id	sid	tid	token	lemma	pos
bracis-33567	1	1	comparing	compare	VERB
bracis-33567	1	2	neural	neural	ADJ
bracis-33567	1	3	network	network	NOUN
bracis-33567	1	4	encodings	encoding	NOUN
bracis-33567	1	5	for	for	ADP
bracis-33567	1	6	 	 	SPACE
bracis-33567	1	7	logic	logic	NOUN
bracis-33567	1	8	-	-	PUNCT
bracis-33567	1	9	based	base	VERB
bracis-33567	1	10	explainability	explainability	NOUN
bracis-33567	1	11	|	|	NOUN
bracis-33567	1	12	springer	springer	NOUN
bracis-33567	1	13	nature	nature	PROPN
bracis-33567	1	14	link	link	PROPN
bracis-33567	1	15	(	(	PUNCT
bracis-33567	1	16	formerly	formerly	ADV
bracis-33567	1	17	springerlink	springerlink	NOUN
bracis-33567	1	18	)	)	PUNCT
bracis-33567	1	19	skip	skip	VERB
bracis-33567	1	20	to	to	ADP
bracis-33567	1	21	main	main	ADJ
bracis-33567	1	22	content	content	NOUN
bracis-33567	1	23	advertisement	advertisement	NOUN
bracis-33567	1	24	log	log	NOUN
bracis-33567	1	25	in	in	ADP
bracis-33567	1	26	menu	menu	NOUN
bracis-33567	1	27	find	find	VERB
bracis-33567	1	28	a	a	DET
bracis-33567	1	29	journal	journal	NOUN
bracis-33567	1	30	publish	publish	VERB
bracis-33567	1	31	with	with	ADP
bracis-33567	1	32	us	we	PRON
bracis-33567	1	33	track	track	VERB
bracis-33567	1	34	your	your	PRON
bracis-33567	1	35	research	research	NOUN
bracis-33567	1	36	search	search	NOUN
bracis-33567	1	37	cart	cart	NOUN
bracis-33567	1	38	home	home	NOUN
bracis-33567	1	39	intelligent	intelligent	ADJ
bracis-33567	1	40	systems	system	NOUN
bracis-33567	1	41	conference	conference	NOUN
bracis-33567	1	42	paper	paper	NOUN
bracis-33567	1	43	comparing	compare	VERB
bracis-33567	1	44	neural	neural	ADJ
bracis-33567	1	45	network	network	NOUN
bracis-33567	1	46	encodings	encoding	NOUN
bracis-33567	1	47	for	for	ADP
bracis-33567	1	48	 	 	SPACE
bracis-33567	1	49	logic	logic	NOUN
bracis-33567	1	50	-	-	PUNCT
bracis-33567	1	51	based	base	VERB
bracis-33567	1	52	explainability	explainability	NOUN
bracis-33567	1	53	conference	conference	NOUN
bracis-33567	1	54	paper	paper	NOUN
bracis-33567	1	55	first	first	ADV
bracis-33567	1	56	online	online	ADV
bracis-33567	1	57	:	:	PUNCT
bracis-33567	1	58	30	30	NUM
bracis-33567	1	59	january	january	NOUN
bracis-33567	1	60	2025	2025	NUM
bracis-33567	1	61	pp	pp	NUM
bracis-33567	1	62	281–295	281–295	NUM
bracis-33567	1	63	cite	cite	VERB
bracis-33567	1	64	this	this	DET
bracis-33567	1	65	conference	conference	NOUN
bracis-33567	1	66	paper	paper	NOUN
bracis-33567	1	67	access	access	NOUN
bracis-33567	1	68	provided	provide	VERB
bracis-33567	1	69	by	by	ADP
bracis-33567	1	70	university	university	PROPN
bracis-33567	1	71	of	of	ADP
bracis-33567	1	72	notre	notre	PROPN
bracis-33567	1	73	dame	dame	PROPN
bracis-33567	1	74	hesburgh	hesburgh	PROPN
bracis-33567	1	75	library	library	PROPN
bracis-33567	1	76	download	download	PROPN
bracis-33567	1	77	book	book	NOUN
bracis-33567	1	78	pdf	pdf	PROPN
bracis-33567	1	79	download	download	NOUN
bracis-33567	1	80	book	book	NOUN
bracis-33567	1	81	epub	epub	PROPN
bracis-33567	1	82	intelligent	intelligent	ADJ
bracis-33567	1	83	systems	system	NOUN
bracis-33567	1	84	(	(	PUNCT
bracis-33567	1	85	bracis	bracis	NOUN
bracis-33567	1	86	2024	2024	NUM
bracis-33567	1	87	)	)	PUNCT
bracis-33567	1	88	comparing	compare	VERB
bracis-33567	1	89	neural	neural	ADJ
bracis-33567	1	90	network	network	NOUN
bracis-33567	1	91	encodings	encoding	NOUN
bracis-33567	1	92	for	for	ADP
bracis-33567	1	93	 	 	SPACE
bracis-33567	1	94	logic	logic	NOUN
bracis-33567	1	95	-	-	PUNCT
bracis-33567	1	96	based	base	VERB
bracis-33567	1	97	explainability	explainability	NOUN
bracis-33567	1	98	download	download	NOUN
bracis-33567	1	99	book	book	PROPN
bracis-33567	1	100	pdf	pdf	PROPN
bracis-33567	1	101	download	download	NOUN
bracis-33567	1	102	book	book	PROPN
bracis-33567	1	103	epub	epub	PROPN
bracis-33567	1	104	levi	levi	PROPN
bracis-33567	1	105	cordeiro	cordeiro	PROPN
bracis-33567	1	106	carvalho9	carvalho9	PROPN
bracis-33567	1	107	,	,	PUNCT
bracis-33567	1	108	saulo	saulo	PROPN
bracis-33567	1	109	a.	a.	PROPN
bracis-33567	1	110	f.	f.	PROPN
bracis-33567	1	111	oliveira9	oliveira9	PROPN
bracis-33567	1	112	&	&	CCONJ
bracis-33567	1	113	thiago	thiago	PROPN
bracis-33567	1	114	alves	alves	PROPN
bracis-33567	1	115	rocha9	rocha9	PROPN
bracis-33567	1	116	  	  	SPACE
bracis-33567	1	117	part	part	NOUN
bracis-33567	1	118	of	of	ADP
bracis-33567	1	119	the	the	DET
bracis-33567	1	120	book	book	NOUN
bracis-33567	1	121	series	series	NOUN
bracis-33567	1	122	:	:	PUNCT
bracis-33567	1	123	lecture	lecture	NOUN
bracis-33567	1	124	notes	note	NOUN
bracis-33567	1	125	in	in	ADP
bracis-33567	1	126	computer	computer	NOUN
bracis-33567	1	127	science	science	NOUN
bracis-33567	1	128	(	(	PUNCT
bracis-33567	1	129	(	(	PUNCT
bracis-33567	1	130	lnai	lnai	ADJ
bracis-33567	1	131	,	,	PUNCT
bracis-33567	1	132	volume	volume	NOUN
bracis-33567	1	133	15412	15412	NUM
bracis-33567	1	134	)	)	PUNCT
bracis-33567	1	135	)	)	PUNCT
bracis-33567	1	136	included	include	VERB
bracis-33567	1	137	in	in	ADP
bracis-33567	1	138	the	the	DET
bracis-33567	1	139	following	follow	VERB
bracis-33567	1	140	conference	conference	NOUN
bracis-33567	1	141	series	series	NOUN
bracis-33567	1	142	:	:	PUNCT
bracis-33567	1	143	brazilian	brazilian	ADJ
bracis-33567	1	144	conference	conference	NOUN
bracis-33567	1	145	on	on	ADP
bracis-33567	1	146	intelligent	intelligent	ADJ
bracis-33567	1	147	systems	system	NOUN
bracis-33567	1	148	476	476	NUM
bracis-33567	1	149	accesses	access	VERB
bracis-33567	1	150	9	9	NUM
bracis-33567	1	151	altmetric	altmetric	ADJ
bracis-33567	1	152	abstract	abstract	NOUN
bracis-33567	1	153	providing	provide	VERB
bracis-33567	1	154	explanations	explanation	NOUN
bracis-33567	1	155	for	for	ADP
bracis-33567	1	156	the	the	DET
bracis-33567	1	157	outputs	output	NOUN
bracis-33567	1	158	of	of	ADP
bracis-33567	1	159	artificial	artificial	ADJ
bracis-33567	1	160	neural	neural	ADJ
bracis-33567	1	161	networks	network	NOUN
bracis-33567	1	162	(	(	PUNCT
bracis-33567	1	163	anns	anns	PROPN
bracis-33567	1	164	)	)	PUNCT
bracis-33567	1	165	is	be	AUX
bracis-33567	1	166	crucial	crucial	ADJ
bracis-33567	1	167	in	in	ADP
bracis-33567	1	168	many	many	ADJ
bracis-33567	1	169	contexts	context	NOUN
bracis-33567	1	170	,	,	PUNCT
bracis-33567	1	171	such	such	ADJ
bracis-33567	1	172	as	as	ADP
bracis-33567	1	173	critical	critical	ADJ
bracis-33567	1	174	systems	system	NOUN
bracis-33567	1	175	,	,	PUNCT
bracis-33567	1	176	data	datum	NOUN
bracis-33567	1	177	protection	protection	NOUN
bracis-33567	1	178	laws	law	NOUN
bracis-33567	1	179	and	and	CCONJ
bracis-33567	1	180	handling	handle	VERB
bracis-33567	1	181	adversarial	adversarial	ADJ
bracis-33567	1	182	examples	example	NOUN
bracis-33567	1	183	.	.	PUNCT
bracis-33567	2	1	logic	logic	NOUN
bracis-33567	2	2	-	-	PUNCT
bracis-33567	2	3	based	base	VERB
bracis-33567	2	4	methods	method	NOUN
bracis-33567	2	5	can	can	AUX
bracis-33567	2	6	offer	offer	VERB
bracis-33567	2	7	explanations	explanation	NOUN
bracis-33567	2	8	with	with	ADP
bracis-33567	2	9	correctness	correctness	NOUN
bracis-33567	2	10	guarantees	guarantee	NOUN
bracis-33567	2	11	,	,	PUNCT
bracis-33567	2	12	but	but	CCONJ
bracis-33567	2	13	face	face	VERB
bracis-33567	2	14	scalability	scalability	NOUN
bracis-33567	2	15	challenges	challenge	NOUN
bracis-33567	2	16	.	.	PUNCT
bracis-33567	3	1	due	due	ADP
bracis-33567	3	2	to	to	ADP
bracis-33567	3	3	these	these	DET
bracis-33567	3	4	issues	issue	NOUN
bracis-33567	3	5	,	,	PUNCT
bracis-33567	3	6	it	it	PRON
bracis-33567	3	7	is	be	AUX
bracis-33567	3	8	necessary	necessary	ADJ
bracis-33567	3	9	to	to	PART
bracis-33567	3	10	compare	compare	VERB
bracis-33567	3	11	different	different	ADJ
bracis-33567	3	12	encodings	encoding	NOUN
bracis-33567	3	13	of	of	ADP
bracis-33567	3	14	anns	ann	NOUN
bracis-33567	3	15	into	into	ADP
bracis-33567	3	16	logical	logical	ADJ
bracis-33567	3	17	constraints	constraint	NOUN
bracis-33567	3	18	,	,	PUNCT
bracis-33567	3	19	which	which	PRON
bracis-33567	3	20	are	be	AUX
bracis-33567	3	21	used	use	VERB
bracis-33567	3	22	in	in	ADP
bracis-33567	3	23	logic	logic	NOUN
bracis-33567	3	24	-	-	PUNCT
bracis-33567	3	25	based	base	VERB
bracis-33567	3	26	explainability	explainability	NOUN
bracis-33567	3	27	.	.	PUNCT
bracis-33567	4	1	this	this	DET
bracis-33567	4	2	work	work	NOUN
bracis-33567	4	3	compares	compare	VERB
bracis-33567	4	4	two	two	NUM
bracis-33567	4	5	encodings	encoding	NOUN
bracis-33567	4	6	of	of	ADP
bracis-33567	4	7	anns	ann	NOUN
bracis-33567	4	8	:	:	PUNCT
bracis-33567	4	9	one	one	NUM
bracis-33567	4	10	has	have	AUX
bracis-33567	4	11	been	be	AUX
bracis-33567	4	12	used	use	VERB
bracis-33567	4	13	in	in	ADP
bracis-33567	4	14	the	the	DET
bracis-33567	4	15	literature	literature	NOUN
bracis-33567	4	16	to	to	PART
bracis-33567	4	17	provide	provide	VERB
bracis-33567	4	18	explanations	explanation	NOUN
bracis-33567	4	19	,	,	PUNCT
bracis-33567	4	20	while	while	SCONJ
bracis-33567	4	21	the	the	DET
bracis-33567	4	22	other	other	ADJ
bracis-33567	4	23	will	will	AUX
bracis-33567	4	24	be	be	AUX
bracis-33567	4	25	adapted	adapt	VERB
bracis-33567	4	26	for	for	ADP
bracis-33567	4	27	our	our	PRON
bracis-33567	4	28	context	context	NOUN
bracis-33567	4	29	of	of	ADP
bracis-33567	4	30	explainability	explainability	NOUN
bracis-33567	4	31	.	.	PUNCT
bracis-33567	5	1	additionally	additionally	ADV
bracis-33567	5	2	,	,	PUNCT
bracis-33567	5	3	the	the	DET
bracis-33567	5	4	second	second	ADJ
bracis-33567	5	5	encoding	encoding	NOUN
bracis-33567	5	6	uses	use	VERB
bracis-33567	5	7	fewer	few	ADJ
bracis-33567	5	8	variables	variable	NOUN
bracis-33567	5	9	and	and	CCONJ
bracis-33567	5	10	constraints	constraint	NOUN
bracis-33567	5	11	,	,	PUNCT
bracis-33567	5	12	thus	thus	ADV
bracis-33567	5	13	,	,	PUNCT
bracis-33567	5	14	potentially	potentially	ADV
bracis-33567	5	15	enhancing	enhance	VERB
bracis-33567	5	16	efficiency	efficiency	NOUN
bracis-33567	5	17	.	.	PUNCT
bracis-33567	6	1	experiments	experiment	NOUN
bracis-33567	6	2	showed	show	VERB
bracis-33567	6	3	similar	similar	ADJ
bracis-33567	6	4	running	running	NOUN
bracis-33567	6	5	times	time	NOUN
bracis-33567	6	6	for	for	ADP
bracis-33567	6	7	computing	computing	NOUN
bracis-33567	6	8	explanations	explanation	NOUN
bracis-33567	6	9	,	,	PUNCT
bracis-33567	6	10	but	but	CCONJ
bracis-33567	6	11	the	the	DET
bracis-33567	6	12	adapted	adapt	VERB
bracis-33567	6	13	encoding	encoding	NOUN
bracis-33567	6	14	performed	perform	VERB
bracis-33567	6	15	up	up	ADP
bracis-33567	6	16	to	to	PART
bracis-33567	6	17	18	18	NUM
bracis-33567	6	18	%	%	NOUN
bracis-33567	6	19	better	well	ADV
bracis-33567	6	20	in	in	ADP
bracis-33567	6	21	building	build	VERB
bracis-33567	6	22	logical	logical	ADJ
bracis-33567	6	23	constraints	constraint	NOUN
bracis-33567	6	24	and	and	CCONJ
bracis-33567	6	25	up	up	ADP
bracis-33567	6	26	to	to	PART
bracis-33567	6	27	16	16	NUM
bracis-33567	6	28	%	%	NOUN
bracis-33567	6	29	better	well	ADV
bracis-33567	6	30	in	in	ADP
bracis-33567	6	31	overall	overall	ADJ
bracis-33567	6	32	time	time	NOUN
bracis-33567	6	33	.	.	PUNCT
bracis-33567	7	1	access	access	NOUN
bracis-33567	7	2	provided	provide	VERB
bracis-33567	7	3	by	by	ADP
bracis-33567	7	4	university	university	PROPN
bracis-33567	7	5	of	of	ADP
bracis-33567	7	6	notre	notre	PROPN
bracis-33567	7	7	dame	dame	PROPN
bracis-33567	7	8	hesburgh	hesburgh	PROPN
bracis-33567	7	9	library	library	PROPN
bracis-33567	7	10	.	.	PUNCT
bracis-33567	8	1	download	download	PROPN
bracis-33567	8	2	conference	conference	NOUN
bracis-33567	8	3	paper	paper	NOUN
bracis-33567	8	4	pdf	pdf	NOUN
bracis-33567	8	5	similar	similar	ADJ
bracis-33567	8	6	content	content	NOUN
bracis-33567	8	7	being	be	AUX
bracis-33567	8	8	viewed	view	VERB
bracis-33567	8	9	by	by	ADP
bracis-33567	8	10	others	other	NOUN
bracis-33567	8	11	ontology	ontology	NOUN
bracis-33567	8	12	-	-	PUNCT
bracis-33567	8	13	based	base	VERB
bracis-33567	8	14	explanations	explanation	NOUN
bracis-33567	8	15	of	of	ADP
bracis-33567	8	16	 	 	SPACE
bracis-33567	8	17	neural	neural	ADJ
bracis-33567	8	18	networks	network	NOUN
bracis-33567	8	19	:	:	PUNCT
bracis-33567	8	20	a	a	DET
bracis-33567	8	21	user	user	NOUN
bracis-33567	8	22	perspective	perspective	NOUN
bracis-33567	8	23	chapter	chapter	NOUN
bracis-33567	8	24	©	©	PROPN
bracis-33567	8	25	2024	2024	NUM
bracis-33567	8	26	correction	correction	NOUN
bracis-33567	8	27	of	of	ADP
bracis-33567	8	28	neural	neural	ADJ
bracis-33567	8	29	network	network	NOUN
bracis-33567	8	30	solutions	solution	NOUN
bracis-33567	8	31	by	by	ADP
bracis-33567	8	32	logical	logical	ADJ
bracis-33567	8	33	analysis	analysis	NOUN
bracis-33567	8	34	methods	method	NOUN
bracis-33567	8	35	chapter	chapter	NOUN
bracis-33567	8	36	©	©	PROPN
bracis-33567	8	37	2023	2023	NUM
bracis-33567	8	38	differentiable	differentiable	ADJ
bracis-33567	8	39	logics	logic	NOUN
bracis-33567	8	40	for	for	ADP
bracis-33567	8	41	neural	neural	ADJ
bracis-33567	8	42	network	network	NOUN
bracis-33567	8	43	training	training	NOUN
bracis-33567	8	44	and	and	CCONJ
bracis-33567	8	45	verification	verification	NOUN
bracis-33567	8	46	chapter	chapter	NOUN
bracis-33567	8	47	©	©	NOUN
bracis-33567	8	48	2022	2022	NUM
bracis-33567	8	49	1	1	NUM
bracis-33567	8	50	introduction	introduction	NOUN
bracis-33567	8	51	artificial	artificial	ADJ
bracis-33567	8	52	neural	neural	ADJ
bracis-33567	8	53	networks	network	NOUN
bracis-33567	8	54	(	(	PUNCT
bracis-33567	8	55	anns	anns	PROPN
bracis-33567	8	56	)	)	PUNCT
bracis-33567	8	57	are	be	AUX
bracis-33567	8	58	widely	widely	ADV
bracis-33567	8	59	applied	apply	VERB
bracis-33567	8	60	in	in	ADP
bracis-33567	8	61	tasks	task	NOUN
bracis-33567	8	62	like	like	ADP
bracis-33567	8	63	computer	computer	NOUN
bracis-33567	8	64	vision	vision	NOUN
bracis-33567	8	65	,	,	PUNCT
bracis-33567	8	66	speech	speech	NOUN
bracis-33567	8	67	recognition	recognition	NOUN
bracis-33567	8	68	,	,	PUNCT
bracis-33567	8	69	and	and	CCONJ
bracis-33567	8	70	pattern	pattern	NOUN
bracis-33567	8	71	recognition	recognition	NOUN
bracis-33567	9	1	[	[	X
bracis-33567	9	2	13	13	NUM
bracis-33567	9	3	]	]	PUNCT
bracis-33567	9	4	.	.	PUNCT
bracis-33567	10	1	despite	despite	SCONJ
bracis-33567	10	2	their	their	PRON
bracis-33567	10	3	success	success	NOUN
bracis-33567	10	4	,	,	PUNCT
bracis-33567	10	5	anns	ann	NOUN
bracis-33567	10	6	are	be	AUX
bracis-33567	10	7	often	often	ADV
bracis-33567	10	8	considered	consider	VERB
bracis-33567	10	9	black	black	ADJ
bracis-33567	10	10	-	-	PUNCT
bracis-33567	10	11	box	box	NOUN
bracis-33567	10	12	algorithms	algorithm	NOUN
bracis-33567	10	13	.	.	PUNCT
bracis-33567	11	1	such	such	DET
bracis-33567	11	2	a	a	DET
bracis-33567	11	3	lack	lack	NOUN
bracis-33567	11	4	of	of	ADP
bracis-33567	11	5	interpretability	interpretability	NOUN
bracis-33567	11	6	poses	pose	VERB
bracis-33567	11	7	risks	risk	NOUN
bracis-33567	11	8	in	in	ADP
bracis-33567	11	9	critical	critical	ADJ
bracis-33567	11	10	domains	domain	NOUN
bracis-33567	11	11	such	such	ADJ
bracis-33567	11	12	as	as	ADP
bracis-33567	11	13	medical	medical	ADJ
bracis-33567	11	14	and	and	CCONJ
bracis-33567	11	15	financial	financial	ADJ
bracis-33567	11	16	applications	application	NOUN
bracis-33567	11	17	,	,	PUNCT
bracis-33567	11	18	where	where	SCONJ
bracis-33567	11	19	understanding	understanding	NOUN
bracis-33567	11	20	model	model	NOUN
bracis-33567	11	21	decisions	decision	NOUN
bracis-33567	11	22	is	be	AUX
bracis-33567	11	23	crucial	crucial	ADJ
bracis-33567	11	24	.	.	PUNCT
bracis-33567	12	1	additionally	additionally	ADV
bracis-33567	12	2	,	,	PUNCT
bracis-33567	12	3	the	the	DET
bracis-33567	12	4	presence	presence	NOUN
bracis-33567	12	5	of	of	ADP
bracis-33567	12	6	adversarial	adversarial	ADJ
bracis-33567	12	7	examples	example	NOUN
bracis-33567	12	8	highlights	highlight	VERB
bracis-33567	12	9	the	the	DET
bracis-33567	12	10	need	need	NOUN
bracis-33567	12	11	for	for	ADP
bracis-33567	12	12	explainability	explainability	NOUN
bracis-33567	12	13	in	in	ADP
bracis-33567	12	14	machine	machine	NOUN
bracis-33567	12	15	learning	learning	NOUN
bracis-33567	12	16	algorithms	algorithm	NOUN
bracis-33567	12	17	,	,	PUNCT
bracis-33567	12	18	including	include	VERB
bracis-33567	12	19	neural	neural	ADJ
bracis-33567	12	20	networks	network	NOUN
bracis-33567	12	21	.	.	PUNCT
bracis-33567	13	1	an	an	DET
bracis-33567	13	2	adversarial	adversarial	ADJ
bracis-33567	13	3	example	example	NOUN
bracis-33567	13	4	is	be	AUX
bracis-33567	13	5	an	an	DET
bracis-33567	13	6	instance	instance	NOUN
bracis-33567	13	7	misclassified	misclassifie	VERB
bracis-33567	13	8	by	by	ADP
bracis-33567	13	9	a	a	DET
bracis-33567	13	10	machine	machine	NOUN
bracis-33567	13	11	learning	learning	NOUN
bracis-33567	13	12	model	model	NOUN
bracis-33567	13	13	and	and	CCONJ
bracis-33567	13	14	also	also	ADV
bracis-33567	13	15	slightly	slightly	ADV
bracis-33567	13	16	different	different	ADJ
bracis-33567	13	17	from	from	ADP
bracis-33567	13	18	another	another	DET
bracis-33567	13	19	correctly	correctly	ADV
bracis-33567	13	20	classified	classified	ADJ
bracis-33567	13	21	instance	instance	NOUN
bracis-33567	13	22	[	[	X
bracis-33567	13	23	6	6	NUM
bracis-33567	13	24	]	]	PUNCT
bracis-33567	13	25	.	.	PUNCT
bracis-33567	14	1	in	in	ADP
bracis-33567	14	2	this	this	DET
bracis-33567	14	3	work	work	NOUN
bracis-33567	14	4	,	,	PUNCT
bracis-33567	14	5	an	an	DET
bracis-33567	14	6	explanation	explanation	NOUN
bracis-33567	14	7	for	for	ADP
bracis-33567	14	8	a	a	DET
bracis-33567	14	9	prediction	prediction	NOUN
bracis-33567	14	10	made	make	VERB
bracis-33567	14	11	by	by	ADP
bracis-33567	14	12	an	an	DET
bracis-33567	14	13	ann	ann	PROPN
bracis-33567	14	14	is	be	AUX
bracis-33567	14	15	a	a	DET
bracis-33567	14	16	subset	subset	NOUN
bracis-33567	14	17	of	of	ADP
bracis-33567	14	18	features	feature	NOUN
bracis-33567	14	19	and	and	CCONJ
bracis-33567	14	20	their	their	PRON
bracis-33567	14	21	values	value	NOUN
bracis-33567	14	22	that	that	SCONJ
bracis-33567	14	23	alone	alone	ADV
bracis-33567	14	24	suffice	suffice	VERB
bracis-33567	14	25	for	for	ADP
bracis-33567	14	26	the	the	DET
bracis-33567	14	27	prediction	prediction	NOUN
bracis-33567	14	28	.	.	PUNCT
bracis-33567	15	1	if	if	SCONJ
bracis-33567	15	2	an	an	DET
bracis-33567	15	3	instance	instance	NOUN
bracis-33567	15	4	has	have	VERB
bracis-33567	15	5	the	the	DET
bracis-33567	15	6	features	feature	NOUN
bracis-33567	15	7	in	in	ADP
bracis-33567	15	8	this	this	DET
bracis-33567	15	9	subset	subset	NOUN
bracis-33567	15	10	,	,	PUNCT
bracis-33567	15	11	the	the	DET
bracis-33567	15	12	ann	ann	PROPN
bracis-33567	15	13	makes	make	VERB
bracis-33567	15	14	the	the	DET
bracis-33567	15	15	same	same	ADJ
bracis-33567	15	16	prediction	prediction	NOUN
bracis-33567	15	17	,	,	PUNCT
bracis-33567	15	18	regardless	regardless	ADV
bracis-33567	15	19	of	of	ADP
bracis-33567	15	20	the	the	DET
bracis-33567	15	21	values	value	NOUN
bracis-33567	15	22	of	of	ADP
bracis-33567	15	23	other	other	ADJ
bracis-33567	15	24	features	feature	NOUN
bracis-33567	15	25	.	.	PUNCT
bracis-33567	16	1	for	for	ADP
bracis-33567	16	2	example	example	NOUN
bracis-33567	16	3	,	,	PUNCT
bracis-33567	16	4	given	give	VERB
bracis-33567	16	5	an	an	DET
bracis-33567	16	6	instance	instance	NOUN
bracis-33567	16	7	\(\{sneeze	\(\{sneeze	NOUN
bracis-33567	16	8	=	=	NOUN
bracis-33567	16	9	true\	true\	NUM
bracis-33567	16	10	)	)	PUNCT
bracis-33567	16	11	,	,	PUNCT
bracis-33567	16	12	\(weight=70	\(weight=70	NOUN
bracis-33567	16	13	\	\	PROPN
bracis-33567	16	14	kg\	kg\	PROPN
bracis-33567	16	15	)	)	PUNCT
bracis-33567	16	16	,	,	PUNCT
bracis-33567	16	17	\(headache	\(headache	NOUN
bracis-33567	16	18	=	=	NOUN
bracis-33567	16	19	true\	true\	NUM
bracis-33567	16	20	)	)	PUNCT
bracis-33567	16	21	,	,	PUNCT
bracis-33567	16	22	\(age=40	\(age=40	PROPN
bracis-33567	16	23	\	\	PROPN
bracis-33567	16	24	years\}\	years\}\	PROPN
bracis-33567	16	25	)	)	PUNCT
bracis-33567	16	26	and	and	CCONJ
bracis-33567	16	27	its	its	PRON
bracis-33567	16	28	ann	ann	PROPN
bracis-33567	16	29	output	output	NOUN
bracis-33567	16	30	flu	flu	PROPN
bracis-33567	16	31	,	,	PUNCT
bracis-33567	16	32	a	a	DET
bracis-33567	16	33	possible	possible	ADJ
bracis-33567	16	34	explanation	explanation	NOUN
bracis-33567	16	35	could	could	AUX
bracis-33567	16	36	be	be	AUX
bracis-33567	16	37	\(\{sneeze	\(\{sneeze	VERB
bracis-33567	16	38	=	=	NOUN
bracis-33567	16	39	true	true	ADJ
bracis-33567	16	40	,	,	PUNCT
bracis-33567	16	41	headache	headache	NOUN
bracis-33567	16	42	=	=	SYM
bracis-33567	16	43	true\}\	true\}\	NOUN
bracis-33567	16	44	)	)	PUNCT
bracis-33567	16	45	.	.	PUNCT
bracis-33567	17	1	that	that	PRON
bracis-33567	17	2	is	be	AUX
bracis-33567	17	3	,	,	PUNCT
bracis-33567	17	4	if	if	SCONJ
bracis-33567	17	5	an	an	DET
bracis-33567	17	6	instance	instance	NOUN
bracis-33567	17	7	has	have	VERB
bracis-33567	17	8	the	the	DET
bracis-33567	17	9	features	feature	NOUN
bracis-33567	17	10	\(sneeze	\(sneeze	ADJ
bracis-33567	17	11	=	=	NOUN
bracis-33567	17	12	true\	true\	NUM
bracis-33567	17	13	)	)	PUNCT
bracis-33567	17	14	and	and	CCONJ
bracis-33567	17	15	\(headache	\(headache	NOUN
bracis-33567	17	16	=	=	NOUN
bracis-33567	17	17	true\	true\	NUM
bracis-33567	17	18	)	)	PUNCT
bracis-33567	17	19	,	,	PUNCT
bracis-33567	17	20	the	the	DET
bracis-33567	17	21	ann	ann	PROPN
bracis-33567	17	22	prediction	prediction	NOUN
bracis-33567	17	23	is	be	AUX
bracis-33567	17	24	flu	flu	NOUN
bracis-33567	17	25	,	,	PUNCT
bracis-33567	17	26	regardless	regardless	ADV
bracis-33567	17	27	of	of	ADP
bracis-33567	17	28	weight	weight	NOUN
bracis-33567	17	29	and	and	CCONJ
bracis-33567	17	30	age	age	NOUN
bracis-33567	17	31	values	value	NOUN
bracis-33567	17	32	.	.	PUNCT
bracis-33567	18	1	a	a	DET
bracis-33567	18	2	minimal	minimal	ADJ
bracis-33567	18	3	explanation	explanation	NOUN
bracis-33567	18	4	avoids	avoid	VERB
bracis-33567	18	5	redundancy	redundancy	NOUN
bracis-33567	18	6	by	by	ADP
bracis-33567	18	7	including	include	VERB
bracis-33567	18	8	only	only	ADJ
bracis-33567	18	9	essential	essential	ADJ
bracis-33567	18	10	information	information	NOUN
bracis-33567	18	11	.	.	PUNCT
bracis-33567	19	1	an	an	DET
bracis-33567	19	2	explanation	explanation	NOUN
bracis-33567	19	3	is	be	AUX
bracis-33567	19	4	considered	consider	VERB
bracis-33567	19	5	minimal	minimal	ADJ
bracis-33567	19	6	when	when	SCONJ
bracis-33567	19	7	removing	remove	VERB
bracis-33567	19	8	any	any	DET
bracis-33567	19	9	feature	feature	NOUN
bracis-33567	19	10	results	result	NOUN
bracis-33567	19	11	in	in	ADP
bracis-33567	19	12	the	the	DET
bracis-33567	19	13	loss	loss	NOUN
bracis-33567	19	14	of	of	ADP
bracis-33567	19	15	assurance	assurance	NOUN
bracis-33567	19	16	that	that	PRON
bracis-33567	19	17	every	every	DET
bracis-33567	19	18	instance	instance	NOUN
bracis-33567	19	19	satisfying	satisfy	VERB
bracis-33567	19	20	the	the	DET
bracis-33567	19	21	explanation	explanation	NOUN
bracis-33567	19	22	maintains	maintain	VERB
bracis-33567	19	23	the	the	DET
bracis-33567	19	24	same	same	ADJ
bracis-33567	19	25	output	output	NOUN
bracis-33567	19	26	.	.	PUNCT
bracis-33567	20	1	then	then	ADV
bracis-33567	20	2	,	,	PUNCT
bracis-33567	20	3	a	a	DET
bracis-33567	20	4	minimal	minimal	ADJ
bracis-33567	20	5	explanation	explanation	NOUN
bracis-33567	20	6	avoids	avoid	VERB
bracis-33567	20	7	redundancy	redundancy	NOUN
bracis-33567	20	8	,	,	PUNCT
bracis-33567	20	9	providing	provide	VERB
bracis-33567	20	10	only	only	ADJ
bracis-33567	20	11	essential	essential	ADJ
bracis-33567	20	12	information	information	NOUN
bracis-33567	20	13	.	.	PUNCT
bracis-33567	21	1	heuristic	heuristic	ADJ
bracis-33567	21	2	methods	method	NOUN
bracis-33567	21	3	,	,	PUNCT
bracis-33567	21	4	such	such	ADJ
bracis-33567	21	5	as	as	ADP
bracis-33567	21	6	anchor	anchor	NOUN
bracis-33567	21	7	[	[	X
bracis-33567	21	8	15	15	NUM
bracis-33567	21	9	]	]	PUNCT
bracis-33567	21	10	and	and	CCONJ
bracis-33567	21	11	lime	lime	NOUN
bracis-33567	22	1	[	[	X
bracis-33567	22	2	14	14	NUM
bracis-33567	22	3	]	]	PUNCT
bracis-33567	22	4	,	,	PUNCT
bracis-33567	22	5	have	have	AUX
bracis-33567	22	6	been	be	AUX
bracis-33567	22	7	used	use	VERB
bracis-33567	22	8	to	to	PART
bracis-33567	22	9	provide	provide	VERB
bracis-33567	22	10	explanations	explanation	NOUN
bracis-33567	22	11	for	for	ADP
bracis-33567	22	12	machine	machine	NOUN
bracis-33567	22	13	learning	learning	NOUN
bracis-33567	22	14	models	model	NOUN
bracis-33567	22	15	.	.	PUNCT
bracis-33567	23	1	however	however	ADV
bracis-33567	23	2	,	,	PUNCT
bracis-33567	23	3	these	these	DET
bracis-33567	23	4	approaches	approach	NOUN
bracis-33567	23	5	explore	explore	VERB
bracis-33567	23	6	the	the	DET
bracis-33567	23	7	instance	instance	NOUN
bracis-33567	23	8	space	space	NOUN
bracis-33567	23	9	locally	locally	ADV
bracis-33567	23	10	,	,	PUNCT
bracis-33567	23	11	not	not	PART
bracis-33567	23	12	resulting	result	VERB
bracis-33567	23	13	in	in	ADP
bracis-33567	23	14	explanations	explanation	NOUN
bracis-33567	23	15	that	that	PRON
bracis-33567	23	16	have	have	VERB
bracis-33567	23	17	minimal	minimal	ADJ
bracis-33567	23	18	sizes	size	NOUN
bracis-33567	23	19	and	and	CCONJ
bracis-33567	23	20	formal	formal	ADJ
bracis-33567	23	21	guarantees	guarantee	NOUN
bracis-33567	23	22	of	of	ADP
bracis-33567	23	23	correctness	correctness	NOUN
bracis-33567	23	24	.	.	PUNCT
bracis-33567	24	1	correctness	correctness	NOUN
bracis-33567	24	2	guarantees	guarantee	NOUN
bracis-33567	24	3	are	be	AUX
bracis-33567	24	4	provided	provide	VERB
bracis-33567	24	5	when	when	SCONJ
bracis-33567	24	6	there	there	PRON
bracis-33567	24	7	are	be	VERB
bracis-33567	24	8	no	no	DET
bracis-33567	24	9	instances	instance	NOUN
bracis-33567	24	10	with	with	ADP
bracis-33567	24	11	the	the	DET
bracis-33567	24	12	values	value	NOUN
bracis-33567	24	13	specified	specify	VERB
bracis-33567	24	14	in	in	ADP
bracis-33567	24	15	the	the	DET
bracis-33567	24	16	explanation	explanation	NOUN
bracis-33567	24	17	such	such	ADJ
bracis-33567	24	18	that	that	SCONJ
bracis-33567	24	19	the	the	DET
bracis-33567	24	20	ann	ann	PROPN
bracis-33567	24	21	makes	make	VERB
bracis-33567	24	22	a	a	DET
bracis-33567	24	23	different	different	ADJ
bracis-33567	24	24	prediction	prediction	NOUN
bracis-33567	24	25	.	.	PUNCT
bracis-33567	25	1	moreover	moreover	ADV
bracis-33567	25	2	,	,	PUNCT
bracis-33567	25	3	minimal	minimal	ADJ
bracis-33567	25	4	explanations	explanation	NOUN
bracis-33567	25	5	are	be	AUX
bracis-33567	25	6	desired	desire	VERB
bracis-33567	25	7	since	since	SCONJ
bracis-33567	25	8	they	they	PRON
bracis-33567	25	9	do	do	AUX
bracis-33567	25	10	not	not	PART
bracis-33567	25	11	contain	contain	VERB
bracis-33567	25	12	redundancy	redundancy	NOUN
bracis-33567	25	13	,	,	PUNCT
bracis-33567	25	14	making	make	VERB
bracis-33567	25	15	them	they	PRON
bracis-33567	25	16	easier	easy	ADJ
bracis-33567	25	17	to	to	PART
bracis-33567	25	18	understand	understand	VERB
bracis-33567	25	19	and	and	CCONJ
bracis-33567	25	20	interpret	interpret	VERB
bracis-33567	25	21	.	.	PUNCT
bracis-33567	26	1	some	some	DET
bracis-33567	26	2	approaches	approach	NOUN
bracis-33567	26	3	aim	aim	VERB
bracis-33567	26	4	to	to	PART
bracis-33567	26	5	provide	provide	VERB
bracis-33567	26	6	explanations	explanation	NOUN
bracis-33567	26	7	for	for	ADP
bracis-33567	26	8	machine	machine	NOUN
bracis-33567	26	9	learning	learning	NOUN
bracis-33567	26	10	models	model	NOUN
bracis-33567	26	11	with	with	ADP
bracis-33567	26	12	formal	formal	ADJ
bracis-33567	26	13	guarantees	guarantee	NOUN
bracis-33567	26	14	of	of	ADP
bracis-33567	26	15	correctness	correctness	NOUN
bracis-33567	26	16	[	[	X
bracis-33567	26	17	1	1	NUM
bracis-33567	26	18	,	,	PUNCT
bracis-33567	26	19	4	4	NUM
bracis-33567	26	20	,	,	PUNCT
bracis-33567	26	21	7	7	NUM
bracis-33567	26	22	,	,	PUNCT
bracis-33567	26	23	8	8	NUM
bracis-33567	26	24	,	,	PUNCT
bracis-33567	26	25	16	16	NUM
bracis-33567	26	26	,	,	PUNCT
bracis-33567	26	27	18	18	NUM
bracis-33567	26	28	]	]	PUNCT
bracis-33567	26	29	.	.	PUNCT
bracis-33567	27	1	ignatiev	ignatiev	PROPN
bracis-33567	27	2	et	et	PROPN
bracis-33567	27	3	al	al	PROPN
bracis-33567	27	4	.	.	PUNCT
bracis-33567	28	1	[	[	X
bracis-33567	28	2	8	8	NUM
bracis-33567	28	3	]	]	PUNCT
bracis-33567	28	4	proposed	propose	VERB
bracis-33567	28	5	a	a	DET
bracis-33567	28	6	logic	logic	NOUN
bracis-33567	28	7	-	-	PUNCT
bracis-33567	28	8	based	base	VERB
bracis-33567	28	9	algorithm	algorithm	NOUN
bracis-33567	28	10	that	that	PRON
bracis-33567	28	11	gives	give	VERB
bracis-33567	28	12	minimal	minimal	ADJ
bracis-33567	28	13	and	and	CCONJ
bracis-33567	28	14	correct	correct	ADJ
bracis-33567	28	15	explanations	explanation	NOUN
bracis-33567	28	16	for	for	ADP
bracis-33567	28	17	anns	ann	NOUN
bracis-33567	28	18	,	,	PUNCT
bracis-33567	28	19	utilizing	utilize	VERB
bracis-33567	28	20	logical	logical	ADJ
bracis-33567	28	21	constraints	constraint	NOUN
bracis-33567	28	22	originally	originally	ADV
bracis-33567	28	23	designed	design	VERB
bracis-33567	28	24	for	for	ADP
bracis-33567	28	25	finding	find	VERB
bracis-33567	28	26	adversarial	adversarial	ADJ
bracis-33567	28	27	examples	example	NOUN
bracis-33567	28	28	fischetti	fischetti	ADJ
bracis-33567	28	29	and	and	CCONJ
bracis-33567	28	30	jo	jo	NOUN
bracis-33567	29	1	[	[	X
bracis-33567	29	2	5	5	NUM
bracis-33567	29	3	]	]	PUNCT
bracis-33567	29	4	.	.	PUNCT
bracis-33567	30	1	these	these	DET
bracis-33567	30	2	constraints	constraint	NOUN
bracis-33567	30	3	include	include	VERB
bracis-33567	30	4	linear	linear	PROPN
bracis-33567	30	5	equations	equation	NOUN
bracis-33567	30	6	,	,	PUNCT
bracis-33567	30	7	inequalities	inequality	NOUN
bracis-33567	30	8	,	,	PUNCT
bracis-33567	30	9	and	and	CCONJ
bracis-33567	30	10	logical	logical	ADJ
bracis-33567	30	11	implications	implication	NOUN
bracis-33567	30	12	,	,	PUNCT
bracis-33567	30	13	solved	solve	VERB
bracis-33567	30	14	using	use	VERB
bracis-33567	30	15	a	a	DET
bracis-33567	30	16	mixed	mixed	ADJ
bracis-33567	30	17	integer	integer	NOUN
bracis-33567	30	18	linear	linear	PROPN
bracis-33567	30	19	programming	programming	NOUN
bracis-33567	30	20	(	(	PUNCT
bracis-33567	30	21	milp	milp	NOUN
bracis-33567	30	22	)	)	PUNCT
bracis-33567	30	23	solver	solver	ADV
bracis-33567	30	24	.	.	PUNCT
bracis-33567	31	1	however	however	ADV
bracis-33567	31	2	,	,	PUNCT
bracis-33567	31	3	scalability	scalability	NOUN
bracis-33567	31	4	issues	issue	NOUN
bracis-33567	31	5	arise	arise	VERB
bracis-33567	31	6	,	,	PUNCT
bracis-33567	31	7	particularly	particularly	ADV
bracis-33567	31	8	with	with	ADP
bracis-33567	31	9	large	large	ADJ
bracis-33567	31	10	anns	ann	NOUN
bracis-33567	31	11	,	,	PUNCT
bracis-33567	31	12	necessitating	necessitate	VERB
bracis-33567	31	13	further	further	ADJ
bracis-33567	31	14	development	development	NOUN
bracis-33567	31	15	before	before	ADP
bracis-33567	31	16	deployment	deployment	NOUN
bracis-33567	31	17	in	in	ADP
bracis-33567	31	18	large	large	ADJ
bracis-33567	31	19	-	-	PUNCT
bracis-33567	31	20	scale	scale	NOUN
bracis-33567	31	21	production	production	NOUN
bracis-33567	31	22	environments	environment	NOUN
bracis-33567	31	23	.	.	PUNCT
bracis-33567	32	1	this	this	DET
bracis-33567	32	2	work	work	NOUN
bracis-33567	32	3	explores	explore	VERB
bracis-33567	32	4	two	two	NUM
bracis-33567	32	5	different	different	ADJ
bracis-33567	32	6	encodings	encoding	NOUN
bracis-33567	32	7	to	to	PART
bracis-33567	32	8	improve	improve	VERB
bracis-33567	32	9	the	the	DET
bracis-33567	32	10	scalability	scalability	NOUN
bracis-33567	32	11	of	of	ADP
bracis-33567	32	12	providing	provide	VERB
bracis-33567	32	13	correct	correct	ADJ
bracis-33567	32	14	minimal	minimal	ADJ
bracis-33567	32	15	explanations	explanation	NOUN
bracis-33567	32	16	for	for	ADP
bracis-33567	32	17	anns	ann	NOUN
bracis-33567	32	18	,	,	PUNCT
bracis-33567	32	19	building	build	VERB
bracis-33567	32	20	upon	upon	SCONJ
bracis-33567	32	21	[	[	X
bracis-33567	32	22	8	8	NUM
bracis-33567	32	23	]	]	PUNCT
bracis-33567	32	24	.	.	PUNCT
bracis-33567	33	1	in	in	ADP
bracis-33567	33	2	addition	addition	NOUN
bracis-33567	33	3	to	to	ADP
bracis-33567	33	4	the	the	DET
bracis-33567	33	5	logical	logical	ADJ
bracis-33567	33	6	constraints	constraint	NOUN
bracis-33567	33	7	of	of	ADP
bracis-33567	33	8	[	[	X
bracis-33567	33	9	5	5	NUM
bracis-33567	33	10	]	]	PUNCT
bracis-33567	33	11	,	,	PUNCT
bracis-33567	33	12	we	we	PRON
bracis-33567	33	13	adopt	adopt	VERB
bracis-33567	33	14	the	the	DET
bracis-33567	33	15	encoding	encoding	NOUN
bracis-33567	33	16	proposed	propose	VERB
bracis-33567	33	17	by	by	ADP
bracis-33567	33	18	tjeng	tjeng	PROPN
bracis-33567	33	19	et	et	PROPN
bracis-33567	33	20	al	al	PROPN
bracis-33567	33	21	.	.	PUNCT
bracis-33567	34	1	[	[	X
bracis-33567	34	2	17	17	NUM
bracis-33567	34	3	]	]	PUNCT
bracis-33567	34	4	,	,	PUNCT
bracis-33567	34	5	which	which	PRON
bracis-33567	34	6	uses	use	VERB
bracis-33567	34	7	fewer	few	ADJ
bracis-33567	34	8	variables	variable	NOUN
bracis-33567	34	9	and	and	CCONJ
bracis-33567	34	10	constraints	constraint	NOUN
bracis-33567	34	11	,	,	PUNCT
bracis-33567	34	12	and	and	CCONJ
bracis-33567	34	13	excludes	exclude	VERB
bracis-33567	34	14	logical	logical	ADJ
bracis-33567	34	15	implications	implication	NOUN
bracis-33567	34	16	.	.	PUNCT
bracis-33567	35	1	by	by	ADP
bracis-33567	35	2	reducing	reduce	VERB
bracis-33567	35	3	variables	variable	NOUN
bracis-33567	35	4	and	and	CCONJ
bracis-33567	35	5	constraints	constraint	NOUN
bracis-33567	35	6	compared	compare	VERB
bracis-33567	35	7	to	to	ADP
bracis-33567	35	8	[	[	X
bracis-33567	35	9	5	5	NUM
bracis-33567	35	10	]	]	PUNCT
bracis-33567	35	11	,	,	PUNCT
bracis-33567	35	12	our	our	PRON
bracis-33567	35	13	approach	approach	NOUN
bracis-33567	35	14	aims	aim	VERB
bracis-33567	35	15	to	to	PART
bracis-33567	35	16	enhance	enhance	VERB
bracis-33567	35	17	explanation	explanation	NOUN
bracis-33567	35	18	computation	computation	NOUN
bracis-33567	35	19	performance	performance	NOUN
bracis-33567	35	20	.	.	PUNCT
bracis-33567	36	1	to	to	PART
bracis-33567	36	2	adapt	adapt	VERB
bracis-33567	36	3	the	the	DET
bracis-33567	36	4	approach	approach	NOUN
bracis-33567	36	5	of	of	ADP
bracis-33567	36	6	[	[	X
bracis-33567	36	7	17	17	NUM
bracis-33567	36	8	]	]	PUNCT
bracis-33567	36	9	for	for	ADP
bracis-33567	36	10	explanations	explanation	NOUN
bracis-33567	36	11	,	,	PUNCT
bracis-33567	36	12	we	we	PRON
bracis-33567	36	13	introduce	introduce	VERB
bracis-33567	36	14	new	new	ADJ
bracis-33567	36	15	constraints	constraint	NOUN
bracis-33567	36	16	to	to	PART
bracis-33567	36	17	ensure	ensure	VERB
bracis-33567	36	18	correctness	correctness	NOUN
bracis-33567	36	19	.	.	PUNCT
bracis-33567	37	1	in	in	ADP
bracis-33567	37	2	line	line	NOUN
bracis-33567	37	3	with	with	ADP
bracis-33567	37	4	the	the	DET
bracis-33567	37	5	encodings	encoding	NOUN
bracis-33567	37	6	proposed	propose	VERB
bracis-33567	37	7	by	by	ADP
bracis-33567	37	8	fischetti	fischetti	PROPN
bracis-33567	37	9	and	and	CCONJ
bracis-33567	37	10	jo	jo	NOUN
bracis-33567	38	1	[	[	X
bracis-33567	38	2	5	5	NUM
bracis-33567	38	3	]	]	PUNCT
bracis-33567	38	4	and	and	CCONJ
bracis-33567	38	5	tjeng	tjeng	PROPN
bracis-33567	38	6	et	et	PROPN
bracis-33567	38	7	al	al	PROPN
bracis-33567	38	8	.	.	PUNCT
bracis-33567	39	1	[	[	X
bracis-33567	39	2	17	17	NUM
bracis-33567	39	3	]	]	PUNCT
bracis-33567	39	4	,	,	PUNCT
bracis-33567	39	5	we	we	PRON
bracis-33567	39	6	also	also	ADV
bracis-33567	39	7	compute	compute	VERB
bracis-33567	39	8	lower	low	ADJ
bracis-33567	39	9	and	and	CCONJ
bracis-33567	39	10	upper	upper	ADJ
bracis-33567	39	11	bounds	bound	NOUN
bracis-33567	39	12	for	for	ADP
bracis-33567	39	13	each	each	DET
bracis-33567	39	14	neuron	neuron	NOUN
bracis-33567	39	15	.	.	PUNCT
bracis-33567	40	1	these	these	DET
bracis-33567	40	2	bounds	bound	NOUN
bracis-33567	40	3	are	be	AUX
bracis-33567	40	4	found	find	VERB
bracis-33567	40	5	through	through	ADP
bracis-33567	40	6	optimization	optimization	NOUN
bracis-33567	40	7	using	use	VERB
bracis-33567	40	8	a	a	DET
bracis-33567	40	9	milp	milp	ADJ
bracis-33567	40	10	solver	solver	NOUN
bracis-33567	40	11	.	.	PUNCT
bracis-33567	41	1	moreover	moreover	ADV
bracis-33567	41	2	,	,	PUNCT
bracis-33567	41	3	these	these	DET
bracis-33567	41	4	bounds	bound	NOUN
bracis-33567	41	5	can	can	AUX
bracis-33567	41	6	aid	aid	VERB
bracis-33567	41	7	the	the	DET
bracis-33567	41	8	solver	solver	NOUN
bracis-33567	41	9	in	in	ADP
bracis-33567	41	10	computing	compute	VERB
bracis-33567	41	11	explanations	explanation	NOUN
bracis-33567	41	12	more	more	ADV
bracis-33567	41	13	rapidly	rapidly	ADV
bracis-33567	41	14	.	.	PUNCT
bracis-33567	42	1	in	in	ADP
bracis-33567	42	2	this	this	DET
bracis-33567	42	3	manner	manner	NOUN
bracis-33567	42	4	,	,	PUNCT
bracis-33567	42	5	we	we	PRON
bracis-33567	42	6	compare	compare	VERB
bracis-33567	42	7	the	the	DET
bracis-33567	42	8	time	time	NOUN
bracis-33567	42	9	required	require	VERB
bracis-33567	42	10	for	for	ADP
bracis-33567	42	11	constructing	construct	VERB
bracis-33567	42	12	logical	logical	ADJ
bracis-33567	42	13	constraints	constraint	NOUN
bracis-33567	42	14	with	with	ADP
bracis-33567	42	15	lower	low	ADJ
bracis-33567	42	16	and	and	CCONJ
bracis-33567	42	17	upper	upper	ADJ
bracis-33567	42	18	bounds	bound	NOUN
bracis-33567	42	19	of	of	ADP
bracis-33567	42	20	each	each	DET
bracis-33567	42	21	neuron	neuron	NOUN
bracis-33567	42	22	,	,	PUNCT
bracis-33567	42	23	along	along	ADP
bracis-33567	42	24	with	with	ADP
bracis-33567	42	25	the	the	DET
bracis-33567	42	26	time	time	NOUN
bracis-33567	42	27	needed	need	VERB
bracis-33567	42	28	for	for	ADP
bracis-33567	42	29	computing	computing	NOUN
bracis-33567	42	30	explanations	explanation	NOUN
bracis-33567	42	31	.	.	PUNCT
bracis-33567	43	1	we	we	PRON
bracis-33567	43	2	conducted	conduct	VERB
bracis-33567	43	3	experiments	experiment	NOUN
bracis-33567	43	4	to	to	PART
bracis-33567	43	5	evaluate	evaluate	VERB
bracis-33567	43	6	both	both	DET
bracis-33567	43	7	encodings	encoding	NOUN
bracis-33567	43	8	.	.	PUNCT
bracis-33567	44	1	our	our	PRON
bracis-33567	44	2	adaptation	adaptation	NOUN
bracis-33567	44	3	of	of	ADP
bracis-33567	44	4	the	the	DET
bracis-33567	44	5	encoding	encoding	NOUN
bracis-33567	44	6	proposed	propose	VERB
bracis-33567	44	7	in	in	ADP
bracis-33567	44	8	[	[	X
bracis-33567	44	9	17	17	NUM
bracis-33567	44	10	]	]	PUNCT
bracis-33567	44	11	exhibits	exhibit	VERB
bracis-33567	44	12	a	a	DET
bracis-33567	44	13	better	well	ADJ
bracis-33567	44	14	running	running	NOUN
bracis-33567	44	15	time	time	NOUN
bracis-33567	44	16	in	in	ADP
bracis-33567	44	17	building	building	NOUN
bracis-33567	44	18	encodings	encoding	NOUN
bracis-33567	44	19	for	for	ADP
bracis-33567	44	20	anns	anns	NOUN
bracis-33567	44	21	with	with	ADP
bracis-33567	44	22	two	two	NUM
bracis-33567	44	23	layers	layer	NOUN
bracis-33567	44	24	and	and	CCONJ
bracis-33567	44	25	tens	ten	NOUN
bracis-33567	44	26	of	of	ADP
bracis-33567	44	27	neurons	neuron	NOUN
bracis-33567	44	28	,	,	PUNCT
bracis-33567	44	29	showing	show	VERB
bracis-33567	44	30	an	an	DET
bracis-33567	44	31	improvement	improvement	NOUN
bracis-33567	44	32	of	of	ADP
bracis-33567	44	33	up	up	ADP
bracis-33567	44	34	to	to	PART
bracis-33567	44	35	18	18	NUM
bracis-33567	44	36	%	%	NOUN
bracis-33567	44	37	.	.	PUNCT
bracis-33567	45	1	surprisingly	surprisingly	ADV
bracis-33567	45	2	,	,	PUNCT
bracis-33567	45	3	both	both	DET
bracis-33567	45	4	methods	method	NOUN
bracis-33567	45	5	exhibit	exhibit	VERB
bracis-33567	45	6	similar	similar	ADJ
bracis-33567	45	7	running	running	NOUN
bracis-33567	45	8	times	time	NOUN
bracis-33567	45	9	for	for	ADP
bracis-33567	45	10	computing	computing	NOUN
bracis-33567	45	11	explanations	explanation	NOUN
bracis-33567	45	12	.	.	PUNCT
bracis-33567	46	1	furthermore	furthermore	ADV
bracis-33567	46	2	,	,	PUNCT
bracis-33567	46	3	our	our	PRON
bracis-33567	46	4	adaptation	adaptation	NOUN
bracis-33567	46	5	outperforms	outperform	VERB
bracis-33567	46	6	the	the	DET
bracis-33567	46	7	other	other	ADJ
bracis-33567	46	8	encoding	encoding	NOUN
bracis-33567	46	9	in	in	ADP
bracis-33567	46	10	the	the	DET
bracis-33567	46	11	overall	overall	ADJ
bracis-33567	46	12	time	time	NOUN
bracis-33567	46	13	,	,	PUNCT
bracis-33567	46	14	encompassing	encompass	VERB
bracis-33567	46	15	both	both	PRON
bracis-33567	46	16	building	build	VERB
bracis-33567	46	17	logical	logical	ADJ
bracis-33567	46	18	constraints	constraint	NOUN
bracis-33567	46	19	and	and	CCONJ
bracis-33567	46	20	computing	computing	NOUN
bracis-33567	46	21	explanations	explanation	NOUN
bracis-33567	46	22	.	.	PUNCT
bracis-33567	47	1	in	in	ADP
bracis-33567	47	2	this	this	DET
bracis-33567	47	3	case	case	NOUN
bracis-33567	47	4	,	,	PUNCT
bracis-33567	47	5	the	the	DET
bracis-33567	47	6	results	result	NOUN
bracis-33567	47	7	indicate	indicate	VERB
bracis-33567	47	8	an	an	DET
bracis-33567	47	9	improvement	improvement	NOUN
bracis-33567	47	10	of	of	ADP
bracis-33567	47	11	up	up	ADP
bracis-33567	47	12	to	to	PART
bracis-33567	47	13	16	16	NUM
bracis-33567	47	14	%	%	NOUN
bracis-33567	47	15	.	.	PUNCT
bracis-33567	48	1	in	in	ADP
bracis-33567	48	2	summary	summary	NOUN
bracis-33567	48	3	,	,	PUNCT
bracis-33567	48	4	our	our	PRON
bracis-33567	48	5	main	main	ADJ
bracis-33567	48	6	contributions	contribution	NOUN
bracis-33567	48	7	are	be	AUX
bracis-33567	48	8	described	describe	VERB
bracis-33567	48	9	in	in	ADP
bracis-33567	48	10	the	the	DET
bracis-33567	48	11	following	following	NOUN
bracis-33567	48	12	:	:	PUNCT
bracis-33567	48	13	adaptation	adaptation	NOUN
bracis-33567	48	14	of	of	ADP
bracis-33567	48	15	the	the	DET
bracis-33567	48	16	encoding	encoding	NOUN
bracis-33567	48	17	proposed	propose	VERB
bracis-33567	48	18	in	in	ADP
bracis-33567	48	19	[	[	X
bracis-33567	48	20	17	17	NUM
bracis-33567	48	21	]	]	PUNCT
bracis-33567	48	22	to	to	PART
bracis-33567	48	23	provide	provide	VERB
bracis-33567	48	24	explanations	explanation	NOUN
bracis-33567	48	25	for	for	ADP
bracis-33567	48	26	anns	ann	NOUN
bracis-33567	48	27	;	;	PUNCT
bracis-33567	48	28	additional	additional	ADJ
bracis-33567	48	29	constraints	constraint	NOUN
bracis-33567	48	30	were	be	AUX
bracis-33567	48	31	incorporated	incorporate	VERB
bracis-33567	48	32	to	to	PART
bracis-33567	48	33	address	address	VERB
bracis-33567	48	34	the	the	DET
bracis-33567	48	35	problem	problem	NOUN
bracis-33567	48	36	of	of	ADP
bracis-33567	48	37	computing	computing	NOUN
bracis-33567	48	38	explanations	explanation	NOUN
bracis-33567	48	39	.	.	PUNCT
bracis-33567	49	1	comparative	comparative	ADJ
bracis-33567	49	2	analysis	analysis	NOUN
bracis-33567	49	3	of	of	ADP
bracis-33567	49	4	the	the	DET
bracis-33567	49	5	running	running	ADJ
bracis-33567	49	6	time	time	NOUN
bracis-33567	49	7	for	for	ADP
bracis-33567	49	8	building	build	VERB
bracis-33567	49	9	the	the	DET
bracis-33567	49	10	logical	logical	ADJ
bracis-33567	49	11	constraints	constraint	NOUN
bracis-33567	49	12	between	between	ADP
bracis-33567	49	13	the	the	DET
bracis-33567	49	14	two	two	NUM
bracis-33567	49	15	approaches	approach	NOUN
bracis-33567	49	16	.	.	PUNCT
bracis-33567	50	1	additionally	additionally	ADV
bracis-33567	50	2	,	,	PUNCT
bracis-33567	50	3	we	we	PRON
bracis-33567	50	4	analyze	analyze	VERB
bracis-33567	50	5	the	the	DET
bracis-33567	50	6	time	time	NOUN
bracis-33567	50	7	for	for	ADP
bracis-33567	50	8	generating	generate	VERB
bracis-33567	50	9	explanations	explanation	NOUN
bracis-33567	50	10	using	use	VERB
bracis-33567	50	11	both	both	DET
bracis-33567	50	12	encodings	encoding	NOUN
bracis-33567	50	13	.	.	PUNCT
bracis-33567	51	1	publicly	publicly	ADV
bracis-33567	51	2	available	available	ADJ
bracis-33567	51	3	implementations	implementation	NOUN
bracis-33567	51	4	of	of	ADP
bracis-33567	51	5	both	both	DET
bracis-33567	51	6	encodings	encoding	NOUN
bracis-33567	51	7	for	for	ADP
bracis-33567	51	8	finding	find	VERB
bracis-33567	51	9	explanations	explanation	NOUN
bracis-33567	51	10	for	for	ADP
bracis-33567	51	11	annsfootnote	annsfootnote	NOUN
bracis-33567	51	12	1	1	NUM
bracis-33567	51	13	.	.	PUNCT
bracis-33567	52	1	in	in	ADP
bracis-33567	52	2	the	the	DET
bracis-33567	52	3	next	next	ADJ
bracis-33567	52	4	section	section	NOUN
bracis-33567	52	5	,	,	PUNCT
bracis-33567	52	6	we	we	PRON
bracis-33567	52	7	review	review	VERB
bracis-33567	52	8	some	some	DET
bracis-33567	52	9	concepts	concept	NOUN
bracis-33567	52	10	and	and	CCONJ
bracis-33567	52	11	terminologies	terminology	NOUN
bracis-33567	52	12	about	about	ADP
bracis-33567	52	13	logic	logic	NOUN
bracis-33567	52	14	,	,	PUNCT
bracis-33567	52	15	milp	milp	ADJ
bracis-33567	52	16	and	and	CCONJ
bracis-33567	52	17	anns	ann	NOUN
bracis-33567	52	18	.	.	PUNCT
bracis-33567	53	1	sections	section	NOUN
bracis-33567	53	2	 	 	SPACE
bracis-33567	53	3	3	3	NUM
bracis-33567	53	4	and	and	CCONJ
bracis-33567	53	5	4	4	NUM
bracis-33567	53	6	show	show	VERB
bracis-33567	53	7	how	how	SCONJ
bracis-33567	53	8	to	to	PART
bracis-33567	53	9	compute	compute	VERB
bracis-33567	53	10	explanations	explanation	NOUN
bracis-33567	53	11	with	with	ADP
bracis-33567	53	12	and	and	CCONJ
bracis-33567	53	13	without	without	ADP
bracis-33567	53	14	implications	implication	NOUN
bracis-33567	53	15	,	,	PUNCT
bracis-33567	53	16	respectively	respectively	ADV
bracis-33567	53	17	.	.	PUNCT
bracis-33567	54	1	section	section	NOUN
bracis-33567	54	2	 	 	SPACE
bracis-33567	54	3	4	4	NUM
bracis-33567	54	4	describes	describe	VERB
bracis-33567	54	5	our	our	PRON
bracis-33567	54	6	adaptation	adaptation	NOUN
bracis-33567	54	7	of	of	ADP
bracis-33567	54	8	the	the	DET
bracis-33567	54	9	encoding	encoding	NOUN
bracis-33567	54	10	proposed	propose	VERB
bracis-33567	54	11	in	in	ADP
bracis-33567	54	12	[	[	X
bracis-33567	54	13	17	17	NUM
bracis-33567	54	14	]	]	PUNCT
bracis-33567	54	15	.	.	PUNCT
bracis-33567	55	1	experiments	experiment	NOUN
bracis-33567	55	2	and	and	CCONJ
bracis-33567	55	3	results	result	NOUN
bracis-33567	55	4	are	be	AUX
bracis-33567	55	5	presented	present	VERB
bracis-33567	55	6	in	in	ADP
bracis-33567	55	7	sect	sect	NOUN
bracis-33567	55	8	.	.	PUNCT
bracis-33567	55	9	 	 	SPACE
bracis-33567	56	1	5	5	NUM
bracis-33567	56	2	.	.	PUNCT
bracis-33567	57	1	finally	finally	ADV
bracis-33567	57	2	,	,	PUNCT
bracis-33567	57	3	conclusions	conclusion	NOUN
bracis-33567	57	4	and	and	CCONJ
bracis-33567	57	5	future	future	ADJ
bracis-33567	57	6	work	work	NOUN
bracis-33567	57	7	are	be	AUX
bracis-33567	57	8	described	describe	VERB
bracis-33567	57	9	in	in	ADP
bracis-33567	57	10	sect	sect	NOUN
bracis-33567	57	11	.	.	PUNCT
bracis-33567	57	12	 	 	SPACE
bracis-33567	58	1	6	6	NUM
bracis-33567	58	2	.	.	SYM
bracis-33567	58	3	2	2	NUM
bracis-33567	58	4	background	background	NOUN
bracis-33567	58	5	in	in	ADP
bracis-33567	58	6	this	this	DET
bracis-33567	58	7	section	section	NOUN
bracis-33567	58	8	,	,	PUNCT
bracis-33567	58	9	we	we	PRON
bracis-33567	58	10	introduce	introduce	VERB
bracis-33567	58	11	some	some	DET
bracis-33567	58	12	initial	initial	ADJ
bracis-33567	58	13	concepts	concept	NOUN
bracis-33567	58	14	and	and	CCONJ
bracis-33567	58	15	terminology	terminology	NOUN
bracis-33567	58	16	to	to	PART
bracis-33567	58	17	understand	understand	VERB
bracis-33567	58	18	the	the	DET
bracis-33567	58	19	rest	rest	NOUN
bracis-33567	58	20	of	of	ADP
bracis-33567	58	21	this	this	DET
bracis-33567	58	22	work	work	NOUN
bracis-33567	58	23	.	.	PUNCT
bracis-33567	59	1	2.1	2.1	NUM
bracis-33567	59	2	first	first	ADJ
bracis-33567	59	3	-	-	PUNCT
bracis-33567	59	4	order	order	NOUN
bracis-33567	59	5	logic	logic	NOUN
bracis-33567	59	6	over	over	ADP
bracis-33567	59	7	 	 	SPACE
bracis-33567	59	8	lra	lra	NOUN
bracis-33567	59	9	in	in	ADP
bracis-33567	59	10	this	this	DET
bracis-33567	59	11	work	work	NOUN
bracis-33567	59	12	,	,	PUNCT
bracis-33567	59	13	we	we	PRON
bracis-33567	59	14	use	use	VERB
bracis-33567	59	15	first	first	ADJ
bracis-33567	59	16	-	-	PUNCT
bracis-33567	59	17	order	order	NOUN
bracis-33567	59	18	logic	logic	NOUN
bracis-33567	59	19	(	(	PUNCT
bracis-33567	59	20	fol	fol	NOUN
bracis-33567	59	21	)	)	PUNCT
bracis-33567	59	22	to	to	PART
bracis-33567	59	23	give	give	VERB
bracis-33567	59	24	explanations	explanation	NOUN
bracis-33567	59	25	with	with	ADP
bracis-33567	59	26	guarantees	guarantee	NOUN
bracis-33567	59	27	of	of	ADP
bracis-33567	59	28	correctness	correctness	NOUN
bracis-33567	59	29	.	.	PUNCT
bracis-33567	60	1	we	we	PRON
bracis-33567	60	2	use	use	VERB
bracis-33567	60	3	quantifier	quantifier	NOUN
bracis-33567	60	4	-	-	PUNCT
bracis-33567	60	5	free	free	ADJ
bracis-33567	60	6	first	first	ADJ
bracis-33567	60	7	-	-	PUNCT
bracis-33567	60	8	order	order	NOUN
bracis-33567	60	9	formulas	formula	NOUN
bracis-33567	60	10	over	over	ADP
bracis-33567	60	11	the	the	DET
bracis-33567	60	12	theory	theory	NOUN
bracis-33567	60	13	of	of	ADP
bracis-33567	60	14	linear	linear	PROPN
bracis-33567	60	15	real	real	ADJ
bracis-33567	60	16	arithmetic	arithmetic	ADJ
bracis-33567	60	17	(	(	PUNCT
bracis-33567	60	18	lra	lra	NOUN
bracis-33567	60	19	)	)	PUNCT
bracis-33567	60	20	.	.	PUNCT
bracis-33567	61	1	then	then	ADV
bracis-33567	61	2	,	,	PUNCT
bracis-33567	61	3	first	first	ADJ
bracis-33567	61	4	-	-	PUNCT
bracis-33567	61	5	order	order	NOUN
bracis-33567	61	6	variables	variable	NOUN
bracis-33567	61	7	are	be	AUX
bracis-33567	61	8	allowed	allow	VERB
bracis-33567	61	9	to	to	PART
bracis-33567	61	10	take	take	VERB
bracis-33567	61	11	values	value	NOUN
bracis-33567	61	12	from	from	ADP
bracis-33567	61	13	the	the	DET
bracis-33567	61	14	real	real	ADJ
bracis-33567	61	15	numbers	number	NOUN
bracis-33567	61	16	\(\mathbb	\(\mathbb	VERB
bracis-33567	61	17	{	{	PUNCT
bracis-33567	61	18	r}\	r}\	NUM
bracis-33567	61	19	)	)	PUNCT
bracis-33567	61	20	.	.	PUNCT
bracis-33567	62	1	for	for	ADP
bracis-33567	62	2	details	detail	NOUN
bracis-33567	62	3	,	,	PUNCT
bracis-33567	62	4	see	see	VERB
bracis-33567	62	5	[	[	X
bracis-33567	62	6	11	11	NUM
bracis-33567	62	7	]	]	PUNCT
bracis-33567	62	8	.	.	PUNCT
bracis-33567	63	1	therefore	therefore	ADV
bracis-33567	63	2	,	,	PUNCT
bracis-33567	63	3	we	we	PRON
bracis-33567	63	4	consider	consider	VERB
bracis-33567	63	5	formulas	formula	NOUN
bracis-33567	63	6	as	as	SCONJ
bracis-33567	63	7	defined	define	VERB
bracis-33567	63	8	below	below	ADP
bracis-33567	63	9	:	:	PUNCT
bracis-33567	63	10	$	$	SYM
bracis-33567	63	11	$	$	SYM
bracis-33567	63	12	\begin{aligned	\begin{aligne	VERB
bracis-33567	63	13	}	}	PUNCT
bracis-33567	63	14	\begin{aligned	\begin{aligne	VERB
bracis-33567	63	15	}	}	PUNCT
bracis-33567	63	16	f	f	PROPN
bracis-33567	63	17	,	,	PUNCT
bracis-33567	63	18	g	g	PROPN
bracis-33567	63	19	&	&	CCONJ
bracis-33567	63	20	:	:	PUNCT
bracis-33567	63	21	=	=	X
bracis-33567	63	22	p	p	X
bracis-33567	63	23	\mid	\mid	PROPN
bracis-33567	63	24	(	(	PUNCT
bracis-33567	63	25	f	f	PROPN
bracis-33567	63	26	\wedge	\wedge	PROPN
bracis-33567	63	27	g	g	NOUN
bracis-33567	63	28	)	)	PUNCT
bracis-33567	63	29	\mid	\mid	ADP
bracis-33567	63	30	(	(	PUNCT
bracis-33567	63	31	f	f	PROPN
bracis-33567	63	32	\vee	\vee	PROPN
bracis-33567	63	33	g	g	PROPN
bracis-33567	63	34	)	)	PUNCT
bracis-33567	63	35	\mid	\mid	ADP
bracis-33567	63	36	(	(	PUNCT
bracis-33567	63	37	\lnot	\lnot	PROPN
bracis-33567	63	38	f	f	PROPN
bracis-33567	63	39	)	)	PUNCT
bracis-33567	63	40	\mid	\mid	ADP
bracis-33567	63	41	(	(	PUNCT
bracis-33567	63	42	f	f	PROPN
bracis-33567	63	43	\rightarrow	\rightarrow	PROPN
bracis-33567	63	44	g),\\	g),\\	PROPN
bracis-33567	63	45	p	p	PROPN
bracis-33567	63	46	&	&	CCONJ
bracis-33567	63	47	:	:	PUNCT
bracis-33567	63	48	=	=	SYM
bracis-33567	63	49	\sum	\sum	NOUN
bracis-33567	63	50	^n_{i=1	^n_{i=1	PUNCT
bracis-33567	63	51	}	}	PUNCT
bracis-33567	63	52	w_i	w_i	PROPN
bracis-33567	63	53	x_i	x_i	PRON
bracis-33567	63	54	\le	\le	PROPN
bracis-33567	63	55	b	b	NOUN
bracis-33567	63	56	\mid	\mid	PROPN
bracis-33567	63	57	\sum	\sum	NOUN
bracis-33567	63	58	^n_{i=1	^n_{i=1	PUNCT
bracis-33567	63	59	}	}	PUNCT
bracis-33567	63	60	w_i	w_i	PUNCT
bracis-33567	63	61	x_i	x_i	X
bracis-33567	63	62	<	<	X
bracis-33567	63	63	b	b	PROPN
bracis-33567	63	64	,	,	PUNCT
bracis-33567	63	65	\end{aligned	\end{aligne	VERB
bracis-33567	63	66	}	}	PUNCT
bracis-33567	63	67	\end{aligned}$$	\end{aligned}$$	X
bracis-33567	63	68	(	(	PUNCT
bracis-33567	63	69	1	1	NUM
bracis-33567	63	70	)	)	PUNCT
bracis-33567	63	71	such	such	ADJ
bracis-33567	63	72	that	that	SCONJ
bracis-33567	63	73	f	f	PROPN
bracis-33567	63	74	and	and	CCONJ
bracis-33567	63	75	g	g	PROPN
bracis-33567	63	76	are	be	AUX
bracis-33567	63	77	quantifier	quantifier	NOUN
bracis-33567	63	78	-	-	PUNCT
bracis-33567	63	79	free	free	ADJ
bracis-33567	63	80	first	first	ADJ
bracis-33567	63	81	-	-	PUNCT
bracis-33567	63	82	order	order	NOUN
bracis-33567	63	83	formulas	formula	NOUN
bracis-33567	63	84	over	over	ADP
bracis-33567	63	85	the	the	DET
bracis-33567	63	86	theory	theory	NOUN
bracis-33567	63	87	of	of	ADP
bracis-33567	63	88	linear	linear	PROPN
bracis-33567	63	89	real	real	ADJ
bracis-33567	63	90	arithmetic	arithmetic	ADJ
bracis-33567	63	91	.	.	PUNCT
bracis-33567	64	1	moreover	moreover	ADV
bracis-33567	64	2	,	,	PUNCT
bracis-33567	64	3	p	p	NOUN
bracis-33567	64	4	represents	represent	VERB
bracis-33567	64	5	the	the	DET
bracis-33567	64	6	atomic	atomic	ADJ
bracis-33567	64	7	formulas	formula	NOUN
bracis-33567	64	8	such	such	ADJ
bracis-33567	64	9	that	that	DET
bracis-33567	64	10	\(n	\(n	NOUN
bracis-33567	64	11	\ge	\ge	PROPN
bracis-33567	64	12	1\	1\	NUM
bracis-33567	64	13	)	)	PUNCT
bracis-33567	64	14	,	,	PUNCT
bracis-33567	64	15	each	each	DET
bracis-33567	64	16	\(w_i\	\(w_i\	NOUN
bracis-33567	64	17	)	)	PUNCT
bracis-33567	64	18	and	and	CCONJ
bracis-33567	64	19	b	b	NOUN
bracis-33567	64	20	are	be	AUX
bracis-33567	64	21	fixed	fix	VERB
bracis-33567	64	22	real	real	ADJ
bracis-33567	64	23	numbers	number	NOUN
bracis-33567	64	24	,	,	PUNCT
bracis-33567	64	25	and	and	CCONJ
bracis-33567	64	26	each	each	DET
bracis-33567	64	27	\(x_i\	\(x_i\	NOUN
bracis-33567	64	28	)	)	PUNCT
bracis-33567	64	29	is	be	AUX
bracis-33567	64	30	a	a	DET
bracis-33567	64	31	first	first	ADJ
bracis-33567	64	32	-	-	PUNCT
bracis-33567	64	33	order	order	NOUN
bracis-33567	64	34	variable	variable	NOUN
bracis-33567	64	35	.	.	PUNCT
bracis-33567	65	1	observe	observe	VERB
bracis-33567	65	2	that	that	SCONJ
bracis-33567	65	3	we	we	PRON
bracis-33567	65	4	allow	allow	VERB
bracis-33567	65	5	the	the	DET
bracis-33567	65	6	use	use	NOUN
bracis-33567	65	7	of	of	ADP
bracis-33567	65	8	other	other	ADJ
bracis-33567	65	9	letters	letter	NOUN
bracis-33567	65	10	for	for	ADP
bracis-33567	65	11	variables	variable	NOUN
bracis-33567	65	12	instead	instead	ADV
bracis-33567	65	13	of	of	ADP
bracis-33567	65	14	\(x_i\	\(x_i\	NOUN
bracis-33567	65	15	)	)	PUNCT
bracis-33567	65	16	,	,	PUNCT
bracis-33567	65	17	such	such	ADJ
bracis-33567	65	18	as	as	ADP
bracis-33567	65	19	\(s_i\	\(s_i\	NOUN
bracis-33567	65	20	)	)	PUNCT
bracis-33567	65	21	,	,	PUNCT
bracis-33567	65	22	\(z_i\	\(z_i\	NOUN
bracis-33567	65	23	)	)	PUNCT
bracis-33567	65	24	,	,	PUNCT
bracis-33567	65	25	\(q_i\	\(q_i\	NOUN
bracis-33567	65	26	)	)	PUNCT
bracis-33567	65	27	.	.	PUNCT
bracis-33567	66	1	for	for	ADP
bracis-33567	66	2	example	example	NOUN
bracis-33567	66	3	,	,	PUNCT
bracis-33567	66	4	\((2.5x_1	\((2.5x_1	PROPN
bracis-33567	66	5	+	+	CCONJ
bracis-33567	66	6	3.1x_2	3.1x_2	NUM
bracis-33567	66	7	\ge	\ge	PROPN
bracis-33567	66	8	6	6	NUM
bracis-33567	66	9	)	)	PUNCT
bracis-33567	66	10	\wedge	\wedge	PROPN
bracis-33567	66	11	(	(	PUNCT
bracis-33567	66	12	x_1=1	x_1=1	PROPN
bracis-33567	66	13	\vee	\vee	PROPN
bracis-33567	66	14	x_1=2	x_1=2	PROPN
bracis-33567	66	15	)	)	PUNCT
bracis-33567	66	16	\wedge	\wedge	PROPN
bracis-33567	66	17	(	(	PUNCT
bracis-33567	66	18	x_1=2	x_1=2	PROPN
bracis-33567	66	19	\rightarrow	\rightarrow	PROPN
bracis-33567	66	20	x_2	x_2	PROPN
bracis-33567	66	21	\le	\le	PROPN
bracis-33567	66	22	1.1)\	1.1)\	NUM
bracis-33567	66	23	)	)	PUNCT
bracis-33567	66	24	is	be	AUX
bracis-33567	66	25	a	a	DET
bracis-33567	66	26	formula	formula	NOUN
bracis-33567	66	27	by	by	ADP
bracis-33567	66	28	this	this	DET
bracis-33567	66	29	definition	definition	NOUN
bracis-33567	66	30	.	.	PUNCT
bracis-33567	67	1	observe	observe	VERB
bracis-33567	67	2	that	that	SCONJ
bracis-33567	67	3	we	we	PRON
bracis-33567	67	4	allow	allow	VERB
bracis-33567	67	5	standard	standard	ADJ
bracis-33567	67	6	abbreviations	abbreviation	NOUN
bracis-33567	67	7	as	as	ADP
bracis-33567	67	8	\(\lnot	\(\lnot	NOUN
bracis-33567	67	9	(	(	PUNCT
bracis-33567	67	10	2.5x_1	2.5x_1	NUM
bracis-33567	67	11	+	+	CCONJ
bracis-33567	67	12	3.1x_2	3.1x_2	NUM
bracis-33567	67	13	<	<	X
bracis-33567	67	14	6)\	6)\	NUM
bracis-33567	67	15	)	)	PUNCT
bracis-33567	67	16	for	for	ADP
bracis-33567	67	17	\(2.5x_1	\(2.5x_1	PROPN
bracis-33567	67	18	+	+	NOUN
bracis-33567	67	19	3.1x_2	3.1x_2	NUM
bracis-33567	67	20	\ge	\ge	PROPN
bracis-33567	67	21	6\	6\	NUM
bracis-33567	67	22	)	)	PUNCT
bracis-33567	67	23	.	.	PUNCT
bracis-33567	68	1	since	since	SCONJ
bracis-33567	68	2	we	we	PRON
bracis-33567	68	3	are	be	AUX
bracis-33567	68	4	assuming	assume	VERB
bracis-33567	68	5	the	the	DET
bracis-33567	68	6	semantics	semantic	NOUN
bracis-33567	68	7	of	of	ADP
bracis-33567	68	8	formulas	formula	NOUN
bracis-33567	68	9	over	over	ADP
bracis-33567	68	10	the	the	DET
bracis-33567	68	11	domain	domain	NOUN
bracis-33567	68	12	of	of	ADP
bracis-33567	68	13	real	real	ADJ
bracis-33567	68	14	numbers	number	NOUN
bracis-33567	68	15	,	,	PUNCT
bracis-33567	68	16	an	an	DET
bracis-33567	68	17	assignment	assignment	NOUN
bracis-33567	68	18	\(\mathcal	\(\mathcal	ADJ
bracis-33567	68	19	{	{	PUNCT
bracis-33567	68	20	a}\	a}\	NUM
bracis-33567	68	21	)	)	PUNCT
bracis-33567	68	22	for	for	ADP
bracis-33567	68	23	a	a	DET
bracis-33567	68	24	formula	formula	NOUN
bracis-33567	68	25	f	f	NOUN
bracis-33567	68	26	is	be	AUX
bracis-33567	68	27	a	a	DET
bracis-33567	68	28	mapping	mapping	NOUN
bracis-33567	68	29	from	from	ADP
bracis-33567	68	30	the	the	DET
bracis-33567	68	31	first	first	ADJ
bracis-33567	68	32	-	-	PUNCT
bracis-33567	68	33	order	order	NOUN
bracis-33567	68	34	variables	variable	NOUN
bracis-33567	68	35	of	of	ADP
bracis-33567	68	36	f	f	PROPN
bracis-33567	68	37	to	to	ADP
bracis-33567	68	38	elements	element	NOUN
bracis-33567	68	39	in	in	ADP
bracis-33567	68	40	the	the	DET
bracis-33567	68	41	domain	domain	NOUN
bracis-33567	68	42	of	of	ADP
bracis-33567	68	43	real	real	ADJ
bracis-33567	68	44	numbers	number	NOUN
bracis-33567	68	45	.	.	PUNCT
bracis-33567	69	1	for	for	ADP
bracis-33567	69	2	instance	instance	NOUN
bracis-33567	69	3	,	,	PUNCT
bracis-33567	69	4	\(\{x_1	\(\{x_1	PROPN
bracis-33567	69	5	\mapsto	\mapsto	PROPN
bracis-33567	69	6	2.3	2.3	NUM
bracis-33567	69	7	,	,	PUNCT
bracis-33567	69	8	x_2	x_2	PROPN
bracis-33567	69	9	\mapsto	\mapsto	PROPN
bracis-33567	69	10	1\}\	1\}\	NUM
bracis-33567	69	11	)	)	PUNCT
bracis-33567	69	12	is	be	AUX
bracis-33567	69	13	an	an	DET
bracis-33567	69	14	assignment	assignment	NOUN
bracis-33567	69	15	for	for	ADP
bracis-33567	69	16	\((2.5x_1	\((2.5x_1	PROPN
bracis-33567	69	17	+	+	CCONJ
bracis-33567	69	18	3.1x_2	3.1x_2	NUM
bracis-33567	69	19	\ge	\ge	PROPN
bracis-33567	69	20	6	6	NUM
bracis-33567	69	21	)	)	PUNCT
bracis-33567	69	22	\wedge	\wedge	PROPN
bracis-33567	69	23	(	(	PUNCT
bracis-33567	69	24	x_1=1	x_1=1	PROPN
bracis-33567	69	25	\vee	\vee	PROPN
bracis-33567	69	26	x_1=2	x_1=2	PROPN
bracis-33567	69	27	)	)	PUNCT
bracis-33567	69	28	\wedge	\wedge	PROPN
bracis-33567	69	29	(	(	PUNCT
bracis-33567	69	30	x_1=2	x_1=2	PROPN
bracis-33567	69	31	\rightarrow	\rightarrow	PROPN
bracis-33567	69	32	x_2	x_2	PROPN
bracis-33567	69	33	\le	\le	PROPN
bracis-33567	69	34	1.1)\	1.1)\	NUM
bracis-33567	69	35	)	)	PUNCT
bracis-33567	69	36	.	.	PUNCT
bracis-33567	70	1	an	an	DET
bracis-33567	70	2	assignment	assignment	NOUN
bracis-33567	70	3	\(\mathcal	\(\mathcal	ADJ
bracis-33567	70	4	{	{	PUNCT
bracis-33567	70	5	a}\	a}\	NUM
bracis-33567	70	6	)	)	PUNCT
bracis-33567	70	7	satisfies	satisfy	VERB
bracis-33567	70	8	a	a	DET
bracis-33567	70	9	formula	formula	NOUN
bracis-33567	70	10	f	f	NOUN
bracis-33567	71	1	if	if	SCONJ
bracis-33567	71	2	f	f	PROPN
bracis-33567	71	3	is	be	AUX
bracis-33567	71	4	true	true	ADJ
bracis-33567	71	5	under	under	ADP
bracis-33567	71	6	this	this	DET
bracis-33567	71	7	assignment	assignment	NOUN
bracis-33567	71	8	.	.	PUNCT
bracis-33567	72	1	for	for	ADP
bracis-33567	72	2	example	example	NOUN
bracis-33567	72	3	,	,	PUNCT
bracis-33567	72	4	\(\{x_1	\(\{x_1	PROPN
bracis-33567	72	5	\mapsto	\mapsto	PROPN
bracis-33567	72	6	2	2	NUM
bracis-33567	72	7	,	,	PUNCT
bracis-33567	72	8	x_2	x_2	PROPN
bracis-33567	72	9	\mapsto	\mapsto	PROPN
bracis-33567	72	10	1.05\}\	1.05\}\	NUM
bracis-33567	72	11	)	)	PUNCT
bracis-33567	72	12	satisfies	satisfy	VERB
bracis-33567	72	13	the	the	DET
bracis-33567	72	14	formula	formula	NOUN
bracis-33567	72	15	in	in	ADP
bracis-33567	72	16	the	the	DET
bracis-33567	72	17	above	above	ADJ
bracis-33567	72	18	example	example	NOUN
bracis-33567	72	19	,	,	PUNCT
bracis-33567	72	20	whereas	whereas	SCONJ
bracis-33567	72	21	\(\{x_1	\(\{x_1	PROPN
bracis-33567	72	22	\mapsto	\mapsto	PROPN
bracis-33567	72	23	2.3	2.3	NUM
bracis-33567	72	24	,	,	PUNCT
bracis-33567	72	25	x_2	x_2	PROPN
bracis-33567	72	26	\mapsto	\mapsto	PROPN
bracis-33567	72	27	1\}\	1\}\	NUM
bracis-33567	72	28	)	)	PUNCT
bracis-33567	72	29	does	do	AUX
bracis-33567	72	30	not	not	PART
bracis-33567	72	31	satisfy	satisfy	VERB
bracis-33567	72	32	it	it	PRON
bracis-33567	72	33	.	.	PUNCT
bracis-33567	73	1	a	a	DET
bracis-33567	73	2	formula	formula	NOUN
bracis-33567	73	3	f	f	NOUN
bracis-33567	73	4	is	be	AUX
bracis-33567	73	5	satisfiable	satisfiable	ADJ
bracis-33567	73	6	if	if	SCONJ
bracis-33567	73	7	there	there	PRON
bracis-33567	73	8	exists	exist	VERB
bracis-33567	73	9	a	a	DET
bracis-33567	73	10	satisfying	satisfy	VERB
bracis-33567	73	11	assignment	assignment	NOUN
bracis-33567	73	12	of	of	ADP
bracis-33567	73	13	f.	f.	PROPN
bracis-33567	73	14	to	to	PART
bracis-33567	73	15	give	give	VERB
bracis-33567	73	16	an	an	DET
bracis-33567	73	17	example	example	NOUN
bracis-33567	73	18	,	,	PUNCT
bracis-33567	73	19	the	the	DET
bracis-33567	73	20	formula	formula	NOUN
bracis-33567	73	21	in	in	ADP
bracis-33567	73	22	the	the	DET
bracis-33567	73	23	above	above	ADJ
bracis-33567	73	24	example	example	NOUN
bracis-33567	73	25	is	be	AUX
bracis-33567	73	26	satisfiable	satisfiable	ADJ
bracis-33567	73	27	since	since	SCONJ
bracis-33567	73	28	\(\{x_1	\(\{x_1	PROPN
bracis-33567	73	29	\mapsto	\mapsto	PROPN
bracis-33567	73	30	2	2	NUM
bracis-33567	73	31	,	,	PUNCT
bracis-33567	73	32	x_2	x_2	PROPN
bracis-33567	73	33	\mapsto	\mapsto	PROPN
bracis-33567	73	34	1.05\}\	1.05\}\	NUM
bracis-33567	73	35	)	)	PUNCT
bracis-33567	73	36	satisfies	satisfy	VERB
bracis-33567	73	37	it	it	PRON
bracis-33567	73	38	.	.	PUNCT
bracis-33567	74	1	as	as	ADP
bracis-33567	74	2	another	another	DET
bracis-33567	74	3	example	example	NOUN
bracis-33567	74	4	,	,	PUNCT
bracis-33567	74	5	the	the	DET
bracis-33567	74	6	formula	formula	NOUN
bracis-33567	74	7	\((x_1	\((x_1	PROPN
bracis-33567	74	8	\ge	\ge	PROPN
bracis-33567	74	9	2	2	NUM
bracis-33567	74	10	)	)	PUNCT
bracis-33567	74	11	\wedge	\wedge	PROPN
bracis-33567	74	12	(	(	PUNCT
bracis-33567	74	13	x_1	x_1	X
bracis-33567	74	14	<	<	X
bracis-33567	74	15	1)\	1)\	NUM
bracis-33567	74	16	)	)	PUNCT
bracis-33567	74	17	is	be	AUX
bracis-33567	74	18	unsatisfiable	unsatisfiable	ADJ
bracis-33567	74	19	since	since	SCONJ
bracis-33567	74	20	no	no	DET
bracis-33567	74	21	assignment	assignment	NOUN
bracis-33567	74	22	satisfies	satisfy	VERB
bracis-33567	74	23	it	it	PRON
bracis-33567	74	24	.	.	PUNCT
bracis-33567	75	1	given	give	VERB
bracis-33567	75	2	formulas	formula	NOUN
bracis-33567	75	3	f	f	PROPN
bracis-33567	75	4	and	and	CCONJ
bracis-33567	75	5	g	g	PROPN
bracis-33567	75	6	,	,	PUNCT
bracis-33567	75	7	the	the	DET
bracis-33567	75	8	notation	notation	NOUN
bracis-33567	75	9	\(f	\(f	PRON
bracis-33567	75	10	\models	\models	PROPN
bracis-33567	75	11	g\	g\	PROPN
bracis-33567	75	12	)	)	PUNCT
bracis-33567	75	13	is	be	AUX
bracis-33567	75	14	used	use	VERB
bracis-33567	75	15	to	to	PART
bracis-33567	75	16	denote	denote	VERB
bracis-33567	75	17	logical	logical	ADJ
bracis-33567	75	18	consequence	consequence	NOUN
bracis-33567	75	19	or	or	CCONJ
bracis-33567	75	20	entailment	entailment	ADJ
bracis-33567	75	21	,	,	PUNCT
bracis-33567	75	22	i.e.	i.e.	X
bracis-33567	75	23	,	,	PUNCT
bracis-33567	75	24	each	each	DET
bracis-33567	75	25	assignment	assignment	NOUN
bracis-33567	75	26	that	that	SCONJ
bracis-33567	75	27	satisfies	satisfy	VERB
bracis-33567	75	28	f	f	PROPN
bracis-33567	75	29	also	also	ADV
bracis-33567	75	30	satisfies	satisfy	VERB
bracis-33567	75	31	g.	g.	PROPN
bracis-33567	75	32	as	as	ADP
bracis-33567	75	33	an	an	DET
bracis-33567	75	34	illustrative	illustrative	ADJ
bracis-33567	75	35	example	example	NOUN
bracis-33567	75	36	,	,	PUNCT
bracis-33567	75	37	let	let	VERB
bracis-33567	75	38	\(f	\(f	ADJ
bracis-33567	75	39	=	=	SYM
bracis-33567	75	40	(	(	PUNCT
bracis-33567	75	41	x_1	x_1	NOUN
bracis-33567	75	42	=	=	SYM
bracis-33567	75	43	2	2	NUM
bracis-33567	75	44	\wedge	\wedge	PROPN
bracis-33567	75	45	x_2	x_2	PROPN
bracis-33567	75	46	\ge	\ge	PROPN
bracis-33567	75	47	1)\	1)\	NUM
bracis-33567	75	48	)	)	PUNCT
bracis-33567	75	49	and	and	CCONJ
bracis-33567	75	50	\(g	\(g	NOUN
bracis-33567	75	51	=	=	SYM
bracis-33567	75	52	(	(	PUNCT
bracis-33567	75	53	2.5x_1	2.5x_1	NUM
bracis-33567	75	54	+	+	CCONJ
bracis-33567	75	55	x_2	x_2	PROPN
bracis-33567	75	56	\ge	\ge	PROPN
bracis-33567	75	57	5	5	NUM
bracis-33567	75	58	)	)	PUNCT
bracis-33567	75	59	\wedge	\wedge	PROPN
bracis-33567	75	60	(	(	PUNCT
bracis-33567	75	61	x_1=1	x_1=1	PROPN
bracis-33567	75	62	\vee	\vee	PROPN
bracis-33567	75	63	x_1=2)\	x_1=2)\	NUM
bracis-33567	75	64	)	)	PUNCT
bracis-33567	75	65	.	.	PUNCT
bracis-33567	76	1	then	then	ADV
bracis-33567	76	2	,	,	PUNCT
bracis-33567	76	3	\(f	\(f	X
bracis-33567	76	4	\models	\models	PROPN
bracis-33567	76	5	g\	g\	PROPN
bracis-33567	76	6	)	)	PUNCT
bracis-33567	76	7	.	.	PUNCT
bracis-33567	77	1	the	the	DET
bracis-33567	77	2	essence	essence	NOUN
bracis-33567	77	3	of	of	ADP
bracis-33567	77	4	entailment	entailment	PROPN
bracis-33567	77	5	lies	lie	VERB
bracis-33567	77	6	in	in	ADP
bracis-33567	77	7	ensuring	ensure	VERB
bracis-33567	77	8	the	the	DET
bracis-33567	77	9	correctness	correctness	NOUN
bracis-33567	77	10	of	of	ADP
bracis-33567	77	11	the	the	DET
bracis-33567	77	12	conclusion	conclusion	NOUN
bracis-33567	77	13	g	g	PROPN
bracis-33567	77	14	based	base	VERB
bracis-33567	77	15	on	on	ADP
bracis-33567	77	16	the	the	DET
bracis-33567	77	17	given	give	VERB
bracis-33567	77	18	premise	premise	NOUN
bracis-33567	77	19	f.	f.	PROPN
bracis-33567	77	20	in	in	ADP
bracis-33567	77	21	the	the	DET
bracis-33567	77	22	context	context	NOUN
bracis-33567	77	23	of	of	ADP
bracis-33567	77	24	computing	computing	NOUN
bracis-33567	77	25	explanations	explanation	NOUN
bracis-33567	77	26	,	,	PUNCT
bracis-33567	77	27	as	as	SCONJ
bracis-33567	77	28	presented	present	VERB
bracis-33567	77	29	in	in	ADP
bracis-33567	77	30	[	[	X
bracis-33567	77	31	8	8	NUM
bracis-33567	77	32	]	]	PUNCT
bracis-33567	77	33	,	,	PUNCT
bracis-33567	77	34	logical	logical	ADJ
bracis-33567	77	35	consequence	consequence	NOUN
bracis-33567	77	36	serves	serve	VERB
bracis-33567	77	37	as	as	ADP
bracis-33567	77	38	a	a	DET
bracis-33567	77	39	fundamental	fundamental	ADJ
bracis-33567	77	40	tool	tool	NOUN
bracis-33567	77	41	for	for	ADP
bracis-33567	77	42	guaranteeing	guarantee	VERB
bracis-33567	77	43	the	the	DET
bracis-33567	77	44	correctness	correctness	NOUN
bracis-33567	77	45	of	of	ADP
bracis-33567	77	46	predictions	prediction	NOUN
bracis-33567	77	47	made	make	VERB
bracis-33567	77	48	by	by	ADP
bracis-33567	77	49	anns	ann	NOUN
bracis-33567	77	50	.	.	PUNCT
bracis-33567	78	1	therefore	therefore	ADV
bracis-33567	78	2	,	,	PUNCT
bracis-33567	78	3	our	our	PRON
bracis-33567	78	4	adaptation	adaptation	NOUN
bracis-33567	78	5	of	of	ADP
bracis-33567	78	6	the	the	DET
bracis-33567	78	7	encoding	encoding	NOUN
bracis-33567	78	8	proposed	propose	VERB
bracis-33567	78	9	by	by	ADP
bracis-33567	78	10	tjeng	tjeng	PROPN
bracis-33567	78	11	et	et	PROPN
bracis-33567	78	12	al	al	PROPN
bracis-33567	78	13	.	.	PUNCT
bracis-33567	79	1	[	[	X
bracis-33567	79	2	17	17	NUM
bracis-33567	79	3	]	]	PUNCT
bracis-33567	79	4	also	also	ADV
bracis-33567	79	5	incorporates	incorporate	VERB
bracis-33567	79	6	the	the	DET
bracis-33567	79	7	principles	principle	NOUN
bracis-33567	79	8	of	of	ADP
bracis-33567	79	9	entailment	entailment	NOUN
bracis-33567	79	10	for	for	ADP
bracis-33567	79	11	computing	computing	NOUN
bracis-33567	79	12	explanations	explanation	NOUN
bracis-33567	79	13	.	.	PUNCT
bracis-33567	80	1	the	the	DET
bracis-33567	80	2	relationship	relationship	NOUN
bracis-33567	80	3	between	between	ADP
bracis-33567	80	4	satisfiability	satisfiability	NOUN
bracis-33567	80	5	and	and	CCONJ
bracis-33567	80	6	entailment	entailment	NOUN
bracis-33567	80	7	is	be	AUX
bracis-33567	80	8	a	a	DET
bracis-33567	80	9	fundamental	fundamental	ADJ
bracis-33567	80	10	aspect	aspect	NOUN
bracis-33567	80	11	of	of	ADP
bracis-33567	80	12	logic	logic	NOUN
bracis-33567	80	13	.	.	PUNCT
bracis-33567	81	1	it	it	PRON
bracis-33567	81	2	is	be	AUX
bracis-33567	81	3	widely	widely	ADV
bracis-33567	81	4	known	know	VERB
bracis-33567	81	5	that	that	SCONJ
bracis-33567	81	6	,	,	PUNCT
bracis-33567	81	7	for	for	ADP
bracis-33567	81	8	all	all	DET
bracis-33567	81	9	formulas	formula	NOUN
bracis-33567	81	10	f	f	PROPN
bracis-33567	81	11	and	and	CCONJ
bracis-33567	81	12	g	g	NOUN
bracis-33567	81	13	,	,	PUNCT
bracis-33567	81	14	it	it	PRON
bracis-33567	81	15	holds	hold	VERB
bracis-33567	81	16	that	that	SCONJ
bracis-33567	81	17	\(f	\(f	ADJ
bracis-33567	81	18	\models	\models	PROPN
bracis-33567	81	19	g\	g\	PROPN
bracis-33567	81	20	)	)	PUNCT
bracis-33567	81	21	iff	iff	PROPN
bracis-33567	81	22	\(f	\(f	ADJ
bracis-33567	81	23	\wedge	\wedge	PROPN
bracis-33567	81	24	\lnot	\lnot	PROPN
bracis-33567	81	25	g\	g\	PROPN
bracis-33567	81	26	)	)	PUNCT
bracis-33567	81	27	is	be	AUX
bracis-33567	81	28	unsatisfiable	unsatisfiable	ADJ
bracis-33567	81	29	.	.	PUNCT
bracis-33567	82	1	for	for	ADP
bracis-33567	82	2	instance	instance	NOUN
bracis-33567	82	3	,	,	PUNCT
bracis-33567	82	4	\	\	PROPN
bracis-33567	82	5	(	(	PUNCT
bracis-33567	82	6	(	(	PUNCT
bracis-33567	82	7	x_1	x_1	X
bracis-33567	82	8	=	=	SYM
bracis-33567	82	9	2	2	NUM
bracis-33567	82	10	\wedge	\wedge	PROPN
bracis-33567	82	11	x_2	x_2	PROPN
bracis-33567	82	12	\ge	\ge	PROPN
bracis-33567	82	13	1	1	NUM
bracis-33567	82	14	)	)	PUNCT
bracis-33567	82	15	\wedge	\wedge	PROPN
bracis-33567	82	16	\lnot	\lnot	PROPN
bracis-33567	82	17	(	(	PUNCT
bracis-33567	82	18	(	(	PUNCT
bracis-33567	82	19	2.5x_1	2.5x_1	NUM
bracis-33567	82	20	+	+	CCONJ
bracis-33567	82	21	x_2	x_2	PROPN
bracis-33567	82	22	\ge	\ge	PROPN
bracis-33567	82	23	5	5	NUM
bracis-33567	82	24	)	)	PUNCT
bracis-33567	82	25	\wedge	\wedge	PROPN
bracis-33567	82	26	(	(	PUNCT
bracis-33567	82	27	x_1=1	x_1=1	PROPN
bracis-33567	82	28	\vee	\vee	PROPN
bracis-33567	82	29	x_1=2))\	x_1=2))\	PROPN
bracis-33567	82	30	)	)	PUNCT
bracis-33567	82	31	has	have	VERB
bracis-33567	82	32	no	no	DET
bracis-33567	82	33	satisfying	satisfying	ADJ
bracis-33567	82	34	assignment	assignment	NOUN
bracis-33567	82	35	since	since	SCONJ
bracis-33567	82	36	an	an	DET
bracis-33567	82	37	assignment	assignment	NOUN
bracis-33567	82	38	that	that	PRON
bracis-33567	82	39	satisfies	satisfy	VERB
bracis-33567	82	40	\((x_1	\((x_1	PROPN
bracis-33567	82	41	=	=	SYM
bracis-33567	82	42	2	2	NUM
bracis-33567	82	43	\wedge	\wedge	PROPN
bracis-33567	82	44	x_2	x_2	PROPN
bracis-33567	82	45	\ge	\ge	PROPN
bracis-33567	82	46	1)\	1)\	NUM
bracis-33567	82	47	)	)	PUNCT
bracis-33567	82	48	also	also	ADV
bracis-33567	82	49	satisfies	satisfy	VERB
bracis-33567	82	50	\((2.5x_1	\((2.5x_1	PROPN
bracis-33567	82	51	+	+	CCONJ
bracis-33567	82	52	x_2	x_2	PROPN
bracis-33567	82	53	\ge	\ge	PROPN
bracis-33567	82	54	5	5	NUM
bracis-33567	82	55	)	)	PUNCT
bracis-33567	82	56	\wedge	\wedge	PROPN
bracis-33567	82	57	(	(	PUNCT
bracis-33567	82	58	x_1=1	x_1=1	PROPN
bracis-33567	82	59	\vee	\vee	PROPN
bracis-33567	82	60	x_1=2)\	x_1=2)\	NUM
bracis-33567	82	61	)	)	PUNCT
bracis-33567	82	62	and	and	CCONJ
bracis-33567	82	63	,	,	PUNCT
bracis-33567	82	64	therefore	therefore	ADV
bracis-33567	82	65	,	,	PUNCT
bracis-33567	82	66	does	do	AUX
bracis-33567	82	67	not	not	PART
bracis-33567	82	68	satisfy	satisfy	VERB
bracis-33567	82	69	\(\lnot	\(\lnot	ADV
bracis-33567	82	70	(	(	PUNCT
bracis-33567	82	71	(	(	PUNCT
bracis-33567	82	72	2.5x_1	2.5x_1	NUM
bracis-33567	82	73	+	+	NUM
bracis-33567	82	74	x_2	x_2	PROPN
bracis-33567	82	75	\ge	\ge	PROPN
bracis-33567	82	76	5	5	NUM
bracis-33567	82	77	)	)	PUNCT
bracis-33567	82	78	\wedge	\wedge	PROPN
bracis-33567	82	79	(	(	PUNCT
bracis-33567	82	80	x_1=1	x_1=1	PROPN
bracis-33567	82	81	\vee	\vee	PROPN
bracis-33567	82	82	x_1=2))\	x_1=2))\	PROPN
bracis-33567	82	83	)	)	PUNCT
bracis-33567	82	84	.	.	PUNCT
bracis-33567	83	1	since	since	SCONJ
bracis-33567	83	2	our	our	PRON
bracis-33567	83	3	approach	approach	NOUN
bracis-33567	83	4	builds	build	VERB
bracis-33567	83	5	upon	upon	SCONJ
bracis-33567	83	6	the	the	DET
bracis-33567	83	7	concept	concept	NOUN
bracis-33567	83	8	of	of	ADP
bracis-33567	83	9	logical	logical	ADJ
bracis-33567	83	10	consequence	consequence	NOUN
bracis-33567	83	11	,	,	PUNCT
bracis-33567	83	12	we	we	PRON
bracis-33567	83	13	can	can	AUX
bracis-33567	83	14	leverage	leverage	VERB
bracis-33567	83	15	this	this	DET
bracis-33567	83	16	connection	connection	NOUN
bracis-33567	83	17	in	in	ADP
bracis-33567	83	18	the	the	DET
bracis-33567	83	19	context	context	NOUN
bracis-33567	83	20	of	of	ADP
bracis-33567	83	21	computing	compute	VERB
bracis-33567	83	22	explanations	explanation	NOUN
bracis-33567	83	23	for	for	ADP
bracis-33567	83	24	anns	ann	NOUN
bracis-33567	83	25	.	.	PUNCT
bracis-33567	84	1	2.2	2.2	NUM
bracis-33567	84	2	mixed	mixed	ADJ
bracis-33567	84	3	integer	integer	NOUN
bracis-33567	84	4	linear	linear	NOUN
bracis-33567	84	5	programming	programming	NOUN
bracis-33567	84	6	in	in	ADP
bracis-33567	84	7	mixed	mixed	ADJ
bracis-33567	84	8	integer	integer	NOUN
bracis-33567	84	9	linear	linear	PROPN
bracis-33567	84	10	programming	programming	NOUN
bracis-33567	84	11	(	(	PUNCT
bracis-33567	84	12	milp	milp	NOUN
bracis-33567	84	13	)	)	PUNCT
bracis-33567	84	14	,	,	PUNCT
bracis-33567	84	15	the	the	DET
bracis-33567	84	16	objective	objective	NOUN
bracis-33567	84	17	is	be	AUX
bracis-33567	84	18	to	to	PART
bracis-33567	84	19	optimize	optimize	VERB
bracis-33567	84	20	a	a	DET
bracis-33567	84	21	linear	linear	ADJ
bracis-33567	84	22	function	function	NOUN
bracis-33567	84	23	subject	subject	ADJ
bracis-33567	84	24	to	to	ADP
bracis-33567	84	25	linear	linear	ADJ
bracis-33567	84	26	constraints	constraint	NOUN
bracis-33567	84	27	,	,	PUNCT
bracis-33567	84	28	where	where	SCONJ
bracis-33567	84	29	some	some	PRON
bracis-33567	84	30	or	or	CCONJ
bracis-33567	84	31	all	all	PRON
bracis-33567	84	32	of	of	ADP
bracis-33567	84	33	the	the	DET
bracis-33567	84	34	variables	variable	NOUN
bracis-33567	84	35	are	be	AUX
bracis-33567	84	36	required	require	VERB
bracis-33567	84	37	to	to	PART
bracis-33567	84	38	be	be	AUX
bracis-33567	84	39	integers	integer	NOUN
bracis-33567	84	40	[	[	X
bracis-33567	84	41	2	2	NUM
bracis-33567	84	42	]	]	PUNCT
bracis-33567	84	43	.	.	PUNCT
bracis-33567	85	1	milp	milp	PROPN
bracis-33567	85	2	is	be	AUX
bracis-33567	85	3	a	a	DET
bracis-33567	85	4	crucial	crucial	ADJ
bracis-33567	85	5	technique	technique	NOUN
bracis-33567	85	6	in	in	ADP
bracis-33567	85	7	our	our	PRON
bracis-33567	85	8	work	work	NOUN
bracis-33567	85	9	for	for	ADP
bracis-33567	85	10	determining	determine	VERB
bracis-33567	85	11	the	the	DET
bracis-33567	85	12	lower	low	ADJ
bracis-33567	85	13	and	and	CCONJ
bracis-33567	85	14	upper	upper	ADJ
bracis-33567	85	15	bounds	bound	NOUN
bracis-33567	85	16	of	of	ADP
bracis-33567	85	17	each	each	DET
bracis-33567	85	18	neuron	neuron	NOUN
bracis-33567	85	19	in	in	ADP
bracis-33567	85	20	the	the	DET
bracis-33567	85	21	anns	ann	NOUN
bracis-33567	85	22	.	.	PUNCT
bracis-33567	86	1	for	for	ADP
bracis-33567	86	2	example	example	NOUN
bracis-33567	86	3	,	,	PUNCT
bracis-33567	86	4	we	we	PRON
bracis-33567	86	5	utilize	utilize	VERB
bracis-33567	86	6	a	a	DET
bracis-33567	86	7	minimization	minimization	NOUN
bracis-33567	86	8	problem	problem	NOUN
bracis-33567	86	9	to	to	PART
bracis-33567	86	10	determine	determine	VERB
bracis-33567	86	11	the	the	DET
bracis-33567	86	12	lower	low	ADJ
bracis-33567	86	13	bound	bind	VERB
bracis-33567	86	14	of	of	ADP
bracis-33567	86	15	neurons	neuron	NOUN
bracis-33567	86	16	within	within	ADP
bracis-33567	86	17	anns	ann	NOUN
bracis-33567	86	18	.	.	PUNCT
bracis-33567	87	1	this	this	DET
bracis-33567	87	2	process	process	NOUN
bracis-33567	87	3	involves	involve	VERB
bracis-33567	87	4	formulating	formulate	VERB
bracis-33567	87	5	an	an	DET
bracis-33567	87	6	objective	objective	ADJ
bracis-33567	87	7	function	function	NOUN
bracis-33567	87	8	that	that	PRON
bracis-33567	87	9	seeks	seek	VERB
bracis-33567	87	10	to	to	PART
bracis-33567	87	11	minimize	minimize	VERB
bracis-33567	87	12	the	the	PRON
bracis-33567	87	13	lower	lower	ADV
bracis-33567	87	14	bound	bind	VERB
bracis-33567	87	15	,	,	PUNCT
bracis-33567	87	16	subject	subject	ADJ
bracis-33567	87	17	to	to	ADP
bracis-33567	87	18	constraints	constraint	NOUN
bracis-33567	87	19	that	that	PRON
bracis-33567	87	20	reflect	reflect	VERB
bracis-33567	87	21	the	the	DET
bracis-33567	87	22	behaviour	behaviour	NOUN
bracis-33567	87	23	of	of	ADP
bracis-33567	87	24	anns	ann	NOUN
bracis-33567	87	25	.	.	PUNCT
bracis-33567	88	1	to	to	PART
bracis-33567	88	2	illustrate	illustrate	VERB
bracis-33567	88	3	the	the	DET
bracis-33567	88	4	structure	structure	NOUN
bracis-33567	88	5	of	of	ADP
bracis-33567	88	6	a	a	DET
bracis-33567	88	7	milp	milp	NOUN
bracis-33567	88	8	,	,	PUNCT
bracis-33567	88	9	we	we	PRON
bracis-33567	88	10	provide	provide	VERB
bracis-33567	88	11	an	an	DET
bracis-33567	88	12	example	example	NOUN
bracis-33567	88	13	below	below	ADP
bracis-33567	88	14	:	:	PUNCT
bracis-33567	88	15	$	$	SYM
bracis-33567	88	16	$	$	SYM
bracis-33567	88	17	\begin{aligned	\begin{aligne	VERB
bracis-33567	88	18	}	}	PUNCT
bracis-33567	88	19	\begin{aligned	\begin{aligne	VERB
bracis-33567	88	20	}	}	PUNCT
bracis-33567	88	21	\min	\min	NOUN
bracis-33567	88	22	\quad	\quad	PROPN
bracis-33567	88	23	&	&	CCONJ
bracis-33567	88	24	y_1	y_1	PROPN
bracis-33567	88	25	\\	\\	NOUN
bracis-33567	88	26	\text	\text	PROPN
bracis-33567	88	27	{	{	PUNCT
bracis-33567	88	28	s.t	s.t	PROPN
bracis-33567	88	29	.	.	PROPN
bracis-33567	88	30	}	}	PUNCT
bracis-33567	88	31	\quad	\quad	PROPN
bracis-33567	88	32	&	&	CCONJ
bracis-33567	88	33	1	1	NUM
bracis-33567	88	34	\le	\le	PROPN
bracis-33567	88	35	x_1	x_1	PROPN
bracis-33567	88	36	\le	\le	PROPN
bracis-33567	88	37	3\\	3\\	NUM
bracis-33567	88	38	&	&	CCONJ
bracis-33567	88	39	3x_1	3x_1	NUM
bracis-33567	89	1	+	+	CCONJ
bracis-33567	89	2	s_1	s_1	PROPN
bracis-33567	89	3	2	2	X
bracis-33567	89	4	=	=	SYM
bracis-33567	89	5	y_1	y_1	PROPN
bracis-33567	89	6	\\	\\	NOUN
bracis-33567	89	7	&	&	CCONJ
bracis-33567	89	8	0	0	NUM
bracis-33567	89	9	\le	\le	PROPN
bracis-33567	89	10	y_1	y_1	PROPN
bracis-33567	89	11	\le	\le	X
bracis-33567	89	12	3x_1	3x_1	NUM
bracis-33567	89	13	2	2	NUM
bracis-33567	89	14	\\	\\	NOUN
bracis-33567	89	15	&	&	CCONJ
bracis-33567	89	16	0	0	NUM
bracis-33567	89	17	\le	\le	PROPN
bracis-33567	89	18	s_1	s_1	PROPN
bracis-33567	89	19	\le	\le	PROPN
bracis-33567	89	20	3x_1	3x_1	NUM
bracis-33567	89	21	2\\	2\\	NUM
bracis-33567	89	22	&	&	CCONJ
bracis-33567	89	23	z_1	z_1	PROPN
bracis-33567	89	24	=	=	SYM
bracis-33567	90	1	1	1	NUM
bracis-33567	90	2	\rightarrow	\rightarrow	PROPN
bracis-33567	90	3	y_1	y_1	PROPN
bracis-33567	90	4	\le	\le	PROPN
bracis-33567	90	5	0	0	NUM
bracis-33567	90	6	\\	\\	NOUN
bracis-33567	90	7	&	&	CCONJ
bracis-33567	90	8	z_1	z_1	PROPN
bracis-33567	91	1	=	=	SYM
bracis-33567	92	1	0	0	NUM
bracis-33567	93	1	\rightarrow	\rightarrow	PROPN
bracis-33567	93	2	s_1	s_1	PROPN
bracis-33567	93	3	\le	\le	PROPN
bracis-33567	93	4	0	0	NUM
bracis-33567	93	5	\\	\\	NOUN
bracis-33567	93	6	&	&	CCONJ
bracis-33567	93	7	z_1	z_1	PROPN
bracis-33567	93	8	\in	\in	PROPN
bracis-33567	93	9	\{0	\{0	NOUN
bracis-33567	93	10	,	,	PUNCT
bracis-33567	93	11	1\	1\	NUM
bracis-33567	93	12	}	}	PUNCT
bracis-33567	93	13	\end{aligned	\end{aligne	VERB
bracis-33567	93	14	}	}	PUNCT
bracis-33567	93	15	\end{aligned}$$	\end{aligned}$$	X
bracis-33567	93	16	(	(	PUNCT
bracis-33567	93	17	2	2	NUM
bracis-33567	93	18	)	)	PUNCT
bracis-33567	93	19	in	in	ADP
bracis-33567	93	20	the	the	DET
bracis-33567	93	21	milp	milp	NOUN
bracis-33567	93	22	in	in	ADP
bracis-33567	93	23	(	(	PUNCT
bracis-33567	93	24	2	2	NUM
bracis-33567	93	25	)	)	PUNCT
bracis-33567	93	26	,	,	PUNCT
bracis-33567	93	27	we	we	PRON
bracis-33567	93	28	want	want	VERB
bracis-33567	93	29	to	to	PART
bracis-33567	93	30	find	find	VERB
bracis-33567	93	31	values	value	NOUN
bracis-33567	93	32	for	for	ADP
bracis-33567	93	33	variables	variable	NOUN
bracis-33567	93	34	\(x_1	\(x_1	PROPN
bracis-33567	93	35	,	,	PUNCT
bracis-33567	93	36	y_1	y_1	PROPN
bracis-33567	93	37	,	,	PUNCT
bracis-33567	93	38	s_1	s_1	PROPN
bracis-33567	93	39	,	,	PUNCT
bracis-33567	93	40	z_1\	z_1\	NUM
bracis-33567	93	41	)	)	PUNCT
bracis-33567	93	42	minimizing	minimize	VERB
bracis-33567	93	43	the	the	DET
bracis-33567	93	44	value	value	NOUN
bracis-33567	93	45	of	of	ADP
bracis-33567	93	46	the	the	DET
bracis-33567	93	47	objective	objective	ADJ
bracis-33567	93	48	function	function	NOUN
bracis-33567	93	49	\(y_1\	\(y_1\	PROPN
bracis-33567	93	50	)	)	PUNCT
bracis-33567	93	51	among	among	ADP
bracis-33567	93	52	all	all	DET
bracis-33567	93	53	values	value	NOUN
bracis-33567	93	54	that	that	PRON
bracis-33567	93	55	satisfy	satisfy	VERB
bracis-33567	93	56	the	the	DET
bracis-33567	93	57	constraints	constraint	NOUN
bracis-33567	93	58	.	.	PUNCT
bracis-33567	94	1	variable	variable	ADJ
bracis-33567	94	2	\(z_1\	\(z_1\	PROPN
bracis-33567	94	3	)	)	PUNCT
bracis-33567	94	4	is	be	AUX
bracis-33567	94	5	binary	binary	ADJ
bracis-33567	94	6	since	since	SCONJ
bracis-33567	94	7	\(z_1	\(z_1	PROPN
bracis-33567	94	8	\in	\in	PROPN
bracis-33567	94	9	\{0	\{0	NOUN
bracis-33567	94	10	,	,	PUNCT
bracis-33567	94	11	1\}\	1\}\	NUM
bracis-33567	94	12	)	)	PUNCT
bracis-33567	94	13	is	be	AUX
bracis-33567	94	14	a	a	DET
bracis-33567	94	15	constraint	constraint	NOUN
bracis-33567	94	16	in	in	ADP
bracis-33567	94	17	the	the	DET
bracis-33567	94	18	milp	milp	NOUN
bracis-33567	94	19	,	,	PUNCT
bracis-33567	94	20	while	while	SCONJ
bracis-33567	94	21	variables	variables	PROPN
bracis-33567	94	22	\(x_1	\(x_1	PROPN
bracis-33567	94	23	,	,	PUNCT
bracis-33567	94	24	y_1	y_1	PROPN
bracis-33567	94	25	,	,	PUNCT
bracis-33567	94	26	s_1\	s_1\	PROPN
bracis-33567	94	27	)	)	PUNCT
bracis-33567	94	28	have	have	VERB
bracis-33567	94	29	the	the	DET
bracis-33567	94	30	real	real	ADJ
bracis-33567	94	31	numbers	number	NOUN
bracis-33567	94	32	\(\mathbb	\(\mathbb	VERB
bracis-33567	94	33	{	{	PUNCT
bracis-33567	94	34	r}\	r}\	NUM
bracis-33567	94	35	)	)	PUNCT
bracis-33567	94	36	as	as	ADP
bracis-33567	94	37	their	their	PRON
bracis-33567	94	38	domain	domain	NOUN
bracis-33567	94	39	.	.	PUNCT
bracis-33567	95	1	the	the	DET
bracis-33567	95	2	constraints	constraint	NOUN
bracis-33567	95	3	in	in	ADP
bracis-33567	95	4	a	a	DET
bracis-33567	95	5	milp	milp	NOUN
bracis-33567	95	6	may	may	AUX
bracis-33567	95	7	appear	appear	VERB
bracis-33567	95	8	as	as	ADP
bracis-33567	95	9	linear	linear	PROPN
bracis-33567	95	10	equations	equation	NOUN
bracis-33567	95	11	,	,	PUNCT
bracis-33567	95	12	linear	linear	ADJ
bracis-33567	95	13	inequalities	inequality	NOUN
bracis-33567	95	14	,	,	PUNCT
bracis-33567	95	15	and	and	CCONJ
bracis-33567	95	16	indicator	indicator	NOUN
bracis-33567	95	17	constraints	constraint	NOUN
bracis-33567	95	18	.	.	PUNCT
bracis-33567	96	1	indicator	indicator	NOUN
bracis-33567	96	2	constraints	constraint	NOUN
bracis-33567	96	3	can	can	AUX
bracis-33567	96	4	be	be	AUX
bracis-33567	96	5	seen	see	VERB
bracis-33567	96	6	as	as	ADP
bracis-33567	96	7	logical	logical	ADJ
bracis-33567	96	8	implications	implication	NOUN
bracis-33567	96	9	of	of	ADP
bracis-33567	96	10	the	the	DET
bracis-33567	96	11	form	form	NOUN
bracis-33567	96	12	\(z	\(z	PROPN
bracis-33567	96	13	=	=	SYM
bracis-33567	96	14	v	v	ADP
bracis-33567	96	15	\rightarrow	\rightarrow	PROPN
bracis-33567	96	16	\sum	\sum	NOUN
bracis-33567	96	17	^n_{i=1	^n_{i=1	PUNCT
bracis-33567	96	18	}	}	PUNCT
bracis-33567	96	19	w_i	w_i	PROPN
bracis-33567	96	20	x_i	x_i	PROPN
bracis-33567	96	21	\le	\le	PROPN
bracis-33567	96	22	b\	b\	NOUN
bracis-33567	96	23	)	)	PUNCT
bracis-33567	96	24	such	such	ADJ
bracis-33567	96	25	that	that	SCONJ
bracis-33567	96	26	z	z	PROPN
bracis-33567	96	27	is	be	AUX
bracis-33567	96	28	a	a	DET
bracis-33567	96	29	binary	binary	ADJ
bracis-33567	96	30	variable	variable	NOUN
bracis-33567	96	31	,	,	PUNCT
bracis-33567	96	32	v	v	NOUN
bracis-33567	96	33	is	be	AUX
bracis-33567	96	34	a	a	DET
bracis-33567	96	35	constant	constant	ADJ
bracis-33567	96	36	0	0	NUM
bracis-33567	96	37	or	or	CCONJ
bracis-33567	96	38	1	1	NUM
bracis-33567	96	39	[	[	X
bracis-33567	96	40	3	3	NUM
bracis-33567	96	41	]	]	PUNCT
bracis-33567	96	42	.	.	PUNCT
bracis-33567	97	1	an	an	DET
bracis-33567	97	2	important	important	ADJ
bracis-33567	97	3	observation	observation	NOUN
bracis-33567	97	4	is	be	AUX
bracis-33567	97	5	that	that	SCONJ
bracis-33567	97	6	a	a	DET
bracis-33567	97	7	milp	milp	ADJ
bracis-33567	97	8	problem	problem	NOUN
bracis-33567	97	9	without	without	ADP
bracis-33567	97	10	an	an	DET
bracis-33567	97	11	objective	objective	ADJ
bracis-33567	97	12	function	function	NOUN
bracis-33567	97	13	corresponds	correspond	VERB
bracis-33567	97	14	to	to	ADP
bracis-33567	97	15	a	a	DET
bracis-33567	97	16	satisfiability	satisfiability	NOUN
bracis-33567	97	17	problem	problem	NOUN
bracis-33567	97	18	,	,	PUNCT
bracis-33567	97	19	as	as	SCONJ
bracis-33567	97	20	discussed	discuss	VERB
bracis-33567	97	21	in	in	ADP
bracis-33567	97	22	sect	sect	NOUN
bracis-33567	97	23	.	.	PUNCT
bracis-33567	97	24	 	 	SPACE
bracis-33567	97	25	2.1	2.1	NUM
bracis-33567	97	26	.	.	PUNCT
bracis-33567	98	1	given	give	VERB
bracis-33567	98	2	that	that	SCONJ
bracis-33567	98	3	the	the	DET
bracis-33567	98	4	approach	approach	NOUN
bracis-33567	98	5	for	for	ADP
bracis-33567	98	6	computing	computing	NOUN
bracis-33567	98	7	explanations	explanation	NOUN
bracis-33567	98	8	relies	rely	VERB
bracis-33567	98	9	on	on	ADP
bracis-33567	98	10	logical	logical	ADJ
bracis-33567	98	11	consequence	consequence	NOUN
bracis-33567	98	12	,	,	PUNCT
bracis-33567	98	13	and	and	CCONJ
bracis-33567	98	14	considering	consider	VERB
bracis-33567	98	15	the	the	DET
bracis-33567	98	16	connection	connection	NOUN
bracis-33567	98	17	between	between	ADP
bracis-33567	98	18	satisfiability	satisfiability	NOUN
bracis-33567	98	19	and	and	CCONJ
bracis-33567	98	20	logical	logical	ADJ
bracis-33567	98	21	consequence	consequence	NOUN
bracis-33567	98	22	,	,	PUNCT
bracis-33567	98	23	we	we	PRON
bracis-33567	98	24	employ	employ	VERB
bracis-33567	98	25	a	a	DET
bracis-33567	98	26	milp	milp	PROPN
bracis-33567	98	27	solver	solver	NOUN
bracis-33567	98	28	to	to	PART
bracis-33567	98	29	address	address	VERB
bracis-33567	98	30	explanation	explanation	NOUN
bracis-33567	98	31	tasks	task	NOUN
bracis-33567	98	32	.	.	PUNCT
bracis-33567	99	1	additionally	additionally	ADV
bracis-33567	99	2	,	,	PUNCT
bracis-33567	99	3	throughout	throughout	ADP
bracis-33567	99	4	the	the	DET
bracis-33567	99	5	construction	construction	NOUN
bracis-33567	99	6	of	of	ADP
bracis-33567	99	7	the	the	DET
bracis-33567	99	8	milp	milp	PROPN
bracis-33567	99	9	model	model	PROPN
bracis-33567	99	10	,	,	PUNCT
bracis-33567	99	11	we	we	PRON
bracis-33567	99	12	utilize	utilize	VERB
bracis-33567	99	13	optimization	optimization	NOUN
bracis-33567	99	14	,	,	PUNCT
bracis-33567	99	15	specifically	specifically	ADV
bracis-33567	99	16	employing	employ	VERB
bracis-33567	99	17	a	a	DET
bracis-33567	99	18	milp	milp	ADJ
bracis-33567	99	19	solver	solver	NOUN
bracis-33567	99	20	,	,	PUNCT
bracis-33567	99	21	to	to	PART
bracis-33567	99	22	determine	determine	VERB
bracis-33567	99	23	tight	tight	ADV
bracis-33567	99	24	lower	low	ADJ
bracis-33567	99	25	and	and	CCONJ
bracis-33567	99	26	upper	upper	ADJ
bracis-33567	99	27	bounds	bound	NOUN
bracis-33567	99	28	for	for	ADP
bracis-33567	99	29	the	the	DET
bracis-33567	99	30	neurons	neuron	NOUN
bracis-33567	99	31	of	of	ADP
bracis-33567	99	32	anns	ann	NOUN
bracis-33567	99	33	.	.	PUNCT
bracis-33567	100	1	2.3	2.3	NUM
bracis-33567	100	2	classification	classification	NOUN
bracis-33567	100	3	problems	problem	NOUN
bracis-33567	100	4	and	and	CCONJ
bracis-33567	100	5	 	 	SPACE
bracis-33567	100	6	artificial	artificial	ADJ
bracis-33567	100	7	neural	neural	ADJ
bracis-33567	100	8	networks	network	NOUN
bracis-33567	100	9	in	in	ADP
bracis-33567	100	10	machine	machine	NOUN
bracis-33567	100	11	learning	learning	NOUN
bracis-33567	100	12	,	,	PUNCT
bracis-33567	100	13	classification	classification	NOUN
bracis-33567	100	14	problems	problem	NOUN
bracis-33567	100	15	are	be	AUX
bracis-33567	100	16	defined	define	VERB
bracis-33567	100	17	over	over	ADP
bracis-33567	100	18	a	a	DET
bracis-33567	100	19	set	set	NOUN
bracis-33567	100	20	of	of	ADP
bracis-33567	100	21	n	n	PRON
bracis-33567	100	22	features	feature	VERB
bracis-33567	100	23	\(\mathcal	\(\mathcal	ADJ
bracis-33567	100	24	{	{	PUNCT
bracis-33567	100	25	f	f	NOUN
bracis-33567	100	26	}	}	PUNCT
bracis-33567	100	27	=	=	SYM
bracis-33567	100	28	\{x_1	\{x_1	NOUN
bracis-33567	100	29	,	,	PUNCT
bracis-33567	100	30	...	...	PUNCT
bracis-33567	100	31	,	,	PUNCT
bracis-33567	100	32	x_n\}\	x_n\}\	X
bracis-33567	100	33	)	)	PUNCT
bracis-33567	100	34	and	and	CCONJ
bracis-33567	100	35	a	a	DET
bracis-33567	100	36	set	set	NOUN
bracis-33567	100	37	of	of	ADP
bracis-33567	100	38	\(\mathcal	\(\mathcal	ADJ
bracis-33567	100	39	{	{	PUNCT
bracis-33567	100	40	n}\	n}\	NOUN
bracis-33567	100	41	)	)	PUNCT
bracis-33567	100	42	classes	class	NOUN
bracis-33567	100	43	\(\mathcal	\(\mathcal	ADJ
bracis-33567	100	44	{	{	PUNCT
bracis-33567	100	45	k	k	NOUN
bracis-33567	100	46	}	}	PUNCT
bracis-33567	100	47	=	=	SYM
bracis-33567	100	48	\{c_1	\{c_1	NOUN
bracis-33567	100	49	,	,	PUNCT
bracis-33567	100	50	c_2,	c_2,	NOUN
bracis-33567	100	51	...	...	PUNCT
bracis-33567	100	52	,c_\mathcal	,c_\mathcal	PUNCT
bracis-33567	100	53	{	{	PUNCT
bracis-33567	100	54	n}\}\	n}\}\	NOUN
bracis-33567	100	55	)	)	PUNCT
bracis-33567	100	56	.	.	PUNCT
bracis-33567	101	1	in	in	ADP
bracis-33567	101	2	this	this	DET
bracis-33567	101	3	work	work	NOUN
bracis-33567	101	4	,	,	PUNCT
bracis-33567	101	5	we	we	PRON
bracis-33567	101	6	consider	consider	VERB
bracis-33567	101	7	that	that	SCONJ
bracis-33567	101	8	each	each	PRON
bracis-33567	101	9	feature	feature	VERB
bracis-33567	101	10	\(x_i	\(x_i	PROPN
bracis-33567	101	11	\in	\in	PROPN
bracis-33567	101	12	\mathcal	\mathcal	PROPN
bracis-33567	101	13	{	{	PUNCT
bracis-33567	101	14	f}\	f}\	NOUN
bracis-33567	101	15	)	)	PUNCT
bracis-33567	101	16	takes	take	VERB
bracis-33567	101	17	its	its	PRON
bracis-33567	101	18	values	value	NOUN
bracis-33567	101	19	\(v_i\	\(v_i\	NOUN
bracis-33567	101	20	)	)	PUNCT
bracis-33567	101	21	from	from	ADP
bracis-33567	101	22	the	the	DET
bracis-33567	101	23	domain	domain	NOUN
bracis-33567	101	24	of	of	ADP
bracis-33567	101	25	real	real	ADJ
bracis-33567	101	26	numbers	number	NOUN
bracis-33567	101	27	.	.	PUNCT
bracis-33567	102	1	moreover	moreover	ADV
bracis-33567	102	2	,	,	PUNCT
bracis-33567	102	3	each	each	DET
bracis-33567	102	4	feature	feature	NOUN
bracis-33567	102	5	\(x_i\	\(x_i\	NOUN
bracis-33567	102	6	)	)	PUNCT
bracis-33567	102	7	has	have	VERB
bracis-33567	102	8	an	an	DET
bracis-33567	102	9	upper	upper	ADJ
bracis-33567	102	10	bound	bind	VERB
bracis-33567	102	11	\(u_i\	\(u_i\	NOUN
bracis-33567	102	12	)	)	PUNCT
bracis-33567	102	13	and	and	CCONJ
bracis-33567	102	14	a	a	DET
bracis-33567	102	15	lower	lower	ADV
bracis-33567	102	16	bound	bind	VERB
bracis-33567	102	17	\(l_i\	\(l_i\	NOUN
bracis-33567	102	18	)	)	PUNCT
bracis-33567	102	19	such	such	ADJ
bracis-33567	102	20	that	that	SCONJ
bracis-33567	102	21	\(l_i	\(l_i	ADJ
bracis-33567	102	22	\le	\le	PROPN
bracis-33567	102	23	x_i	x_i	SYM
bracis-33567	102	24	\le	\le	PROPN
bracis-33567	102	25	u_i\	u_i\	PROPN
bracis-33567	102	26	)	)	PUNCT
bracis-33567	102	27	,	,	PUNCT
bracis-33567	102	28	and	and	CCONJ
bracis-33567	102	29	its	its	PRON
bracis-33567	102	30	domain	domain	NOUN
bracis-33567	102	31	is	be	AUX
bracis-33567	102	32	the	the	DET
bracis-33567	102	33	closed	closed	ADJ
bracis-33567	102	34	interval	interval	NOUN
bracis-33567	102	35	\([l_i	\([l_i	NOUN
bracis-33567	102	36	,	,	PUNCT
bracis-33567	102	37	u_i]\	u_i]\	NOUN
bracis-33567	102	38	)	)	PUNCT
bracis-33567	102	39	.	.	PUNCT
bracis-33567	103	1	this	this	PRON
bracis-33567	103	2	is	be	AUX
bracis-33567	103	3	represented	represent	VERB
bracis-33567	103	4	as	as	ADP
bracis-33567	103	5	a	a	DET
bracis-33567	103	6	set	set	NOUN
bracis-33567	103	7	of	of	ADP
bracis-33567	103	8	domain	domain	NOUN
bracis-33567	103	9	constraints	constraint	NOUN
bracis-33567	103	10	or	or	CCONJ
bracis-33567	103	11	feature	feature	NOUN
bracis-33567	103	12	space	space	NOUN
bracis-33567	103	13	\(d	\(d	NOUN
bracis-33567	103	14	=	=	SYM
bracis-33567	103	15	\{l_1	\{l_1	ADP
bracis-33567	103	16	\le	\le	PROPN
bracis-33567	103	17	x_1	x_1	PROPN
bracis-33567	103	18	\le	\le	PROPN
bracis-33567	103	19	u_1,\text	u_1,\text	ADP
bracis-33567	103	20	l_2	l_2	PROPN
bracis-33567	103	21	\le	\le	PROPN
bracis-33567	103	22	x_2	x_2	PROPN
bracis-33567	103	23	\le	\le	PROPN
bracis-33567	103	24	u_2	u_2	PROPN
bracis-33567	103	25	,	,	PUNCT
bracis-33567	103	26	...	...	PUNCT
bracis-33567	103	27	,	,	PUNCT
bracis-33567	103	28	l_n	l_n	PROPN
bracis-33567	104	1	\le	\le	PROPN
bracis-33567	104	2	x_n	x_n	PROPN
bracis-33567	104	3	\le	\le	PROPN
bracis-33567	104	4	u_n	u_n	SYM
bracis-33567	104	5	\}\	\}\	NOUN
bracis-33567	104	6	)	)	PUNCT
bracis-33567	104	7	.	.	PUNCT
bracis-33567	105	1	for	for	ADP
bracis-33567	105	2	example	example	NOUN
bracis-33567	105	3	,	,	PUNCT
bracis-33567	105	4	a	a	DET
bracis-33567	105	5	feature	feature	NOUN
bracis-33567	105	6	for	for	ADP
bracis-33567	105	7	the	the	DET
bracis-33567	105	8	height	height	NOUN
bracis-33567	105	9	of	of	ADP
bracis-33567	105	10	a	a	DET
bracis-33567	105	11	person	person	NOUN
bracis-33567	105	12	belongs	belong	VERB
bracis-33567	105	13	to	to	ADP
bracis-33567	105	14	the	the	DET
bracis-33567	105	15	real	real	ADJ
bracis-33567	105	16	numbers	number	NOUN
bracis-33567	105	17	and	and	CCONJ
bracis-33567	105	18	may	may	AUX
bracis-33567	105	19	have	have	VERB
bracis-33567	105	20	lower	low	ADJ
bracis-33567	105	21	and	and	CCONJ
bracis-33567	105	22	upper	upper	ADJ
bracis-33567	105	23	bounds	bound	NOUN
bracis-33567	105	24	of	of	ADP
bracis-33567	105	25	0.5	0.5	NUM
bracis-33567	105	26	and	and	CCONJ
bracis-33567	105	27	2.1	2.1	NUM
bracis-33567	105	28	meters	meter	NOUN
bracis-33567	105	29	,	,	PUNCT
bracis-33567	105	30	respectively	respectively	ADV
bracis-33567	105	31	.	.	PUNCT
bracis-33567	106	1	furthermore	furthermore	ADV
bracis-33567	106	2	,	,	PUNCT
bracis-33567	106	3	\(\{x_1	\(\{x_1	PROPN
bracis-33567	106	4	=	=	PUNCT
bracis-33567	106	5	v_1	v_1	PROPN
bracis-33567	106	6	,	,	PUNCT
bracis-33567	106	7	x_2	x_2	PROPN
bracis-33567	106	8	=	=	PUNCT
bracis-33567	106	9	v_2	v_2	PROPN
bracis-33567	106	10	,	,	PUNCT
bracis-33567	106	11	...	...	PUNCT
bracis-33567	106	12	,	,	PUNCT
bracis-33567	106	13	x_n	x_n	PROPN
bracis-33567	106	14	=	=	SYM
bracis-33567	106	15	v_n\}\	v_n\}\	X
bracis-33567	106	16	)	)	PUNCT
bracis-33567	106	17	represents	represent	VERB
bracis-33567	106	18	a	a	DET
bracis-33567	106	19	specific	specific	ADJ
bracis-33567	106	20	point	point	NOUN
bracis-33567	106	21	or	or	CCONJ
bracis-33567	106	22	instance	instance	NOUN
bracis-33567	106	23	of	of	ADP
bracis-33567	106	24	the	the	DET
bracis-33567	106	25	feature	feature	NOUN
bracis-33567	106	26	space	space	NOUN
bracis-33567	106	27	such	such	ADJ
bracis-33567	106	28	that	that	SCONJ
bracis-33567	106	29	each	each	DET
bracis-33567	106	30	\(v_i\	\(v_i\	NOUN
bracis-33567	106	31	)	)	PUNCT
bracis-33567	106	32	is	be	AUX
bracis-33567	106	33	in	in	ADP
bracis-33567	106	34	the	the	DET
bracis-33567	106	35	domain	domain	NOUN
bracis-33567	106	36	of	of	ADP
bracis-33567	106	37	\(x_i\	\(x_i\	NOUN
bracis-33567	106	38	)	)	PUNCT
bracis-33567	106	39	.	.	PUNCT
bracis-33567	107	1	an	an	DET
bracis-33567	107	2	ann	ann	PROPN
bracis-33567	107	3	is	be	AUX
bracis-33567	107	4	a	a	DET
bracis-33567	107	5	function	function	NOUN
bracis-33567	107	6	that	that	PRON
bracis-33567	107	7	maps	map	VERB
bracis-33567	107	8	elements	element	NOUN
bracis-33567	107	9	in	in	ADP
bracis-33567	107	10	the	the	DET
bracis-33567	107	11	feature	feature	NOUN
bracis-33567	107	12	space	space	NOUN
bracis-33567	107	13	into	into	ADP
bracis-33567	107	14	the	the	DET
bracis-33567	107	15	set	set	NOUN
bracis-33567	107	16	of	of	ADP
bracis-33567	107	17	classes	class	NOUN
bracis-33567	107	18	\(\mathcal	\(\mathcal	ADJ
bracis-33567	107	19	{	{	PUNCT
bracis-33567	107	20	k}\	k}\	NOUN
bracis-33567	107	21	)	)	PUNCT
bracis-33567	107	22	.	.	PUNCT
bracis-33567	108	1	a	a	DET
bracis-33567	108	2	feedforward	feedforward	NOUN
bracis-33567	108	3	ann	ann	PROPN
bracis-33567	108	4	is	be	AUX
bracis-33567	108	5	composed	compose	VERB
bracis-33567	108	6	of	of	ADP
bracis-33567	108	7	\(l+1\	\(l+1\	NOUN
bracis-33567	108	8	)	)	PUNCT
bracis-33567	108	9	layers	layer	NOUN
bracis-33567	108	10	of	of	ADP
bracis-33567	108	11	neurons	neuron	NOUN
bracis-33567	108	12	.	.	PUNCT
bracis-33567	109	1	each	each	DET
bracis-33567	109	2	layer	layer	NOUN
bracis-33567	109	3	\(l	\(l	PRON
bracis-33567	109	4	\in	\in	NOUN
bracis-33567	109	5	\{0	\{0	NOUN
bracis-33567	109	6	,	,	PUNCT
bracis-33567	109	7	1	1	NUM
bracis-33567	109	8	,	,	PUNCT
bracis-33567	109	9	...	...	PUNCT
bracis-33567	109	10	,	,	PUNCT
bracis-33567	109	11	l\}\	l\}\	NOUN
bracis-33567	109	12	)	)	PUNCT
bracis-33567	109	13	is	be	AUX
bracis-33567	109	14	composed	compose	VERB
bracis-33567	109	15	of	of	ADP
bracis-33567	109	16	\(n_l\	\(n_l\	NOUN
bracis-33567	109	17	)	)	PUNCT
bracis-33567	109	18	neurons	neuron	NOUN
bracis-33567	109	19	,	,	PUNCT
bracis-33567	109	20	numbered	number	VERB
bracis-33567	109	21	from	from	ADP
bracis-33567	109	22	1	1	NUM
bracis-33567	109	23	to	to	ADP
bracis-33567	109	24	\(n_l\	\(n_l\	PROPN
bracis-33567	109	25	)	)	PUNCT
bracis-33567	109	26	.	.	PUNCT
bracis-33567	110	1	layer	layer	NOUN
bracis-33567	110	2	0	0	NUM
bracis-33567	110	3	is	be	AUX
bracis-33567	110	4	fictitious	fictitious	ADJ
bracis-33567	110	5	and	and	CCONJ
bracis-33567	110	6	corresponds	correspond	VERB
bracis-33567	110	7	to	to	ADP
bracis-33567	110	8	the	the	DET
bracis-33567	110	9	input	input	NOUN
bracis-33567	110	10	of	of	ADP
bracis-33567	110	11	the	the	DET
bracis-33567	110	12	ann	ann	PROPN
bracis-33567	110	13	,	,	PUNCT
bracis-33567	110	14	while	while	SCONJ
bracis-33567	110	15	the	the	DET
bracis-33567	110	16	last	last	ADJ
bracis-33567	110	17	layer	layer	NOUN
bracis-33567	110	18	,	,	PUNCT
bracis-33567	110	19	k	k	PROPN
bracis-33567	110	20	corresponds	correspond	VERB
bracis-33567	110	21	to	to	ADP
bracis-33567	110	22	its	its	PRON
bracis-33567	110	23	outputs	output	NOUN
bracis-33567	110	24	.	.	PUNCT
bracis-33567	111	1	layers	layer	NOUN
bracis-33567	111	2	1	1	NUM
bracis-33567	111	3	to	to	ADP
bracis-33567	111	4	\(l-1\	\(l-1\	VERB
bracis-33567	111	5	)	)	PUNCT
bracis-33567	111	6	are	be	AUX
bracis-33567	111	7	typically	typically	ADV
bracis-33567	111	8	referred	refer	VERB
bracis-33567	111	9	to	to	ADP
bracis-33567	111	10	as	as	ADP
bracis-33567	111	11	hidden	hide	VERB
bracis-33567	111	12	layers	layer	NOUN
bracis-33567	111	13	.	.	PUNCT
bracis-33567	112	1	let	let	AUX
bracis-33567	112	2	\(x^l_i\	\(x^l_i\	NOUN
bracis-33567	112	3	)	)	PUNCT
bracis-33567	112	4	be	be	AUX
bracis-33567	112	5	the	the	DET
bracis-33567	112	6	output	output	NOUN
bracis-33567	112	7	of	of	ADP
bracis-33567	112	8	the	the	DET
bracis-33567	112	9	ith	ith	PROPN
bracis-33567	112	10	neuron	neuron	NOUN
bracis-33567	112	11	of	of	ADP
bracis-33567	112	12	the	the	DET
bracis-33567	112	13	lth	lth	NOUN
bracis-33567	112	14	layer	layer	NOUN
bracis-33567	112	15	,	,	PUNCT
bracis-33567	112	16	with	with	ADP
bracis-33567	112	17	\(i	\(i	X
bracis-33567	112	18	\in	\in	PROPN
bracis-33567	112	19	\{1,	\{1,	ADJ
bracis-33567	112	20	...	...	PUNCT
bracis-33567	112	21	,n_l\}\	,n_l\}\	NUM
bracis-33567	112	22	)	)	PUNCT
bracis-33567	112	23	.	.	PUNCT
bracis-33567	113	1	the	the	DET
bracis-33567	113	2	inputs	input	NOUN
bracis-33567	113	3	to	to	ADP
bracis-33567	113	4	the	the	DET
bracis-33567	113	5	ann	ann	PROPN
bracis-33567	113	6	can	can	AUX
bracis-33567	113	7	be	be	AUX
bracis-33567	113	8	represented	represent	VERB
bracis-33567	113	9	as	as	ADP
bracis-33567	113	10	\(x^0_i\	\(x^0_i\	NOUN
bracis-33567	113	11	)	)	PUNCT
bracis-33567	113	12	or	or	CCONJ
bracis-33567	113	13	simply	simply	ADV
bracis-33567	113	14	\(x_i\	\(x_i\	NOUN
bracis-33567	113	15	)	)	PUNCT
bracis-33567	113	16	.	.	PUNCT
bracis-33567	114	1	moreover	moreover	ADV
bracis-33567	114	2	,	,	PUNCT
bracis-33567	114	3	we	we	PRON
bracis-33567	114	4	represent	represent	VERB
bracis-33567	114	5	the	the	DET
bracis-33567	114	6	outputs	output	NOUN
bracis-33567	114	7	as	as	ADP
bracis-33567	114	8	\(x^l_i\	\(x^l_i\	NOUN
bracis-33567	114	9	)	)	PUNCT
bracis-33567	114	10	or	or	CCONJ
bracis-33567	114	11	simply	simply	ADV
bracis-33567	114	12	\(o_i\	\(o_i\	NOUN
bracis-33567	114	13	)	)	PUNCT
bracis-33567	114	14	.	.	PUNCT
bracis-33567	115	1	the	the	DET
bracis-33567	115	2	values	value	NOUN
bracis-33567	115	3	\(x^l_i\	\(x^l_i\	NOUN
bracis-33567	115	4	)	)	PUNCT
bracis-33567	115	5	of	of	ADP
bracis-33567	115	6	the	the	DET
bracis-33567	115	7	neurons	neuron	NOUN
bracis-33567	115	8	in	in	ADP
bracis-33567	115	9	a	a	DET
bracis-33567	115	10	given	give	VERB
bracis-33567	115	11	layer	layer	NOUN
bracis-33567	115	12	l	l	NOUN
bracis-33567	115	13	are	be	AUX
bracis-33567	115	14	computed	compute	VERB
bracis-33567	115	15	through	through	ADP
bracis-33567	115	16	the	the	DET
bracis-33567	115	17	output	output	NOUN
bracis-33567	115	18	values	value	NOUN
bracis-33567	115	19	\(x^{l-1}_j\	\(x^{l-1}_j\	PROPN
bracis-33567	115	20	)	)	PUNCT
bracis-33567	115	21	of	of	ADP
bracis-33567	115	22	the	the	DET
bracis-33567	115	23	previous	previous	ADJ
bracis-33567	115	24	layer	layer	NOUN
bracis-33567	115	25	,	,	PUNCT
bracis-33567	115	26	with	with	ADP
bracis-33567	115	27	\(j	\(j	X
bracis-33567	115	28	\in	\in	PROPN
bracis-33567	115	29	\{1,	\{1,	ADJ
bracis-33567	115	30	...	...	PUNCT
bracis-33567	115	31	,n_{l-1}\}\	,n_{l-1}\}\	NUM
bracis-33567	115	32	)	)	PUNCT
bracis-33567	115	33	.	.	PUNCT
bracis-33567	116	1	each	each	DET
bracis-33567	116	2	neuron	neuron	NOUN
bracis-33567	116	3	applies	apply	VERB
bracis-33567	116	4	a	a	DET
bracis-33567	116	5	linear	linear	ADJ
bracis-33567	116	6	combination	combination	NOUN
bracis-33567	116	7	of	of	ADP
bracis-33567	116	8	the	the	DET
bracis-33567	116	9	output	output	NOUN
bracis-33567	116	10	of	of	ADP
bracis-33567	116	11	the	the	DET
bracis-33567	116	12	neurons	neuron	NOUN
bracis-33567	116	13	in	in	ADP
bracis-33567	116	14	the	the	DET
bracis-33567	116	15	previous	previous	ADJ
bracis-33567	116	16	layer	layer	NOUN
bracis-33567	116	17	.	.	PUNCT
bracis-33567	117	1	then	then	ADV
bracis-33567	117	2	,	,	PUNCT
bracis-33567	117	3	the	the	DET
bracis-33567	117	4	neuron	neuron	NOUN
bracis-33567	117	5	applies	apply	VERB
bracis-33567	117	6	a	a	DET
bracis-33567	117	7	nonlinear	nonlinear	ADJ
bracis-33567	117	8	function	function	NOUN
bracis-33567	117	9	,	,	PUNCT
bracis-33567	117	10	also	also	ADV
bracis-33567	117	11	known	know	VERB
bracis-33567	117	12	as	as	ADP
bracis-33567	117	13	an	an	DET
bracis-33567	117	14	activation	activation	NOUN
bracis-33567	117	15	function	function	NOUN
bracis-33567	117	16	.	.	PUNCT
bracis-33567	118	1	the	the	DET
bracis-33567	118	2	output	output	NOUN
bracis-33567	118	3	of	of	ADP
bracis-33567	118	4	the	the	DET
bracis-33567	118	5	linear	linear	ADJ
bracis-33567	118	6	part	part	NOUN
bracis-33567	118	7	is	be	AUX
bracis-33567	118	8	represented	represent	VERB
bracis-33567	118	9	as	as	ADP
bracis-33567	118	10	\(\sum	\(\sum	ADV
bracis-33567	118	11	_	_	PRON
bracis-33567	118	12	{	{	PUNCT
bracis-33567	118	13	j=1}^{n_{l-1	j=1}^{n_{l-1	ADJ
bracis-33567	118	14	}	}	PUNCT
bracis-33567	118	15	}	}	PUNCT
bracis-33567	118	16	w^{l}_{i	w^{l}_{i	NOUN
bracis-33567	118	17	,	,	PUNCT
bracis-33567	118	18	j	j	NOUN
bracis-33567	118	19	}	}	PUNCT
bracis-33567	118	20	x^{l-1}_{j	x^{l-1}_{j	NOUN
bracis-33567	118	21	}	}	PUNCT
bracis-33567	118	22	+	+	CCONJ
bracis-33567	118	23	b^{l}_{i}\	b^{l}_{i}\	X
bracis-33567	118	24	)	)	PUNCT
bracis-33567	118	25	where	where	SCONJ
bracis-33567	118	26	\(w^{l}_{i	\(w^{l}_{i	NOUN
bracis-33567	118	27	,	,	PUNCT
bracis-33567	118	28	j}\	j}\	PROPN
bracis-33567	118	29	)	)	PUNCT
bracis-33567	118	30	and	and	CCONJ
bracis-33567	118	31	\(b^{l}_{i}\	\(b^{l}_{i}\	NOUN
bracis-33567	118	32	)	)	PUNCT
bracis-33567	118	33	denote	denote	VERB
bracis-33567	118	34	the	the	DET
bracis-33567	118	35	weights	weight	NOUN
bracis-33567	118	36	and	and	CCONJ
bracis-33567	118	37	bias	bias	NOUN
bracis-33567	118	38	,	,	PUNCT
bracis-33567	118	39	respectively	respectively	ADV
bracis-33567	118	40	,	,	PUNCT
bracis-33567	118	41	serving	serve	VERB
bracis-33567	118	42	as	as	ADP
bracis-33567	118	43	parameters	parameter	NOUN
bracis-33567	118	44	of	of	ADP
bracis-33567	118	45	the	the	DET
bracis-33567	118	46	ith	ith	PROPN
bracis-33567	118	47	neuron	neuron	NOUN
bracis-33567	118	48	of	of	ADP
bracis-33567	118	49	layer	layer	NOUN
bracis-33567	118	50	l.	l.	NOUN
bracis-33567	118	51	in	in	ADP
bracis-33567	118	52	this	this	DET
bracis-33567	118	53	work	work	NOUN
bracis-33567	118	54	,	,	PUNCT
bracis-33567	118	55	we	we	PRON
bracis-33567	118	56	consider	consider	VERB
bracis-33567	118	57	only	only	ADV
bracis-33567	118	58	feedforward	feedforward	NOUN
bracis-33567	118	59	anns	ann	NOUN
bracis-33567	118	60	with	with	ADP
bracis-33567	118	61	the	the	DET
bracis-33567	118	62	rectified	rectified	ADJ
bracis-33567	118	63	linear	linear	NOUN
bracis-33567	118	64	unit	unit	NOUN
bracis-33567	118	65	(	(	PUNCT
bracis-33567	118	66	\(\textrm{relu}\	\(\textrm{relu}\	PROPN
bracis-33567	118	67	)	)	PUNCT
bracis-33567	118	68	)	)	PUNCT
bracis-33567	118	69	as	as	ADP
bracis-33567	118	70	activation	activation	NOUN
bracis-33567	118	71	function	function	NOUN
bracis-33567	118	72	because	because	SCONJ
bracis-33567	118	73	it	it	PRON
bracis-33567	118	74	can	can	AUX
bracis-33567	118	75	be	be	AUX
bracis-33567	118	76	represented	represent	VERB
bracis-33567	118	77	by	by	ADP
bracis-33567	118	78	linear	linear	PROPN
bracis-33567	118	79	constraints	constraint	NOUN
bracis-33567	118	80	due	due	ADP
bracis-33567	118	81	to	to	ADP
bracis-33567	118	82	its	its	PRON
bracis-33567	118	83	piecewise	piecewise	NOUN
bracis-33567	118	84	-	-	PUNCT
bracis-33567	118	85	linear	linear	NOUN
bracis-33567	118	86	nature	nature	NOUN
bracis-33567	118	87	.	.	PUNCT
bracis-33567	119	1	this	this	DET
bracis-33567	119	2	function	function	NOUN
bracis-33567	119	3	is	be	AUX
bracis-33567	119	4	a	a	DET
bracis-33567	119	5	widely	widely	ADV
bracis-33567	119	6	used	use	VERB
bracis-33567	119	7	activation	activation	NOUN
bracis-33567	119	8	whose	whose	DET
bracis-33567	119	9	output	output	NOUN
bracis-33567	119	10	is	be	AUX
bracis-33567	119	11	the	the	DET
bracis-33567	119	12	maximum	maximum	NOUN
bracis-33567	119	13	between	between	ADP
bracis-33567	119	14	its	its	PRON
bracis-33567	119	15	input	input	NOUN
bracis-33567	119	16	value	value	NOUN
bracis-33567	119	17	and	and	CCONJ
bracis-33567	119	18	zero	zero	NUM
bracis-33567	119	19	.	.	PUNCT
bracis-33567	120	1	then	then	ADV
bracis-33567	120	2	,	,	PUNCT
bracis-33567	120	3	\(x^{l}_{i	\(x^{l}_{i	NOUN
bracis-33567	120	4	}	}	PUNCT
bracis-33567	120	5	=	=	PUNCT
bracis-33567	120	6	\textrm{relu}(\sum	\textrm{relu}(\sum	NOUN
bracis-33567	120	7	_	_	NOUN
bracis-33567	120	8	{	{	PUNCT
bracis-33567	120	9	j=1}^{n_{l-1	j=1}^{n_{l-1	ADJ
bracis-33567	120	10	}	}	PUNCT
bracis-33567	120	11	}	}	PUNCT
bracis-33567	120	12	w^{l}_{i	w^{l}_{i	NOUN
bracis-33567	120	13	,	,	PUNCT
bracis-33567	120	14	j	j	NOUN
bracis-33567	120	15	}	}	PUNCT
bracis-33567	120	16	x^{l-1}_{j	x^{l-1}_{j	NOUN
bracis-33567	120	17	}	}	PUNCT
bracis-33567	120	18	+	+	CCONJ
bracis-33567	120	19	b^{l}_{i})\	b^{l}_{i})\	NOUN
bracis-33567	120	20	)	)	PUNCT
bracis-33567	120	21	is	be	AUX
bracis-33567	120	22	the	the	DET
bracis-33567	120	23	output	output	NOUN
bracis-33567	120	24	of	of	ADP
bracis-33567	120	25	the	the	DET
bracis-33567	120	26	\(\textrm{relu}\	\(\textrm{relu}\	NOUN
bracis-33567	120	27	)	)	PUNCT
bracis-33567	120	28	.	.	PUNCT
bracis-33567	121	1	for	for	ADP
bracis-33567	121	2	classification	classification	NOUN
bracis-33567	121	3	tasks	task	NOUN
bracis-33567	121	4	,	,	PUNCT
bracis-33567	121	5	the	the	DET
bracis-33567	121	6	last	last	ADJ
bracis-33567	121	7	layer	layer	NOUN
bracis-33567	121	8	l	l	NOUN
bracis-33567	121	9	is	be	AUX
bracis-33567	121	10	composed	compose	VERB
bracis-33567	121	11	of	of	ADP
bracis-33567	121	12	\(n_l	\(n_l	NOUN
bracis-33567	121	13	=	=	PUNCT
bracis-33567	121	14	\mathcal	\mathcal	PROPN
bracis-33567	121	15	{	{	PUNCT
bracis-33567	121	16	n}\	n}\	NOUN
bracis-33567	121	17	)	)	PUNCT
bracis-33567	121	18	neurons	neuron	NOUN
bracis-33567	121	19	,	,	PUNCT
bracis-33567	121	20	one	one	NUM
bracis-33567	121	21	for	for	ADP
bracis-33567	121	22	each	each	DET
bracis-33567	121	23	class	class	NOUN
bracis-33567	121	24	.	.	PUNCT
bracis-33567	122	1	moreover	moreover	ADV
bracis-33567	122	2	,	,	PUNCT
bracis-33567	122	3	it	it	PRON
bracis-33567	122	4	is	be	AUX
bracis-33567	122	5	common	common	ADJ
bracis-33567	122	6	to	to	PART
bracis-33567	122	7	normalize	normalize	VERB
bracis-33567	122	8	the	the	DET
bracis-33567	122	9	output	output	NOUN
bracis-33567	122	10	layer	layer	NOUN
bracis-33567	122	11	using	use	VERB
bracis-33567	122	12	a	a	DET
bracis-33567	122	13	softmax	softmax	NOUN
bracis-33567	122	14	layer	layer	NOUN
bracis-33567	122	15	.	.	PUNCT
bracis-33567	123	1	consequently	consequently	ADV
bracis-33567	123	2	,	,	PUNCT
bracis-33567	123	3	these	these	DET
bracis-33567	123	4	values	value	NOUN
bracis-33567	123	5	represent	represent	VERB
bracis-33567	123	6	the	the	DET
bracis-33567	123	7	probabilities	probability	NOUN
bracis-33567	123	8	associated	associate	VERB
bracis-33567	123	9	with	with	ADP
bracis-33567	123	10	each	each	DET
bracis-33567	123	11	class	class	NOUN
bracis-33567	123	12	.	.	PUNCT
bracis-33567	124	1	the	the	DET
bracis-33567	124	2	class	class	NOUN
bracis-33567	124	3	with	with	ADP
bracis-33567	124	4	the	the	DET
bracis-33567	124	5	highest	high	ADJ
bracis-33567	124	6	probability	probability	NOUN
bracis-33567	124	7	is	be	AUX
bracis-33567	124	8	chosen	choose	VERB
bracis-33567	124	9	as	as	ADP
bracis-33567	124	10	the	the	DET
bracis-33567	124	11	predicted	predict	VERB
bracis-33567	124	12	class	class	NOUN
bracis-33567	124	13	.	.	PUNCT
bracis-33567	125	1	however	however	ADV
bracis-33567	125	2	,	,	PUNCT
bracis-33567	125	3	we	we	PRON
bracis-33567	125	4	do	do	AUX
bracis-33567	125	5	not	not	PART
bracis-33567	125	6	need	need	VERB
bracis-33567	125	7	to	to	PART
bracis-33567	125	8	consider	consider	VERB
bracis-33567	125	9	this	this	DET
bracis-33567	125	10	normalization	normalization	NOUN
bracis-33567	125	11	transformation	transformation	NOUN
bracis-33567	125	12	as	as	SCONJ
bracis-33567	125	13	it	it	PRON
bracis-33567	125	14	does	do	AUX
bracis-33567	125	15	not	not	PART
bracis-33567	125	16	change	change	VERB
bracis-33567	125	17	the	the	DET
bracis-33567	125	18	maximum	maximum	ADJ
bracis-33567	125	19	value	value	NOUN
bracis-33567	125	20	of	of	ADP
bracis-33567	125	21	the	the	DET
bracis-33567	125	22	last	last	ADJ
bracis-33567	125	23	layer	layer	NOUN
bracis-33567	125	24	.	.	PUNCT
bracis-33567	126	1	thus	thus	ADV
bracis-33567	126	2	,	,	PUNCT
bracis-33567	126	3	the	the	DET
bracis-33567	126	4	predicted	predict	VERB
bracis-33567	126	5	class	class	NOUN
bracis-33567	126	6	is	be	AUX
bracis-33567	126	7	\(c_i	\(c_i	PROPN
bracis-33567	126	8	\in	\in	PROPN
bracis-33567	126	9	\mathcal	\mathcal	PROPN
bracis-33567	126	10	{	{	PUNCT
bracis-33567	126	11	k}\	k}\	NOUN
bracis-33567	126	12	)	)	PUNCT
bracis-33567	126	13	such	such	ADJ
bracis-33567	126	14	that	that	DET
bracis-33567	126	15	\(i	\(i	NOUN
bracis-33567	126	16	=	=	SYM
bracis-33567	126	17	\mathop	\mathop	PROPN
bracis-33567	126	18	{	{	PUNCT
bracis-33567	126	19	\mathrm	\mathrm	PROPN
bracis-33567	126	20	{	{	PUNCT
bracis-33567	126	21	arg\,max}}\nolimits	arg\,max}}\nolimits	X
bracis-33567	126	22	_	_	PUNCT
bracis-33567	126	23	{	{	PUNCT
bracis-33567	126	24	j	j	PROPN
bracis-33567	126	25	\in	\in	PROPN
bracis-33567	126	26	\{1	\{1	PROPN
bracis-33567	126	27	,	,	PUNCT
bracis-33567	126	28	...	...	PUNCT
bracis-33567	126	29	,	,	PUNCT
bracis-33567	126	30	\mathcal	\mathcal	PROPN
bracis-33567	126	31	{	{	PUNCT
bracis-33567	126	32	n}\	n}\	NOUN
bracis-33567	126	33	}	}	PUNCT
bracis-33567	126	34	}	}	PUNCT
bracis-33567	126	35	x^l_j\	x^l_j\	PROPN
bracis-33567	126	36	)	)	PUNCT
bracis-33567	126	37	.	.	PUNCT
bracis-33567	127	1	3	3	NUM
bracis-33567	127	2	explanations	explanation	NOUN
bracis-33567	127	3	for	for	ADP
bracis-33567	127	4	 	 	SPACE
bracis-33567	127	5	anns	anns	NOUN
bracis-33567	127	6	with	with	ADP
bracis-33567	127	7	 	 	SPACE
bracis-33567	127	8	logical	logical	ADJ
bracis-33567	127	9	implications	implication	NOUN
bracis-33567	127	10	ignatiev	ignatiev	PROPN
bracis-33567	127	11	et	et	PROPN
bracis-33567	127	12	al	al	PROPN
bracis-33567	127	13	.	.	PUNCT
bracis-33567	128	1	[	[	X
bracis-33567	128	2	8	8	NUM
bracis-33567	128	3	]	]	PUNCT
bracis-33567	128	4	proposed	propose	VERB
bracis-33567	128	5	an	an	DET
bracis-33567	128	6	algorithm	algorithm	NOUN
bracis-33567	128	7	that	that	PRON
bracis-33567	128	8	computes	compute	VERB
bracis-33567	128	9	minimal	minimal	ADJ
bracis-33567	128	10	explanations	explanation	NOUN
bracis-33567	128	11	for	for	ADP
bracis-33567	128	12	anns	ann	NOUN
bracis-33567	128	13	,	,	PUNCT
bracis-33567	128	14	yielding	yield	VERB
bracis-33567	128	15	a	a	DET
bracis-33567	128	16	subset	subset	NOUN
bracis-33567	128	17	of	of	ADP
bracis-33567	128	18	the	the	DET
bracis-33567	128	19	input	input	NOUN
bracis-33567	128	20	features	feature	VERB
bracis-33567	128	21	sufficient	sufficient	ADJ
bracis-33567	128	22	for	for	ADP
bracis-33567	128	23	the	the	DET
bracis-33567	128	24	prediction	prediction	NOUN
bracis-33567	128	25	.	.	PUNCT
bracis-33567	129	1	this	this	DET
bracis-33567	129	2	approach	approach	NOUN
bracis-33567	129	3	is	be	AUX
bracis-33567	129	4	based	base	VERB
bracis-33567	129	5	on	on	ADP
bracis-33567	129	6	logic	logic	NOUN
bracis-33567	129	7	with	with	ADP
bracis-33567	129	8	guarantees	guarantee	NOUN
bracis-33567	129	9	on	on	ADP
bracis-33567	129	10	the	the	DET
bracis-33567	129	11	correctness	correctness	NOUN
bracis-33567	129	12	and	and	CCONJ
bracis-33567	129	13	minimality	minimality	NOUN
bracis-33567	129	14	of	of	ADP
bracis-33567	129	15	explanations	explanation	NOUN
bracis-33567	129	16	.	.	PUNCT
bracis-33567	130	1	a	a	DET
bracis-33567	130	2	flowchart	flowchart	NOUN
bracis-33567	130	3	for	for	ADP
bracis-33567	130	4	computing	computing	NOUN
bracis-33567	130	5	explanations	explanation	NOUN
bracis-33567	130	6	using	use	VERB
bracis-33567	130	7	such	such	DET
bracis-33567	130	8	an	an	DET
bracis-33567	130	9	algorithm	algorithm	NOUN
bracis-33567	130	10	is	be	AUX
bracis-33567	130	11	shown	show	VERB
bracis-33567	130	12	in	in	ADP
bracis-33567	130	13	fig	fig	NOUN
bracis-33567	130	14	.	.	PUNCT
bracis-33567	130	15	 	 	SPACE
bracis-33567	131	1	1	1	NUM
bracis-33567	131	2	.	.	PUNCT
bracis-33567	131	3	fig	fig	NOUN
bracis-33567	131	4	.	.	PUNCT
bracis-33567	132	1	1	1	X
bracis-33567	132	2	.	.	X
bracis-33567	132	3	flowchart	flowchart	NOUN
bracis-33567	132	4	for	for	ADP
bracis-33567	132	5	calculating	calculate	VERB
bracis-33567	132	6	explanations	explanation	NOUN
bracis-33567	132	7	.	.	PUNCT
bracis-33567	133	1	full	full	ADJ
bracis-33567	133	2	size	size	NOUN
bracis-33567	133	3	image	image	NOUN
bracis-33567	133	4	first	first	ADV
bracis-33567	133	5	,	,	PUNCT
bracis-33567	133	6	the	the	DET
bracis-33567	133	7	ann	ann	PROPN
bracis-33567	133	8	and	and	CCONJ
bracis-33567	133	9	the	the	DET
bracis-33567	133	10	feature	feature	NOUN
bracis-33567	133	11	space	space	NOUN
bracis-33567	133	12	\(\{l_1	\(\{l_1	PROPN
bracis-33567	133	13	\le	\le	PROPN
bracis-33567	133	14	x_1	x_1	PROPN
bracis-33567	133	15	\le	\le	PROPN
bracis-33567	133	16	u_1,\text	u_1,\text	ADP
bracis-33567	133	17	l_2	l_2	PROPN
bracis-33567	133	18	\le	\le	PROPN
bracis-33567	133	19	x_2	x_2	PROPN
bracis-33567	133	20	\le	\le	PROPN
bracis-33567	133	21	u_2	u_2	PROPN
bracis-33567	133	22	,	,	PUNCT
bracis-33567	133	23	...	...	PUNCT
bracis-33567	133	24	,	,	PUNCT
bracis-33567	133	25	l_n	l_n	PROPN
bracis-33567	133	26	\le	\le	PROPN
bracis-33567	133	27	x_n	x_n	PROPN
bracis-33567	133	28	\le	\le	PROPN
bracis-33567	133	29	u_n	u_n	SYM
bracis-33567	133	30	\}\	\}\	NOUN
bracis-33567	133	31	)	)	PUNCT
bracis-33567	133	32	are	be	AUX
bracis-33567	133	33	encoded	encode	VERB
bracis-33567	133	34	as	as	ADP
bracis-33567	133	35	a	a	DET
bracis-33567	133	36	formula	formula	NOUN
bracis-33567	133	37	f	f	NOUN
bracis-33567	133	38	,	,	PUNCT
bracis-33567	133	39	an	an	DET
bracis-33567	133	40	instance	instance	NOUN
bracis-33567	133	41	\(\{x_1	\(\{x_1	PROPN
bracis-33567	133	42	=	=	PUNCT
bracis-33567	133	43	v_1	v_1	PROPN
bracis-33567	133	44	,	,	PUNCT
bracis-33567	133	45	x_2	x_2	PROPN
bracis-33567	133	46	=	=	PUNCT
bracis-33567	133	47	v_2	v_2	PROPN
bracis-33567	133	48	,	,	PUNCT
bracis-33567	133	49	...	...	PUNCT
bracis-33567	133	50	,	,	PUNCT
bracis-33567	133	51	x_n	x_n	PROPN
bracis-33567	133	52	=	=	SYM
bracis-33567	134	1	v_n\}\	v_n\}\	NOUN
bracis-33567	134	2	)	)	PUNCT
bracis-33567	134	3	of	of	ADP
bracis-33567	134	4	the	the	DET
bracis-33567	134	5	feature	feature	NOUN
bracis-33567	134	6	space	space	NOUN
bracis-33567	134	7	is	be	AUX
bracis-33567	134	8	encoded	encode	VERB
bracis-33567	134	9	as	as	ADP
bracis-33567	134	10	a	a	DET
bracis-33567	134	11	conjunction	conjunction	NOUN
bracis-33567	134	12	in	in	ADP
bracis-33567	134	13	a	a	DET
bracis-33567	134	14	formula	formula	NOUN
bracis-33567	134	15	c	c	NOUN
bracis-33567	134	16	,	,	PUNCT
bracis-33567	134	17	and	and	CCONJ
bracis-33567	134	18	the	the	DET
bracis-33567	134	19	associated	associated	ADJ
bracis-33567	134	20	prediction	prediction	NOUN
bracis-33567	134	21	by	by	ADP
bracis-33567	134	22	the	the	DET
bracis-33567	134	23	ann	ann	PROPN
bracis-33567	134	24	is	be	AUX
bracis-33567	134	25	encoded	encode	VERB
bracis-33567	134	26	as	as	ADP
bracis-33567	134	27	a	a	DET
bracis-33567	134	28	formula	formula	NOUN
bracis-33567	134	29	e.	e.	PROPN
bracis-33567	135	1	then	then	ADV
bracis-33567	135	2	,	,	PUNCT
bracis-33567	135	3	it	it	PRON
bracis-33567	135	4	holds	hold	VERB
bracis-33567	135	5	that	that	SCONJ
bracis-33567	135	6	\(c	\(c	NUM
bracis-33567	135	7	\wedge	\wedge	PROPN
bracis-33567	135	8	f	f	PROPN
bracis-33567	135	9	\models	\models	PROPN
bracis-33567	135	10	e\	e\	PROPN
bracis-33567	135	11	)	)	PUNCT
bracis-33567	135	12	.	.	PUNCT
bracis-33567	136	1	the	the	DET
bracis-33567	136	2	minimal	minimal	ADJ
bracis-33567	136	3	explanation	explanation	NOUN
bracis-33567	136	4	\(c_m\	\(c_m\	NOUN
bracis-33567	136	5	)	)	PUNCT
bracis-33567	136	6	of	of	ADP
bracis-33567	136	7	c	c	PROPN
bracis-33567	136	8	is	be	AUX
bracis-33567	136	9	calculated	calculate	VERB
bracis-33567	136	10	removing	remove	VERB
bracis-33567	136	11	feature	feature	NOUN
bracis-33567	136	12	by	by	ADP
bracis-33567	136	13	feature	feature	NOUN
bracis-33567	136	14	from	from	ADP
bracis-33567	136	15	c.	c.	NOUN
bracis-33567	136	16	for	for	ADP
bracis-33567	136	17	example	example	NOUN
bracis-33567	136	18	,	,	PUNCT
bracis-33567	136	19	given	give	VERB
bracis-33567	136	20	a	a	DET
bracis-33567	136	21	feature	feature	NOUN
bracis-33567	136	22	\(x_i\	\(x_i\	NOUN
bracis-33567	136	23	)	)	PUNCT
bracis-33567	136	24	with	with	ADP
bracis-33567	136	25	value	value	NOUN
bracis-33567	136	26	v	v	NOUN
bracis-33567	136	27	in	in	ADP
bracis-33567	136	28	c	c	NOUN
bracis-33567	136	29	,	,	PUNCT
bracis-33567	136	30	if	if	SCONJ
bracis-33567	136	31	\(c	\(c	ADJ
bracis-33567	136	32	\setminus	\setminus	PROPN
bracis-33567	136	33	\{x_i	\{x_i	NOUN
bracis-33567	136	34	=	=	SYM
bracis-33567	136	35	v\	v\	NOUN
bracis-33567	136	36	}	}	PUNCT
bracis-33567	136	37	\wedge	\wedge	PROPN
bracis-33567	136	38	f	f	PROPN
bracis-33567	136	39	\models	\models	PROPN
bracis-33567	136	40	e\	e\	PROPN
bracis-33567	136	41	)	)	PUNCT
bracis-33567	136	42	,	,	PUNCT
bracis-33567	136	43	feature	feature	NOUN
bracis-33567	136	44	\(x_i\	\(x_i\	NOUN
bracis-33567	136	45	)	)	PUNCT
bracis-33567	136	46	may	may	AUX
bracis-33567	136	47	be	be	AUX
bracis-33567	136	48	considered	consider	VERB
bracis-33567	136	49	as	as	ADP
bracis-33567	136	50	irrelevant	irrelevant	ADJ
bracis-33567	136	51	in	in	ADP
bracis-33567	136	52	the	the	DET
bracis-33567	136	53	explanation	explanation	NOUN
bracis-33567	136	54	and	and	CCONJ
bracis-33567	136	55	is	be	AUX
bracis-33567	136	56	removed	remove	VERB
bracis-33567	136	57	from	from	ADP
bracis-33567	136	58	c.	c.	PROPN
bracis-33567	136	59	otherwise	otherwise	ADV
bracis-33567	136	60	,	,	PUNCT
bracis-33567	136	61	if	if	SCONJ
bracis-33567	136	62	\(c	\(c	ADJ
bracis-33567	136	63	\setminus	\setminus	PROPN
bracis-33567	136	64	\{x_i	\{x_i	NOUN
bracis-33567	136	65	=	=	SYM
bracis-33567	136	66	v\	v\	NOUN
bracis-33567	136	67	}	}	PUNCT
bracis-33567	136	68	\wedge	\wedge	PROPN
bracis-33567	136	69	f	f	PROPN
bracis-33567	136	70	\not	\not	ADV
bracis-33567	136	71	\models	\models	PROPN
bracis-33567	136	72	e\	e\	PROPN
bracis-33567	136	73	)	)	PUNCT
bracis-33567	136	74	,	,	PUNCT
bracis-33567	136	75	then	then	ADV
bracis-33567	136	76	\(x_i\	\(x_i\	VERB
bracis-33567	136	77	)	)	PUNCT
bracis-33567	136	78	is	be	AUX
bracis-33567	136	79	kept	keep	VERB
bracis-33567	136	80	in	in	ADP
bracis-33567	136	81	c	c	PROPN
bracis-33567	136	82	since	since	SCONJ
bracis-33567	136	83	the	the	DET
bracis-33567	136	84	same	same	ADJ
bracis-33567	136	85	class	class	NOUN
bracis-33567	136	86	can	can	AUX
bracis-33567	136	87	not	not	PART
bracis-33567	136	88	be	be	AUX
bracis-33567	136	89	guaranteed	guarantee	VERB
bracis-33567	136	90	.	.	PUNCT
bracis-33567	137	1	this	this	DET
bracis-33567	137	2	\(c	\(c	ADJ
bracis-33567	137	3	\setminus	\setminus	PROPN
bracis-33567	137	4	\{x_i	\{x_i	NOUN
bracis-33567	137	5	=	=	SYM
bracis-33567	137	6	v\}\	v\}\	NOUN
bracis-33567	137	7	)	)	PUNCT
bracis-33567	137	8	notation	notation	NOUN
bracis-33567	137	9	represents	represent	VERB
bracis-33567	137	10	the	the	DET
bracis-33567	137	11	removal	removal	NOUN
bracis-33567	137	12	of	of	ADP
bracis-33567	137	13	\(x_i	\(x_i	ADJ
bracis-33567	137	14	=	=	SYM
bracis-33567	137	15	v\	v\	NOUN
bracis-33567	137	16	)	)	PUNCT
bracis-33567	137	17	from	from	ADP
bracis-33567	137	18	formula	formula	NOUN
bracis-33567	137	19	c.	c.	NOUN
bracis-33567	137	20	this	this	DET
bracis-33567	137	21	process	process	NOUN
bracis-33567	137	22	is	be	AUX
bracis-33567	137	23	described	describe	VERB
bracis-33567	137	24	in	in	ADP
bracis-33567	137	25	algorithm	algorithm	PROPN
bracis-33567	137	26	 	 	SPACE
bracis-33567	137	27	1	1	NUM
bracis-33567	137	28	and	and	CCONJ
bracis-33567	137	29	is	be	AUX
bracis-33567	137	30	performed	perform	VERB
bracis-33567	137	31	for	for	ADP
bracis-33567	137	32	all	all	DET
bracis-33567	137	33	features	feature	NOUN
bracis-33567	137	34	.	.	PUNCT
bracis-33567	138	1	then	then	ADV
bracis-33567	138	2	,	,	PUNCT
bracis-33567	138	3	\(c_m\	\(c_m\	PROPN
bracis-33567	138	4	)	)	PUNCT
bracis-33567	138	5	is	be	AUX
bracis-33567	138	6	the	the	DET
bracis-33567	138	7	result	result	NOUN
bracis-33567	138	8	at	at	ADP
bracis-33567	138	9	the	the	DET
bracis-33567	138	10	end	end	NOUN
bracis-33567	138	11	of	of	ADP
bracis-33567	138	12	this	this	DET
bracis-33567	138	13	procedure	procedure	NOUN
bracis-33567	138	14	.	.	PUNCT
bracis-33567	139	1	this	this	PRON
bracis-33567	139	2	means	mean	VERB
bracis-33567	139	3	that	that	SCONJ
bracis-33567	139	4	for	for	ADP
bracis-33567	139	5	the	the	DET
bracis-33567	139	6	values	value	NOUN
bracis-33567	139	7	of	of	ADP
bracis-33567	139	8	the	the	DET
bracis-33567	139	9	features	feature	NOUN
bracis-33567	139	10	in	in	ADP
bracis-33567	139	11	\(c_m\	\(c_m\	NOUN
bracis-33567	139	12	)	)	PUNCT
bracis-33567	139	13	,	,	PUNCT
bracis-33567	139	14	the	the	DET
bracis-33567	139	15	ann	ann	PROPN
bracis-33567	139	16	makes	make	VERB
bracis-33567	139	17	the	the	DET
bracis-33567	139	18	same	same	ADJ
bracis-33567	139	19	classification	classification	NOUN
bracis-33567	139	20	,	,	PUNCT
bracis-33567	139	21	whatever	whatever	PRON
bracis-33567	139	22	the	the	DET
bracis-33567	139	23	values	value	NOUN
bracis-33567	139	24	of	of	ADP
bracis-33567	139	25	the	the	DET
bracis-33567	139	26	remaining	remain	VERB
bracis-33567	139	27	features	feature	NOUN
bracis-33567	139	28	.	.	PUNCT
bracis-33567	140	1	since	since	SCONJ
bracis-33567	140	2	to	to	PART
bracis-33567	140	3	check	check	VERB
bracis-33567	140	4	entailments	entailment	NOUN
bracis-33567	140	5	\(c	\(c	ADJ
bracis-33567	140	6	\wedge	\wedge	PROPN
bracis-33567	140	7	f	f	PROPN
bracis-33567	140	8	\models	\models	PROPN
bracis-33567	140	9	e\	e\	PROPN
bracis-33567	140	10	)	)	PUNCT
bracis-33567	140	11	is	be	AUX
bracis-33567	140	12	equivalent	equivalent	ADJ
bracis-33567	140	13	to	to	PART
bracis-33567	140	14	test	test	VERB
bracis-33567	140	15	whether	whether	SCONJ
bracis-33567	140	16	\(c	\(c	NUM
bracis-33567	140	17	\wedge	\wedge	PROPN
bracis-33567	140	18	f	f	PROPN
bracis-33567	140	19	\wedge	\wedge	PROPN
bracis-33567	140	20	\lnot	\lnot	PROPN
bracis-33567	140	21	e\	e\	PROPN
bracis-33567	140	22	)	)	PUNCT
bracis-33567	140	23	is	be	AUX
bracis-33567	140	24	unsatisfiable	unsatisfiable	ADJ
bracis-33567	140	25	and	and	CCONJ
bracis-33567	140	26	f	f	NUM
bracis-33567	140	27	,	,	PUNCT
bracis-33567	140	28	c	c	NOUN
bracis-33567	140	29	and	and	CCONJ
bracis-33567	140	30	\(\lnot	\(\lnot	ADV
bracis-33567	140	31	e\	e\	NOUN
bracis-33567	140	32	)	)	PUNCT
bracis-33567	140	33	are	be	AUX
bracis-33567	140	34	encoded	encode	VERB
bracis-33567	140	35	as	as	ADP
bracis-33567	140	36	linear	linear	ADJ
bracis-33567	140	37	constraints	constraint	NOUN
bracis-33567	140	38	and	and	CCONJ
bracis-33567	140	39	indicator	indicator	NOUN
bracis-33567	140	40	constraints	constraint	NOUN
bracis-33567	140	41	,	,	PUNCT
bracis-33567	140	42	such	such	DET
bracis-33567	140	43	a	a	DET
bracis-33567	140	44	entailment	entailment	NOUN
bracis-33567	140	45	can	can	AUX
bracis-33567	140	46	be	be	AUX
bracis-33567	140	47	addressed	address	VERB
bracis-33567	140	48	by	by	ADP
bracis-33567	140	49	a	a	DET
bracis-33567	140	50	milp	milp	PROPN
bracis-33567	140	51	solver	solver	NOUN
bracis-33567	140	52	.	.	PUNCT
bracis-33567	141	1	the	the	DET
bracis-33567	141	2	encoding	encoding	NOUN
bracis-33567	141	3	of	of	ADP
bracis-33567	141	4	anns	ann	NOUN
bracis-33567	141	5	used	use	VERB
bracis-33567	141	6	in	in	ADP
bracis-33567	141	7	[	[	X
bracis-33567	141	8	8	8	NUM
bracis-33567	141	9	]	]	PUNCT
bracis-33567	141	10	and	and	CCONJ
bracis-33567	141	11	originally	originally	ADV
bracis-33567	141	12	proposed	propose	VERB
bracis-33567	141	13	by	by	ADP
bracis-33567	141	14	fischetti	fischetti	PROPN
bracis-33567	141	15	and	and	CCONJ
bracis-33567	141	16	jo	jo	NOUN
bracis-33567	142	1	[	[	X
bracis-33567	142	2	5	5	NUM
bracis-33567	142	3	]	]	PUNCT
bracis-33567	142	4	uses	use	VERB
bracis-33567	142	5	implications	implication	NOUN
bracis-33567	142	6	to	to	PART
bracis-33567	142	7	represent	represent	VERB
bracis-33567	142	8	the	the	DET
bracis-33567	142	9	behavior	behavior	NOUN
bracis-33567	142	10	of	of	ADP
bracis-33567	142	11	the	the	DET
bracis-33567	142	12	\(\textrm{relu}\	\(\textrm{relu}\	PROPN
bracis-33567	142	13	)	)	PUNCT
bracis-33567	142	14	activation	activation	NOUN
bracis-33567	142	15	function	function	NOUN
bracis-33567	142	16	.	.	PUNCT
bracis-33567	143	1	we	we	PRON
bracis-33567	143	2	encode	encode	VERB
bracis-33567	143	3	an	an	DET
bracis-33567	143	4	ann	ann	NOUN
bracis-33567	143	5	with	with	ADP
bracis-33567	143	6	\(l+1\	\(l+1\	NOUN
bracis-33567	143	7	)	)	PUNCT
bracis-33567	143	8	layers	layer	NOUN
bracis-33567	143	9	as	as	ADP
bracis-33567	143	10	in	in	ADP
bracis-33567	143	11	eqs	eqs	PROPN
bracis-33567	143	12	.	.	PUNCT
bracis-33567	144	1	(	(	PUNCT
bracis-33567	144	2	3)–(5	3)–(5	NOUN
bracis-33567	144	3	)	)	PUNCT
bracis-33567	144	4	.	.	PUNCT
bracis-33567	145	1	in	in	ADP
bracis-33567	145	2	the	the	DET
bracis-33567	145	3	following	following	NOUN
bracis-33567	145	4	,	,	PUNCT
bracis-33567	145	5	we	we	PRON
bracis-33567	145	6	explain	explain	VERB
bracis-33567	145	7	the	the	DET
bracis-33567	145	8	notation	notation	NOUN
bracis-33567	145	9	.	.	PUNCT
bracis-33567	146	1	the	the	DET
bracis-33567	146	2	encoding	encoding	NOUN
bracis-33567	146	3	uses	use	VERB
bracis-33567	146	4	variables	variable	NOUN
bracis-33567	146	5	\(x^{l}_{i}\	\(x^{l}_{i}\	NOUN
bracis-33567	146	6	)	)	PUNCT
bracis-33567	146	7	and	and	CCONJ
bracis-33567	146	8	\(o_n\	\(o_n\	NOUN
bracis-33567	146	9	)	)	PUNCT
bracis-33567	146	10	with	with	ADP
bracis-33567	146	11	the	the	DET
bracis-33567	146	12	same	same	ADJ
bracis-33567	146	13	meaning	meaning	NOUN
bracis-33567	146	14	as	as	ADP
bracis-33567	146	15	in	in	ADP
bracis-33567	146	16	the	the	DET
bracis-33567	146	17	notation	notation	NOUN
bracis-33567	146	18	for	for	ADP
bracis-33567	146	19	anns	ann	NOUN
bracis-33567	146	20	.	.	PUNCT
bracis-33567	147	1	auxiliary	auxiliary	PROPN
bracis-33567	147	2	variables	variable	NOUN
bracis-33567	147	3	\(s^{l}_{i}\	\(s^{l}_{i}\	PROPN
bracis-33567	147	4	)	)	PUNCT
bracis-33567	147	5	and	and	CCONJ
bracis-33567	147	6	\(z^{l}_{i}\	\(z^{l}_{i}\	PROPN
bracis-33567	147	7	)	)	PUNCT
bracis-33567	147	8	control	control	VERB
bracis-33567	147	9	the	the	DET
bracis-33567	147	10	behaviour	behaviour	NOUN
bracis-33567	147	11	of	of	ADP
bracis-33567	147	12	\(\textrm{relu}\	\(\textrm{relu}\	PROPN
bracis-33567	147	13	)	)	PUNCT
bracis-33567	147	14	activations	activation	NOUN
bracis-33567	147	15	.	.	PUNCT
bracis-33567	148	1	variable	variable	PROPN
bracis-33567	148	2	\(z^{l}_{i}\	\(z^{l}_{i}\	PROPN
bracis-33567	148	3	)	)	PUNCT
bracis-33567	148	4	is	be	AUX
bracis-33567	148	5	binary	binary	ADJ
bracis-33567	148	6	and	and	CCONJ
bracis-33567	148	7	if	if	SCONJ
bracis-33567	148	8	\(z^{l}_{i}\	\(z^{l}_{i}\	NOUN
bracis-33567	148	9	)	)	PUNCT
bracis-33567	148	10	is	be	AUX
bracis-33567	148	11	equal	equal	ADJ
bracis-33567	148	12	to	to	ADP
bracis-33567	148	13	1	1	NUM
bracis-33567	148	14	,	,	PUNCT
bracis-33567	148	15	the	the	DET
bracis-33567	148	16	\(\textrm{relu}\	\(\textrm{relu}\	PROPN
bracis-33567	148	17	)	)	PUNCT
bracis-33567	148	18	output	output	PROPN
bracis-33567	148	19	\(x^{l}_{i}\	\(x^{l}_{i}\	PROPN
bracis-33567	148	20	)	)	PUNCT
bracis-33567	148	21	is	be	AUX
bracis-33567	148	22	0	0	NUM
bracis-33567	148	23	and	and	CCONJ
bracis-33567	148	24	\(s^{l}_{i}\	\(s^{l}_{i}\	NOUN
bracis-33567	148	25	)	)	PUNCT
bracis-33567	148	26	is	be	AUX
bracis-33567	148	27	equal	equal	ADJ
bracis-33567	148	28	to	to	ADP
bracis-33567	148	29	the	the	DET
bracis-33567	148	30	linear	linear	ADJ
bracis-33567	148	31	part	part	NOUN
bracis-33567	148	32	.	.	PUNCT
bracis-33567	149	1	otherwise	otherwise	ADV
bracis-33567	149	2	,	,	PUNCT
bracis-33567	149	3	the	the	DET
bracis-33567	149	4	output	output	PROPN
bracis-33567	149	5	\(x^{l}_{i}\	\(x^{l}_{i}\	NOUN
bracis-33567	149	6	)	)	PUNCT
bracis-33567	149	7	is	be	AUX
bracis-33567	149	8	equal	equal	ADJ
bracis-33567	149	9	to	to	ADP
bracis-33567	149	10	the	the	DET
bracis-33567	149	11	linear	linear	ADJ
bracis-33567	149	12	part	part	NOUN
bracis-33567	149	13	and	and	CCONJ
bracis-33567	149	14	\(s^{l}_{i}\	\(s^{l}_{i}\	NOUN
bracis-33567	149	15	)	)	PUNCT
bracis-33567	149	16	is	be	AUX
bracis-33567	149	17	equal	equal	ADJ
bracis-33567	149	18	to	to	ADP
bracis-33567	149	19	0	0	NUM
bracis-33567	149	20	.	.	PUNCT
bracis-33567	150	1	the	the	DET
bracis-33567	150	2	constant	constant	ADJ
bracis-33567	150	3	\(ub^{l}_{s	\(ub^{l}_{s	PROPN
bracis-33567	150	4	,	,	PUNCT
bracis-33567	150	5	i}\	i}\	NUM
bracis-33567	150	6	)	)	PUNCT
bracis-33567	150	7	is	be	AUX
bracis-33567	150	8	the	the	DET
bracis-33567	150	9	upper	upper	ADJ
bracis-33567	150	10	bound	bind	VERB
bracis-33567	150	11	of	of	ADP
bracis-33567	150	12	variable	variable	ADJ
bracis-33567	150	13	\(s^{l}_{i}\	\(s^{l}_{i}\	NOUN
bracis-33567	150	14	)	)	PUNCT
bracis-33567	150	15	,	,	PUNCT
bracis-33567	150	16	and	and	CCONJ
bracis-33567	150	17	the	the	DET
bracis-33567	150	18	constant	constant	ADJ
bracis-33567	150	19	\(ub^{l}_{x	\(ub^{l}_{x	PROPN
bracis-33567	150	20	,	,	PUNCT
bracis-33567	150	21	i}\	i}\	NUM
bracis-33567	150	22	)	)	PUNCT
bracis-33567	150	23	is	be	AUX
bracis-33567	150	24	the	the	DET
bracis-33567	150	25	upper	upper	ADJ
bracis-33567	150	26	bound	bind	VERB
bracis-33567	150	27	of	of	ADP
bracis-33567	150	28	variable	variable	ADJ
bracis-33567	150	29	\(x^{l}_{i}\	\(x^{l}_{i}\	PROPN
bracis-33567	150	30	)	)	PUNCT
bracis-33567	150	31	.	.	PUNCT
bracis-33567	151	1	each	each	DET
bracis-33567	151	2	variable	variable	PROPN
bracis-33567	151	3	\(x^{0}_{i}\	\(x^{0}_{i}\	PROPN
bracis-33567	151	4	)	)	PUNCT
bracis-33567	151	5	has	have	VERB
bracis-33567	151	6	also	also	ADV
bracis-33567	151	7	lower	low	ADJ
bracis-33567	151	8	and	and	CCONJ
bracis-33567	151	9	upper	upper	ADJ
bracis-33567	151	10	bounds	bound	NOUN
bracis-33567	151	11	\(l_i\	\(l_i\	NOUN
bracis-33567	151	12	)	)	PUNCT
bracis-33567	151	13	,	,	PUNCT
bracis-33567	151	14	\(u_i\	\(u_i\	NOUN
bracis-33567	151	15	)	)	PUNCT
bracis-33567	151	16	,	,	PUNCT
bracis-33567	151	17	respectively	respectively	ADV
bracis-33567	151	18	,	,	PUNCT
bracis-33567	151	19	defined	define	VERB
bracis-33567	151	20	by	by	ADP
bracis-33567	151	21	the	the	DET
bracis-33567	151	22	domain	domain	NOUN
bracis-33567	151	23	of	of	ADP
bracis-33567	151	24	the	the	DET
bracis-33567	151	25	features	feature	NOUN
bracis-33567	151	26	.	.	PUNCT
bracis-33567	152	1	$	$	SYM
bracis-33567	152	2	$	$	SYM
bracis-33567	152	3	\begin{aligned	\begin{aligne	VERB
bracis-33567	152	4	}	}	PUNCT
bracis-33567	152	5	\left	\left	PROPN
bracis-33567	152	6	.	.	PROPN
bracis-33567	152	7	\begin{aligned	\begin{aligne	VERB
bracis-33567	152	8	}	}	PUNCT
bracis-33567	152	9	&	&	CCONJ
bracis-33567	152	10	\sum	\sum	NOUN
bracis-33567	152	11	_	_	PUNCT
bracis-33567	152	12	{	{	PUNCT
bracis-33567	152	13	j=1}^{n_{l-1	j=1}^{n_{l-1	ADJ
bracis-33567	152	14	}	}	PUNCT
bracis-33567	152	15	}	}	PUNCT
bracis-33567	152	16	w^{l}_{i	w^{l}_{i	NOUN
bracis-33567	152	17	,	,	PUNCT
bracis-33567	152	18	j	j	NOUN
bracis-33567	152	19	}	}	PUNCT
bracis-33567	152	20	x^{l-1}_i	x^{l-1}_i	PROPN
bracis-33567	153	1	+	+	CCONJ
bracis-33567	153	2	b^{l}_{i	b^{l}_{i	NOUN
bracis-33567	153	3	}	}	PUNCT
bracis-33567	153	4	=	=	SYM
bracis-33567	153	5	x^{l}_{i	x^{l}_{i	ADJ
bracis-33567	153	6	}	}	PUNCT
bracis-33567	153	7	s^{l}_{i}\\	s^{l}_{i}\\	PROPN
bracis-33567	153	8	&	&	CCONJ
bracis-33567	153	9	z^{l}_{i	z^{l}_{i	NOUN
bracis-33567	153	10	}	}	PUNCT
bracis-33567	153	11	=	=	SYM
bracis-33567	153	12	1	1	NUM
bracis-33567	153	13	\rightarrow	\rightarrow	PROPN
bracis-33567	153	14	x^{l}_{n	x^{l}_{n	PROPN
bracis-33567	153	15	}	}	PUNCT
bracis-33567	153	16	\le	\le	PROPN
bracis-33567	153	17	0	0	NUM
bracis-33567	153	18	\\	\\	NOUN
bracis-33567	153	19	&	&	CCONJ
bracis-33567	153	20	z^{l}_{i	z^{l}_{i	NOUN
bracis-33567	153	21	}	}	PUNCT
bracis-33567	153	22	=	=	SYM
bracis-33567	153	23	0	0	NUM
bracis-33567	153	24	\rightarrow	\rightarrow	PROPN
bracis-33567	153	25	s^{l}_{n	s^{l}_{n	NOUN
bracis-33567	153	26	}	}	PUNCT
bracis-33567	153	27	\le	\le	PROPN
bracis-33567	153	28	0	0	NUM
bracis-33567	153	29	\\	\\	NOUN
bracis-33567	153	30	&	&	CCONJ
bracis-33567	153	31	z^{l}_{i	z^{l}_{i	NOUN
bracis-33567	153	32	}	}	PUNCT
bracis-33567	153	33	\in	\in	PROPN
bracis-33567	153	34	\{0	\{0	NOUN
bracis-33567	153	35	,	,	PUNCT
bracis-33567	153	36	1\	1\	NUM
bracis-33567	153	37	}	}	PUNCT
bracis-33567	153	38	\\	\\	NOUN
bracis-33567	153	39	&	&	CCONJ
bracis-33567	153	40	0	0	PROPN
bracis-33567	153	41	\le	\le	PROPN
bracis-33567	153	42	x^{l}_{i	x^{l}_{i	ADJ
bracis-33567	153	43	}	}	PUNCT
bracis-33567	153	44	\le	\le	PROPN
bracis-33567	153	45	ub^{l}_{x	ub^{l}_{x	PROPN
bracis-33567	153	46	,	,	PUNCT
bracis-33567	153	47	i	i	PROPN
bracis-33567	153	48	}	}	PUNCT
bracis-33567	153	49	\\	\\	NOUN
bracis-33567	153	50	&	&	CCONJ
bracis-33567	153	51	0	0	PROPN
bracis-33567	153	52	\le	\le	PROPN
bracis-33567	153	53	s^{l}_{i	s^{l}_{i	NOUN
bracis-33567	153	54	}	}	PUNCT
bracis-33567	153	55	\le	\le	PROPN
bracis-33567	153	56	ub^{l}_{s	ub^{l}_{s	ADJ
bracis-33567	153	57	,	,	PUNCT
bracis-33567	153	58	i	i	PRON
bracis-33567	153	59	}	}	PUNCT
bracis-33567	153	60	\\	\\	NOUN
bracis-33567	153	61	\end{aligned	\end{aligne	VERB
bracis-33567	153	62	}	}	PUNCT
bracis-33567	153	63	\right\	\right\	ADJ
bracis-33567	153	64	}	}	PUNCT
bracis-33567	153	65	l	l	NOUN
bracis-33567	153	66	=	=	SYM
bracis-33567	153	67	1	1	NUM
bracis-33567	153	68	,	,	PUNCT
bracis-33567	153	69	...	...	PUNCT
bracis-33567	153	70	,	,	PUNCT
bracis-33567	153	71	l-1	l-1	NUM
bracis-33567	153	72	,	,	PUNCT
bracis-33567	153	73	\	\	PUNCT
bracis-33567	154	1	i	i	NOUN
bracis-33567	154	2	=	=	NOUN
bracis-33567	154	3	1	1	NUM
bracis-33567	154	4	,	,	PUNCT
bracis-33567	154	5	...	...	PUNCT
bracis-33567	154	6	,	,	PUNCT
bracis-33567	154	7	n_l	n_l	PUNCT
bracis-33567	154	8	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33567	154	9	(	(	PUNCT
bracis-33567	154	10	3	3	NUM
bracis-33567	154	11	)	)	PUNCT
bracis-33567	154	12	$	$	SYM
bracis-33567	154	13	$	$	SYM
bracis-33567	154	14	\begin{aligned	\begin{aligne	VERB
bracis-33567	154	15	}	}	PUNCT
bracis-33567	154	16	&	&	CCONJ
bracis-33567	154	17	l_i	l_i	PROPN
bracis-33567	154	18	\le	\le	PROPN
bracis-33567	154	19	x_{i	x_{i	PROPN
bracis-33567	154	20	}	}	PUNCT
bracis-33567	154	21	\le	\le	NOUN
bracis-33567	154	22	u_i,\quad	u_i,\quad	NOUN
bracis-33567	154	23	i	i	NOUN
bracis-33567	154	24	=	=	NOUN
bracis-33567	154	25	1	1	NUM
bracis-33567	154	26	,	,	PUNCT
bracis-33567	154	27	...	...	PUNCT
bracis-33567	154	28	,	,	PUNCT
bracis-33567	154	29	n_0\end{aligned}$$	n_0\end{aligned}$$	ADP
bracis-33567	154	30	(	(	PUNCT
bracis-33567	154	31	4	4	NUM
bracis-33567	154	32	)	)	PUNCT
bracis-33567	154	33	$	$	SYM
bracis-33567	154	34	$	$	SYM
bracis-33567	154	35	\begin{aligned	\begin{aligne	VERB
bracis-33567	154	36	}	}	PUNCT
bracis-33567	154	37	&	&	CCONJ
bracis-33567	154	38	o_i	o_i	PROPN
bracis-33567	154	39	=	=	SYM
bracis-33567	154	40	\sum	\sum	NOUN
bracis-33567	154	41	_	_	PUNCT
bracis-33567	154	42	{	{	PUNCT
bracis-33567	154	43	j=1}^{n_{l-1	j=1}^{n_{l-1	ADJ
bracis-33567	154	44	}	}	PUNCT
bracis-33567	154	45	}	}	PUNCT
bracis-33567	154	46	w^{l}_{i	w^{l}_{i	NOUN
bracis-33567	154	47	,	,	PUNCT
bracis-33567	154	48	j	j	NOUN
bracis-33567	154	49	}	}	PUNCT
bracis-33567	154	50	x^{l-1}_i	x^{l-1}_i	PROPN
bracis-33567	155	1	+	+	CCONJ
bracis-33567	155	2	b^{l}_{i},\quad	b^{l}_{i},\quad	VERB
bracis-33567	155	3	i	i	NOUN
bracis-33567	155	4	=	=	NOUN
bracis-33567	155	5	1	1	NUM
bracis-33567	155	6	,	,	PUNCT
bracis-33567	155	7	...	...	PUNCT
bracis-33567	155	8	,	,	PUNCT
bracis-33567	155	9	n_l	n_l	PUNCT
bracis-33567	155	10	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33567	155	11	(	(	PUNCT
bracis-33567	155	12	5	5	NUM
bracis-33567	155	13	)	)	PUNCT
bracis-33567	155	14	the	the	DET
bracis-33567	155	15	constraints	constraint	NOUN
bracis-33567	155	16	in	in	ADP
bracis-33567	155	17	(	(	PUNCT
bracis-33567	155	18	3)–(5	3)–(5	NOUN
bracis-33567	155	19	)	)	PUNCT
bracis-33567	155	20	represent	represent	VERB
bracis-33567	155	21	the	the	DET
bracis-33567	155	22	formula	formula	NOUN
bracis-33567	155	23	f.	f.	NOUN
bracis-33567	156	1	the	the	DET
bracis-33567	156	2	bounds	bound	NOUN
bracis-33567	156	3	\(ub^{l}_{x	\(ub^{l}_{x	PROPN
bracis-33567	156	4	,	,	PUNCT
bracis-33567	156	5	i}\	i}\	NUM
bracis-33567	156	6	)	)	PUNCT
bracis-33567	156	7	are	be	AUX
bracis-33567	156	8	defined	define	VERB
bracis-33567	156	9	by	by	ADP
bracis-33567	156	10	isolating	isolate	VERB
bracis-33567	156	11	variable	variable	ADJ
bracis-33567	156	12	\(x^{l}_{i}\	\(x^{l}_{i}\	NOUN
bracis-33567	156	13	)	)	PUNCT
bracis-33567	156	14	from	from	ADP
bracis-33567	156	15	other	other	ADJ
bracis-33567	156	16	constraints	constraint	NOUN
bracis-33567	156	17	in	in	ADP
bracis-33567	156	18	subsequent	subsequent	ADJ
bracis-33567	156	19	layers	layer	NOUN
bracis-33567	156	20	.	.	PUNCT
bracis-33567	157	1	then	then	ADV
bracis-33567	157	2	,	,	PUNCT
bracis-33567	157	3	\(x^{l}_{i}\	\(x^{l}_{i}\	PROPN
bracis-33567	157	4	)	)	PUNCT
bracis-33567	157	5	is	be	AUX
bracis-33567	157	6	maximized	maximize	VERB
bracis-33567	157	7	to	to	PART
bracis-33567	157	8	find	find	VERB
bracis-33567	157	9	its	its	PRON
bracis-33567	157	10	upper	upper	ADJ
bracis-33567	157	11	bound	bind	VERB
bracis-33567	157	12	.	.	PUNCT
bracis-33567	158	1	a	a	DET
bracis-33567	158	2	similar	similar	ADJ
bracis-33567	158	3	process	process	NOUN
bracis-33567	158	4	is	be	AUX
bracis-33567	158	5	applied	apply	VERB
bracis-33567	158	6	to	to	PART
bracis-33567	158	7	find	find	VERB
bracis-33567	158	8	the	the	DET
bracis-33567	158	9	bounds	bound	NOUN
bracis-33567	158	10	\(ub^{l}_{s	\(ub^{l}_{s	PROPN
bracis-33567	158	11	,	,	PUNCT
bracis-33567	158	12	i}\	i}\	NUM
bracis-33567	158	13	)	)	PUNCT
bracis-33567	158	14	for	for	ADP
bracis-33567	158	15	variables	variable	NOUN
bracis-33567	158	16	\(s^{l}_{i}\	\(s^{l}_{i}\	NOUN
bracis-33567	158	17	)	)	PUNCT
bracis-33567	158	18	.	.	PUNCT
bracis-33567	159	1	this	this	DET
bracis-33567	159	2	optimization	optimization	NOUN
bracis-33567	159	3	is	be	AUX
bracis-33567	159	4	possible	possible	ADJ
bracis-33567	159	5	due	due	ADP
bracis-33567	159	6	to	to	ADP
bracis-33567	159	7	the	the	DET
bracis-33567	159	8	bounds	bound	NOUN
bracis-33567	159	9	of	of	ADP
bracis-33567	159	10	the	the	DET
bracis-33567	159	11	features	feature	NOUN
bracis-33567	159	12	.	.	PUNCT
bracis-33567	160	1	furthermore	furthermore	ADV
bracis-33567	160	2	,	,	PUNCT
bracis-33567	160	3	these	these	DET
bracis-33567	160	4	bounds	bound	NOUN
bracis-33567	160	5	can	can	AUX
bracis-33567	160	6	assist	assist	VERB
bracis-33567	160	7	the	the	DET
bracis-33567	160	8	solver	solver	NOUN
bracis-33567	160	9	in	in	ADP
bracis-33567	160	10	accelerating	accelerate	VERB
bracis-33567	160	11	the	the	DET
bracis-33567	160	12	computation	computation	NOUN
bracis-33567	160	13	of	of	ADP
bracis-33567	160	14	explanations	explanation	NOUN
bracis-33567	160	15	.	.	PUNCT
bracis-33567	161	1	therefore	therefore	ADV
bracis-33567	161	2	,	,	PUNCT
bracis-33567	161	3	the	the	DET
bracis-33567	161	4	time	time	NOUN
bracis-33567	161	5	required	require	VERB
bracis-33567	161	6	for	for	ADP
bracis-33567	161	7	this	this	DET
bracis-33567	161	8	process	process	NOUN
bracis-33567	161	9	must	must	AUX
bracis-33567	161	10	be	be	AUX
bracis-33567	161	11	considered	consider	VERB
bracis-33567	161	12	when	when	SCONJ
bracis-33567	161	13	building	build	VERB
bracis-33567	161	14	f.	f.	PROPN
bracis-33567	161	15	to	to	PART
bracis-33567	161	16	check	check	VERB
bracis-33567	161	17	the	the	DET
bracis-33567	161	18	unsatisfiability	unsatisfiability	NOUN
bracis-33567	161	19	of	of	ADP
bracis-33567	161	20	the	the	DET
bracis-33567	161	21	expression	expression	NOUN
bracis-33567	161	22	\(c	\(c	PROPN
bracis-33567	161	23	\wedge	\wedge	PROPN
bracis-33567	161	24	f	f	PROPN
bracis-33567	161	25	\wedge	\wedge	PROPN
bracis-33567	161	26	\lnot	\lnot	PROPN
bracis-33567	161	27	e\	e\	PROPN
bracis-33567	161	28	)	)	PUNCT
bracis-33567	161	29	,	,	PUNCT
bracis-33567	161	30	we	we	PRON
bracis-33567	161	31	still	still	ADV
bracis-33567	161	32	need	need	VERB
bracis-33567	161	33	to	to	PART
bracis-33567	161	34	take	take	VERB
bracis-33567	161	35	into	into	ADP
bracis-33567	161	36	account	account	NOUN
bracis-33567	161	37	the	the	DET
bracis-33567	161	38	formula	formula	NOUN
bracis-33567	161	39	\(\lnot	\(\lnot	ADV
bracis-33567	161	40	e\	e\	ADV
bracis-33567	161	41	)	)	PUNCT
bracis-33567	161	42	,	,	PUNCT
bracis-33567	161	43	referring	refer	VERB
bracis-33567	161	44	to	to	ADP
bracis-33567	161	45	the	the	DET
bracis-33567	161	46	prediction	prediction	NOUN
bracis-33567	161	47	of	of	ADP
bracis-33567	161	48	the	the	DET
bracis-33567	161	49	ann	ann	PROPN
bracis-33567	161	50	.	.	PROPN
bracis-33567	162	1	given	give	VERB
bracis-33567	162	2	an	an	DET
bracis-33567	162	3	input	input	NOUN
bracis-33567	162	4	c	c	NOUN
bracis-33567	162	5	predicted	predict	VERB
bracis-33567	162	6	as	as	ADP
bracis-33567	162	7	class	class	NOUN
bracis-33567	162	8	\(c_i\	\(c_i\	NOUN
bracis-33567	162	9	)	)	PUNCT
bracis-33567	162	10	by	by	ADP
bracis-33567	162	11	the	the	DET
bracis-33567	162	12	ann	ann	PROPN
bracis-33567	162	13	,	,	PUNCT
bracis-33567	162	14	formula	formula	NOUN
bracis-33567	162	15	e	e	NOUN
bracis-33567	162	16	must	must	AUX
bracis-33567	162	17	be	be	AUX
bracis-33567	162	18	equivalent	equivalent	ADJ
bracis-33567	162	19	to	to	PART
bracis-33567	162	20	\(\bigwedge	\(\bigwedge	VERB
bracis-33567	162	21	_	_	PRON
bracis-33567	162	22	{	{	PUNCT
bracis-33567	162	23	j=1	j=1	PROPN
bracis-33567	162	24	,	,	PUNCT
bracis-33567	162	25	j	j	PROPN
bracis-33567	162	26	\ne	\ne	PROPN
bracis-33567	162	27	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	162	28	{	{	PUNCT
bracis-33567	162	29	n	n	CCONJ
bracis-33567	162	30	}	}	PUNCT
bracis-33567	162	31	}	}	PUNCT
bracis-33567	162	32	o_i	o_i	PROPN
bracis-33567	162	33	>	>	X
bracis-33567	162	34	o_j\	o_j\	PROPN
bracis-33567	162	35	)	)	PUNCT
bracis-33567	162	36	.	.	PUNCT
bracis-33567	163	1	this	this	DET
bracis-33567	163	2	formula	formula	NOUN
bracis-33567	163	3	asserts	assert	VERB
bracis-33567	163	4	that	that	SCONJ
bracis-33567	163	5	the	the	DET
bracis-33567	163	6	maximum	maximum	ADJ
bracis-33567	163	7	value	value	NOUN
bracis-33567	163	8	of	of	ADP
bracis-33567	163	9	the	the	DET
bracis-33567	163	10	last	last	ADJ
bracis-33567	163	11	layer	layer	NOUN
bracis-33567	163	12	is	be	AUX
bracis-33567	163	13	in	in	ADP
bracis-33567	163	14	output	output	NOUN
bracis-33567	163	15	\(o_i\	\(o_i\	NOUN
bracis-33567	163	16	)	)	PUNCT
bracis-33567	163	17	.	.	PUNCT
bracis-33567	164	1	therefore	therefore	ADV
bracis-33567	164	2	,	,	PUNCT
bracis-33567	164	3	\(\lnot	\(\lnot	ADV
bracis-33567	164	4	e\	e\	NOUN
bracis-33567	164	5	)	)	PUNCT
bracis-33567	164	6	must	must	AUX
bracis-33567	164	7	ensure	ensure	VERB
bracis-33567	164	8	that	that	SCONJ
bracis-33567	164	9	\(\bigvee	\(\bigvee	PROPN
bracis-33567	164	10	_	_	PUNCT
bracis-33567	164	11	{	{	PUNCT
bracis-33567	164	12	j=1	j=1	PROPN
bracis-33567	164	13	,	,	PUNCT
bracis-33567	164	14	j	j	PROPN
bracis-33567	164	15	\ne	\ne	PROPN
bracis-33567	164	16	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	164	17	{	{	PUNCT
bracis-33567	164	18	n	n	CCONJ
bracis-33567	164	19	}	}	PUNCT
bracis-33567	164	20	}	}	PUNCT
bracis-33567	164	21	o_i	o_i	PROPN
bracis-33567	164	22	\le	\le	PROPN
bracis-33567	164	23	o_j\	o_j\	NOUN
bracis-33567	164	24	)	)	PUNCT
bracis-33567	164	25	.	.	PUNCT
bracis-33567	165	1	since	since	SCONJ
bracis-33567	165	2	milp	milp	ADJ
bracis-33567	165	3	solvers	solver	NOUN
bracis-33567	165	4	can	can	AUX
bracis-33567	165	5	not	not	PART
bracis-33567	165	6	directly	directly	ADV
bracis-33567	165	7	represent	represent	VERB
bracis-33567	165	8	disjunctions	disjunction	NOUN
bracis-33567	165	9	,	,	PUNCT
bracis-33567	165	10	we	we	PRON
bracis-33567	165	11	use	use	VERB
bracis-33567	165	12	implications	implication	NOUN
bracis-33567	165	13	(	(	PUNCT
bracis-33567	165	14	6	6	NUM
bracis-33567	165	15	)	)	PUNCT
bracis-33567	165	16	and	and	CCONJ
bracis-33567	165	17	a	a	DET
bracis-33567	165	18	linear	linear	ADJ
bracis-33567	165	19	constraint	constraint	NOUN
bracis-33567	165	20	(	(	PUNCT
bracis-33567	165	21	7	7	NUM
bracis-33567	165	22	)	)	PUNCT
bracis-33567	165	23	over	over	ADP
bracis-33567	165	24	binary	binary	ADJ
bracis-33567	165	25	variables	variable	NOUN
bracis-33567	165	26	to	to	PART
bracis-33567	165	27	define	define	VERB
bracis-33567	165	28	\(\lnot	\(\lnot	ADV
bracis-33567	165	29	e\	e\	NOUN
bracis-33567	165	30	)	)	PUNCT
bracis-33567	165	31	.	.	PUNCT
bracis-33567	166	1	$	$	SYM
bracis-33567	166	2	$	$	SYM
bracis-33567	166	3	\begin{aligned	\begin{aligne	VERB
bracis-33567	166	4	}	}	PUNCT
bracis-33567	166	5	&	&	CCONJ
bracis-33567	166	6	q_j	q_j	CCONJ
bracis-33567	166	7	=	=	SYM
bracis-33567	166	8	1	1	NUM
bracis-33567	166	9	\rightarrow	\rightarrow	PROPN
bracis-33567	166	10	o_i	o_i	PROPN
bracis-33567	166	11	\le	\le	PROPN
bracis-33567	166	12	o_j	o_j	SYM
bracis-33567	166	13	,	,	PUNCT
bracis-33567	166	14	\quad	\quad	PROPN
bracis-33567	166	15	j	j	PROPN
bracis-33567	166	16	\in	\in	PROPN
bracis-33567	166	17	\{1	\{1	PROPN
bracis-33567	166	18	,	,	PUNCT
bracis-33567	166	19	...	...	PUNCT
bracis-33567	166	20	,	,	PUNCT
bracis-33567	166	21	\mathcal	\mathcal	PROPN
bracis-33567	166	22	{	{	PUNCT
bracis-33567	166	23	n}\	n}\	NOUN
bracis-33567	166	24	}	}	PUNCT
bracis-33567	166	25	\setminus	\setminus	PROPN
bracis-33567	166	26	\{i\	\{i\	PROPN
bracis-33567	166	27	}	}	PUNCT
bracis-33567	166	28	\end{aligned}$$	\end{aligned}$$	X
bracis-33567	166	29	(	(	PUNCT
bracis-33567	166	30	6	6	NUM
bracis-33567	166	31	)	)	PUNCT
bracis-33567	166	32	$	$	SYM
bracis-33567	166	33	$	$	SYM
bracis-33567	166	34	\begin{aligned	\begin{aligne	VERB
bracis-33567	166	35	}	}	PUNCT
bracis-33567	166	36	&	&	CCONJ
bracis-33567	166	37	\sum	\sum	NOUN
bracis-33567	166	38	_	_	PUNCT
bracis-33567	166	39	{	{	PUNCT
bracis-33567	166	40	j=1	j=1	PROPN
bracis-33567	166	41	,	,	PUNCT
bracis-33567	166	42	j	j	PROPN
bracis-33567	166	43	\ne	\ne	PROPN
bracis-33567	166	44	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	166	45	{	{	PUNCT
bracis-33567	166	46	n	n	CCONJ
bracis-33567	166	47	}	}	PUNCT
bracis-33567	166	48	}	}	PUNCT
bracis-33567	166	49	q_j	q_j	CCONJ
bracis-33567	166	50	\ge	\ge	PROPN
bracis-33567	166	51	1\end{aligned}$$	1\end{aligned}$$	NUM
bracis-33567	166	52	(	(	PUNCT
bracis-33567	166	53	7	7	NUM
bracis-33567	166	54	)	)	PUNCT
bracis-33567	166	55	$	$	SYM
bracis-33567	166	56	$	$	SYM
bracis-33567	166	57	\begin{aligned	\begin{aligne	VERB
bracis-33567	166	58	}	}	PUNCT
bracis-33567	166	59	&	&	CCONJ
bracis-33567	166	60	q_{j	q_{j	ADJ
bracis-33567	166	61	}	}	PUNCT
bracis-33567	166	62	\in	\in	PROPN
bracis-33567	166	63	\{0	\{0	NOUN
bracis-33567	166	64	,	,	PUNCT
bracis-33567	166	65	1\	1\	NUM
bracis-33567	166	66	}	}	PUNCT
bracis-33567	166	67	,	,	PUNCT
bracis-33567	166	68	\quad	\quad	PROPN
bracis-33567	166	69	j	j	PROPN
bracis-33567	166	70	\in	\in	PROPN
bracis-33567	166	71	\{1	\{1	PROPN
bracis-33567	166	72	,	,	PUNCT
bracis-33567	166	73	...	...	PUNCT
bracis-33567	166	74	,	,	PUNCT
bracis-33567	166	75	\mathcal	\mathcal	PROPN
bracis-33567	166	76	{	{	PUNCT
bracis-33567	166	77	n}\	n}\	NOUN
bracis-33567	166	78	}	}	PUNCT
bracis-33567	166	79	\setminus	\setminus	PROPN
bracis-33567	166	80	\{i\	\{i\	PROPN
bracis-33567	166	81	}	}	PUNCT
bracis-33567	166	82	\end{aligned}$$	\end{aligned}$$	X
bracis-33567	167	1	(	(	PUNCT
bracis-33567	167	2	8)	8)	NUM
bracis-33567	167	3	if	if	SCONJ
bracis-33567	167	4	an	an	DET
bracis-33567	167	5	assignment	assignment	NOUN
bracis-33567	167	6	\(\mathcal	\(\mathcal	ADJ
bracis-33567	167	7	{	{	PUNCT
bracis-33567	167	8	a}\	a}\	NUM
bracis-33567	167	9	)	)	PUNCT
bracis-33567	167	10	satisfies	satisfy	VERB
bracis-33567	167	11	\(\bigvee	\(\bigvee	PROPN
bracis-33567	167	12	_	_	PUNCT
bracis-33567	167	13	{	{	PUNCT
bracis-33567	167	14	j=1	j=1	PROPN
bracis-33567	167	15	,	,	PUNCT
bracis-33567	167	16	j	j	PROPN
bracis-33567	167	17	\ne	\ne	PROPN
bracis-33567	167	18	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	167	19	{	{	PUNCT
bracis-33567	167	20	n	n	CCONJ
bracis-33567	167	21	}	}	PUNCT
bracis-33567	167	22	}	}	PUNCT
bracis-33567	167	23	o_i	o_i	PROPN
bracis-33567	167	24	\le	\le	PROPN
bracis-33567	167	25	o_j\	o_j\	PROPN
bracis-33567	167	26	)	)	PUNCT
bracis-33567	167	27	,	,	PUNCT
bracis-33567	167	28	then	then	ADV
bracis-33567	167	29	\(o_i	\(o_i	VERB
bracis-33567	167	30	\le	\le	PROPN
bracis-33567	167	31	o_j\	o_j\	NOUN
bracis-33567	167	32	)	)	PUNCT
bracis-33567	167	33	is	be	AUX
bracis-33567	167	34	true	true	ADJ
bracis-33567	167	35	under	under	ADP
bracis-33567	167	36	\(\mathcal	\(\mathcal	ADJ
bracis-33567	167	37	{	{	PUNCT
bracis-33567	167	38	a}\	a}\	NUM
bracis-33567	167	39	)	)	PUNCT
bracis-33567	167	40	for	for	ADP
bracis-33567	167	41	some	some	DET
bracis-33567	167	42	j.	j.	PROPN
bracis-33567	167	43	therefore	therefore	ADV
bracis-33567	167	44	,	,	PUNCT
bracis-33567	167	45	the	the	DET
bracis-33567	167	46	assignment	assignment	NOUN
bracis-33567	167	47	\(\mathcal	\(\mathcal	ADJ
bracis-33567	167	48	{	{	PUNCT
bracis-33567	167	49	a	a	DET
bracis-33567	167	50	}	}	PUNCT
bracis-33567	167	51	\cup	\cup	NOUN
bracis-33567	167	52	\{q_j	\{q_j	NOUN
bracis-33567	167	53	\mapsto	\mapsto	PROPN
bracis-33567	167	54	1\}\	1\}\	NUM
bracis-33567	167	55	)	)	PUNCT
bracis-33567	167	56	satisfies	satisfy	VERB
bracis-33567	167	57	the	the	DET
bracis-33567	167	58	eqs	eqs	PROPN
bracis-33567	167	59	.	.	PUNCT
bracis-33567	168	1	(	(	PUNCT
bracis-33567	168	2	6)–(8	6)–(8	NUM
bracis-33567	168	3	)	)	PUNCT
bracis-33567	168	4	.	.	PUNCT
bracis-33567	169	1	conversely	conversely	ADV
bracis-33567	169	2	,	,	PUNCT
bracis-33567	169	3	if	if	SCONJ
bracis-33567	169	4	an	an	DET
bracis-33567	169	5	assignment	assignment	NOUN
bracis-33567	169	6	\(\mathcal	\(\mathcal	ADJ
bracis-33567	169	7	{	{	PUNCT
bracis-33567	169	8	a}\	a}\	NUM
bracis-33567	169	9	)	)	PUNCT
bracis-33567	169	10	satisfies	satisfy	VERB
bracis-33567	169	11	eqs	eqs	X
bracis-33567	169	12	.	.	PUNCT
bracis-33567	170	1	(	(	PUNCT
bracis-33567	170	2	6)–(8	6)–(8	NUM
bracis-33567	170	3	)	)	PUNCT
bracis-33567	170	4	,	,	PUNCT
bracis-33567	170	5	it	it	PRON
bracis-33567	170	6	clearly	clearly	ADV
bracis-33567	170	7	also	also	ADV
bracis-33567	170	8	satisfies	satisfy	VERB
bracis-33567	170	9	\(\bigvee	\(\bigvee	PROPN
bracis-33567	170	10	_	_	PUNCT
bracis-33567	170	11	{	{	PUNCT
bracis-33567	170	12	j=1	j=1	PROPN
bracis-33567	170	13	,	,	PUNCT
bracis-33567	170	14	j	j	PROPN
bracis-33567	170	15	\ne	\ne	PROPN
bracis-33567	170	16	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	170	17	{	{	PUNCT
bracis-33567	170	18	n	n	CCONJ
bracis-33567	170	19	}	}	PUNCT
bracis-33567	170	20	}	}	PUNCT
bracis-33567	171	1	o_i	o_i	PROPN
bracis-33567	171	2	\le	\le	PROPN
bracis-33567	171	3	o_j\	o_j\	NOUN
bracis-33567	171	4	)	)	PUNCT
bracis-33567	171	5	.	.	PUNCT
bracis-33567	172	1	we	we	PRON
bracis-33567	172	2	conclude	conclude	VERB
bracis-33567	172	3	this	this	DET
bracis-33567	172	4	section	section	NOUN
bracis-33567	172	5	with	with	ADP
bracis-33567	172	6	a	a	DET
bracis-33567	172	7	proposition	proposition	NOUN
bracis-33567	172	8	regarding	regard	VERB
bracis-33567	172	9	the	the	DET
bracis-33567	172	10	number	number	NOUN
bracis-33567	172	11	of	of	ADP
bracis-33567	172	12	variables	variable	NOUN
bracis-33567	172	13	and	and	CCONJ
bracis-33567	172	14	constraints	constraint	NOUN
bracis-33567	172	15	of	of	ADP
bracis-33567	172	16	the	the	DET
bracis-33567	172	17	encoding	encoding	NOUN
bracis-33567	172	18	discussed	discuss	VERB
bracis-33567	172	19	above	above	ADV
bracis-33567	172	20	.	.	PUNCT
bracis-33567	173	1	proposition	proposition	NOUN
bracis-33567	173	2	1	1	NUM
bracis-33567	173	3	let	let	VERB
bracis-33567	173	4	c	c	PRON
bracis-33567	173	5	be	be	AUX
bracis-33567	173	6	an	an	DET
bracis-33567	173	7	instance	instance	NOUN
bracis-33567	173	8	predicted	predict	VERB
bracis-33567	173	9	as	as	ADP
bracis-33567	173	10	a	a	DET
bracis-33567	173	11	class	class	NOUN
bracis-33567	173	12	\(c	\(c	PROPN
bracis-33567	173	13	\in	\in	PROPN
bracis-33567	173	14	\mathcal	\mathcal	PROPN
bracis-33567	173	15	{	{	PUNCT
bracis-33567	173	16	k}\	k}\	NOUN
bracis-33567	173	17	)	)	PUNCT
bracis-33567	173	18	by	by	ADP
bracis-33567	173	19	an	an	DET
bracis-33567	173	20	ann	ann	PROPN
bracis-33567	173	21	,	,	PUNCT
bracis-33567	173	22	the	the	DET
bracis-33567	173	23	formula	formula	NOUN
bracis-33567	173	24	\(c	\(c	NUM
bracis-33567	173	25	\wedge	\wedge	PROPN
bracis-33567	173	26	f	f	PROPN
bracis-33567	173	27	\wedge	\wedge	PROPN
bracis-33567	173	28	\lnot	\lnot	PROPN
bracis-33567	173	29	e\	e\	PROPN
bracis-33567	173	30	)	)	PUNCT
bracis-33567	173	31	has	have	VERB
bracis-33567	173	32	\(n_0	\(n_0	PROPN
bracis-33567	173	33	+	+	PUNCT
bracis-33567	173	34	n_l	n_l	PUNCT
bracis-33567	174	1	+	+	PUNCT
bracis-33567	174	2	2\sum	2\sum	NUM
bracis-33567	174	3	_	_	PUNCT
bracis-33567	174	4	{	{	PUNCT
bracis-33567	174	5	l=1}^{n_{l-1	l=1}^{n_{l-1	ADJ
bracis-33567	174	6	}	}	PUNCT
bracis-33567	174	7	}	}	PUNCT
bracis-33567	174	8	n_l\	n_l\	NOUN
bracis-33567	174	9	)	)	PUNCT
bracis-33567	174	10	real	real	ADJ
bracis-33567	174	11	variables	variable	NOUN
bracis-33567	174	12	and	and	CCONJ
bracis-33567	174	13	\(n_l	\(n_l	AUX
bracis-33567	174	14	1	1	NUM
bracis-33567	174	15	+	+	NUM
bracis-33567	174	16	\sum	\sum	NOUN
bracis-33567	174	17	_	_	PUNCT
bracis-33567	174	18	{	{	PUNCT
bracis-33567	174	19	l=1}^{n_{l-1	l=1}^{n_{l-1	NOUN
bracis-33567	174	20	}	}	PUNCT
bracis-33567	174	21	}	}	PUNCT
bracis-33567	174	22	n_l\	n_l\	NOUN
bracis-33567	174	23	)	)	PUNCT
bracis-33567	174	24	binary	binary	ADJ
bracis-33567	174	25	variables	variable	NOUN
bracis-33567	174	26	.	.	PUNCT
bracis-33567	175	1	also	also	ADV
bracis-33567	175	2	,	,	PUNCT
bracis-33567	175	3	the	the	DET
bracis-33567	175	4	formula	formula	NOUN
bracis-33567	175	5	has	have	VERB
bracis-33567	175	6	\(n_0	\(n_0	PROPN
bracis-33567	175	7	+	+	CCONJ
bracis-33567	175	8	2n_l	2n_l	NUM
bracis-33567	176	1	+	+	CCONJ
bracis-33567	176	2	5\sum	5\sum	NUM
bracis-33567	176	3	_	_	PUNCT
bracis-33567	176	4	{	{	PUNCT
bracis-33567	176	5	l=1}^{n_{l-1}}\	l=1}^{n_{l-1}}\	NOUN
bracis-33567	176	6	)	)	PUNCT
bracis-33567	176	7	constraints	constraint	NOUN
bracis-33567	176	8	.	.	PUNCT
bracis-33567	177	1	4	4	NUM
bracis-33567	177	2	explanations	explanation	NOUN
bracis-33567	177	3	for	for	ADP
bracis-33567	177	4	 	 	SPACE
bracis-33567	177	5	anns	ann	NOUN
bracis-33567	177	6	without	without	ADP
bracis-33567	177	7	implications	implication	NOUN
bracis-33567	177	8	in	in	ADP
bracis-33567	177	9	this	this	DET
bracis-33567	177	10	section	section	NOUN
bracis-33567	177	11	,	,	PUNCT
bracis-33567	177	12	we	we	PRON
bracis-33567	177	13	present	present	VERB
bracis-33567	177	14	an	an	DET
bracis-33567	177	15	adaptation	adaptation	NOUN
bracis-33567	177	16	of	of	ADP
bracis-33567	177	17	the	the	DET
bracis-33567	177	18	encoding	encoding	NOUN
bracis-33567	177	19	proposed	propose	VERB
bracis-33567	177	20	by	by	ADP
bracis-33567	177	21	tjeng	tjeng	PROPN
bracis-33567	177	22	et	et	PROPN
bracis-33567	177	23	al	al	PROPN
bracis-33567	177	24	.	.	PUNCT
bracis-33567	178	1	[	[	X
bracis-33567	178	2	17	17	NUM
bracis-33567	178	3	]	]	PUNCT
bracis-33567	178	4	for	for	ADP
bracis-33567	178	5	logic	logic	NOUN
bracis-33567	178	6	-	-	PUNCT
bracis-33567	178	7	based	base	VERB
bracis-33567	178	8	explainability	explainability	NOUN
bracis-33567	178	9	.	.	PUNCT
bracis-33567	179	1	in	in	ADP
bracis-33567	179	2	such	such	DET
bracis-33567	179	3	a	a	DET
bracis-33567	179	4	work	work	NOUN
bracis-33567	179	5	,	,	PUNCT
bracis-33567	179	6	the	the	DET
bracis-33567	179	7	authors	author	NOUN
bracis-33567	179	8	originally	originally	ADV
bracis-33567	179	9	used	use	VERB
bracis-33567	179	10	the	the	DET
bracis-33567	179	11	encoding	encoding	NOUN
bracis-33567	179	12	to	to	PART
bracis-33567	179	13	find	find	VERB
bracis-33567	179	14	adversarial	adversarial	ADJ
bracis-33567	179	15	examples	example	NOUN
bracis-33567	179	16	without	without	ADP
bracis-33567	179	17	using	use	VERB
bracis-33567	179	18	logical	logical	ADJ
bracis-33567	179	19	implications	implication	NOUN
bracis-33567	179	20	.	.	PUNCT
bracis-33567	180	1	even	even	ADV
bracis-33567	180	2	more	more	ADV
bracis-33567	180	3	importantly	importantly	ADV
bracis-33567	180	4	,	,	PUNCT
bracis-33567	180	5	such	such	DET
bracis-33567	180	6	an	an	DET
bracis-33567	180	7	encoding	encoding	NOUN
bracis-33567	180	8	uses	use	VERB
bracis-33567	180	9	fewer	few	ADJ
bracis-33567	180	10	variables	variable	NOUN
bracis-33567	180	11	and	and	CCONJ
bracis-33567	180	12	constraints	constraint	NOUN
bracis-33567	180	13	compared	compare	VERB
bracis-33567	180	14	to	to	ADP
bracis-33567	180	15	[	[	X
bracis-33567	180	16	5	5	NUM
bracis-33567	180	17	]	]	PUNCT
bracis-33567	180	18	.	.	PUNCT
bracis-33567	181	1	then	then	ADV
bracis-33567	181	2	,	,	PUNCT
bracis-33567	181	3	we	we	PRON
bracis-33567	181	4	expect	expect	VERB
bracis-33567	181	5	that	that	SCONJ
bracis-33567	181	6	our	our	PRON
bracis-33567	181	7	adaptation	adaptation	NOUN
bracis-33567	181	8	can	can	AUX
bracis-33567	181	9	lead	lead	VERB
bracis-33567	181	10	to	to	ADP
bracis-33567	181	11	a	a	DET
bracis-33567	181	12	better	well	ADJ
bracis-33567	181	13	execution	execution	NOUN
bracis-33567	181	14	time	time	NOUN
bracis-33567	181	15	for	for	ADP
bracis-33567	181	16	both	both	PRON
bracis-33567	181	17	building	build	VERB
bracis-33567	181	18	the	the	DET
bracis-33567	181	19	logical	logical	ADJ
bracis-33567	181	20	constraints	constraint	NOUN
bracis-33567	181	21	and	and	CCONJ
bracis-33567	181	22	computing	computing	NOUN
bracis-33567	181	23	explanations	explanation	NOUN
bracis-33567	181	24	.	.	PUNCT
bracis-33567	182	1	adapting	adapt	VERB
bracis-33567	182	2	the	the	DET
bracis-33567	182	3	encoding	encoding	NOUN
bracis-33567	182	4	in	in	ADP
bracis-33567	182	5	[	[	X
bracis-33567	182	6	17	17	NUM
bracis-33567	182	7	]	]	PUNCT
bracis-33567	182	8	to	to	ADP
bracis-33567	182	9	the	the	DET
bracis-33567	182	10	context	context	NOUN
bracis-33567	182	11	of	of	ADP
bracis-33567	182	12	computing	computing	NOUN
bracis-33567	182	13	explanations	explanation	NOUN
bracis-33567	182	14	requires	require	VERB
bracis-33567	182	15	incorporating	incorporate	VERB
bracis-33567	182	16	additional	additional	ADJ
bracis-33567	182	17	constraints	constraint	NOUN
bracis-33567	182	18	that	that	PRON
bracis-33567	182	19	were	be	AUX
bracis-33567	182	20	not	not	PART
bracis-33567	182	21	part	part	NOUN
bracis-33567	182	22	of	of	ADP
bracis-33567	182	23	the	the	DET
bracis-33567	182	24	original	original	ADJ
bracis-33567	182	25	work	work	NOUN
bracis-33567	182	26	.	.	PUNCT
bracis-33567	183	1	these	these	DET
bracis-33567	183	2	new	new	ADJ
bracis-33567	183	3	constraints	constraint	NOUN
bracis-33567	183	4	represent	represent	VERB
bracis-33567	183	5	the	the	DET
bracis-33567	183	6	class	class	NOUN
bracis-33567	183	7	predicted	predict	VERB
bracis-33567	183	8	by	by	ADP
bracis-33567	183	9	the	the	DET
bracis-33567	183	10	ann	ann	PROPN
bracis-33567	183	11	as	as	ADP
bracis-33567	183	12	a	a	DET
bracis-33567	183	13	formula	formula	NOUN
bracis-33567	183	14	e	e	NOUN
bracis-33567	183	15	,	,	PUNCT
bracis-33567	183	16	as	as	SCONJ
bracis-33567	183	17	seen	see	VERB
bracis-33567	183	18	in	in	ADP
bracis-33567	183	19	sect	sect	NOUN
bracis-33567	183	20	.	.	PUNCT
bracis-33567	183	21	 	 	SPACE
bracis-33567	184	1	3	3	X
bracis-33567	184	2	.	.	PUNCT
bracis-33567	185	1	however	however	ADV
bracis-33567	185	2	,	,	PUNCT
bracis-33567	185	3	to	to	PART
bracis-33567	185	4	maintain	maintain	VERB
bracis-33567	185	5	the	the	DET
bracis-33567	185	6	concept	concept	NOUN
bracis-33567	185	7	of	of	ADP
bracis-33567	185	8	the	the	DET
bracis-33567	185	9	original	original	ADJ
bracis-33567	185	10	encoding	encoding	NOUN
bracis-33567	185	11	without	without	ADP
bracis-33567	185	12	implications	implication	NOUN
bracis-33567	185	13	,	,	PUNCT
bracis-33567	185	14	we	we	PRON
bracis-33567	185	15	define	define	VERB
bracis-33567	185	16	these	these	DET
bracis-33567	185	17	additional	additional	ADJ
bracis-33567	185	18	constraints	constraint	NOUN
bracis-33567	185	19	without	without	ADP
bracis-33567	185	20	implications	implication	NOUN
bracis-33567	185	21	.	.	PUNCT
bracis-33567	186	1	in	in	ADP
bracis-33567	186	2	the	the	DET
bracis-33567	186	3	following	following	NOUN
bracis-33567	186	4	,	,	PUNCT
bracis-33567	186	5	we	we	PRON
bracis-33567	186	6	apply	apply	VERB
bracis-33567	186	7	the	the	DET
bracis-33567	186	8	same	same	ADJ
bracis-33567	186	9	algorithm	algorithm	NOUN
bracis-33567	186	10	from	from	ADP
bracis-33567	186	11	fig	fig	NOUN
bracis-33567	186	12	.	.	PUNCT
bracis-33567	186	13	 	 	SPACE
bracis-33567	186	14	1	1	NUM
bracis-33567	186	15	,	,	PUNCT
bracis-33567	186	16	but	but	CCONJ
bracis-33567	186	17	replacing	replace	VERB
bracis-33567	186	18	the	the	DET
bracis-33567	186	19	encoding	encoding	NOUN
bracis-33567	186	20	of	of	ADP
bracis-33567	186	21	f	f	PROPN
bracis-33567	186	22	as	as	ADP
bracis-33567	186	23	in	in	ADP
bracis-33567	186	24	[	[	X
bracis-33567	186	25	5	5	NUM
bracis-33567	186	26	]	]	PUNCT
bracis-33567	186	27	with	with	ADP
bracis-33567	186	28	the	the	DET
bracis-33567	186	29	one	one	NUM
bracis-33567	186	30	in	in	ADP
bracis-33567	186	31	[	[	X
bracis-33567	186	32	17	17	NUM
bracis-33567	186	33	]	]	PUNCT
bracis-33567	186	34	.	.	PUNCT
bracis-33567	187	1	we	we	PRON
bracis-33567	187	2	encode	encode	VERB
bracis-33567	187	3	an	an	DET
bracis-33567	187	4	ann	ann	NOUN
bracis-33567	187	5	with	with	ADP
bracis-33567	187	6	\(l+1\	\(l+1\	NOUN
bracis-33567	187	7	)	)	PUNCT
bracis-33567	187	8	layers	layer	NOUN
bracis-33567	187	9	as	as	ADP
bracis-33567	187	10	in	in	ADP
bracis-33567	187	11	eqs	eqs	PROPN
bracis-33567	187	12	.	.	PUNCT
bracis-33567	188	1	(	(	PUNCT
bracis-33567	188	2	9	9	NUM
bracis-33567	188	3	)	)	PUNCT
bracis-33567	188	4	,	,	PUNCT
bracis-33567	188	5	(	(	PUNCT
bracis-33567	188	6	4	4	NUM
bracis-33567	188	7	)	)	PUNCT
bracis-33567	188	8	and	and	CCONJ
bracis-33567	188	9	(	(	PUNCT
bracis-33567	188	10	5	5	NUM
bracis-33567	188	11	)	)	PUNCT
bracis-33567	188	12	.	.	PUNCT
bracis-33567	189	1	the	the	DET
bracis-33567	189	2	variables	variables	PROPN
bracis-33567	189	3	\(x^{l}_{i}\	\(x^{l}_{i}\	PROPN
bracis-33567	189	4	)	)	PUNCT
bracis-33567	189	5	and	and	CCONJ
bracis-33567	189	6	\(o_i\	\(o_i\	NOUN
bracis-33567	189	7	)	)	PUNCT
bracis-33567	189	8	have	have	VERB
bracis-33567	189	9	the	the	DET
bracis-33567	189	10	same	same	ADJ
bracis-33567	189	11	meaning	meaning	NOUN
bracis-33567	189	12	as	as	ADP
bracis-33567	189	13	in	in	ADP
bracis-33567	189	14	eqs	eqs	PROPN
bracis-33567	189	15	.	.	PUNCT
bracis-33567	190	1	(	(	PUNCT
bracis-33567	190	2	3)–(5	3)–(5	NOUN
bracis-33567	190	3	)	)	PUNCT
bracis-33567	190	4	.	.	PUNCT
bracis-33567	191	1	furthermore	furthermore	ADV
bracis-33567	191	2	,	,	PUNCT
bracis-33567	191	3	auxiliary	auxiliary	ADJ
bracis-33567	191	4	variables	variable	NOUN
bracis-33567	191	5	\(s^l_i\	\(s^l_i\	NOUN
bracis-33567	191	6	)	)	PUNCT
bracis-33567	191	7	are	be	AUX
bracis-33567	191	8	not	not	PART
bracis-33567	191	9	required	require	VERB
bracis-33567	191	10	,	,	PUNCT
bracis-33567	191	11	as	as	SCONJ
bracis-33567	191	12	observed	observe	VERB
bracis-33567	191	13	in	in	ADP
bracis-33567	191	14	the	the	DET
bracis-33567	191	15	encoding	encoding	NOUN
bracis-33567	191	16	by	by	ADP
bracis-33567	191	17	fischetti	fischetti	PROPN
bracis-33567	191	18	and	and	CCONJ
bracis-33567	191	19	jo	jo	NOUN
bracis-33567	192	1	[	[	X
bracis-33567	192	2	5	5	NUM
bracis-33567	192	3	]	]	PUNCT
bracis-33567	192	4	.	.	PUNCT
bracis-33567	193	1	constants	constants	PROPN
bracis-33567	193	2	\(lb^{l}_{i}\	\(lb^{l}_{i}\	PROPN
bracis-33567	193	3	)	)	PUNCT
bracis-33567	193	4	and	and	CCONJ
bracis-33567	193	5	\(ub^{l}_{i}\	\(ub^{l}_{i}\	PROPN
bracis-33567	193	6	)	)	PUNCT
bracis-33567	193	7	are	be	AUX
bracis-33567	193	8	,	,	PUNCT
bracis-33567	193	9	respectively	respectively	ADV
bracis-33567	193	10	,	,	PUNCT
bracis-33567	193	11	the	the	DET
bracis-33567	193	12	lower	low	ADJ
bracis-33567	193	13	and	and	CCONJ
bracis-33567	193	14	upper	upper	ADJ
bracis-33567	193	15	bounds	bound	NOUN
bracis-33567	193	16	of	of	ADP
bracis-33567	193	17	\(\sum	\(\sum	NOUN
bracis-33567	194	1	_	_	PRON
bracis-33567	194	2	{	{	PUNCT
bracis-33567	194	3	j=1}^{n_{l-1	j=1}^{n_{l-1	ADJ
bracis-33567	194	4	}	}	PUNCT
bracis-33567	194	5	}	}	PUNCT
bracis-33567	194	6	w^{l}_{i	w^{l}_{i	NOUN
bracis-33567	194	7	,	,	PUNCT
bracis-33567	194	8	j	j	NOUN
bracis-33567	194	9	}	}	PUNCT
bracis-33567	194	10	x^{l-1}_j	x^{l-1}_j	PROPN
bracis-33567	194	11	+	+	PROPN
bracis-33567	194	12	b^{l}_{i}\	b^{l}_{i}\	X
bracis-33567	194	13	)	)	PUNCT
bracis-33567	194	14	.	.	PUNCT
bracis-33567	195	1	again	again	ADV
bracis-33567	195	2	,	,	PUNCT
bracis-33567	195	3	we	we	PRON
bracis-33567	195	4	find	find	VERB
bracis-33567	195	5	such	such	ADJ
bracis-33567	195	6	bounds	bound	NOUN
bracis-33567	195	7	via	via	ADP
bracis-33567	195	8	a	a	DET
bracis-33567	195	9	milp	milp	PROPN
bracis-33567	195	10	solver	solver	NOUN
bracis-33567	195	11	.	.	PUNCT
bracis-33567	196	1	the	the	DET
bracis-33567	196	2	behavior	behavior	NOUN
bracis-33567	196	3	of	of	ADP
bracis-33567	196	4	\(\textrm{relu}\	\(\textrm{relu}\	PROPN
bracis-33567	196	5	)	)	PUNCT
bracis-33567	196	6	is	be	AUX
bracis-33567	196	7	modeled	model	VERB
bracis-33567	196	8	using	use	VERB
bracis-33567	196	9	these	these	DET
bracis-33567	196	10	bounds	bound	NOUN
bracis-33567	196	11	and	and	CCONJ
bracis-33567	196	12	binary	binary	ADJ
bracis-33567	196	13	variables	variable	NOUN
bracis-33567	196	14	\(z^{l}_{i}\	\(z^{l}_{i}\	PROPN
bracis-33567	196	15	)	)	PUNCT
bracis-33567	196	16	.	.	PUNCT
bracis-33567	197	1	if	if	SCONJ
bracis-33567	197	2	\(z^{l}_{i}\	\(z^{l}_{i}\	NOUN
bracis-33567	197	3	)	)	PUNCT
bracis-33567	197	4	is	be	AUX
bracis-33567	197	5	equal	equal	ADJ
bracis-33567	197	6	to	to	ADP
bracis-33567	197	7	0	0	NUM
bracis-33567	197	8	,	,	PUNCT
bracis-33567	197	9	the	the	DET
bracis-33567	197	10	\(\textrm{relu}\	\(\textrm{relu}\	PROPN
bracis-33567	197	11	)	)	PUNCT
bracis-33567	197	12	output	output	PROPN
bracis-33567	197	13	\(x^{l}_{i}\	\(x^{l}_{i}\	PROPN
bracis-33567	197	14	)	)	PUNCT
bracis-33567	197	15	is	be	AUX
bracis-33567	197	16	0	0	NUM
bracis-33567	197	17	.	.	PUNCT
bracis-33567	198	1	otherwise	otherwise	ADV
bracis-33567	198	2	,	,	PUNCT
bracis-33567	198	3	\(x^{l}_{i}\	\(x^{l}_{i}\	PROPN
bracis-33567	198	4	)	)	PUNCT
bracis-33567	198	5	is	be	AUX
bracis-33567	198	6	equal	equal	ADJ
bracis-33567	198	7	to	to	PART
bracis-33567	198	8	\(\sum	\(\sum	VERB
bracis-33567	198	9	_	_	PRON
bracis-33567	198	10	{	{	PUNCT
bracis-33567	198	11	j=1}^{n_{l-1	j=1}^{n_{l-1	ADJ
bracis-33567	198	12	}	}	PUNCT
bracis-33567	198	13	}	}	PUNCT
bracis-33567	198	14	w^{l}_{i	w^{l}_{i	NOUN
bracis-33567	198	15	,	,	PUNCT
bracis-33567	198	16	j	j	NOUN
bracis-33567	198	17	}	}	PUNCT
bracis-33567	198	18	x^{l-1}_j	x^{l-1}_j	PROPN
bracis-33567	198	19	+	+	PROPN
bracis-33567	198	20	b^{l}_{i}\	b^{l}_{i}\	NUM
bracis-33567	198	21	)	)	PUNCT
bracis-33567	198	22	.	.	PUNCT
bracis-33567	199	1	the	the	DET
bracis-33567	199	2	bounds	bound	NOUN
bracis-33567	199	3	\(lb^{l}{i}\	\(lb^{l}{i}\	PROPN
bracis-33567	199	4	)	)	PUNCT
bracis-33567	199	5	and	and	CCONJ
bracis-33567	199	6	\(ub^{l}{i}\	\(ub^{l}{i}\	NUM
bracis-33567	199	7	)	)	PUNCT
bracis-33567	199	8	are	be	AUX
bracis-33567	199	9	necessary	necessary	ADJ
bracis-33567	199	10	to	to	PART
bracis-33567	199	11	maintain	maintain	VERB
bracis-33567	199	12	the	the	DET
bracis-33567	199	13	integrity	integrity	NOUN
bracis-33567	199	14	of	of	ADP
bracis-33567	199	15	the	the	DET
bracis-33567	199	16	set	set	NOUN
bracis-33567	199	17	of	of	ADP
bracis-33567	199	18	constraints	constraint	NOUN
bracis-33567	199	19	for	for	ADP
bracis-33567	199	20	the	the	DET
bracis-33567	199	21	entire	entire	ADJ
bracis-33567	199	22	feature	feature	NOUN
bracis-33567	199	23	space	space	NOUN
bracis-33567	199	24	.	.	PUNCT
bracis-33567	200	1	regardless	regardless	ADV
bracis-33567	200	2	of	of	ADP
bracis-33567	200	3	the	the	DET
bracis-33567	200	4	value	value	NOUN
bracis-33567	200	5	of	of	ADP
bracis-33567	200	6	\(z^{l}{i}\	\(z^{l}{i}\	PROPN
bracis-33567	200	7	)	)	PUNCT
bracis-33567	200	8	,	,	PUNCT
bracis-33567	200	9	the	the	DET
bracis-33567	200	10	bounds	bound	NOUN
bracis-33567	200	11	ensure	ensure	VERB
bracis-33567	200	12	that	that	SCONJ
bracis-33567	200	13	the	the	DET
bracis-33567	200	14	constraints	constraint	NOUN
bracis-33567	200	15	remain	remain	VERB
bracis-33567	200	16	valid	valid	ADJ
bracis-33567	200	17	for	for	ADP
bracis-33567	200	18	the	the	DET
bracis-33567	200	19	entire	entire	ADJ
bracis-33567	200	20	feature	feature	NOUN
bracis-33567	200	21	space	space	NOUN
bracis-33567	200	22	.	.	PUNCT
bracis-33567	201	1	$	$	SYM
bracis-33567	201	2	$	$	SYM
bracis-33567	201	3	\begin{aligned	\begin{aligne	VERB
bracis-33567	201	4	}	}	PUNCT
bracis-33567	201	5	\left	\left	PROPN
bracis-33567	201	6	.	.	PROPN
bracis-33567	201	7	\begin{aligned	\begin{aligne	VERB
bracis-33567	201	8	}	}	PUNCT
bracis-33567	201	9	&	&	CCONJ
bracis-33567	201	10	x^{l}_{i	x^{l}_{i	ADJ
bracis-33567	201	11	}	}	PUNCT
bracis-33567	201	12	\le	\le	NOUN
bracis-33567	201	13	\sum	\sum	NOUN
bracis-33567	202	1	_	_	PUNCT
bracis-33567	202	2	{	{	PUNCT
bracis-33567	202	3	j=1}^{n_{l-1	j=1}^{n_{l-1	ADJ
bracis-33567	202	4	}	}	PUNCT
bracis-33567	202	5	}	}	PUNCT
bracis-33567	202	6	w^{l}_{i	w^{l}_{i	NOUN
bracis-33567	202	7	,	,	PUNCT
bracis-33567	202	8	j	j	NOUN
bracis-33567	202	9	}	}	PUNCT
bracis-33567	202	10	x^{l-1}_j	x^{l-1}_j	PROPN
bracis-33567	202	11	+	+	CCONJ
bracis-33567	202	12	b^{l}_{i	b^{l}_{i	NOUN
bracis-33567	202	13	}	}	PUNCT
bracis-33567	202	14	lb^{l}_{i	lb^{l}_{i	VERB
bracis-33567	202	15	}	}	PUNCT
bracis-33567	202	16	(	(	PUNCT
bracis-33567	202	17	1	1	NUM
bracis-33567	202	18	z^{l}_{i})\\	z^{l}_{i})\\	NUM
bracis-33567	202	19	&	&	CCONJ
bracis-33567	202	20	x^{l}_{i	x^{l}_{i	PROPN
bracis-33567	202	21	}	}	PUNCT
bracis-33567	202	22	\ge	\ge	PROPN
bracis-33567	202	23	\sum	\sum	NOUN
bracis-33567	202	24	_	_	PUNCT
bracis-33567	202	25	{	{	PUNCT
bracis-33567	202	26	j=1}^{n_{l-1	j=1}^{n_{l-1	ADJ
bracis-33567	202	27	}	}	PUNCT
bracis-33567	202	28	}	}	PUNCT
bracis-33567	202	29	w^{l}_{i	w^{l}_{i	NOUN
bracis-33567	202	30	,	,	PUNCT
bracis-33567	202	31	j	j	NOUN
bracis-33567	202	32	}	}	PUNCT
bracis-33567	202	33	x^{l-1}_j	x^{l-1}_j	PROPN
bracis-33567	202	34	+	+	CCONJ
bracis-33567	202	35	b^{l}_{i	b^{l}_{i	NOUN
bracis-33567	202	36	}	}	PUNCT
bracis-33567	202	37	\\	\\	NOUN
bracis-33567	202	38	&	&	CCONJ
bracis-33567	202	39	x^{l}_{i	x^{l}_{i	PROPN
bracis-33567	202	40	}	}	PUNCT
bracis-33567	202	41	\le	\le	PROPN
bracis-33567	202	42	ub^{l}_{i	ub^{l}_{i	ADJ
bracis-33567	202	43	}	}	PUNCT
bracis-33567	202	44	z^{l}_{i	z^{l}_{i	VERB
bracis-33567	202	45	}	}	PUNCT
bracis-33567	202	46	\\	\\	NOUN
bracis-33567	202	47	&	&	CCONJ
bracis-33567	202	48	z^{l}_{i	z^{l}_{i	NOUN
bracis-33567	202	49	}	}	PUNCT
bracis-33567	202	50	\in	\in	PROPN
bracis-33567	202	51	\{0	\{0	NOUN
bracis-33567	202	52	,	,	PUNCT
bracis-33567	202	53	1\	1\	NUM
bracis-33567	202	54	}	}	PUNCT
bracis-33567	202	55	\\	\\	NOUN
bracis-33567	202	56	&	&	CCONJ
bracis-33567	202	57	x^{l}_{i	x^{l}_{i	PROPN
bracis-33567	202	58	}	}	PUNCT
bracis-33567	202	59	\ge	\ge	PROPN
bracis-33567	202	60	0	0	NUM
bracis-33567	202	61	\\	\\	NOUN
bracis-33567	202	62	\end{aligned	\end{aligne	VERB
bracis-33567	202	63	}	}	PUNCT
bracis-33567	202	64	\right\	\right\	ADJ
bracis-33567	202	65	}	}	PUNCT
bracis-33567	202	66	l	l	NOUN
bracis-33567	203	1	=	=	SYM
bracis-33567	203	2	1	1	NUM
bracis-33567	203	3	,	,	PUNCT
bracis-33567	203	4	...	...	PUNCT
bracis-33567	203	5	,	,	PUNCT
bracis-33567	203	6	l-1	l-1	NUM
bracis-33567	203	7	,	,	PUNCT
bracis-33567	203	8	\	\	PUNCT
bracis-33567	204	1	i	i	NOUN
bracis-33567	204	2	=	=	NOUN
bracis-33567	204	3	1	1	NUM
bracis-33567	204	4	,	,	PUNCT
bracis-33567	204	5	...	...	PUNCT
bracis-33567	204	6	,	,	PUNCT
bracis-33567	204	7	n_l	n_l	PUNCT
bracis-33567	204	8	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33567	204	9	(	(	PUNCT
bracis-33567	204	10	9	9	NUM
bracis-33567	204	11	)	)	PUNCT
bracis-33567	204	12	in	in	ADP
bracis-33567	204	13	our	our	PRON
bracis-33567	204	14	proposal	proposal	NOUN
bracis-33567	204	15	for	for	ADP
bracis-33567	204	16	computing	compute	VERB
bracis-33567	204	17	explanations	explanation	NOUN
bracis-33567	204	18	,	,	PUNCT
bracis-33567	204	19	constraints	constraint	NOUN
bracis-33567	204	20	in	in	ADP
bracis-33567	204	21	eqs	eqs	PROPN
bracis-33567	204	22	.	.	PUNCT
bracis-33567	205	1	(	(	PUNCT
bracis-33567	205	2	9	9	NUM
bracis-33567	205	3	)	)	PUNCT
bracis-33567	205	4	,	,	PUNCT
bracis-33567	205	5	(	(	PUNCT
bracis-33567	205	6	4	4	NUM
bracis-33567	205	7	)	)	PUNCT
bracis-33567	205	8	and	and	CCONJ
bracis-33567	205	9	(	(	PUNCT
bracis-33567	205	10	5	5	X
bracis-33567	205	11	)	)	PUNCT
bracis-33567	205	12	represent	represent	VERB
bracis-33567	205	13	the	the	DET
bracis-33567	205	14	formula	formula	NOUN
bracis-33567	205	15	f.	f.	NOUN
bracis-33567	205	16	as	as	ADP
bracis-33567	205	17	in	in	ADP
bracis-33567	205	18	sect	sect	NOUN
bracis-33567	205	19	.	.	PUNCT
bracis-33567	205	20	 	 	SPACE
bracis-33567	206	1	3	3	NUM
bracis-33567	206	2	,	,	PUNCT
bracis-33567	206	3	an	an	DET
bracis-33567	206	4	instance	instance	NOUN
bracis-33567	206	5	is	be	AUX
bracis-33567	206	6	a	a	DET
bracis-33567	206	7	conjunction	conjunction	NOUN
bracis-33567	206	8	c	c	NOUN
bracis-33567	206	9	,	,	PUNCT
bracis-33567	206	10	and	and	CCONJ
bracis-33567	206	11	the	the	DET
bracis-33567	206	12	associated	associated	ADJ
bracis-33567	206	13	prediction	prediction	NOUN
bracis-33567	206	14	by	by	ADP
bracis-33567	206	15	the	the	DET
bracis-33567	206	16	ann	ann	PROPN
bracis-33567	206	17	is	be	AUX
bracis-33567	206	18	a	a	DET
bracis-33567	206	19	formula	formula	NOUN
bracis-33567	206	20	e.	e.	NOUN
bracis-33567	206	21	given	give	VERB
bracis-33567	206	22	an	an	DET
bracis-33567	206	23	input	input	NOUN
bracis-33567	206	24	c	c	NOUN
bracis-33567	206	25	predicted	predict	VERB
bracis-33567	206	26	as	as	ADP
bracis-33567	206	27	class	class	NOUN
bracis-33567	206	28	\(c_i\	\(c_i\	NOUN
bracis-33567	206	29	)	)	PUNCT
bracis-33567	206	30	by	by	ADP
bracis-33567	206	31	the	the	DET
bracis-33567	206	32	ann	ann	PROPN
bracis-33567	206	33	,	,	PUNCT
bracis-33567	206	34	again	again	ADV
bracis-33567	206	35	formula	formula	VERB
bracis-33567	206	36	\(\lnot	\(\lnot	ADV
bracis-33567	206	37	e\	e\	NOUN
bracis-33567	206	38	)	)	PUNCT
bracis-33567	206	39	must	must	AUX
bracis-33567	206	40	ensure	ensure	VERB
bracis-33567	206	41	that	that	SCONJ
bracis-33567	206	42	\(\bigvee	\(\bigvee	PROPN
bracis-33567	206	43	_	_	PUNCT
bracis-33567	206	44	{	{	PUNCT
bracis-33567	206	45	j=1	j=1	PROPN
bracis-33567	206	46	,	,	PUNCT
bracis-33567	206	47	j	j	PROPN
bracis-33567	206	48	\ne	\ne	PROPN
bracis-33567	206	49	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	206	50	{	{	PUNCT
bracis-33567	206	51	n	n	CCONJ
bracis-33567	206	52	}	}	PUNCT
bracis-33567	206	53	}	}	PUNCT
bracis-33567	206	54	o_i	o_i	PROPN
bracis-33567	206	55	\le	\le	PROPN
bracis-33567	206	56	o_j\	o_j\	NOUN
bracis-33567	206	57	)	)	PUNCT
bracis-33567	206	58	.	.	PUNCT
bracis-33567	207	1	therefore	therefore	ADV
bracis-33567	207	2	,	,	PUNCT
bracis-33567	207	3	we	we	PRON
bracis-33567	207	4	must	must	AUX
bracis-33567	207	5	add	add	VERB
bracis-33567	207	6	new	new	ADJ
bracis-33567	207	7	constraints	constraint	NOUN
bracis-33567	207	8	to	to	PART
bracis-33567	207	9	represent	represent	VERB
bracis-33567	207	10	\(\lnot	\(\lnot	ADV
bracis-33567	207	11	e\	e\	NOUN
bracis-33567	207	12	)	)	PUNCT
bracis-33567	207	13	.	.	PUNCT
bracis-33567	208	1	maintaining	maintain	VERB
bracis-33567	208	2	the	the	DET
bracis-33567	208	3	concept	concept	NOUN
bracis-33567	208	4	of	of	ADP
bracis-33567	208	5	the	the	DET
bracis-33567	208	6	original	original	ADJ
bracis-33567	208	7	encoding	encoding	NOUN
bracis-33567	208	8	in	in	ADP
bracis-33567	208	9	[	[	X
bracis-33567	208	10	17	17	NUM
bracis-33567	208	11	]	]	PUNCT
bracis-33567	208	12	without	without	ADP
bracis-33567	208	13	implications	implication	NOUN
bracis-33567	208	14	,	,	PUNCT
bracis-33567	208	15	we	we	PRON
bracis-33567	208	16	define	define	VERB
bracis-33567	208	17	these	these	DET
bracis-33567	208	18	additional	additional	ADJ
bracis-33567	208	19	constraints	constraint	NOUN
bracis-33567	208	20	accordingly	accordingly	ADV
bracis-33567	208	21	.	.	PUNCT
bracis-33567	209	1	we	we	PRON
bracis-33567	209	2	employ	employ	VERB
bracis-33567	209	3	binary	binary	ADJ
bracis-33567	209	4	variables	variable	NOUN
bracis-33567	209	5	\(q_j\	\(q_j\	NOUN
bracis-33567	209	6	)	)	PUNCT
bracis-33567	209	7	and	and	CCONJ
bracis-33567	209	8	the	the	DET
bracis-33567	209	9	upper	upper	ADJ
bracis-33567	209	10	and	and	CCONJ
bracis-33567	209	11	lower	low	ADJ
bracis-33567	209	12	bounds	bound	NOUN
bracis-33567	209	13	\(ub_j\	\(ub_j\	PROPN
bracis-33567	209	14	)	)	PUNCT
bracis-33567	209	15	and	and	CCONJ
bracis-33567	209	16	\(lb_j\	\(lb_j\	PROPN
bracis-33567	209	17	)	)	PUNCT
bracis-33567	209	18	of	of	ADP
bracis-33567	209	19	variables	variable	NOUN
bracis-33567	209	20	\(o_j\	\(o_j\	PROPN
bracis-33567	209	21	)	)	PUNCT
bracis-33567	209	22	.	.	PUNCT
bracis-33567	210	1	as	as	ADP
bracis-33567	210	2	for	for	ADP
bracis-33567	210	3	\(lb^{l}_{i}\	\(lb^{l}_{i}\	ADJ
bracis-33567	210	4	)	)	PUNCT
bracis-33567	210	5	and	and	CCONJ
bracis-33567	210	6	\(ub^{l}_{i}\	\(ub^{l}_{i}\	PROPN
bracis-33567	210	7	)	)	PUNCT
bracis-33567	210	8	,	,	PUNCT
bracis-33567	210	9	we	we	PRON
bracis-33567	210	10	find	find	VERB
bracis-33567	210	11	the	the	DET
bracis-33567	210	12	bounds	bound	NOUN
bracis-33567	210	13	\(ub_j\	\(ub_j\	PROPN
bracis-33567	210	14	)	)	PUNCT
bracis-33567	210	15	and	and	CCONJ
bracis-33567	210	16	\(lb_j\	\(lb_j\	PROPN
bracis-33567	210	17	)	)	PUNCT
bracis-33567	210	18	through	through	ADP
bracis-33567	210	19	a	a	DET
bracis-33567	210	20	milp	milp	PROPN
bracis-33567	210	21	solver	solver	NOUN
bracis-33567	210	22	.	.	PUNCT
bracis-33567	211	1	we	we	PRON
bracis-33567	211	2	recall	recall	VERB
bracis-33567	211	3	such	such	ADJ
bracis-33567	211	4	elements	element	NOUN
bracis-33567	211	5	are	be	AUX
bracis-33567	211	6	not	not	PART
bracis-33567	211	7	originally	originally	ADV
bracis-33567	211	8	present	present	ADJ
bracis-33567	211	9	in	in	ADP
bracis-33567	211	10	[	[	X
bracis-33567	211	11	17	17	NUM
bracis-33567	211	12	]	]	PUNCT
bracis-33567	211	13	.	.	PUNCT
bracis-33567	212	1	however	however	ADV
bracis-33567	212	2	,	,	PUNCT
bracis-33567	212	3	they	they	PRON
bracis-33567	212	4	are	be	AUX
bracis-33567	212	5	necessary	necessary	ADJ
bracis-33567	212	6	 	 	SPACE
bracis-33567	212	7	for	for	ADP
bracis-33567	212	8	the	the	DET
bracis-33567	212	9	context	context	NOUN
bracis-33567	212	10	of	of	ADP
bracis-33567	212	11	computing	compute	VERB
bracis-33567	212	12	explanations	explanation	NOUN
bracis-33567	212	13	for	for	ADP
bracis-33567	212	14	anns	ann	NOUN
bracis-33567	212	15	.	.	PUNCT
bracis-33567	213	1	in	in	ADP
bracis-33567	213	2	equations	equation	NOUN
bracis-33567	213	3	(	(	PUNCT
bracis-33567	213	4	10)-(12	10)-(12	NUM
bracis-33567	213	5	)	)	PUNCT
bracis-33567	213	6	we	we	PRON
bracis-33567	213	7	represent	represent	VERB
bracis-33567	213	8	our	our	PRON
bracis-33567	213	9	proposal	proposal	NOUN
bracis-33567	213	10	for	for	ADP
bracis-33567	213	11	encoding	encode	VERB
bracis-33567	213	12	formula	formula	NOUN
bracis-33567	213	13	\(\lnot	\(\lnot	ADV
bracis-33567	213	14	e\	e\	NOUN
bracis-33567	213	15	)	)	PUNCT
bracis-33567	213	16	,	,	PUNCT
bracis-33567	213	17	where	where	SCONJ
bracis-33567	213	18	the	the	DET
bracis-33567	213	19	prediction	prediction	NOUN
bracis-33567	213	20	associated	associate	VERB
bracis-33567	213	21	with	with	ADP
bracis-33567	213	22	an	an	DET
bracis-33567	213	23	input	input	NOUN
bracis-33567	213	24	c	c	NOUN
bracis-33567	213	25	is	be	AUX
bracis-33567	213	26	class	class	NOUN
bracis-33567	213	27	\(c_i\	\(c_i\	NOUN
bracis-33567	213	28	)	)	PUNCT
bracis-33567	213	29	.	.	PUNCT
bracis-33567	214	1	$	$	SYM
bracis-33567	214	2	$	$	SYM
bracis-33567	214	3	\begin{aligned	\begin{aligne	VERB
bracis-33567	214	4	}	}	PUNCT
bracis-33567	214	5	&	&	CCONJ
bracis-33567	214	6	o_i	o_i	PROPN
bracis-33567	214	7	o_j	o_j	PUNCT
bracis-33567	214	8	\le	\le	PROPN
bracis-33567	214	9	(	(	PUNCT
bracis-33567	214	10	ub_i	ub_i	PROPN
bracis-33567	214	11	lb_j	lb_j	NUM
bracis-33567	214	12	)	)	PUNCT
bracis-33567	214	13	(	(	PUNCT
bracis-33567	214	14	1	1	NUM
bracis-33567	214	15	q_j	q_j	NUM
bracis-33567	214	16	)	)	PUNCT
bracis-33567	214	17	,	,	PUNCT
bracis-33567	214	18	\quad	\quad	PROPN
bracis-33567	214	19	j	j	PROPN
bracis-33567	214	20	\in	\in	PROPN
bracis-33567	214	21	\{1	\{1	PROPN
bracis-33567	214	22	,	,	PUNCT
bracis-33567	214	23	...	...	PUNCT
bracis-33567	214	24	,	,	PUNCT
bracis-33567	214	25	\mathcal	\mathcal	PROPN
bracis-33567	214	26	{	{	PUNCT
bracis-33567	214	27	n}\	n}\	NOUN
bracis-33567	214	28	}	}	PUNCT
bracis-33567	214	29	\setminus	\setminus	PROPN
bracis-33567	214	30	\{i\	\{i\	PROPN
bracis-33567	214	31	}	}	PUNCT
bracis-33567	214	32	\end{aligned}$$	\end{aligned}$$	X
bracis-33567	214	33	(	(	PUNCT
bracis-33567	214	34	10	10	NUM
bracis-33567	214	35	)	)	PUNCT
bracis-33567	214	36	$	$	SYM
bracis-33567	214	37	$	$	SYM
bracis-33567	214	38	\begin{aligned	\begin{aligne	VERB
bracis-33567	214	39	}	}	PUNCT
bracis-33567	214	40	&	&	CCONJ
bracis-33567	214	41	\sum	\sum	NOUN
bracis-33567	214	42	_	_	PUNCT
bracis-33567	214	43	{	{	PUNCT
bracis-33567	214	44	j=1	j=1	PROPN
bracis-33567	214	45	,	,	PUNCT
bracis-33567	214	46	j	j	PROPN
bracis-33567	214	47	\ne	\ne	PROPN
bracis-33567	214	48	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	214	49	{	{	PUNCT
bracis-33567	214	50	n	n	CCONJ
bracis-33567	214	51	}	}	PUNCT
bracis-33567	214	52	}	}	PUNCT
bracis-33567	214	53	q_j	q_j	CCONJ
bracis-33567	214	54	\ge	\ge	PROPN
bracis-33567	214	55	1	1	NUM
bracis-33567	214	56	\end{aligned}$$	\end{aligned}$$	NOUN
bracis-33567	214	57	(	(	PUNCT
bracis-33567	214	58	11	11	NUM
bracis-33567	214	59	)	)	PUNCT
bracis-33567	214	60	$	$	SYM
bracis-33567	214	61	$	$	SYM
bracis-33567	214	62	\begin{aligned	\begin{aligne	VERB
bracis-33567	214	63	}	}	PUNCT
bracis-33567	214	64	&	&	CCONJ
bracis-33567	214	65	q_{j	q_{j	ADJ
bracis-33567	214	66	}	}	PUNCT
bracis-33567	214	67	\in	\in	PROPN
bracis-33567	214	68	\{0	\{0	NOUN
bracis-33567	214	69	,	,	PUNCT
bracis-33567	214	70	1\	1\	NUM
bracis-33567	214	71	}	}	PUNCT
bracis-33567	214	72	,	,	PUNCT
bracis-33567	214	73	\quad	\quad	PROPN
bracis-33567	214	74	j	j	PROPN
bracis-33567	214	75	\in	\in	PROPN
bracis-33567	214	76	\{1	\{1	PROPN
bracis-33567	214	77	,	,	PUNCT
bracis-33567	214	78	...	...	PUNCT
bracis-33567	214	79	,	,	PUNCT
bracis-33567	214	80	\mathcal	\mathcal	PROPN
bracis-33567	214	81	{	{	PUNCT
bracis-33567	214	82	n}\	n}\	NOUN
bracis-33567	214	83	}	}	PUNCT
bracis-33567	214	84	\setminus	\setminus	PROPN
bracis-33567	214	85	\{i\	\{i\	PROPN
bracis-33567	214	86	}	}	PUNCT
bracis-33567	214	87	\end{aligned}$$	\end{aligned}$$	X
bracis-33567	214	88	(	(	PUNCT
bracis-33567	214	89	12	12	NUM
bracis-33567	214	90	)	)	PUNCT
bracis-33567	214	91	in	in	ADP
bracis-33567	214	92	what	what	PRON
bracis-33567	214	93	follows	follow	VERB
bracis-33567	214	94	,	,	PUNCT
bracis-33567	214	95	we	we	PRON
bracis-33567	214	96	prove	prove	VERB
bracis-33567	214	97	that	that	SCONJ
bracis-33567	214	98	equations	equation	NOUN
bracis-33567	214	99	(	(	PUNCT
bracis-33567	214	100	10)-(12	10)-(12	NUM
bracis-33567	214	101	)	)	PUNCT
bracis-33567	214	102	correctly	correctly	ADV
bracis-33567	214	103	ensure	ensure	VERB
bracis-33567	214	104	that	that	SCONJ
bracis-33567	214	105	\(\bigvee	\(\bigvee	NOUN
bracis-33567	214	106	_	_	PUNCT
bracis-33567	214	107	{	{	PUNCT
bracis-33567	214	108	j=1	j=1	PROPN
bracis-33567	214	109	,	,	PUNCT
bracis-33567	214	110	j	j	PROPN
bracis-33567	214	111	\ne	\ne	PROPN
bracis-33567	214	112	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	214	113	{	{	PUNCT
bracis-33567	214	114	n	n	CCONJ
bracis-33567	214	115	}	}	PUNCT
bracis-33567	214	116	}	}	PUNCT
bracis-33567	214	117	o_i	o_i	PROPN
bracis-33567	214	118	\le	\le	PROPN
bracis-33567	214	119	o_j\	o_j\	NOUN
bracis-33567	214	120	)	)	PUNCT
bracis-33567	214	121	.	.	PUNCT
bracis-33567	215	1	proposition	proposition	NOUN
bracis-33567	215	2	2	2	NUM
bracis-33567	215	3	let	let	VERB
bracis-33567	215	4	\(\lnot	\(\lnot	ADV
bracis-33567	215	5	e\	e\	ADV
bracis-33567	215	6	)	)	PUNCT
bracis-33567	215	7	be	be	AUX
bracis-33567	215	8	defined	define	VERB
bracis-33567	215	9	as	as	ADP
bracis-33567	215	10	in	in	ADP
bracis-33567	215	11	equations	equation	NOUN
bracis-33567	215	12	(	(	PUNCT
bracis-33567	215	13	10)-(12	10)-(12	NUM
bracis-33567	215	14	)	)	PUNCT
bracis-33567	215	15	.	.	PUNCT
bracis-33567	216	1	let	let	VERB
bracis-33567	216	2	\(i	\(i	PROPN
bracis-33567	216	3	\in	\in	PROPN
bracis-33567	216	4	\{1	\{1	PROPN
bracis-33567	216	5	,	,	PUNCT
bracis-33567	216	6	...	...	PUNCT
bracis-33567	216	7	,	,	PUNCT
bracis-33567	216	8	\mathcal	\mathcal	PROPN
bracis-33567	216	9	{	{	PUNCT
bracis-33567	216	10	n}\}\	n}\}\	NOUN
bracis-33567	216	11	)	)	PUNCT
bracis-33567	216	12	be	be	AUX
bracis-33567	216	13	fixed	fix	VERB
bracis-33567	216	14	and	and	CCONJ
bracis-33567	216	15	\(ub_i\	\(ub_i\	NOUN
bracis-33567	216	16	)	)	PUNCT
bracis-33567	216	17	be	be	VERB
bracis-33567	216	18	such	such	ADJ
bracis-33567	216	19	that	that	SCONJ
bracis-33567	216	20	\(o_i	\(o_i	VERB
bracis-33567	216	21	\le	\le	PROPN
bracis-33567	216	22	ub_i\	ub_i\	NOUN
bracis-33567	216	23	)	)	PUNCT
bracis-33567	216	24	.	.	PUNCT
bracis-33567	217	1	let	let	VERB
bracis-33567	217	2	\(lb_j\	\(lb_j\	PROPN
bracis-33567	217	3	)	)	PUNCT
bracis-33567	217	4	be	be	AUX
bracis-33567	217	5	such	such	ADJ
bracis-33567	217	6	that	that	DET
bracis-33567	217	7	\(lb_j	\(lb_j	NOUN
bracis-33567	217	8	\le	\le	PROPN
bracis-33567	217	9	o_j\	o_j\	PROPN
bracis-33567	217	10	)	)	PUNCT
bracis-33567	217	11	,	,	PUNCT
bracis-33567	217	12	for	for	ADP
bracis-33567	217	13	\(j	\(j	NUM
bracis-33567	217	14	\in	\in	PROPN
bracis-33567	217	15	\{1	\{1	PROPN
bracis-33567	217	16	,	,	PUNCT
bracis-33567	217	17	...	...	PUNCT
bracis-33567	217	18	,	,	PUNCT
bracis-33567	217	19	\mathcal	\mathcal	PROPN
bracis-33567	217	20	{	{	PUNCT
bracis-33567	217	21	n}\	n}\	NOUN
bracis-33567	217	22	}	}	PUNCT
bracis-33567	217	23	\setminus	\setminus	PROPN
bracis-33567	217	24	\{i\}\	\{i\}\	ADJ
bracis-33567	217	25	)	)	PUNCT
bracis-33567	217	26	.	.	PUNCT
bracis-33567	218	1	therefore	therefore	ADV
bracis-33567	218	2	,	,	PUNCT
bracis-33567	218	3	$	$	SYM
bracis-33567	218	4	$	$	SYM
bracis-33567	218	5	\lnot	\lnot	PROPN
bracis-33567	218	6	e	e	SYM
bracis-33567	218	7	\text	\text	NOUN
bracis-33567	218	8	{	{	PUNCT
bracis-33567	218	9	is	be	AUX
bracis-33567	218	10	satisfiable	satisfiable	ADJ
bracis-33567	218	11	iff	iff	VERB
bracis-33567	218	12	}	}	PUNCT
bracis-33567	218	13	\bigvee	\bigvee	ADP
bracis-33567	218	14	_	_	PRON
bracis-33567	218	15	{	{	PUNCT
bracis-33567	218	16	j=1	j=1	PROPN
bracis-33567	218	17	,	,	PUNCT
bracis-33567	218	18	j	j	PROPN
bracis-33567	218	19	\ne	\ne	PROPN
bracis-33567	218	20	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	218	21	{	{	PUNCT
bracis-33567	218	22	n	n	CCONJ
bracis-33567	218	23	}	}	PUNCT
bracis-33567	218	24	}	}	PUNCT
bracis-33567	218	25	o_i	o_i	PROPN
bracis-33567	218	26	\le	\le	NOUN
bracis-33567	218	27	o_j	o_j	SYM
bracis-33567	219	1	\text	\text	ADV
bracis-33567	219	2	{	{	PUNCT
bracis-33567	219	3	is	be	AUX
bracis-33567	219	4	satisfiable	satisfiable	ADJ
bracis-33567	219	5	.	.	PUNCT
bracis-33567	220	1	}	}	PUNCT
bracis-33567	220	2	$	$	SYM
bracis-33567	220	3	$	$	SYM
bracis-33567	220	4	proof	proof	NOUN
bracis-33567	220	5	if	if	SCONJ
bracis-33567	220	6	an	an	DET
bracis-33567	220	7	assignment	assignment	NOUN
bracis-33567	220	8	\(\mathcal	\(\mathcal	ADJ
bracis-33567	220	9	{	{	PUNCT
bracis-33567	220	10	a}\	a}\	NUM
bracis-33567	220	11	)	)	PUNCT
bracis-33567	220	12	satisfies	satisfy	VERB
bracis-33567	220	13	\(\bigvee	\(\bigvee	PROPN
bracis-33567	220	14	_	_	PUNCT
bracis-33567	220	15	{	{	PUNCT
bracis-33567	220	16	j=1	j=1	PROPN
bracis-33567	220	17	,	,	PUNCT
bracis-33567	220	18	j	j	PROPN
bracis-33567	220	19	\ne	\ne	PROPN
bracis-33567	220	20	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	220	21	{	{	PUNCT
bracis-33567	220	22	n	n	CCONJ
bracis-33567	220	23	}	}	PUNCT
bracis-33567	220	24	}	}	PUNCT
bracis-33567	220	25	o_i	o_i	PROPN
bracis-33567	220	26	\le	\le	PROPN
bracis-33567	220	27	o_j\	o_j\	PROPN
bracis-33567	220	28	)	)	PUNCT
bracis-33567	220	29	,	,	PUNCT
bracis-33567	220	30	then	then	ADV
bracis-33567	220	31	\(o_i	\(o_i	VERB
bracis-33567	220	32	\le	\le	PROPN
bracis-33567	220	33	o_j'\	o_j'\	NUM
bracis-33567	220	34	)	)	PUNCT
bracis-33567	220	35	is	be	AUX
bracis-33567	220	36	true	true	ADJ
bracis-33567	220	37	under	under	ADP
bracis-33567	220	38	\(\mathcal	\(\mathcal	ADJ
bracis-33567	220	39	{	{	PUNCT
bracis-33567	220	40	a}\	a}\	NUM
bracis-33567	220	41	)	)	PUNCT
bracis-33567	220	42	for	for	ADP
bracis-33567	220	43	\(j	\(j	PROPN
bracis-33567	220	44	'	'	PART
bracis-33567	220	45	\ne	\ne	PROPN
bracis-33567	220	46	i\	i\	PROPN
bracis-33567	220	47	)	)	PUNCT
bracis-33567	220	48	.	.	PUNCT
bracis-33567	221	1	let	let	VERB
bracis-33567	221	2	\(\mathcal	\(\mathcal	ADJ
bracis-33567	221	3	{	{	PUNCT
bracis-33567	221	4	a	a	NOUN
bracis-33567	221	5	}	}	PUNCT
bracis-33567	221	6	'	'	PUNCT
bracis-33567	221	7	=	=	SYM
bracis-33567	221	8	\mathcal	\mathcal	ADJ
bracis-33567	221	9	{	{	PUNCT
bracis-33567	221	10	a	a	PRON
bracis-33567	221	11	}	}	PUNCT
bracis-33567	221	12	\cup	\cup	VERB
bracis-33567	221	13	\{q_{j	\{q_{j	NOUN
bracis-33567	221	14	}	}	PUNCT
bracis-33567	221	15	\mapsto	\mapsto	PROPN
bracis-33567	221	16	v	v	NUM
bracis-33567	221	17	\mid	\mid	NOUN
bracis-33567	221	18	v=1	v=1	PROPN
bracis-33567	222	1	\text	\text	ADV
bracis-33567	222	2	{	{	PUNCT
bracis-33567	222	3	if	if	SCONJ
bracis-33567	222	4	}	}	PUNCT
bracis-33567	222	5	j	j	PROPN
bracis-33567	222	6	=	=	PROPN
bracis-33567	222	7	j	j	PROPN
bracis-33567	222	8	'	'	PUNCT
bracis-33567	222	9	,	,	PUNCT
bracis-33567	222	10	\text	\text	PROPN
bracis-33567	222	11	{	{	PUNCT
bracis-33567	222	12	else	else	ADV
bracis-33567	222	13	}	}	PUNCT
bracis-33567	222	14	v=0	v=0	VERB
bracis-33567	222	15	,	,	PUNCT
bracis-33567	222	16	\text	\text	ADP
bracis-33567	222	17	{	{	PUNCT
bracis-33567	222	18	for	for	ADP
bracis-33567	222	19	}	}	PUNCT
bracis-33567	222	20	j	j	PROPN
bracis-33567	222	21	\in	\in	PROPN
bracis-33567	222	22	\{1	\{1	PROPN
bracis-33567	222	23	,	,	PUNCT
bracis-33567	222	24	...	...	PUNCT
bracis-33567	222	25	,	,	PUNCT
bracis-33567	222	26	\mathcal	\mathcal	PROPN
bracis-33567	222	27	{	{	PUNCT
bracis-33567	222	28	n}\	n}\	NOUN
bracis-33567	222	29	}	}	PUNCT
bracis-33567	222	30	\setminus	\setminus	PROPN
bracis-33567	222	31	\{i\}\}\	\{i\}\}\	NOUN
bracis-33567	222	32	)	)	PUNCT
bracis-33567	222	33	be	be	AUX
bracis-33567	222	34	an	an	DET
bracis-33567	222	35	assignment	assignment	NOUN
bracis-33567	222	36	.	.	PUNCT
bracis-33567	223	1	then	then	ADV
bracis-33567	223	2	,	,	PUNCT
bracis-33567	223	3	\(\mathcal	\(\mathcal	ADJ
bracis-33567	223	4	{	{	PUNCT
bracis-33567	223	5	a}'\	a}'\	NUM
bracis-33567	223	6	)	)	PUNCT
bracis-33567	223	7	imposes	impose	VERB
bracis-33567	223	8	that	that	PRON
bracis-33567	223	9	\(o_i	\(o_i	VERB
bracis-33567	223	10	\le	\le	PROPN
bracis-33567	223	11	o_j'\	o_j'\	NUM
bracis-33567	223	12	)	)	PUNCT
bracis-33567	223	13	in	in	ADP
bracis-33567	223	14	equation	equation	NOUN
bracis-33567	223	15	 	 	SPACE
bracis-33567	223	16	(	(	PUNCT
bracis-33567	223	17	10	10	NUM
bracis-33567	223	18	)	)	PUNCT
bracis-33567	223	19	for	for	ADP
bracis-33567	223	20	\(j	\(j	PROPN
bracis-33567	223	21	=	=	SYM
bracis-33567	223	22	j'\	j'\	NOUN
bracis-33567	223	23	)	)	PUNCT
bracis-33567	223	24	,	,	PUNCT
bracis-33567	223	25	which	which	PRON
bracis-33567	223	26	in	in	ADP
bracis-33567	223	27	clearly	clearly	ADV
bracis-33567	223	28	true	true	ADJ
bracis-33567	223	29	under	under	ADP
bracis-33567	223	30	this	this	DET
bracis-33567	223	31	assignment	assignment	NOUN
bracis-33567	223	32	.	.	PUNCT
bracis-33567	224	1	for	for	ADP
bracis-33567	224	2	\(j	\(j	PROPN
bracis-33567	224	3	\ne	\ne	PROPN
bracis-33567	224	4	j'\	j'\	PROPN
bracis-33567	224	5	)	)	PUNCT
bracis-33567	224	6	,	,	PUNCT
bracis-33567	224	7	it	it	PRON
bracis-33567	224	8	follows	follow	VERB
bracis-33567	224	9	that	that	SCONJ
bracis-33567	224	10	\(o_i	\(o_i	VERB
bracis-33567	224	11	o_j	o_j	PUNCT
bracis-33567	224	12	\le	\le	PROPN
bracis-33567	224	13	(	(	PUNCT
bracis-33567	224	14	ub_i	ub_i	NOUN
bracis-33567	224	15	lb_j)\	lb_j)\	NOUN
bracis-33567	224	16	)	)	PUNCT
bracis-33567	224	17	must	must	AUX
bracis-33567	224	18	hold	hold	VERB
bracis-33567	224	19	,	,	PUNCT
bracis-33567	224	20	which	which	PRON
bracis-33567	224	21	is	be	AUX
bracis-33567	224	22	also	also	ADV
bracis-33567	224	23	true	true	ADJ
bracis-33567	224	24	under	under	ADP
bracis-33567	224	25	\(\mathcal	\(\mathcal	ADJ
bracis-33567	224	26	{	{	PUNCT
bracis-33567	224	27	a}'\	a}'\	NUM
bracis-33567	224	28	)	)	PUNCT
bracis-33567	224	29	since	since	SCONJ
bracis-33567	224	30	\(lb_j	\(lb_j	VERB
bracis-33567	224	31	\le	\le	PROPN
bracis-33567	224	32	o_j\	o_j\	NOUN
bracis-33567	224	33	)	)	PUNCT
bracis-33567	224	34	and	and	CCONJ
bracis-33567	224	35	\(o_i	\(o_i	VERB
bracis-33567	224	36	\le	\le	PROPN
bracis-33567	224	37	ub_i\	ub_i\	NOUN
bracis-33567	224	38	)	)	PUNCT
bracis-33567	224	39	.	.	PUNCT
bracis-33567	225	1	conversely	conversely	ADV
bracis-33567	225	2	,	,	PUNCT
bracis-33567	225	3	if	if	SCONJ
bracis-33567	225	4	an	an	DET
bracis-33567	225	5	assignment	assignment	NOUN
bracis-33567	225	6	\(\mathcal	\(\mathcal	ADJ
bracis-33567	225	7	{	{	PUNCT
bracis-33567	225	8	a}\	a}\	NUM
bracis-33567	225	9	)	)	PUNCT
bracis-33567	225	10	satisfies	satisfy	VERB
bracis-33567	225	11	equations	equation	NOUN
bracis-33567	225	12	(	(	PUNCT
bracis-33567	225	13	10)-(12	10)-(12	NUM
bracis-33567	225	14	)	)	PUNCT
bracis-33567	225	15	,	,	PUNCT
bracis-33567	225	16	it	it	PRON
bracis-33567	225	17	satisfies	satisfy	VERB
bracis-33567	225	18	some	some	DET
bracis-33567	225	19	\(q_j'\	\(q_j'\	PROPN
bracis-33567	225	20	)	)	PUNCT
bracis-33567	225	21	,	,	PUNCT
bracis-33567	225	22	for	for	ADP
bracis-33567	225	23	\(j	\(j	PROPN
bracis-33567	225	24	'	'	PART
bracis-33567	225	25	\ne	\ne	PROPN
bracis-33567	225	26	i\	i\	PROPN
bracis-33567	225	27	)	)	PUNCT
bracis-33567	225	28	by	by	ADP
bracis-33567	225	29	equation	equation	NOUN
bracis-33567	225	30	 	 	SPACE
bracis-33567	225	31	(	(	PUNCT
bracis-33567	225	32	11	11	NUM
bracis-33567	225	33	)	)	PUNCT
bracis-33567	225	34	.	.	PUNCT
bracis-33567	226	1	moreover	moreover	ADV
bracis-33567	226	2	,	,	PUNCT
bracis-33567	226	3	\(\mathcal	\(\mathcal	ADJ
bracis-33567	226	4	{	{	PUNCT
bracis-33567	226	5	a}\	a}\	NUM
bracis-33567	226	6	)	)	PUNCT
bracis-33567	226	7	satisfies	satisfie	NOUN
bracis-33567	226	8	\(o_i	\(o_i	VERB
bracis-33567	226	9	\le	\le	PROPN
bracis-33567	226	10	o_{j'}\	o_{j'}\	PROPN
bracis-33567	226	11	)	)	PUNCT
bracis-33567	226	12	by	by	ADP
bracis-33567	226	13	equation	equation	NOUN
bracis-33567	226	14	 	 	SPACE
bracis-33567	226	15	(	(	PUNCT
bracis-33567	226	16	10	10	NUM
bracis-33567	226	17	)	)	PUNCT
bracis-33567	226	18	,	,	PUNCT
bracis-33567	226	19	for	for	ADP
bracis-33567	226	20	\(j	\(j	PROPN
bracis-33567	226	21	=	=	SYM
bracis-33567	226	22	j'\	j'\	NOUN
bracis-33567	226	23	)	)	PUNCT
bracis-33567	226	24	.	.	PUNCT
bracis-33567	227	1	therefore	therefore	ADV
bracis-33567	227	2	,	,	PUNCT
bracis-33567	227	3	\(\mathcal	\(\mathcal	ADJ
bracis-33567	227	4	{	{	PUNCT
bracis-33567	227	5	a}\	a}\	NUM
bracis-33567	227	6	)	)	PUNCT
bracis-33567	227	7	also	also	ADV
bracis-33567	227	8	satisfies	satisfy	VERB
bracis-33567	227	9	\(\bigvee	\(\bigvee	PROPN
bracis-33567	227	10	_	_	PUNCT
bracis-33567	227	11	{	{	PUNCT
bracis-33567	227	12	j=1	j=1	PROPN
bracis-33567	227	13	,	,	PUNCT
bracis-33567	227	14	j	j	PROPN
bracis-33567	227	15	\ne	\ne	PROPN
bracis-33567	227	16	i}^{\mathcal	i}^{\mathcal	ADJ
bracis-33567	227	17	{	{	PUNCT
bracis-33567	227	18	n	n	CCONJ
bracis-33567	227	19	}	}	PUNCT
bracis-33567	227	20	}	}	PUNCT
bracis-33567	227	21	o_i	o_i	PROPN
bracis-33567	227	22	\le	\le	PROPN
bracis-33567	227	23	o_j\	o_j\	NOUN
bracis-33567	227	24	)	)	PUNCT
bracis-33567	227	25	.	.	PUNCT
bracis-33567	228	1	finally	finally	ADV
bracis-33567	228	2	,	,	PUNCT
bracis-33567	228	3	we	we	PRON
bracis-33567	228	4	give	give	VERB
bracis-33567	228	5	a	a	DET
bracis-33567	228	6	proposition	proposition	NOUN
bracis-33567	228	7	on	on	ADP
bracis-33567	228	8	the	the	DET
bracis-33567	228	9	number	number	NOUN
bracis-33567	228	10	of	of	ADP
bracis-33567	228	11	variables	variable	NOUN
bracis-33567	228	12	and	and	CCONJ
bracis-33567	228	13	constraints	constraint	NOUN
bracis-33567	228	14	in	in	ADP
bracis-33567	228	15	our	our	PRON
bracis-33567	228	16	adaptation	adaptation	NOUN
bracis-33567	228	17	of	of	ADP
bracis-33567	228	18	the	the	DET
bracis-33567	228	19	encoding	encoding	NOUN
bracis-33567	228	20	in	in	ADP
bracis-33567	228	21	[	[	X
bracis-33567	228	22	17	17	NUM
bracis-33567	228	23	]	]	PUNCT
bracis-33567	228	24	.	.	PUNCT
bracis-33567	229	1	proposition	proposition	NOUN
bracis-33567	229	2	3	3	NUM
bracis-33567	229	3	let	let	VERB
bracis-33567	229	4	c	c	PRON
bracis-33567	229	5	be	be	AUX
bracis-33567	229	6	an	an	DET
bracis-33567	229	7	instance	instance	NOUN
bracis-33567	229	8	predicted	predict	VERB
bracis-33567	229	9	as	as	ADP
bracis-33567	229	10	a	a	DET
bracis-33567	229	11	class	class	NOUN
bracis-33567	229	12	\(c	\(c	PROPN
bracis-33567	229	13	\in	\in	PROPN
bracis-33567	229	14	\mathcal	\mathcal	PROPN
bracis-33567	229	15	{	{	PUNCT
bracis-33567	229	16	k}\	k}\	NOUN
bracis-33567	229	17	)	)	PUNCT
bracis-33567	229	18	by	by	ADP
bracis-33567	229	19	an	an	DET
bracis-33567	229	20	ann	ann	PROPN
bracis-33567	229	21	,	,	PUNCT
bracis-33567	229	22	then	then	ADV
bracis-33567	229	23	formula	formula	VERB
bracis-33567	229	24	\(c	\(c	NUM
bracis-33567	229	25	\wedge	\wedge	PROPN
bracis-33567	229	26	f	f	PROPN
bracis-33567	229	27	\wedge	\wedge	PROPN
bracis-33567	229	28	\lnot	\lnot	PROPN
bracis-33567	229	29	e\	e\	PROPN
bracis-33567	229	30	)	)	PUNCT
bracis-33567	229	31	has	have	VERB
bracis-33567	229	32	\(n_0	\(n_0	PROPN
bracis-33567	229	33	+	+	NUM
bracis-33567	229	34	n_l	n_l	PUNCT
bracis-33567	230	1	+	+	NUM
bracis-33567	230	2	\sum	\sum	NOUN
bracis-33567	230	3	_	_	PUNCT
bracis-33567	230	4	{	{	PUNCT
bracis-33567	230	5	l=1}^{n_{l-1	l=1}^{n_{l-1	NOUN
bracis-33567	230	6	}	}	PUNCT
bracis-33567	230	7	}	}	PUNCT
bracis-33567	230	8	n_l\	n_l\	NOUN
bracis-33567	230	9	)	)	PUNCT
bracis-33567	230	10	real	real	ADJ
bracis-33567	230	11	variables	variable	NOUN
bracis-33567	230	12	and	and	CCONJ
bracis-33567	230	13	\(n_l	\(n_l	AUX
bracis-33567	230	14	1	1	NUM
bracis-33567	230	15	+	+	NUM
bracis-33567	230	16	\sum	\sum	NOUN
bracis-33567	230	17	_	_	PUNCT
bracis-33567	230	18	{	{	PUNCT
bracis-33567	230	19	l=1}^{n_{l-1	l=1}^{n_{l-1	NOUN
bracis-33567	230	20	}	}	PUNCT
bracis-33567	230	21	}	}	PUNCT
bracis-33567	230	22	n_l\	n_l\	NOUN
bracis-33567	230	23	)	)	PUNCT
bracis-33567	230	24	binary	binary	ADJ
bracis-33567	230	25	variables	variable	NOUN
bracis-33567	230	26	.	.	PUNCT
bracis-33567	231	1	moreover	moreover	ADV
bracis-33567	231	2	,	,	PUNCT
bracis-33567	231	3	the	the	DET
bracis-33567	231	4	formula	formula	NOUN
bracis-33567	231	5	has	have	VERB
bracis-33567	231	6	\(n_0	\(n_0	PROPN
bracis-33567	231	7	+	+	CCONJ
bracis-33567	231	8	2n_l	2n_l	NUM
bracis-33567	231	9	+	+	CCONJ
bracis-33567	231	10	4\sum	4\sum	NUM
bracis-33567	231	11	_	_	PUNCT
bracis-33567	231	12	{	{	PUNCT
bracis-33567	231	13	l=1}^{n_{l-1	l=1}^{n_{l-1	ADJ
bracis-33567	231	14	}	}	PUNCT
bracis-33567	231	15	}	}	PUNCT
bracis-33567	231	16	n_l\	n_l\	NOUN
bracis-33567	231	17	)	)	PUNCT
bracis-33567	231	18	constraints	constraint	NOUN
bracis-33567	231	19	.	.	PUNCT
bracis-33567	232	1	therefore	therefore	ADV
bracis-33567	232	2	,	,	PUNCT
bracis-33567	232	3	this	this	DET
bracis-33567	232	4	encoding	encoding	NOUN
bracis-33567	232	5	has	have	AUX
bracis-33567	232	6	\(\sum	\(\sum	VERB
bracis-33567	232	7	_	_	PRON
bracis-33567	232	8	{	{	PUNCT
bracis-33567	232	9	l=1}^{n_{l-1	l=1}^{n_{l-1	NOUN
bracis-33567	232	10	}	}	PUNCT
bracis-33567	232	11	}	}	PUNCT
bracis-33567	232	12	n_l\	n_l\	NOUN
bracis-33567	232	13	)	)	PUNCT
bracis-33567	232	14	fewer	few	ADJ
bracis-33567	232	15	variables	variable	NOUN
bracis-33567	232	16	than	than	ADP
bracis-33567	232	17	the	the	DET
bracis-33567	232	18	one	one	NOUN
bracis-33567	232	19	presented	present	VERB
bracis-33567	232	20	in	in	ADP
bracis-33567	232	21	sect	sect	NOUN
bracis-33567	232	22	.	.	PUNCT
bracis-33567	232	23	 	 	SPACE
bracis-33567	233	1	3	3	X
bracis-33567	233	2	.	.	PUNCT
bracis-33567	233	3	additionally	additionally	ADV
bracis-33567	233	4	,	,	PUNCT
bracis-33567	233	5	this	this	DET
bracis-33567	233	6	encoding	encoding	NOUN
bracis-33567	233	7	has	have	AUX
bracis-33567	233	8	\(\sum	\(\sum	VERB
bracis-33567	233	9	_	_	DET
bracis-33567	233	10	{	{	PUNCT
bracis-33567	233	11	l=1}^{n_{l-1	l=1}^{n_{l-1	NOUN
bracis-33567	233	12	}	}	PUNCT
bracis-33567	233	13	}	}	PUNCT
bracis-33567	233	14	n_l\	n_l\	NOUN
bracis-33567	233	15	)	)	PUNCT
bracis-33567	233	16	fewer	few	ADJ
bracis-33567	233	17	constraints	constraint	NOUN
bracis-33567	233	18	.	.	PUNCT
bracis-33567	234	1	consequently	consequently	ADV
bracis-33567	234	2	,	,	PUNCT
bracis-33567	234	3	one	one	PRON
bracis-33567	234	4	would	would	AUX
bracis-33567	234	5	expect	expect	VERB
bracis-33567	234	6	a	a	DET
bracis-33567	234	7	reduction	reduction	NOUN
bracis-33567	234	8	in	in	ADP
bracis-33567	234	9	running	run	VERB
bracis-33567	234	10	time	time	NOUN
bracis-33567	234	11	for	for	ADP
bracis-33567	234	12	both	both	PRON
bracis-33567	234	13	building	build	VERB
bracis-33567	234	14	the	the	DET
bracis-33567	234	15	logical	logical	ADJ
bracis-33567	234	16	constraints	constraint	NOUN
bracis-33567	234	17	and	and	CCONJ
bracis-33567	234	18	computing	computing	NOUN
bracis-33567	234	19	explanations	explanation	NOUN
bracis-33567	234	20	.	.	PUNCT
bracis-33567	235	1	5	5	NUM
bracis-33567	235	2	experiments	experiment	NOUN
bracis-33567	235	3	in	in	ADP
bracis-33567	235	4	this	this	DET
bracis-33567	235	5	section	section	NOUN
bracis-33567	235	6	,	,	PUNCT
bracis-33567	235	7	we	we	PRON
bracis-33567	235	8	detail	detail	VERB
bracis-33567	235	9	the	the	DET
bracis-33567	235	10	experiments	experiment	NOUN
bracis-33567	235	11	conducted	conduct	VERB
bracis-33567	235	12	to	to	PART
bracis-33567	235	13	compare	compare	VERB
bracis-33567	235	14	our	our	PRON
bracis-33567	235	15	proposal	proposal	NOUN
bracis-33567	235	16	against	against	ADP
bracis-33567	235	17	the	the	DET
bracis-33567	235	18	encoding	encoding	NOUN
bracis-33567	235	19	presented	present	VERB
bracis-33567	235	20	in	in	ADP
bracis-33567	235	21	[	[	X
bracis-33567	235	22	5	5	NUM
bracis-33567	235	23	]	]	PUNCT
bracis-33567	235	24	.	.	PUNCT
bracis-33567	236	1	our	our	PRON
bracis-33567	236	2	evaluation	evaluation	NOUN
bracis-33567	236	3	consists	consist	VERB
bracis-33567	236	4	of	of	ADP
bracis-33567	236	5	two	two	NUM
bracis-33567	236	6	main	main	ADJ
bracis-33567	236	7	experiments	experiment	NOUN
bracis-33567	236	8	.	.	PUNCT
bracis-33567	237	1	in	in	ADP
bracis-33567	237	2	the	the	DET
bracis-33567	237	3	first	first	ADJ
bracis-33567	237	4	one	one	NUM
bracis-33567	237	5	,	,	PUNCT
bracis-33567	237	6	we	we	PRON
bracis-33567	237	7	compare	compare	VERB
bracis-33567	237	8	the	the	DET
bracis-33567	237	9	two	two	NUM
bracis-33567	237	10	encodings	encoding	NOUN
bracis-33567	237	11	using	use	VERB
bracis-33567	237	12	12	12	NUM
bracis-33567	237	13	datasets	dataset	NOUN
bracis-33567	237	14	.	.	PUNCT
bracis-33567	238	1	in	in	ADP
bracis-33567	238	2	the	the	DET
bracis-33567	238	3	second	second	ADJ
bracis-33567	238	4	one	one	NOUN
bracis-33567	238	5	,	,	PUNCT
bracis-33567	238	6	we	we	PRON
bracis-33567	238	7	conduct	conduct	VERB
bracis-33567	238	8	a	a	DET
bracis-33567	238	9	detailed	detailed	ADJ
bracis-33567	238	10	comparison	comparison	NOUN
bracis-33567	238	11	using	use	VERB
bracis-33567	238	12	a	a	DET
bracis-33567	238	13	single	single	ADJ
bracis-33567	238	14	dataset	dataset	NOUN
bracis-33567	238	15	.	.	PUNCT
bracis-33567	239	1	we	we	PRON
bracis-33567	239	2	vary	vary	VERB
bracis-33567	239	3	the	the	DET
bracis-33567	239	4	architecture	architecture	NOUN
bracis-33567	239	5	of	of	ADP
bracis-33567	239	6	the	the	DET
bracis-33567	239	7	trained	train	VERB
bracis-33567	239	8	anns	anns	NOUN
bracis-33567	239	9	to	to	PART
bracis-33567	239	10	explore	explore	VERB
bracis-33567	239	11	the	the	DET
bracis-33567	239	12	effect	effect	NOUN
bracis-33567	239	13	of	of	ADP
bracis-33567	239	14	the	the	DET
bracis-33567	239	15	number	number	NOUN
bracis-33567	239	16	of	of	ADP
bracis-33567	239	17	layers	layer	NOUN
bracis-33567	239	18	and	and	CCONJ
bracis-33567	239	19	neurons	neuron	NOUN
bracis-33567	239	20	.	.	PUNCT
bracis-33567	240	1	we	we	PRON
bracis-33567	240	2	evaluate	evaluate	VERB
bracis-33567	240	3	the	the	DET
bracis-33567	240	4	performance	performance	NOUN
bracis-33567	240	5	of	of	ADP
bracis-33567	240	6	each	each	DET
bracis-33567	240	7	encoding	encoding	NOUN
bracis-33567	240	8	in	in	ADP
bracis-33567	240	9	terms	term	NOUN
bracis-33567	240	10	of	of	ADP
bracis-33567	240	11	time	time	NOUN
bracis-33567	240	12	for	for	ADP
bracis-33567	240	13	building	build	VERB
bracis-33567	240	14	logical	logical	ADJ
bracis-33567	240	15	constraints	constraint	NOUN
bracis-33567	240	16	and	and	CCONJ
bracis-33567	240	17	time	time	NOUN
bracis-33567	240	18	for	for	ADP
bracis-33567	240	19	computing	compute	VERB
bracis-33567	240	20	explanations	explanation	NOUN
bracis-33567	240	21	.	.	PUNCT
bracis-33567	241	1	we	we	PRON
bracis-33567	241	2	explained	explain	VERB
bracis-33567	241	3	all	all	DET
bracis-33567	241	4	instances	instance	NOUN
bracis-33567	241	5	in	in	ADP
bracis-33567	241	6	a	a	DET
bracis-33567	241	7	given	give	VERB
bracis-33567	241	8	dataset	dataset	NOUN
bracis-33567	241	9	and	and	CCONJ
bracis-33567	241	10	calculated	calculate	VERB
bracis-33567	241	11	the	the	DET
bracis-33567	241	12	average	average	ADJ
bracis-33567	241	13	time	time	NOUN
bracis-33567	241	14	and	and	CCONJ
bracis-33567	241	15	standard	standard	ADJ
bracis-33567	241	16	deviation	deviation	NOUN
bracis-33567	241	17	to	to	PART
bracis-33567	241	18	compare	compare	VERB
bracis-33567	241	19	times	time	NOUN
bracis-33567	241	20	for	for	ADP
bracis-33567	241	21	computing	computing	NOUN
bracis-33567	241	22	explanations	explanation	NOUN
bracis-33567	241	23	.	.	PUNCT
bracis-33567	242	1	in	in	ADP
bracis-33567	242	2	the	the	DET
bracis-33567	242	3	other	other	ADJ
bracis-33567	242	4	case	case	NOUN
bracis-33567	242	5	,	,	PUNCT
bracis-33567	242	6	given	give	VERB
bracis-33567	242	7	a	a	DET
bracis-33567	242	8	trained	train	VERB
bracis-33567	242	9	ann	ann	PROPN
bracis-33567	242	10	on	on	ADP
bracis-33567	242	11	a	a	DET
bracis-33567	242	12	dataset	dataset	NOUN
bracis-33567	242	13	,	,	PUNCT
bracis-33567	242	14	we	we	PRON
bracis-33567	242	15	built	build	VERB
bracis-33567	242	16	the	the	DET
bracis-33567	242	17	logical	logical	ADJ
bracis-33567	242	18	constraints	constraint	NOUN
bracis-33567	242	19	10	10	NUM
bracis-33567	242	20	times	time	NOUN
bracis-33567	242	21	and	and	CCONJ
bracis-33567	242	22	calculated	calculate	VERB
bracis-33567	242	23	the	the	DET
bracis-33567	242	24	average	average	ADJ
bracis-33567	242	25	time	time	NOUN
bracis-33567	242	26	and	and	CCONJ
bracis-33567	242	27	standard	standard	ADJ
bracis-33567	242	28	deviation	deviation	NOUN
bracis-33567	242	29	.	.	PUNCT
bracis-33567	243	1	next	next	ADV
bracis-33567	243	2	,	,	PUNCT
bracis-33567	243	3	we	we	PRON
bracis-33567	243	4	present	present	VERB
bracis-33567	243	5	the	the	DET
bracis-33567	243	6	experimental	experimental	ADJ
bracis-33567	243	7	setup	setup	NOUN
bracis-33567	243	8	,	,	PUNCT
bracis-33567	243	9	describing	describe	VERB
bracis-33567	243	10	technologies	technology	NOUN
bracis-33567	243	11	,	,	PUNCT
bracis-33567	243	12	datasets	dataset	NOUN
bracis-33567	243	13	,	,	PUNCT
bracis-33567	243	14	the	the	DET
bracis-33567	243	15	trained	train	VERB
bracis-33567	243	16	anns	ann	NOUN
bracis-33567	243	17	and	and	CCONJ
bracis-33567	243	18	hyperparameters	hyperparameter	NOUN
bracis-33567	243	19	.	.	PUNCT
bracis-33567	244	1	after	after	ADP
bracis-33567	244	2	that	that	PRON
bracis-33567	244	3	,	,	PUNCT
bracis-33567	244	4	we	we	PRON
bracis-33567	244	5	discuss	discuss	VERB
bracis-33567	244	6	the	the	DET
bracis-33567	244	7	results	result	NOUN
bracis-33567	244	8	providing	provide	VERB
bracis-33567	244	9	a	a	DET
bracis-33567	244	10	comparative	comparative	ADJ
bracis-33567	244	11	analysis	analysis	NOUN
bracis-33567	244	12	of	of	ADP
bracis-33567	244	13	the	the	DET
bracis-33567	244	14	running	running	NOUN
bracis-33567	244	15	times	time	NOUN
bracis-33567	244	16	for	for	ADP
bracis-33567	244	17	building	build	VERB
bracis-33567	244	18	logical	logical	ADJ
bracis-33567	244	19	constraints	constraint	NOUN
bracis-33567	244	20	and	and	CCONJ
bracis-33567	244	21	computing	computing	NOUN
bracis-33567	244	22	explanations	explanation	NOUN
bracis-33567	244	23	.	.	PUNCT
bracis-33567	245	1	finally	finally	ADV
bracis-33567	245	2	,	,	PUNCT
bracis-33567	245	3	we	we	PRON
bracis-33567	245	4	highlight	highlight	VERB
bracis-33567	245	5	specific	specific	ADJ
bracis-33567	245	6	improvements	improvement	NOUN
bracis-33567	245	7	observed	observe	VERB
bracis-33567	245	8	in	in	ADP
bracis-33567	245	9	our	our	PRON
bracis-33567	245	10	proposal	proposal	NOUN
bracis-33567	245	11	.	.	PUNCT
bracis-33567	246	1	5.1	5.1	NUM
bracis-33567	246	2	experimental	experimental	ADJ
bracis-33567	246	3	setup	setup	NOUN
bracis-33567	246	4	we	we	PRON
bracis-33567	246	5	used	use	VERB
bracis-33567	246	6	python	python	NOUN
bracis-33567	246	7	to	to	PART
bracis-33567	246	8	implement	implement	VERB
bracis-33567	246	9	the	the	DET
bracis-33567	246	10	approaches	approach	NOUN
bracis-33567	246	11	and	and	CCONJ
bracis-33567	246	12	to	to	PART
bracis-33567	246	13	run	run	VERB
bracis-33567	246	14	the	the	DET
bracis-33567	246	15	experiments	experiment	NOUN
bracis-33567	246	16	.	.	PUNCT
bracis-33567	247	1	tensorflow	tensorflow	NOUN
bracis-33567	247	2	was	be	AUX
bracis-33567	247	3	used	use	VERB
bracis-33567	247	4	to	to	PART
bracis-33567	247	5	manipulate	manipulate	VERB
bracis-33567	247	6	anns	ann	NOUN
bracis-33567	247	7	,	,	PUNCT
bracis-33567	247	8	including	include	VERB
bracis-33567	247	9	the	the	DET
bracis-33567	247	10	training	training	NOUN
bracis-33567	247	11	and	and	CCONJ
bracis-33567	247	12	testing	testing	NOUN
bracis-33567	247	13	steps	step	NOUN
bracis-33567	247	14	.	.	PUNCT
bracis-33567	248	1	cplex	cplex	PROPN
bracis-33567	248	2	was	be	AUX
bracis-33567	248	3	used	use	VERB
bracis-33567	248	4	as	as	ADP
bracis-33567	248	5	the	the	DET
bracis-33567	248	6	milp	milp	PROPN
bracis-33567	248	7	solver	solver	PROPN
bracis-33567	248	8	and	and	CCONJ
bracis-33567	248	9	accessed	access	VERB
bracis-33567	248	10	by	by	ADP
bracis-33567	248	11	the	the	DET
bracis-33567	248	12	docplex	docplex	ADJ
bracis-33567	248	13	library	library	NOUN
bracis-33567	248	14	.	.	PUNCT
bracis-33567	249	1	we	we	PRON
bracis-33567	249	2	used	use	VERB
bracis-33567	249	3	12	12	NUM
bracis-33567	249	4	datasets	dataset	NOUN
bracis-33567	249	5	from	from	ADP
bracis-33567	249	6	the	the	DET
bracis-33567	249	7	uci	uci	PROPN
bracis-33567	249	8	machine	machine	NOUN
bracis-33567	249	9	learning	learning	NOUN
bracis-33567	249	10	repositoryfootnote	repositoryfootnote	VERB
bracis-33567	249	11	2	2	NUM
bracis-33567	249	12	and	and	CCONJ
bracis-33567	249	13	penn	penn	PROPN
bracis-33567	249	14	machine	machine	NOUN
bracis-33567	249	15	learning	learning	PROPN
bracis-33567	249	16	benchmarksfootnote	benchmarksfootnote	NOUN
bracis-33567	249	17	3	3	NUM
bracis-33567	249	18	,	,	PUNCT
bracis-33567	249	19	each	each	PRON
bracis-33567	249	20	ranging	range	VERB
bracis-33567	249	21	from	from	ADP
bracis-33567	249	22	9	9	NUM
bracis-33567	249	23	to	to	ADP
bracis-33567	249	24	32	32	NUM
bracis-33567	249	25	integer	integer	NOUN
bracis-33567	249	26	,	,	PUNCT
bracis-33567	249	27	continuous	continuous	ADJ
bracis-33567	249	28	,	,	PUNCT
bracis-33567	249	29	categorical	categorical	ADJ
bracis-33567	249	30	or	or	CCONJ
bracis-33567	249	31	binary	binary	ADJ
bracis-33567	249	32	features	feature	NOUN
bracis-33567	249	33	.	.	PUNCT
bracis-33567	250	1	the	the	DET
bracis-33567	250	2	number	number	NOUN
bracis-33567	250	3	of	of	ADP
bracis-33567	250	4	instances	instance	NOUN
bracis-33567	250	5	in	in	ADP
bracis-33567	250	6	the	the	DET
bracis-33567	250	7	selected	select	VERB
bracis-33567	250	8	datasets	dataset	NOUN
bracis-33567	250	9	ranges	range	VERB
bracis-33567	250	10	from	from	ADP
bracis-33567	250	11	156	156	NUM
bracis-33567	250	12	to	to	ADP
bracis-33567	250	13	691	691	NUM
bracis-33567	250	14	.	.	PUNCT
bracis-33567	251	1	the	the	DET
bracis-33567	251	2	types	type	NOUN
bracis-33567	251	3	of	of	ADP
bracis-33567	251	4	classification	classification	NOUN
bracis-33567	251	5	problems	problem	NOUN
bracis-33567	251	6	related	relate	VERB
bracis-33567	251	7	to	to	ADP
bracis-33567	251	8	these	these	DET
bracis-33567	251	9	datasets	dataset	NOUN
bracis-33567	251	10	are	be	AUX
bracis-33567	251	11	binary	binary	ADJ
bracis-33567	251	12	and	and	CCONJ
bracis-33567	251	13	multi	multi	ADJ
bracis-33567	251	14	-	-	ADJ
bracis-33567	251	15	class	class	ADJ
bracis-33567	251	16	classification	classification	NOUN
bracis-33567	251	17	.	.	PUNCT
bracis-33567	252	1	the	the	DET
bracis-33567	252	2	preprocessing	preprocessing	NOUN
bracis-33567	252	3	performed	perform	VERB
bracis-33567	252	4	on	on	ADP
bracis-33567	252	5	the	the	DET
bracis-33567	252	6	datasets	dataset	NOUN
bracis-33567	252	7	included	include	VERB
bracis-33567	252	8	one	one	NUM
bracis-33567	252	9	-	-	PUNCT
bracis-33567	252	10	hot	hot	ADJ
bracis-33567	252	11	encoding	encoding	NOUN
bracis-33567	252	12	of	of	ADP
bracis-33567	252	13	the	the	DET
bracis-33567	252	14	categorical	categorical	ADJ
bracis-33567	252	15	data	datum	NOUN
bracis-33567	252	16	and	and	CCONJ
bracis-33567	252	17	normalization	normalization	NOUN
bracis-33567	252	18	of	of	ADP
bracis-33567	252	19	the	the	DET
bracis-33567	252	20	continuous	continuous	ADJ
bracis-33567	252	21	features	feature	NOUN
bracis-33567	252	22	to	to	ADP
bracis-33567	252	23	the	the	DET
bracis-33567	252	24	range	range	NOUN
bracis-33567	252	25	[	[	X
bracis-33567	252	26	0	0	NUM
bracis-33567	252	27	,	,	PUNCT
bracis-33567	252	28	 	 	SPACE
bracis-33567	252	29	1	1	NUM
bracis-33567	252	30	]	]	PUNCT
bracis-33567	252	31	.	.	PUNCT
bracis-33567	253	1	this	this	DET
bracis-33567	253	2	normalization	normalization	NOUN
bracis-33567	253	3	was	be	AUX
bracis-33567	253	4	not	not	PART
bracis-33567	253	5	applied	apply	VERB
bracis-33567	253	6	to	to	ADP
bracis-33567	253	7	the	the	DET
bracis-33567	253	8	integer	integer	NOUN
bracis-33567	253	9	features	feature	VERB
bracis-33567	253	10	to	to	PART
bracis-33567	253	11	avoid	avoid	VERB
bracis-33567	253	12	transforming	transform	VERB
bracis-33567	253	13	their	their	PRON
bracis-33567	253	14	space	space	NOUN
bracis-33567	253	15	into	into	ADP
bracis-33567	253	16	continuous	continuous	ADJ
bracis-33567	253	17	,	,	PUNCT
bracis-33567	253	18	which	which	PRON
bracis-33567	253	19	could	could	AUX
bracis-33567	253	20	compromise	compromise	VERB
bracis-33567	253	21	formal	formal	ADJ
bracis-33567	253	22	guarantees	guarantee	NOUN
bracis-33567	253	23	on	on	ADP
bracis-33567	253	24	the	the	DET
bracis-33567	253	25	correctness	correctness	NOUN
bracis-33567	253	26	of	of	ADP
bracis-33567	253	27	the	the	DET
bracis-33567	253	28	algorithm	algorithm	NOUN
bracis-33567	253	29	.	.	PUNCT
bracis-33567	254	1	as	as	ADV
bracis-33567	254	2	far	far	ADV
bracis-33567	254	3	as	as	SCONJ
bracis-33567	254	4	we	we	PRON
bracis-33567	254	5	know	know	VERB
bracis-33567	254	6	,	,	PUNCT
bracis-33567	254	7	such	such	DET
bracis-33567	254	8	a	a	DET
bracis-33567	254	9	methodology	methodology	NOUN
bracis-33567	254	10	was	be	AUX
bracis-33567	254	11	not	not	PART
bracis-33567	254	12	considered	consider	VERB
bracis-33567	254	13	in	in	ADP
bracis-33567	254	14	earlier	early	ADJ
bracis-33567	254	15	works	work	NOUN
bracis-33567	254	16	.	.	PUNCT
bracis-33567	255	1	the	the	DET
bracis-33567	255	2	anns	anns	PROPN
bracis-33567	255	3	training	training	NOUN
bracis-33567	255	4	was	be	AUX
bracis-33567	255	5	accomplished	accomplish	VERB
bracis-33567	255	6	using	use	VERB
bracis-33567	255	7	a	a	DET
bracis-33567	255	8	batch	batch	NOUN
bracis-33567	255	9	size	size	NOUN
bracis-33567	255	10	of	of	ADP
bracis-33567	255	11	4	4	NUM
bracis-33567	255	12	and	and	CCONJ
bracis-33567	255	13	a	a	DET
bracis-33567	255	14	maximum	maximum	NOUN
bracis-33567	255	15	of	of	ADP
bracis-33567	255	16	100	100	NUM
bracis-33567	255	17	epochs	epoch	NOUN
bracis-33567	255	18	,	,	PUNCT
bracis-33567	255	19	applying	apply	VERB
bracis-33567	255	20	early	early	ADJ
bracis-33567	255	21	stopping	stop	VERB
bracis-33567	255	22	regularization	regularization	NOUN
bracis-33567	255	23	with	with	ADP
bracis-33567	255	24	10	10	NUM
bracis-33567	255	25	epochs	epoch	NOUN
bracis-33567	255	26	based	base	VERB
bracis-33567	255	27	on	on	ADP
bracis-33567	255	28	validation	validation	NOUN
bracis-33567	255	29	loss	loss	NOUN
bracis-33567	255	30	.	.	PUNCT
bracis-33567	256	1	the	the	DET
bracis-33567	256	2	optimization	optimization	NOUN
bracis-33567	256	3	algorithm	algorithm	NOUN
bracis-33567	256	4	used	use	VERB
bracis-33567	256	5	was	be	AUX
bracis-33567	256	6	adam	adam	PROPN
bracis-33567	256	7	and	and	CCONJ
bracis-33567	256	8	the	the	DET
bracis-33567	256	9	learning	learning	NOUN
bracis-33567	256	10	rate	rate	NOUN
bracis-33567	256	11	was	be	AUX
bracis-33567	256	12	0.001	0.001	NUM
bracis-33567	256	13	.	.	PUNCT
bracis-33567	257	1	the	the	DET
bracis-33567	257	2	datasets	dataset	NOUN
bracis-33567	257	3	split	split	VERB
bracis-33567	257	4	was	be	AUX
bracis-33567	257	5	\(80\%\	\(80\%\	NOUN
bracis-33567	257	6	)	)	PUNCT
bracis-33567	257	7	for	for	ADP
bracis-33567	257	8	training	training	NOUN
bracis-33567	257	9	and	and	CCONJ
bracis-33567	257	10	\(20\%\	\(20\%\	NUM
bracis-33567	257	11	)	)	PUNCT
bracis-33567	257	12	for	for	ADP
bracis-33567	257	13	validation	validation	NOUN
bracis-33567	257	14	.	.	PUNCT
bracis-33567	258	1	the	the	DET
bracis-33567	258	2	ann	ann	PROPN
bracis-33567	258	3	architectures	architecture	NOUN
bracis-33567	258	4	were	be	AUX
bracis-33567	258	5	limited	limit	VERB
bracis-33567	258	6	to	to	ADP
bracis-33567	258	7	2	2	NUM
bracis-33567	258	8	layers	layer	NOUN
bracis-33567	258	9	to	to	PART
bracis-33567	258	10	reduce	reduce	VERB
bracis-33567	258	11	the	the	DET
bracis-33567	258	12	total	total	ADJ
bracis-33567	258	13	running	running	NOUN
bracis-33567	258	14	time	time	NOUN
bracis-33567	258	15	,	,	PUNCT
bracis-33567	258	16	because	because	SCONJ
bracis-33567	258	17	many	many	ADJ
bracis-33567	258	18	solver	solver	NOUN
bracis-33567	258	19	calls	call	NOUN
bracis-33567	258	20	were	be	AUX
bracis-33567	258	21	performed	perform	VERB
bracis-33567	258	22	in	in	ADP
bracis-33567	258	23	the	the	DET
bracis-33567	258	24	experiments	experiment	NOUN
bracis-33567	258	25	due	due	ADP
bracis-33567	258	26	to	to	ADP
bracis-33567	258	27	the	the	DET
bracis-33567	258	28	large	large	ADJ
bracis-33567	258	29	number	number	NOUN
bracis-33567	258	30	of	of	ADP
bracis-33567	258	31	instances	instance	NOUN
bracis-33567	258	32	.	.	PUNCT
bracis-33567	259	1	each	each	DET
bracis-33567	259	2	solver	solver	VERB
bracis-33567	259	3	call	call	NOUN
bracis-33567	259	4	deals	deal	NOUN
bracis-33567	259	5	with	with	ADP
bracis-33567	259	6	an	an	DET
bracis-33567	259	7	np	np	NOUN
bracis-33567	259	8	-	-	PUNCT
bracis-33567	259	9	complete	complete	ADJ
bracis-33567	259	10	problem	problem	NOUN
bracis-33567	259	11	,	,	PUNCT
bracis-33567	259	12	therefore	therefore	ADV
bracis-33567	259	13	,	,	PUNCT
bracis-33567	259	14	impacting	impact	VERB
bracis-33567	259	15	the	the	DET
bracis-33567	259	16	experiments	experiment	NOUN
bracis-33567	259	17	running	run	VERB
bracis-33567	259	18	time	time	NOUN
bracis-33567	259	19	.	.	PUNCT
bracis-33567	260	1	the	the	DET
bracis-33567	260	2	first	first	ADJ
bracis-33567	260	3	experiment	experiment	NOUN
bracis-33567	260	4	compared	compare	VERB
bracis-33567	260	5	the	the	DET
bracis-33567	260	6	two	two	NUM
bracis-33567	260	7	encodings	encoding	NOUN
bracis-33567	260	8	presented	present	VERB
bracis-33567	260	9	on	on	ADP
bracis-33567	260	10	the	the	DET
bracis-33567	260	11	12	12	NUM
bracis-33567	260	12	datasets	dataset	NOUN
bracis-33567	260	13	.	.	PUNCT
bracis-33567	261	1	the	the	DET
bracis-33567	261	2	architecture	architecture	NOUN
bracis-33567	261	3	of	of	ADP
bracis-33567	261	4	the	the	DET
bracis-33567	261	5	trained	train	VERB
bracis-33567	261	6	anns	anns	NOUN
bracis-33567	261	7	is	be	AUX
bracis-33567	261	8	two	two	NUM
bracis-33567	261	9	hidden	hidden	ADJ
bracis-33567	261	10	layers	layer	NOUN
bracis-33567	261	11	with	with	ADP
bracis-33567	261	12	20	20	NUM
bracis-33567	261	13	neurons	neuron	NOUN
bracis-33567	261	14	each	each	PRON
bracis-33567	261	15	.	.	PUNCT
bracis-33567	262	1	for	for	ADP
bracis-33567	262	2	each	each	DET
bracis-33567	262	3	dataset	dataset	NOUN
bracis-33567	262	4	and	and	CCONJ
bracis-33567	262	5	the	the	DET
bracis-33567	262	6	associated	associated	PROPN
bracis-33567	262	7	ann	ann	PROPN
bracis-33567	262	8	,	,	PUNCT
bracis-33567	262	9	the	the	DET
bracis-33567	262	10	explanation	explanation	NOUN
bracis-33567	262	11	of	of	ADP
bracis-33567	262	12	each	each	DET
bracis-33567	262	13	instance	instance	NOUN
bracis-33567	262	14	was	be	AUX
bracis-33567	262	15	obtained	obtain	VERB
bracis-33567	262	16	using	use	VERB
bracis-33567	262	17	the	the	DET
bracis-33567	262	18	algorithm	algorithm	NOUN
bracis-33567	262	19	 	 	SPACE
bracis-33567	262	20	1	1	NUM
bracis-33567	262	21	and	and	CCONJ
bracis-33567	262	22	both	both	DET
bracis-33567	262	23	presented	present	VERB
bracis-33567	262	24	encodings	encoding	NOUN
bracis-33567	262	25	.	.	PUNCT
bracis-33567	263	1	the	the	DET
bracis-33567	263	2	second	second	ADJ
bracis-33567	263	3	experiment	experiment	NOUN
bracis-33567	263	4	performed	perform	VERB
bracis-33567	263	5	the	the	DET
bracis-33567	263	6	comparison	comparison	NOUN
bracis-33567	263	7	of	of	ADP
bracis-33567	263	8	the	the	DET
bracis-33567	263	9	two	two	NUM
bracis-33567	263	10	encodings	encoding	NOUN
bracis-33567	263	11	presented	present	VERB
bracis-33567	263	12	using	use	VERB
bracis-33567	263	13	the	the	DET
bracis-33567	263	14	voting	voting	NOUN
bracis-33567	263	15	dataset	dataset	NOUN
bracis-33567	263	16	of	of	ADP
bracis-33567	263	17	the	the	DET
bracis-33567	263	18	first	first	ADJ
bracis-33567	263	19	experiment	experiment	NOUN
bracis-33567	263	20	.	.	PUNCT
bracis-33567	264	1	this	this	DET
bracis-33567	264	2	experiment	experiment	NOUN
bracis-33567	264	3	was	be	AUX
bracis-33567	264	4	conducted	conduct	VERB
bracis-33567	264	5	in	in	ADP
bracis-33567	264	6	two	two	NUM
bracis-33567	264	7	cases	case	NOUN
bracis-33567	264	8	.	.	PUNCT
bracis-33567	265	1	in	in	ADP
bracis-33567	265	2	the	the	DET
bracis-33567	265	3	first	first	ADJ
bracis-33567	265	4	case	case	NOUN
bracis-33567	265	5	,	,	PUNCT
bracis-33567	265	6	the	the	DET
bracis-33567	265	7	trained	train	VERB
bracis-33567	265	8	anns	anns	NOUN
bracis-33567	265	9	consist	consist	VERB
bracis-33567	265	10	of	of	ADP
bracis-33567	265	11	one	one	NUM
bracis-33567	265	12	hidden	hide	VERB
bracis-33567	265	13	layer	layer	NOUN
bracis-33567	265	14	with	with	ADP
bracis-33567	265	15	the	the	DET
bracis-33567	265	16	number	number	NOUN
bracis-33567	265	17	of	of	ADP
bracis-33567	265	18	neurons	neuron	NOUN
bracis-33567	265	19	ranging	range	VERB
bracis-33567	265	20	from	from	ADP
bracis-33567	265	21	10	10	NUM
bracis-33567	265	22	to	to	PART
bracis-33567	265	23	100	100	NUM
bracis-33567	265	24	.	.	PUNCT
bracis-33567	266	1	in	in	ADP
bracis-33567	266	2	the	the	DET
bracis-33567	266	3	second	second	ADJ
bracis-33567	266	4	case	case	NOUN
bracis-33567	266	5	,	,	PUNCT
bracis-33567	266	6	the	the	DET
bracis-33567	266	7	anns	anns	NOUN
bracis-33567	266	8	consist	consist	VERB
bracis-33567	266	9	of	of	ADP
bracis-33567	266	10	two	two	NUM
bracis-33567	266	11	hidden	hidden	ADJ
bracis-33567	266	12	layers	layer	NOUN
bracis-33567	266	13	such	such	ADJ
bracis-33567	266	14	that	that	SCONJ
bracis-33567	266	15	both	both	DET
bracis-33567	266	16	layers	layer	NOUN
bracis-33567	266	17	contains	contain	VERB
bracis-33567	266	18	the	the	DET
bracis-33567	266	19	same	same	ADJ
bracis-33567	266	20	number	number	NOUN
bracis-33567	266	21	of	of	ADP
bracis-33567	266	22	neurons	neuron	NOUN
bracis-33567	266	23	,	,	PUNCT
bracis-33567	266	24	ranging	range	VERB
bracis-33567	266	25	from	from	ADP
bracis-33567	266	26	10	10	NUM
bracis-33567	266	27	to	to	PART
bracis-33567	266	28	40	40	NUM
bracis-33567	266	29	.	.	PUNCT
bracis-33567	267	1	in	in	ADP
bracis-33567	267	2	both	both	DET
bracis-33567	267	3	cases	case	NOUN
bracis-33567	267	4	,	,	PUNCT
bracis-33567	267	5	the	the	DET
bracis-33567	267	6	number	number	NOUN
bracis-33567	267	7	of	of	ADP
bracis-33567	267	8	neurons	neuron	NOUN
bracis-33567	267	9	in	in	ADP
bracis-33567	267	10	the	the	DET
bracis-33567	267	11	layers	layer	NOUN
bracis-33567	267	12	increases	increase	VERB
bracis-33567	267	13	in	in	ADP
bracis-33567	267	14	increments	increment	NOUN
bracis-33567	267	15	of	of	ADP
bracis-33567	267	16	5	5	NUM
bracis-33567	267	17	.	.	PUNCT
bracis-33567	267	18	again	again	ADV
bracis-33567	267	19	,	,	PUNCT
bracis-33567	267	20	the	the	DET
bracis-33567	267	21	explanations	explanation	NOUN
bracis-33567	267	22	of	of	ADP
bracis-33567	267	23	each	each	DET
bracis-33567	267	24	instance	instance	NOUN
bracis-33567	267	25	was	be	AUX
bracis-33567	267	26	obtained	obtain	VERB
bracis-33567	267	27	using	use	VERB
bracis-33567	267	28	algorithm	algorithm	NOUN
bracis-33567	267	29	 	 	SPACE
bracis-33567	267	30	1	1	NUM
bracis-33567	267	31	and	and	CCONJ
bracis-33567	267	32	both	both	DET
bracis-33567	267	33	presented	present	VERB
bracis-33567	267	34	encodings	encoding	NOUN
bracis-33567	267	35	.	.	PUNCT
bracis-33567	268	1	the	the	DET
bracis-33567	268	2	objective	objective	NOUN
bracis-33567	268	3	of	of	ADP
bracis-33567	268	4	this	this	DET
bracis-33567	268	5	experiment	experiment	NOUN
bracis-33567	268	6	is	be	AUX
bracis-33567	268	7	to	to	PART
bracis-33567	268	8	verify	verify	VERB
bracis-33567	268	9	the	the	DET
bracis-33567	268	10	influence	influence	NOUN
bracis-33567	268	11	of	of	ADP
bracis-33567	268	12	the	the	DET
bracis-33567	268	13	number	number	NOUN
bracis-33567	268	14	of	of	ADP
bracis-33567	268	15	layers	layer	NOUN
bracis-33567	268	16	and	and	CCONJ
bracis-33567	268	17	the	the	DET
bracis-33567	268	18	number	number	NOUN
bracis-33567	268	19	of	of	ADP
bracis-33567	268	20	neurons	neuron	NOUN
bracis-33567	268	21	in	in	ADP
bracis-33567	268	22	both	both	DET
bracis-33567	268	23	encodings	encoding	NOUN
bracis-33567	268	24	.	.	PUNCT
bracis-33567	269	1	5.2	5.2	NUM
bracis-33567	269	2	results	result	NOUN
bracis-33567	269	3	table	table	NOUN
bracis-33567	269	4	1	1	NUM
bracis-33567	269	5	.	.	PUNCT
bracis-33567	269	6	comparison	comparison	NOUN
bracis-33567	269	7	of	of	ADP
bracis-33567	269	8	both	both	PRON
bracis-33567	269	9	encodings.full	encodings.full	PROPN
bracis-33567	269	10	size	size	NOUN
bracis-33567	269	11	table	table	NOUN
bracis-33567	269	12	the	the	DET
bracis-33567	269	13	results	result	NOUN
bracis-33567	269	14	of	of	ADP
bracis-33567	269	15	the	the	DET
bracis-33567	269	16	first	first	ADJ
bracis-33567	269	17	experiment	experiment	NOUN
bracis-33567	269	18	are	be	AUX
bracis-33567	269	19	shown	show	VERB
bracis-33567	269	20	in	in	ADP
bracis-33567	269	21	table	table	NOUN
bracis-33567	269	22	 	 	SPACE
bracis-33567	269	23	1	1	NUM
bracis-33567	269	24	.	.	PUNCT
bracis-33567	270	1	for	for	ADP
bracis-33567	270	2	each	each	DET
bracis-33567	270	3	dataset	dataset	NOUN
bracis-33567	270	4	,	,	PUNCT
bracis-33567	270	5	its	its	PRON
bracis-33567	270	6	number	number	NOUN
bracis-33567	270	7	of	of	ADP
bracis-33567	270	8	features	feature	NOUN
bracis-33567	270	9	is	be	AUX
bracis-33567	270	10	indicated	indicate	VERB
bracis-33567	270	11	in	in	ADP
bracis-33567	270	12	parentheses	parenthesis	NOUN
bracis-33567	270	13	.	.	PUNCT
bracis-33567	271	1	the	the	DET
bracis-33567	271	2	column	column	NOUN
bracis-33567	271	3	exp	exp	X
bracis-33567	271	4	(	(	PUNCT
bracis-33567	271	5	s	s	NOUN
bracis-33567	271	6	)	)	PUNCT
bracis-33567	271	7	refers	refer	VERB
bracis-33567	271	8	to	to	ADP
bracis-33567	271	9	the	the	DET
bracis-33567	271	10	average	average	ADJ
bracis-33567	271	11	running	running	NOUN
bracis-33567	271	12	time	time	NOUN
bracis-33567	271	13	for	for	ADP
bracis-33567	271	14	computing	compute	VERB
bracis-33567	271	15	explanations	explanation	NOUN
bracis-33567	271	16	in	in	ADP
bracis-33567	271	17	seconds	second	NOUN
bracis-33567	271	18	,	,	PUNCT
bracis-33567	271	19	and	and	CCONJ
bracis-33567	271	20	the	the	DET
bracis-33567	271	21	standard	standard	ADJ
bracis-33567	271	22	deviation	deviation	NOUN
bracis-33567	271	23	is	be	AUX
bracis-33567	271	24	also	also	ADV
bracis-33567	271	25	presented	present	VERB
bracis-33567	271	26	.	.	PUNCT
bracis-33567	272	1	the	the	DET
bracis-33567	272	2	column	column	NOUN
bracis-33567	272	3	build	build	NOUN
bracis-33567	272	4	(	(	PUNCT
bracis-33567	272	5	s	s	X
bracis-33567	272	6	)	)	PUNCT
bracis-33567	272	7	refers	refer	VERB
bracis-33567	272	8	to	to	ADP
bracis-33567	272	9	the	the	DET
bracis-33567	272	10	average	average	ADJ
bracis-33567	272	11	running	running	NOUN
bracis-33567	272	12	time	time	NOUN
bracis-33567	272	13	,	,	PUNCT
bracis-33567	272	14	in	in	ADP
bracis-33567	272	15	seconds	second	NOUN
bracis-33567	272	16	,	,	PUNCT
bracis-33567	272	17	for	for	ADP
bracis-33567	272	18	building	build	VERB
bracis-33567	272	19	the	the	DET
bracis-33567	272	20	logical	logical	ADJ
bracis-33567	272	21	constraints	constraint	NOUN
bracis-33567	272	22	of	of	ADP
bracis-33567	272	23	the	the	DET
bracis-33567	272	24	trained	train	VERB
bracis-33567	272	25	ann	ann	PROPN
bracis-33567	272	26	.	.	PUNCT
bracis-33567	273	1	the	the	DET
bracis-33567	273	2	running	running	ADJ
bracis-33567	273	3	time	time	NOUN
bracis-33567	273	4	for	for	ADP
bracis-33567	273	5	finding	find	VERB
bracis-33567	273	6	the	the	DET
bracis-33567	273	7	bounds	bound	NOUN
bracis-33567	273	8	of	of	ADP
bracis-33567	273	9	variables	variable	NOUN
bracis-33567	273	10	is	be	AUX
bracis-33567	273	11	included	include	VERB
bracis-33567	273	12	in	in	ADP
bracis-33567	273	13	the	the	DET
bracis-33567	273	14	time	time	NOUN
bracis-33567	273	15	for	for	ADP
bracis-33567	273	16	building	build	VERB
bracis-33567	273	17	the	the	DET
bracis-33567	273	18	encodings	encoding	NOUN
bracis-33567	273	19	.	.	PUNCT
bracis-33567	274	1	despite	despite	SCONJ
bracis-33567	274	2	the	the	DET
bracis-33567	274	3	encoding	encoding	NOUN
bracis-33567	274	4	by	by	ADP
bracis-33567	274	5	fischetti	fischetti	PROPN
bracis-33567	274	6	and	and	CCONJ
bracis-33567	274	7	jo	jo	NOUN
bracis-33567	275	1	[	[	X
bracis-33567	275	2	5	5	NUM
bracis-33567	275	3	]	]	PUNCT
bracis-33567	275	4	achieved	achieve	VERB
bracis-33567	275	5	a	a	DET
bracis-33567	275	6	better	well	ADJ
bracis-33567	275	7	average	average	ADJ
bracis-33567	275	8	running	running	NOUN
bracis-33567	275	9	time	time	NOUN
bracis-33567	275	10	for	for	ADP
bracis-33567	275	11	computing	compute	VERB
bracis-33567	275	12	explanations	explanation	NOUN
bracis-33567	275	13	in	in	ADP
bracis-33567	275	14	7	7	NUM
bracis-33567	275	15	out	out	ADP
bracis-33567	275	16	of	of	ADP
bracis-33567	275	17	12	12	NUM
bracis-33567	275	18	cases	case	NOUN
bracis-33567	275	19	,	,	PUNCT
bracis-33567	275	20	both	both	DET
bracis-33567	275	21	encodings	encoding	NOUN
bracis-33567	275	22	generally	generally	ADV
bracis-33567	275	23	perform	perform	VERB
bracis-33567	275	24	similarly	similarly	ADV
bracis-33567	275	25	when	when	SCONJ
bracis-33567	275	26	considering	consider	VERB
bracis-33567	275	27	the	the	DET
bracis-33567	275	28	variability	variability	NOUN
bracis-33567	275	29	of	of	ADP
bracis-33567	275	30	the	the	DET
bracis-33567	275	31	time	time	NOUN
bracis-33567	275	32	.	.	PUNCT
bracis-33567	276	1	for	for	ADP
bracis-33567	276	2	instance	instance	NOUN
bracis-33567	276	3	,	,	PUNCT
bracis-33567	276	4	in	in	ADP
bracis-33567	276	5	the	the	DET
bracis-33567	276	6	spect	spect	ADJ
bracis-33567	276	7	dataset	dataset	NOUN
bracis-33567	276	8	,	,	PUNCT
bracis-33567	276	9	the	the	DET
bracis-33567	276	10	average	average	ADJ
bracis-33567	276	11	execution	execution	NOUN
bracis-33567	276	12	time	time	NOUN
bracis-33567	276	13	of	of	ADP
bracis-33567	276	14	the	the	DET
bracis-33567	276	15	encoding	encoding	NOUN
bracis-33567	276	16	by	by	ADP
bracis-33567	276	17	fischetti	fischetti	PROPN
bracis-33567	276	18	 	 	SPACE
bracis-33567	276	19	and	and	CCONJ
bracis-33567	276	20	jo	jo	NOUN
bracis-33567	277	1	[	[	X
bracis-33567	277	2	5	5	NUM
bracis-33567	277	3	]	]	PUNCT
bracis-33567	277	4	(	(	PUNCT
bracis-33567	277	5	2.64	2.64	NUM
bracis-33567	277	6	seconds	second	NOUN
bracis-33567	277	7	)	)	PUNCT
bracis-33567	277	8	falls	fall	VERB
bracis-33567	277	9	within	within	ADP
bracis-33567	277	10	the	the	DET
bracis-33567	277	11	range	range	NOUN
bracis-33567	277	12	of	of	ADP
bracis-33567	277	13	the	the	DET
bracis-33567	277	14	average	average	NOUN
bracis-33567	277	15	minus	minus	CCONJ
bracis-33567	277	16	the	the	DET
bracis-33567	277	17	standard	standard	ADJ
bracis-33567	277	18	deviation	deviation	NOUN
bracis-33567	277	19	of	of	ADP
bracis-33567	277	20	our	our	PRON
bracis-33567	277	21	approach	approach	NOUN
bracis-33567	277	22	(	(	PUNCT
bracis-33567	277	23	\(3.21	\(3.21	PROPN
bracis-33567	277	24	1.81\	1.81\	NUM
bracis-33567	277	25	)	)	PUNCT
bracis-33567	277	26	)	)	PUNCT
bracis-33567	277	27	.	.	PUNCT
bracis-33567	278	1	this	this	DET
bracis-33567	278	2	pattern	pattern	NOUN
bracis-33567	278	3	is	be	AUX
bracis-33567	278	4	observed	observe	VERB
bracis-33567	278	5	across	across	ADP
bracis-33567	278	6	several	several	ADJ
bracis-33567	278	7	datasets	dataset	NOUN
bracis-33567	278	8	.	.	PUNCT
bracis-33567	279	1	in	in	ADP
bracis-33567	279	2	summary	summary	NOUN
bracis-33567	279	3	,	,	PUNCT
bracis-33567	279	4	the	the	DET
bracis-33567	279	5	results	result	NOUN
bracis-33567	279	6	indicate	indicate	VERB
bracis-33567	279	7	that	that	SCONJ
bracis-33567	279	8	both	both	DET
bracis-33567	279	9	encodings	encoding	NOUN
bracis-33567	279	10	generally	generally	ADV
bracis-33567	279	11	perform	perform	VERB
bracis-33567	279	12	similarly	similarly	ADV
bracis-33567	279	13	in	in	ADP
bracis-33567	279	14	terms	term	NOUN
bracis-33567	279	15	of	of	ADP
bracis-33567	279	16	running	run	VERB
bracis-33567	279	17	time	time	NOUN
bracis-33567	279	18	for	for	ADP
bracis-33567	279	19	computing	computing	NOUN
bracis-33567	279	20	explanations	explanation	NOUN
bracis-33567	279	21	,	,	PUNCT
bracis-33567	279	22	with	with	ADP
bracis-33567	279	23	minor	minor	ADJ
bracis-33567	279	24	variations	variation	NOUN
bracis-33567	279	25	across	across	ADP
bracis-33567	279	26	different	different	ADJ
bracis-33567	279	27	datasets	dataset	NOUN
bracis-33567	279	28	.	.	PUNCT
bracis-33567	280	1	with	with	ADP
bracis-33567	280	2	respect	respect	NOUN
bracis-33567	280	3	to	to	ADP
bracis-33567	280	4	the	the	DET
bracis-33567	280	5	average	average	ADJ
bracis-33567	280	6	running	running	NOUN
bracis-33567	280	7	time	time	NOUN
bracis-33567	280	8	for	for	ADP
bracis-33567	280	9	building	build	VERB
bracis-33567	280	10	the	the	DET
bracis-33567	280	11	logical	logical	ADJ
bracis-33567	280	12	constraints	constraint	NOUN
bracis-33567	280	13	,	,	PUNCT
bracis-33567	280	14	our	our	PRON
bracis-33567	280	15	adaptation	adaptation	NOUN
bracis-33567	280	16	generally	generally	ADV
bracis-33567	280	17	outperformed	outperform	VERB
bracis-33567	280	18	the	the	DET
bracis-33567	280	19	encoding	encoding	NOUN
bracis-33567	280	20	by	by	ADP
bracis-33567	280	21	fischetti	fischetti	PROPN
bracis-33567	280	22	and	and	CCONJ
bracis-33567	280	23	jo	jo	NOUN
bracis-33567	281	1	[	[	X
bracis-33567	281	2	5	5	NUM
bracis-33567	281	3	]	]	PUNCT
bracis-33567	281	4	.	.	PUNCT
bracis-33567	282	1	however	however	ADV
bracis-33567	282	2	,	,	PUNCT
bracis-33567	282	3	there	there	PRON
bracis-33567	282	4	were	be	VERB
bracis-33567	282	5	exceptions	exception	NOUN
bracis-33567	282	6	noted	note	VERB
bracis-33567	282	7	,	,	PUNCT
bracis-33567	282	8	such	such	ADJ
bracis-33567	282	9	as	as	ADP
bracis-33567	282	10	in	in	ADP
bracis-33567	282	11	the	the	DET
bracis-33567	282	12	spect	spect	ADJ
bracis-33567	282	13	dataset	dataset	NOUN
bracis-33567	282	14	.	.	PUNCT
bracis-33567	283	1	overall	overall	ADV
bracis-33567	283	2	,	,	PUNCT
bracis-33567	283	3	our	our	PRON
bracis-33567	283	4	adaptation	adaptation	NOUN
bracis-33567	283	5	achieved	achieve	VERB
bracis-33567	283	6	an	an	DET
bracis-33567	283	7	improvement	improvement	NOUN
bracis-33567	283	8	of	of	ADP
bracis-33567	283	9	up	up	ADP
bracis-33567	283	10	to	to	ADP
bracis-33567	283	11	\(18\%\	\(18\%\	PRON
bracis-33567	283	12	)	)	PUNCT
bracis-33567	283	13	compared	compare	VERB
bracis-33567	283	14	to	to	ADP
bracis-33567	283	15	the	the	DET
bracis-33567	283	16	other	other	ADJ
bracis-33567	283	17	one	one	NOUN
bracis-33567	283	18	,	,	PUNCT
bracis-33567	283	19	as	as	SCONJ
bracis-33567	283	20	seen	see	VERB
bracis-33567	283	21	in	in	ADP
bracis-33567	283	22	the	the	DET
bracis-33567	283	23	heart	heart	NOUN
bracis-33567	283	24	-	-	PUNCT
bracis-33567	283	25	statlog	statlog	NOUN
bracis-33567	283	26	dataset	dataset	NOUN
bracis-33567	283	27	.	.	PUNCT
bracis-33567	284	1	in	in	ADP
bracis-33567	284	2	summary	summary	NOUN
bracis-33567	284	3	,	,	PUNCT
bracis-33567	284	4	the	the	DET
bracis-33567	284	5	results	result	NOUN
bracis-33567	284	6	indicate	indicate	VERB
bracis-33567	284	7	that	that	SCONJ
bracis-33567	284	8	our	our	PRON
bracis-33567	284	9	adaptation	adaptation	NOUN
bracis-33567	284	10	is	be	AUX
bracis-33567	284	11	consistently	consistently	ADV
bracis-33567	284	12	more	more	ADV
bracis-33567	284	13	efficient	efficient	ADJ
bracis-33567	284	14	than	than	ADP
bracis-33567	284	15	the	the	DET
bracis-33567	284	16	other	other	ADJ
bracis-33567	284	17	approach	approach	NOUN
bracis-33567	284	18	for	for	ADP
bracis-33567	284	19	building	build	VERB
bracis-33567	284	20	logical	logical	ADJ
bracis-33567	284	21	constraints	constraint	NOUN
bracis-33567	284	22	.	.	PUNCT
bracis-33567	285	1	the	the	DET
bracis-33567	285	2	variability	variability	NOUN
bracis-33567	285	3	in	in	ADP
bracis-33567	285	4	the	the	DET
bracis-33567	285	5	results	result	NOUN
bracis-33567	285	6	,	,	PUNCT
bracis-33567	285	7	as	as	SCONJ
bracis-33567	285	8	shown	show	VERB
bracis-33567	285	9	by	by	ADP
bracis-33567	285	10	the	the	DET
bracis-33567	285	11	standard	standard	ADJ
bracis-33567	285	12	deviations	deviation	NOUN
bracis-33567	285	13	,	,	PUNCT
bracis-33567	285	14	further	far	ADV
bracis-33567	285	15	supports	support	VERB
bracis-33567	285	16	this	this	DET
bracis-33567	285	17	conclusion	conclusion	NOUN
bracis-33567	285	18	.	.	PUNCT
bracis-33567	286	1	for	for	ADP
bracis-33567	286	2	instance	instance	NOUN
bracis-33567	286	3	,	,	PUNCT
bracis-33567	286	4	the	the	DET
bracis-33567	286	5	average	average	ADJ
bracis-33567	286	6	running	running	NOUN
bracis-33567	286	7	time	time	NOUN
bracis-33567	286	8	of	of	ADP
bracis-33567	286	9	our	our	PRON
bracis-33567	286	10	proposal	proposal	NOUN
bracis-33567	286	11	is	be	AUX
bracis-33567	286	12	less	less	ADJ
bracis-33567	286	13	than	than	ADP
bracis-33567	286	14	the	the	DET
bracis-33567	286	15	average	average	NOUN
bracis-33567	286	16	minus	minus	CCONJ
bracis-33567	286	17	the	the	DET
bracis-33567	286	18	standard	standard	ADJ
bracis-33567	286	19	deviation	deviation	NOUN
bracis-33567	286	20	of	of	ADP
bracis-33567	286	21	the	the	DET
bracis-33567	286	22	other	other	ADJ
bracis-33567	286	23	approach	approach	NOUN
bracis-33567	286	24	in	in	ADP
bracis-33567	286	25	9	9	NUM
bracis-33567	286	26	out	out	ADP
bracis-33567	286	27	of	of	ADP
bracis-33567	286	28	12	12	NUM
bracis-33567	286	29	datasets	dataset	NOUN
bracis-33567	286	30	.	.	PUNCT
bracis-33567	287	1	these	these	DET
bracis-33567	287	2	cases	case	NOUN
bracis-33567	287	3	are	be	AUX
bracis-33567	287	4	highlighted	highlight	VERB
bracis-33567	287	5	in	in	ADP
bracis-33567	287	6	bold	bold	ADJ
bracis-33567	287	7	in	in	ADP
bracis-33567	287	8	table	table	NOUN
bracis-33567	287	9	 	 	SPACE
bracis-33567	287	10	1	1	NUM
bracis-33567	287	11	.	.	PUNCT
bracis-33567	288	1	it	it	PRON
bracis-33567	288	2	is	be	AUX
bracis-33567	288	3	important	important	ADJ
bracis-33567	288	4	to	to	PART
bracis-33567	288	5	note	note	VERB
bracis-33567	288	6	that	that	SCONJ
bracis-33567	288	7	,	,	PUNCT
bracis-33567	288	8	in	in	ADP
bracis-33567	288	9	the	the	DET
bracis-33567	288	10	spect	spect	ADJ
bracis-33567	288	11	dataset	dataset	NOUN
bracis-33567	288	12	,	,	PUNCT
bracis-33567	288	13	the	the	DET
bracis-33567	288	14	average	average	ADJ
bracis-33567	288	15	running	running	NOUN
bracis-33567	288	16	time	time	NOUN
bracis-33567	288	17	of	of	ADP
bracis-33567	288	18	the	the	DET
bracis-33567	288	19	encoding	encoding	NOUN
bracis-33567	288	20	proposed	propose	VERB
bracis-33567	288	21	by	by	ADP
bracis-33567	288	22	fischetti	fischetti	PROPN
bracis-33567	288	23	and	and	CCONJ
bracis-33567	288	24	jo	jo	NOUN
bracis-33567	289	1	[	[	X
bracis-33567	289	2	5	5	NUM
bracis-33567	289	3	]	]	PUNCT
bracis-33567	289	4	is	be	AUX
bracis-33567	289	5	less	less	ADJ
bracis-33567	289	6	than	than	ADP
bracis-33567	289	7	the	the	DET
bracis-33567	289	8	average	average	NOUN
bracis-33567	289	9	minus	minus	CCONJ
bracis-33567	289	10	the	the	DET
bracis-33567	289	11	standard	standard	ADJ
bracis-33567	289	12	deviation	deviation	NOUN
bracis-33567	289	13	of	of	ADP
bracis-33567	289	14	our	our	PRON
bracis-33567	289	15	adaptation	adaptation	NOUN
bracis-33567	289	16	.	.	PUNCT
bracis-33567	290	1	this	this	PRON
bracis-33567	290	2	indicates	indicate	VERB
bracis-33567	290	3	that	that	SCONJ
bracis-33567	290	4	,	,	PUNCT
bracis-33567	290	5	while	while	SCONJ
bracis-33567	290	6	our	our	PRON
bracis-33567	290	7	proposal	proposal	NOUN
bracis-33567	290	8	appears	appear	VERB
bracis-33567	290	9	generally	generally	ADV
bracis-33567	290	10	more	more	ADV
bracis-33567	290	11	efficient	efficient	ADJ
bracis-33567	290	12	,	,	PUNCT
bracis-33567	290	13	specific	specific	ADJ
bracis-33567	290	14	dataset	dataset	NOUN
bracis-33567	290	15	characteristics	characteristic	NOUN
bracis-33567	290	16	can	can	AUX
bracis-33567	290	17	influence	influence	VERB
bracis-33567	290	18	which	which	PRON
bracis-33567	290	19	encoding	encode	VERB
bracis-33567	290	20	is	be	AUX
bracis-33567	290	21	more	more	ADV
bracis-33567	290	22	advantageous	advantageous	ADJ
bracis-33567	290	23	.	.	PUNCT
bracis-33567	291	1	our	our	PRON
bracis-33567	291	2	adaptation	adaptation	NOUN
bracis-33567	291	3	yielded	yield	VERB
bracis-33567	291	4	notably	notably	ADV
bracis-33567	291	5	superior	superior	ADJ
bracis-33567	291	6	results	result	NOUN
bracis-33567	291	7	not	not	PART
bracis-33567	291	8	only	only	ADV
bracis-33567	291	9	in	in	ADP
bracis-33567	291	10	the	the	DET
bracis-33567	291	11	average	average	ADJ
bracis-33567	291	12	time	time	NOUN
bracis-33567	291	13	for	for	ADP
bracis-33567	291	14	building	build	VERB
bracis-33567	291	15	logical	logical	ADJ
bracis-33567	291	16	constraints	constraint	NOUN
bracis-33567	291	17	but	but	CCONJ
bracis-33567	291	18	also	also	ADV
bracis-33567	291	19	in	in	ADP
bracis-33567	291	20	the	the	DET
bracis-33567	291	21	overall	overall	ADJ
bracis-33567	291	22	time	time	NOUN
bracis-33567	291	23	,	,	PUNCT
bracis-33567	291	24	which	which	PRON
bracis-33567	291	25	includes	include	VERB
bracis-33567	291	26	both	both	DET
bracis-33567	291	27	computing	compute	VERB
bracis-33567	291	28	explanations	explanation	NOUN
bracis-33567	291	29	and	and	CCONJ
bracis-33567	291	30	constructing	construct	VERB
bracis-33567	291	31	logical	logical	ADJ
bracis-33567	291	32	constraints	constraint	NOUN
bracis-33567	291	33	.	.	PUNCT
bracis-33567	292	1	for	for	ADP
bracis-33567	292	2	instance	instance	NOUN
bracis-33567	292	3	,	,	PUNCT
bracis-33567	292	4	it	it	PRON
bracis-33567	292	5	achieved	achieve	VERB
bracis-33567	292	6	an	an	DET
bracis-33567	292	7	improvement	improvement	NOUN
bracis-33567	292	8	of	of	ADP
bracis-33567	292	9	up	up	ADP
bracis-33567	292	10	to	to	ADP
bracis-33567	292	11	\(16\%\	\(16\%\	X
bracis-33567	292	12	)	)	PUNCT
bracis-33567	292	13	compared	compare	VERB
bracis-33567	292	14	to	to	ADP
bracis-33567	292	15	the	the	DET
bracis-33567	292	16	other	other	ADJ
bracis-33567	292	17	approach	approach	NOUN
bracis-33567	292	18	,	,	PUNCT
bracis-33567	292	19	as	as	SCONJ
bracis-33567	292	20	seen	see	VERB
bracis-33567	292	21	in	in	ADP
bracis-33567	292	22	the	the	DET
bracis-33567	292	23	heart	heart	NOUN
bracis-33567	292	24	-	-	PUNCT
bracis-33567	292	25	statlog	statlog	NOUN
bracis-33567	292	26	dataset	dataset	NOUN
bracis-33567	292	27	.	.	PUNCT
bracis-33567	293	1	fig	fig	NOUN
bracis-33567	293	2	.	.	PUNCT
bracis-33567	294	1	2	2	X
bracis-33567	294	2	.	.	X
bracis-33567	294	3	comparison	comparison	NOUN
bracis-33567	294	4	of	of	ADP
bracis-33567	294	5	average	average	ADJ
bracis-33567	294	6	running	running	NOUN
bracis-33567	294	7	time	time	NOUN
bracis-33567	294	8	for	for	ADP
bracis-33567	294	9	computing	computing	NOUN
bracis-33567	294	10	explanations	explanation	NOUN
bracis-33567	294	11	,	,	PUNCT
bracis-33567	294	12	using	use	VERB
bracis-33567	294	13	anns	anns	NOUN
bracis-33567	294	14	with	with	ADP
bracis-33567	294	15	one	one	NUM
bracis-33567	294	16	hidden	hide	VERB
bracis-33567	294	17	layer	layer	NOUN
bracis-33567	294	18	and	and	CCONJ
bracis-33567	294	19	the	the	DET
bracis-33567	294	20	voting	voting	NOUN
bracis-33567	294	21	dataset	dataset	NOUN
bracis-33567	294	22	.	.	PUNCT
bracis-33567	295	1	full	full	ADJ
bracis-33567	295	2	size	size	NOUN
bracis-33567	295	3	image	image	NOUN
bracis-33567	295	4	fig	fig	NOUN
bracis-33567	295	5	.	.	PUNCT
bracis-33567	296	1	3	3	X
bracis-33567	296	2	.	.	X
bracis-33567	296	3	comparison	comparison	NOUN
bracis-33567	296	4	of	of	ADP
bracis-33567	296	5	average	average	ADJ
bracis-33567	296	6	running	running	NOUN
bracis-33567	296	7	time	time	NOUN
bracis-33567	296	8	for	for	ADP
bracis-33567	296	9	computing	computing	NOUN
bracis-33567	296	10	explanations	explanation	NOUN
bracis-33567	296	11	,	,	PUNCT
bracis-33567	296	12	using	use	VERB
bracis-33567	296	13	anns	anns	NOUN
bracis-33567	296	14	with	with	ADP
bracis-33567	296	15	two	two	NUM
bracis-33567	296	16	hidden	hidden	ADJ
bracis-33567	296	17	layers	layer	NOUN
bracis-33567	296	18	and	and	CCONJ
bracis-33567	296	19	the	the	DET
bracis-33567	296	20	voting	voting	NOUN
bracis-33567	296	21	dataset	dataset	NOUN
bracis-33567	296	22	.	.	PUNCT
bracis-33567	297	1	full	full	ADJ
bracis-33567	297	2	size	size	NOUN
bracis-33567	297	3	image	image	NOUN
bracis-33567	297	4	the	the	DET
bracis-33567	297	5	results	result	NOUN
bracis-33567	297	6	of	of	ADP
bracis-33567	297	7	the	the	DET
bracis-33567	297	8	second	second	ADJ
bracis-33567	297	9	experiment	experiment	NOUN
bracis-33567	297	10	are	be	AUX
bracis-33567	297	11	shown	show	VERB
bracis-33567	297	12	in	in	ADP
bracis-33567	297	13	figs	fig	NOUN
bracis-33567	297	14	.	.	PUNCT
bracis-33567	297	15	 	 	SPACE
bracis-33567	297	16	2	2	NUM
bracis-33567	297	17	and	and	CCONJ
bracis-33567	297	18	3	3	NUM
bracis-33567	297	19	.	.	PUNCT
bracis-33567	298	1	the	the	DET
bracis-33567	298	2	x	x	ADJ
bracis-33567	298	3	-	-	ADJ
bracis-33567	298	4	axis	axis	NOUN
bracis-33567	298	5	shows	show	VERB
bracis-33567	298	6	the	the	DET
bracis-33567	298	7	number	number	NOUN
bracis-33567	298	8	of	of	ADP
bracis-33567	298	9	neurons	neuron	NOUN
bracis-33567	298	10	in	in	ADP
bracis-33567	298	11	each	each	DET
bracis-33567	298	12	hidden	hide	VERB
bracis-33567	298	13	layer	layer	NOUN
bracis-33567	298	14	in	in	ADP
bracis-33567	298	15	both	both	DET
bracis-33567	298	16	figures	figure	NOUN
bracis-33567	298	17	.	.	PUNCT
bracis-33567	299	1	while	while	SCONJ
bracis-33567	299	2	the	the	DET
bracis-33567	299	3	y	y	NOUN
bracis-33567	299	4	-	-	PUNCT
bracis-33567	299	5	axis	axis	NOUN
bracis-33567	299	6	shows	show	VERB
bracis-33567	299	7	the	the	DET
bracis-33567	299	8	average	average	ADJ
bracis-33567	299	9	running	running	NOUN
bracis-33567	299	10	time	time	NOUN
bracis-33567	299	11	for	for	ADP
bracis-33567	299	12	computing	computing	NOUN
bracis-33567	299	13	explanations	explanation	NOUN
bracis-33567	299	14	.	.	PUNCT
bracis-33567	300	1	furthermore	furthermore	ADV
bracis-33567	300	2	,	,	PUNCT
bracis-33567	300	3	the	the	DET
bracis-33567	300	4	standard	standard	ADJ
bracis-33567	300	5	deviation	deviation	NOUN
bracis-33567	300	6	is	be	AUX
bracis-33567	300	7	indicated	indicate	VERB
bracis-33567	300	8	by	by	ADP
bracis-33567	300	9	the	the	DET
bracis-33567	300	10	shaded	shaded	ADJ
bracis-33567	300	11	region	region	NOUN
bracis-33567	300	12	in	in	ADP
bracis-33567	300	13	both	both	DET
bracis-33567	300	14	figures	figure	NOUN
bracis-33567	300	15	.	.	PUNCT
bracis-33567	301	1	figure	figure	VERB
bracis-33567	301	2	 	 	SPACE
bracis-33567	301	3	2	2	NUM
bracis-33567	301	4	refers	refer	VERB
bracis-33567	301	5	to	to	ADP
bracis-33567	301	6	anns	anns	NOUN
bracis-33567	301	7	with	with	ADP
bracis-33567	301	8	one	one	NUM
bracis-33567	301	9	hidden	hide	VERB
bracis-33567	301	10	layer	layer	NOUN
bracis-33567	301	11	,	,	PUNCT
bracis-33567	301	12	while	while	SCONJ
bracis-33567	301	13	fig	fig	NOUN
bracis-33567	301	14	.	.	PUNCT
bracis-33567	301	15	 	 	SPACE
bracis-33567	302	1	3	3	NUM
bracis-33567	302	2	refers	refer	VERB
bracis-33567	302	3	to	to	ADP
bracis-33567	302	4	anns	anns	NOUN
bracis-33567	302	5	with	with	ADP
bracis-33567	302	6	two	two	NUM
bracis-33567	302	7	hidden	hidden	ADJ
bracis-33567	302	8	layers	layer	NOUN
bracis-33567	302	9	.	.	PUNCT
bracis-33567	303	1	figure	figure	NOUN
bracis-33567	303	2	 	 	SPACE
bracis-33567	303	3	2	2	NUM
bracis-33567	303	4	suggests	suggest	VERB
bracis-33567	303	5	that	that	SCONJ
bracis-33567	303	6	our	our	PRON
bracis-33567	303	7	proposal	proposal	NOUN
bracis-33567	303	8	,	,	PUNCT
bracis-33567	303	9	for	for	ADP
bracis-33567	303	10	anns	anns	NOUN
bracis-33567	303	11	with	with	ADP
bracis-33567	303	12	one	one	NUM
bracis-33567	303	13	hidden	hide	VERB
bracis-33567	303	14	layer	layer	NOUN
bracis-33567	303	15	,	,	PUNCT
bracis-33567	303	16	achieved	achieve	VERB
bracis-33567	303	17	a	a	DET
bracis-33567	303	18	superior	superior	ADJ
bracis-33567	303	19	average	average	ADJ
bracis-33567	303	20	running	running	NOUN
bracis-33567	303	21	time	time	NOUN
bracis-33567	303	22	for	for	ADP
bracis-33567	303	23	computing	compute	VERB
bracis-33567	303	24	explanations	explanation	NOUN
bracis-33567	303	25	in	in	ADP
bracis-33567	303	26	the	the	DET
bracis-33567	303	27	voting	voting	NOUN
bracis-33567	303	28	dataset	dataset	NOUN
bracis-33567	303	29	.	.	PUNCT
bracis-33567	304	1	this	this	DET
bracis-33567	304	2	encoding	encoding	NOUN
bracis-33567	304	3	outperforms	outperform	VERB
bracis-33567	304	4	the	the	DET
bracis-33567	304	5	other	other	ADJ
bracis-33567	304	6	approach	approach	NOUN
bracis-33567	304	7	with	with	ADP
bracis-33567	304	8	percentage	percentage	NOUN
bracis-33567	304	9	improvements	improvement	NOUN
bracis-33567	304	10	ranging	range	VERB
bracis-33567	304	11	from	from	ADP
bracis-33567	304	12	approximately	approximately	ADV
bracis-33567	304	13	\(7.69\%\	\(7.69\%\	PROPN
bracis-33567	304	14	)	)	PUNCT
bracis-33567	304	15	to	to	ADP
bracis-33567	304	16	\(40.82\%\	\(40.82\%\	PRON
bracis-33567	304	17	)	)	PUNCT
bracis-33567	304	18	.	.	PUNCT
bracis-33567	305	1	the	the	DET
bracis-33567	305	2	most	most	ADV
bracis-33567	305	3	significant	significant	ADJ
bracis-33567	305	4	improvements	improvement	NOUN
bracis-33567	305	5	are	be	AUX
bracis-33567	305	6	observed	observe	VERB
bracis-33567	305	7	with	with	ADP
bracis-33567	305	8	higher	high	ADJ
bracis-33567	305	9	neuron	neuron	NOUN
bracis-33567	305	10	counts	count	NOUN
bracis-33567	305	11	.	.	PUNCT
bracis-33567	306	1	for	for	ADP
bracis-33567	306	2	instance	instance	NOUN
bracis-33567	306	3	,	,	PUNCT
bracis-33567	306	4	with	with	ADP
bracis-33567	306	5	85	85	NUM
bracis-33567	306	6	neurons	neuron	NOUN
bracis-33567	306	7	per	per	ADP
bracis-33567	306	8	layer	layer	NOUN
bracis-33567	306	9	,	,	PUNCT
bracis-33567	306	10	our	our	PRON
bracis-33567	306	11	proposal	proposal	NOUN
bracis-33567	306	12	shows	show	VERB
bracis-33567	306	13	an	an	DET
bracis-33567	306	14	improvement	improvement	NOUN
bracis-33567	306	15	of	of	ADP
bracis-33567	306	16	around	around	ADP
bracis-33567	306	17	\(40.82\%\	\(40.82\%\	PRON
bracis-33567	306	18	)	)	PUNCT
bracis-33567	306	19	,	,	PUNCT
bracis-33567	306	20	and	and	CCONJ
bracis-33567	306	21	with	with	ADP
bracis-33567	306	22	95	95	NUM
bracis-33567	306	23	neurons	neuron	NOUN
bracis-33567	306	24	,	,	PUNCT
bracis-33567	306	25	the	the	DET
bracis-33567	306	26	improvement	improvement	NOUN
bracis-33567	306	27	is	be	AUX
bracis-33567	306	28	about	about	ADP
bracis-33567	306	29	\(31.65\%\	\(31.65\%\	NOUN
bracis-33567	306	30	)	)	PUNCT
bracis-33567	306	31	.	.	PUNCT
bracis-33567	307	1	moreover	moreover	ADV
bracis-33567	307	2	,	,	PUNCT
bracis-33567	307	3	our	our	PRON
bracis-33567	307	4	proposal	proposal	NOUN
bracis-33567	307	5	generally	generally	ADV
bracis-33567	307	6	exhibits	exhibit	VERB
bracis-33567	307	7	similar	similar	ADJ
bracis-33567	307	8	or	or	CCONJ
bracis-33567	307	9	lower	low	ADJ
bracis-33567	307	10	standard	standard	ADJ
bracis-33567	307	11	deviations	deviation	NOUN
bracis-33567	307	12	,	,	PUNCT
bracis-33567	307	13	indicating	indicate	VERB
bracis-33567	307	14	more	more	ADV
bracis-33567	307	15	consistent	consistent	ADJ
bracis-33567	307	16	performance	performance	NOUN
bracis-33567	307	17	across	across	ADP
bracis-33567	307	18	different	different	ADJ
bracis-33567	307	19	number	number	NOUN
bracis-33567	307	20	of	of	ADP
bracis-33567	307	21	neurons	neuron	NOUN
bracis-33567	307	22	.	.	PUNCT
bracis-33567	308	1	on	on	ADP
bracis-33567	308	2	the	the	DET
bracis-33567	308	3	other	other	ADJ
bracis-33567	308	4	hand	hand	NOUN
bracis-33567	308	5	,	,	PUNCT
bracis-33567	308	6	fig	fig	NOUN
bracis-33567	308	7	.	.	PUNCT
bracis-33567	308	8	 	 	SPACE
bracis-33567	308	9	3	3	NUM
bracis-33567	308	10	depicts	depict	VERB
bracis-33567	308	11	comparable	comparable	ADJ
bracis-33567	308	12	results	result	NOUN
bracis-33567	308	13	between	between	ADP
bracis-33567	308	14	both	both	DET
bracis-33567	308	15	encodings	encoding	NOUN
bracis-33567	308	16	for	for	ADP
bracis-33567	308	17	anns	anns	NOUN
bracis-33567	308	18	with	with	ADP
bracis-33567	308	19	two	two	NUM
bracis-33567	308	20	hidden	hidden	ADJ
bracis-33567	308	21	layers	layer	NOUN
bracis-33567	308	22	.	.	PUNCT
bracis-33567	309	1	moreover	moreover	ADV
bracis-33567	309	2	,	,	PUNCT
bracis-33567	309	3	similar	similar	ADJ
bracis-33567	309	4	standard	standard	ADJ
bracis-33567	309	5	deviations	deviation	NOUN
bracis-33567	309	6	were	be	AUX
bracis-33567	309	7	achieved	achieve	VERB
bracis-33567	309	8	for	for	ADP
bracis-33567	309	9	both	both	DET
bracis-33567	309	10	encodings	encoding	NOUN
bracis-33567	309	11	,	,	PUNCT
bracis-33567	309	12	indicating	indicate	VERB
bracis-33567	309	13	comparable	comparable	ADJ
bracis-33567	309	14	levels	level	NOUN
bracis-33567	309	15	of	of	ADP
bracis-33567	309	16	consistency	consistency	NOUN
bracis-33567	309	17	in	in	ADP
bracis-33567	309	18	performance	performance	NOUN
bracis-33567	309	19	.	.	PUNCT
bracis-33567	310	1	the	the	DET
bracis-33567	310	2	variability	variability	NOUN
bracis-33567	310	3	increases	increase	VERB
bracis-33567	310	4	significantly	significantly	ADV
bracis-33567	310	5	with	with	ADP
bracis-33567	310	6	more	more	ADJ
bracis-33567	310	7	complex	complex	ADJ
bracis-33567	310	8	networks	network	NOUN
bracis-33567	310	9	.	.	PUNCT
bracis-33567	311	1	for	for	ADP
bracis-33567	311	2	example	example	NOUN
bracis-33567	311	3	,	,	PUNCT
bracis-33567	311	4	with	with	ADP
bracis-33567	311	5	35	35	NUM
bracis-33567	311	6	and	and	CCONJ
bracis-33567	311	7	40	40	NUM
bracis-33567	311	8	neurons	neuron	NOUN
bracis-33567	311	9	per	per	ADP
bracis-33567	311	10	layer	layer	NOUN
bracis-33567	311	11	,	,	PUNCT
bracis-33567	311	12	both	both	DET
bracis-33567	311	13	encodings	encoding	NOUN
bracis-33567	311	14	exhibit	exhibit	VERB
bracis-33567	311	15	significant	significant	ADJ
bracis-33567	311	16	variability	variability	NOUN
bracis-33567	311	17	.	.	PUNCT
bracis-33567	312	1	furthermore	furthermore	ADV
bracis-33567	312	2	,	,	PUNCT
bracis-33567	312	3	with	with	ADP
bracis-33567	312	4	30	30	NUM
bracis-33567	312	5	neurons	neuron	NOUN
bracis-33567	312	6	per	per	ADP
bracis-33567	312	7	layer	layer	NOUN
bracis-33567	312	8	,	,	PUNCT
bracis-33567	312	9	our	our	PRON
bracis-33567	312	10	adaptation	adaptation	NOUN
bracis-33567	312	11	shows	show	VERB
bracis-33567	312	12	higher	high	ADJ
bracis-33567	312	13	variability	variability	NOUN
bracis-33567	312	14	compared	compare	VERB
bracis-33567	312	15	to	to	ADP
bracis-33567	312	16	the	the	DET
bracis-33567	312	17	other	other	ADJ
bracis-33567	312	18	approach	approach	NOUN
bracis-33567	312	19	.	.	PUNCT
bracis-33567	313	1	6	6	NUM
bracis-33567	313	2	conclusions	conclusion	NOUN
bracis-33567	313	3	and	and	CCONJ
bracis-33567	313	4	 	 	SPACE
bracis-33567	313	5	future	future	ADJ
bracis-33567	313	6	work	work	NOUN
bracis-33567	313	7	explanations	explanation	NOUN
bracis-33567	313	8	for	for	ADP
bracis-33567	313	9	the	the	DET
bracis-33567	313	10	outputs	output	NOUN
bracis-33567	313	11	of	of	ADP
bracis-33567	313	12	anns	ann	NOUN
bracis-33567	313	13	are	be	AUX
bracis-33567	313	14	fundamental	fundamental	ADJ
bracis-33567	313	15	in	in	ADP
bracis-33567	313	16	many	many	ADJ
bracis-33567	313	17	scenarios	scenario	NOUN
bracis-33567	313	18	,	,	PUNCT
bracis-33567	313	19	due	due	ADP
bracis-33567	313	20	to	to	ADP
bracis-33567	313	21	critical	critical	ADJ
bracis-33567	313	22	systems	system	NOUN
bracis-33567	313	23	,	,	PUNCT
bracis-33567	313	24	data	datum	NOUN
bracis-33567	313	25	protection	protection	NOUN
bracis-33567	313	26	laws	law	NOUN
bracis-33567	313	27	,	,	PUNCT
bracis-33567	313	28	adversarial	adversarial	ADJ
bracis-33567	313	29	examples	example	NOUN
bracis-33567	313	30	,	,	PUNCT
bracis-33567	313	31	among	among	ADP
bracis-33567	313	32	others	other	NOUN
bracis-33567	313	33	.	.	PUNCT
bracis-33567	314	1	therefore	therefore	ADV
bracis-33567	314	2	,	,	PUNCT
bracis-33567	314	3	several	several	ADJ
bracis-33567	314	4	heuristic	heuristic	ADJ
bracis-33567	314	5	methods	method	NOUN
bracis-33567	314	6	have	have	AUX
bracis-33567	314	7	been	be	AUX
bracis-33567	314	8	developed	develop	VERB
bracis-33567	314	9	to	to	PART
bracis-33567	314	10	provide	provide	VERB
bracis-33567	314	11	explanations	explanation	NOUN
bracis-33567	314	12	for	for	ADP
bracis-33567	314	13	the	the	DET
bracis-33567	314	14	decisions	decision	NOUN
bracis-33567	314	15	made	make	VERB
bracis-33567	314	16	by	by	ADP
bracis-33567	314	17	anns	ann	NOUN
bracis-33567	314	18	.	.	PUNCT
bracis-33567	315	1	however	however	ADV
bracis-33567	315	2	,	,	PUNCT
bracis-33567	315	3	these	these	DET
bracis-33567	315	4	approaches	approach	NOUN
bracis-33567	315	5	lack	lack	VERB
bracis-33567	315	6	guarantees	guarantee	NOUN
bracis-33567	315	7	of	of	ADP
bracis-33567	315	8	correctness	correctness	NOUN
bracis-33567	315	9	and	and	CCONJ
bracis-33567	315	10	may	may	AUX
bracis-33567	315	11	also	also	ADV
bracis-33567	315	12	produce	produce	VERB
bracis-33567	315	13	redundant	redundant	ADJ
bracis-33567	315	14	explanations	explanation	NOUN
bracis-33567	315	15	.	.	PUNCT
bracis-33567	316	1	logic	logic	NOUN
bracis-33567	316	2	-	-	PUNCT
bracis-33567	316	3	based	base	VERB
bracis-33567	316	4	approaches	approach	NOUN
bracis-33567	316	5	address	address	VERB
bracis-33567	316	6	these	these	DET
bracis-33567	316	7	issues	issue	NOUN
bracis-33567	316	8	but	but	CCONJ
bracis-33567	316	9	often	often	ADV
bracis-33567	316	10	suffer	suffer	VERB
bracis-33567	316	11	from	from	ADP
bracis-33567	316	12	scalability	scalability	NOUN
bracis-33567	316	13	problems	problem	NOUN
bracis-33567	316	14	.	.	PUNCT
bracis-33567	317	1	in	in	ADP
bracis-33567	317	2	this	this	DET
bracis-33567	317	3	work	work	NOUN
bracis-33567	317	4	,	,	PUNCT
bracis-33567	317	5	we	we	PRON
bracis-33567	317	6	compare	compare	VERB
bracis-33567	317	7	two	two	NUM
bracis-33567	317	8	logical	logical	ADJ
bracis-33567	317	9	encodings	encoding	NOUN
bracis-33567	317	10	of	of	ADP
bracis-33567	317	11	anns	ann	NOUN
bracis-33567	317	12	:	:	PUNCT
bracis-33567	317	13	one	one	NUM
bracis-33567	317	14	has	have	AUX
bracis-33567	317	15	been	be	AUX
bracis-33567	317	16	used	use	VERB
bracis-33567	317	17	in	in	ADP
bracis-33567	317	18	the	the	DET
bracis-33567	317	19	literature	literature	NOUN
bracis-33567	317	20	to	to	PART
bracis-33567	317	21	provide	provide	VERB
bracis-33567	317	22	explanations	explanation	NOUN
bracis-33567	317	23	[	[	X
bracis-33567	317	24	5	5	NUM
bracis-33567	317	25	,	,	PUNCT
bracis-33567	317	26	8	8	NUM
bracis-33567	317	27	]	]	PUNCT
bracis-33567	317	28	,	,	PUNCT
bracis-33567	317	29	and	and	CCONJ
bracis-33567	317	30	another	another	PRON
bracis-33567	318	1	[	[	X
bracis-33567	318	2	17	17	NUM
bracis-33567	318	3	]	]	PUNCT
bracis-33567	318	4	that	that	SCONJ
bracis-33567	318	5	we	we	PRON
bracis-33567	318	6	have	have	AUX
bracis-33567	318	7	adapted	adapt	VERB
bracis-33567	318	8	for	for	ADP
bracis-33567	318	9	our	our	PRON
bracis-33567	318	10	context	context	NOUN
bracis-33567	318	11	of	of	ADP
bracis-33567	318	12	explainability	explainability	NOUN
bracis-33567	318	13	.	.	PUNCT
bracis-33567	319	1	our	our	PRON
bracis-33567	319	2	experiments	experiment	NOUN
bracis-33567	319	3	indicate	indicate	VERB
bracis-33567	319	4	that	that	SCONJ
bracis-33567	319	5	both	both	DET
bracis-33567	319	6	encodings	encoding	NOUN
bracis-33567	319	7	have	have	VERB
bracis-33567	319	8	similar	similar	ADJ
bracis-33567	319	9	running	running	NOUN
bracis-33567	319	10	times	time	NOUN
bracis-33567	319	11	for	for	ADP
bracis-33567	319	12	computing	computing	NOUN
bracis-33567	319	13	explanations	explanation	NOUN
bracis-33567	319	14	,	,	PUNCT
bracis-33567	319	15	even	even	ADV
bracis-33567	319	16	as	as	SCONJ
bracis-33567	319	17	the	the	DET
bracis-33567	319	18	number	number	NOUN
bracis-33567	319	19	of	of	ADP
bracis-33567	319	20	neurons	neuron	NOUN
bracis-33567	319	21	and	and	CCONJ
bracis-33567	319	22	layers	layer	NOUN
bracis-33567	319	23	increases	increase	NOUN
bracis-33567	319	24	.	.	PUNCT
bracis-33567	320	1	furthermore	furthermore	ADV
bracis-33567	320	2	,	,	PUNCT
bracis-33567	320	3	our	our	PRON
bracis-33567	320	4	experimental	experimental	ADJ
bracis-33567	320	5	results	result	NOUN
bracis-33567	320	6	suggest	suggest	VERB
bracis-33567	320	7	that	that	SCONJ
bracis-33567	320	8	our	our	PRON
bracis-33567	320	9	adaptation	adaptation	NOUN
bracis-33567	320	10	is	be	AUX
bracis-33567	320	11	generally	generally	ADV
bracis-33567	320	12	more	more	ADV
bracis-33567	320	13	efficient	efficient	ADJ
bracis-33567	320	14	for	for	ADP
bracis-33567	320	15	anns	anns	NOUN
bracis-33567	320	16	with	with	ADP
bracis-33567	320	17	one	one	NUM
bracis-33567	320	18	hidden	hide	VERB
bracis-33567	320	19	layer	layer	NOUN
bracis-33567	320	20	,	,	PUNCT
bracis-33567	320	21	while	while	SCONJ
bracis-33567	320	22	the	the	DET
bracis-33567	320	23	performance	performance	NOUN
bracis-33567	320	24	advantage	advantage	NOUN
bracis-33567	320	25	diminishes	diminish	VERB
bracis-33567	320	26	for	for	ADP
bracis-33567	320	27	anns	anns	NOUN
bracis-33567	320	28	with	with	ADP
bracis-33567	320	29	two	two	NUM
bracis-33567	320	30	hidden	hidden	ADJ
bracis-33567	320	31	layers	layer	NOUN
bracis-33567	320	32	.	.	PUNCT
bracis-33567	321	1	however	however	ADV
bracis-33567	321	2	,	,	PUNCT
bracis-33567	321	3	our	our	PRON
bracis-33567	321	4	proposal	proposal	NOUN
bracis-33567	321	5	achieved	achieve	VERB
bracis-33567	321	6	a	a	DET
bracis-33567	321	7	better	well	ADJ
bracis-33567	321	8	running	running	NOUN
bracis-33567	321	9	time	time	NOUN
bracis-33567	321	10	for	for	ADP
bracis-33567	321	11	building	build	VERB
bracis-33567	321	12	the	the	DET
bracis-33567	321	13	encoding	encoding	NOUN
bracis-33567	321	14	for	for	ADP
bracis-33567	321	15	anns	anns	NOUN
bracis-33567	321	16	with	with	ADP
bracis-33567	321	17	two	two	NUM
bracis-33567	321	18	layers	layer	NOUN
bracis-33567	321	19	,	,	PUNCT
bracis-33567	321	20	showing	show	VERB
bracis-33567	321	21	an	an	DET
bracis-33567	321	22	improvement	improvement	NOUN
bracis-33567	321	23	of	of	ADP
bracis-33567	321	24	up	up	ADP
bracis-33567	321	25	to	to	ADP
bracis-33567	321	26	\(18\%\	\(18\%\	NOUN
bracis-33567	321	27	)	)	PUNCT
bracis-33567	321	28	.	.	PUNCT
bracis-33567	322	1	this	this	PRON
bracis-33567	322	2	can	can	AUX
bracis-33567	322	3	help	help	VERB
bracis-33567	322	4	to	to	PART
bracis-33567	322	5	decrease	decrease	VERB
bracis-33567	322	6	the	the	DET
bracis-33567	322	7	scalability	scalability	NOUN
bracis-33567	322	8	issue	issue	NOUN
bracis-33567	322	9	for	for	ADP
bracis-33567	322	10	building	build	VERB
bracis-33567	322	11	the	the	DET
bracis-33567	322	12	logical	logical	ADJ
bracis-33567	322	13	constraints	constraint	NOUN
bracis-33567	322	14	given	give	VERB
bracis-33567	322	15	an	an	DET
bracis-33567	322	16	ann	ann	PROPN
bracis-33567	322	17	.	.	PUNCT
bracis-33567	323	1	furthermore	furthermore	ADV
bracis-33567	323	2	,	,	PUNCT
bracis-33567	323	3	this	this	DET
bracis-33567	323	4	encoding	encoding	NOUN
bracis-33567	323	5	obtained	obtain	VERB
bracis-33567	323	6	better	well	ADJ
bracis-33567	323	7	results	result	NOUN
bracis-33567	323	8	also	also	ADV
bracis-33567	323	9	in	in	ADP
bracis-33567	323	10	the	the	DET
bracis-33567	323	11	overall	overall	ADJ
bracis-33567	323	12	time	time	NOUN
bracis-33567	323	13	,	,	PUNCT
bracis-33567	323	14	i.e.	i.e.	X
bracis-33567	323	15	,	,	PUNCT
bracis-33567	323	16	the	the	DET
bracis-33567	323	17	time	time	NOUN
bracis-33567	323	18	for	for	ADP
bracis-33567	323	19	computing	compute	VERB
bracis-33567	323	20	explanations	explanation	NOUN
bracis-33567	323	21	plus	plus	CCONJ
bracis-33567	323	22	the	the	DET
bracis-33567	323	23	time	time	NOUN
bracis-33567	323	24	for	for	ADP
bracis-33567	323	25	building	build	VERB
bracis-33567	323	26	the	the	DET
bracis-33567	323	27	logical	logical	ADJ
bracis-33567	323	28	constraints	constraint	NOUN
bracis-33567	323	29	,	,	PUNCT
bracis-33567	323	30	showing	show	VERB
bracis-33567	323	31	an	an	DET
bracis-33567	323	32	improvement	improvement	NOUN
bracis-33567	323	33	of	of	ADP
bracis-33567	323	34	up	up	ADP
bracis-33567	323	35	to	to	ADP
bracis-33567	323	36	\(16\%\	\(16\%\	NOUN
bracis-33567	323	37	)	)	PUNCT
bracis-33567	323	38	.	.	PUNCT
bracis-33567	324	1	in	in	ADP
bracis-33567	324	2	the	the	DET
bracis-33567	324	3	experiments	experiment	NOUN
bracis-33567	324	4	of	of	ADP
bracis-33567	324	5	this	this	DET
bracis-33567	324	6	work	work	NOUN
bracis-33567	324	7	,	,	PUNCT
bracis-33567	324	8	we	we	PRON
bracis-33567	324	9	considered	consider	VERB
bracis-33567	324	10	all	all	DET
bracis-33567	324	11	instances	instance	NOUN
bracis-33567	324	12	of	of	ADP
bracis-33567	324	13	the	the	DET
bracis-33567	324	14	datasets	dataset	NOUN
bracis-33567	324	15	used	use	VERB
bracis-33567	324	16	,	,	PUNCT
bracis-33567	324	17	which	which	PRON
bracis-33567	324	18	considerably	considerably	ADV
bracis-33567	324	19	increased	increase	VERB
bracis-33567	324	20	the	the	DET
bracis-33567	324	21	experiments	experiment	NOUN
bracis-33567	324	22	running	run	VERB
bracis-33567	324	23	time	time	NOUN
bracis-33567	324	24	.	.	PUNCT
bracis-33567	325	1	as	as	ADP
bracis-33567	325	2	future	future	ADJ
bracis-33567	325	3	work	work	NOUN
bracis-33567	325	4	,	,	PUNCT
bracis-33567	325	5	we	we	PRON
bracis-33567	325	6	can	can	AUX
bracis-33567	325	7	change	change	VERB
bracis-33567	325	8	the	the	DET
bracis-33567	325	9	design	design	NOUN
bracis-33567	325	10	of	of	ADP
bracis-33567	325	11	experiments	experiment	NOUN
bracis-33567	325	12	,	,	PUNCT
bracis-33567	325	13	using	use	VERB
bracis-33567	325	14	only	only	ADV
bracis-33567	325	15	a	a	DET
bracis-33567	325	16	subset	subset	NOUN
bracis-33567	325	17	of	of	ADP
bracis-33567	325	18	the	the	DET
bracis-33567	325	19	datasets	dataset	NOUN
bracis-33567	325	20	,	,	PUNCT
bracis-33567	325	21	to	to	PART
bracis-33567	325	22	allow	allow	VERB
bracis-33567	325	23	the	the	DET
bracis-33567	325	24	use	use	NOUN
bracis-33567	325	25	of	of	ADP
bracis-33567	325	26	larger	large	ADJ
bracis-33567	325	27	anns	ann	NOUN
bracis-33567	325	28	.	.	PUNCT
bracis-33567	326	1	more	more	ADJ
bracis-33567	326	2	experiments	experiment	NOUN
bracis-33567	326	3	are	be	AUX
bracis-33567	326	4	necessary	necessary	ADJ
bracis-33567	326	5	,	,	PUNCT
bracis-33567	326	6	especially	especially	ADV
bracis-33567	326	7	with	with	ADP
bracis-33567	326	8	additional	additional	ADJ
bracis-33567	326	9	layers	layer	NOUN
bracis-33567	326	10	and	and	CCONJ
bracis-33567	326	11	neurons	neuron	NOUN
bracis-33567	326	12	,	,	PUNCT
bracis-33567	326	13	to	to	PART
bracis-33567	326	14	further	far	ADV
bracis-33567	326	15	validate	validate	VERB
bracis-33567	326	16	our	our	PRON
bracis-33567	326	17	findings	finding	NOUN
bracis-33567	326	18	and	and	CCONJ
bracis-33567	326	19	understand	understand	VERB
bracis-33567	326	20	the	the	DET
bracis-33567	326	21	performance	performance	NOUN
bracis-33567	326	22	of	of	ADP
bracis-33567	326	23	these	these	DET
bracis-33567	326	24	encodings	encoding	NOUN
bracis-33567	326	25	.	.	PUNCT
bracis-33567	327	1	furthermore	furthermore	ADV
bracis-33567	327	2	,	,	PUNCT
bracis-33567	327	3	others	other	NOUN
bracis-33567	327	4	encodings	encoding	VERB
bracis-33567	327	5	[	[	X
bracis-33567	327	6	9	9	NUM
bracis-33567	327	7	,	,	PUNCT
bracis-33567	327	8	10	10	NUM
bracis-33567	327	9	]	]	PUNCT
bracis-33567	327	10	can	can	AUX
bracis-33567	327	11	be	be	AUX
bracis-33567	327	12	evaluated	evaluate	VERB
bracis-33567	327	13	for	for	ADP
bracis-33567	327	14	computing	compute	VERB
bracis-33567	327	15	logic	logic	NOUN
bracis-33567	327	16	-	-	PUNCT
bracis-33567	327	17	based	base	VERB
bracis-33567	327	18	minimal	minimal	ADJ
bracis-33567	327	19	explanations	explanation	NOUN
bracis-33567	327	20	for	for	ADP
bracis-33567	327	21	anns	ann	NOUN
bracis-33567	327	22	.	.	PUNCT
bracis-33567	328	1	moreover	moreover	ADV
bracis-33567	328	2	,	,	PUNCT
bracis-33567	328	3	in	in	ADP
bracis-33567	328	4	order	order	NOUN
bracis-33567	328	5	to	to	PART
bracis-33567	328	6	improve	improve	VERB
bracis-33567	328	7	the	the	DET
bracis-33567	328	8	scalability	scalability	NOUN
bracis-33567	328	9	of	of	ADP
bracis-33567	328	10	computing	compute	VERB
bracis-33567	328	11	logic	logic	NOUN
bracis-33567	328	12	-	-	PUNCT
bracis-33567	328	13	based	base	VERB
bracis-33567	328	14	explanations	explanation	NOUN
bracis-33567	328	15	,	,	PUNCT
bracis-33567	328	16	the	the	DET
bracis-33567	328	17	anns	anns	NOUN
bracis-33567	328	18	can	can	AUX
bracis-33567	328	19	be	be	AUX
bracis-33567	328	20	simplified	simplify	VERB
bracis-33567	328	21	,	,	PUNCT
bracis-33567	328	22	before	before	ADP
bracis-33567	328	23	or	or	CCONJ
bracis-33567	328	24	during	during	ADP
bracis-33567	328	25	building	build	VERB
bracis-33567	328	26	their	their	PRON
bracis-33567	328	27	encodings	encoding	NOUN
bracis-33567	328	28	,	,	PUNCT
bracis-33567	328	29	via	via	ADP
bracis-33567	328	30	pruning	prune	VERB
bracis-33567	328	31	or	or	CCONJ
bracis-33567	328	32	slicing	slicing	NOUN
bracis-33567	328	33	as	as	SCONJ
bracis-33567	328	34	proposed	propose	VERB
bracis-33567	328	35	by	by	ADP
bracis-33567	328	36	[	[	X
bracis-33567	328	37	12	12	NUM
bracis-33567	328	38	]	]	PUNCT
bracis-33567	328	39	.	.	PUNCT
bracis-33567	329	1	this	this	DET
bracis-33567	329	2	results	result	NOUN
bracis-33567	329	3	in	in	ADP
bracis-33567	329	4	equivalent	equivalent	ADJ
bracis-33567	329	5	anns	ann	NOUN
bracis-33567	329	6	with	with	ADP
bracis-33567	329	7	smaller	small	ADJ
bracis-33567	329	8	sizes	size	NOUN
bracis-33567	329	9	.	.	PUNCT
bracis-33567	330	1	notes	note	NOUN
bracis-33567	330	2	1.https://github.com/levicc8/explications-anns	1.https://github.com/levicc8/explications-anns	NUM
bracis-33567	330	3	.	.	PUNCT
bracis-33567	331	1	2.https://archive.ics.uci.edu/ml/.	2.https://archive.ics.uci.edu/ml/.	NUM
bracis-33567	331	2	3.https://github.com/epistasislab/penn-ml-benchmarks/.	3.https://github.com/epistasislab/penn-ml-benchmarks/.	NUM
bracis-33567	331	3	references	reference	NOUN
bracis-33567	331	4	audemard	audemard	NOUN
bracis-33567	331	5	,	,	PUNCT
bracis-33567	331	6	g.	g.	PROPN
bracis-33567	331	7	,	,	PUNCT
bracis-33567	331	8	lagniez	lagniez	NOUN
bracis-33567	331	9	,	,	PUNCT
bracis-33567	331	10	j.m	j.m	PROPN
bracis-33567	331	11	.	.	PROPN
bracis-33567	331	12	,	,	PUNCT
bracis-33567	331	13	marquis	marquis	PROPN
bracis-33567	331	14	,	,	PUNCT
bracis-33567	331	15	p.	p.	PROPN
bracis-33567	331	16	,	,	PUNCT
bracis-33567	331	17	szczepanski	szczepanski	ADJ
bracis-33567	331	18	,	,	PUNCT
bracis-33567	331	19	n.	n.	NOUN
bracis-33567	331	20	:	:	PUNCT
bracis-33567	331	21	computing	compute	VERB
bracis-33567	331	22	abductive	abductive	ADJ
bracis-33567	331	23	explanations	explanation	NOUN
bracis-33567	331	24	for	for	ADP
bracis-33567	331	25	boosted	boost	VERB
bracis-33567	331	26	trees	tree	NOUN
bracis-33567	331	27	.	.	PUNCT
bracis-33567	332	1	in	in	ADP
bracis-33567	332	2	:	:	PUNCT
bracis-33567	332	3	26th	26th	ADJ
bracis-33567	332	4	aistats	aistat	NOUN
bracis-33567	332	5	(	(	PUNCT
bracis-33567	332	6	2023	2023	NUM
bracis-33567	332	7	)	)	PUNCT
bracis-33567	332	8	google	google	NOUN
bracis-33567	332	9	scholar	scholar	NOUN
bracis-33567	332	10	  	  	SPACE
bracis-33567	332	11	bénichou	bénichou	NOUN
bracis-33567	332	12	,	,	PUNCT
bracis-33567	332	13	m.	m.	NOUN
bracis-33567	332	14	,	,	PUNCT
bracis-33567	332	15	gauthier	gauthier	PROPN
bracis-33567	332	16	,	,	PUNCT
bracis-33567	332	17	j.m	j.m	PROPN
bracis-33567	332	18	.	.	PROPN
bracis-33567	332	19	,	,	PUNCT
bracis-33567	332	20	girodet	girodet	PROPN
bracis-33567	332	21	,	,	PUNCT
bracis-33567	332	22	p.	p.	NOUN
bracis-33567	332	23	,	,	PUNCT
bracis-33567	332	24	hentges	hentge	NOUN
bracis-33567	332	25	,	,	PUNCT
bracis-33567	332	26	g.	g.	PROPN
bracis-33567	332	27	,	,	PUNCT
bracis-33567	332	28	ribière	ribière	VERB
bracis-33567	332	29	,	,	PUNCT
bracis-33567	332	30	g.	g.	PROPN
bracis-33567	332	31	,	,	PUNCT
bracis-33567	332	32	vincent	vincent	PROPN
bracis-33567	332	33	,	,	PUNCT
bracis-33567	332	34	o.	o.	NOUN
bracis-33567	332	35	:	:	PUNCT
bracis-33567	332	36	experiments	experiment	NOUN
bracis-33567	332	37	in	in	ADP
bracis-33567	332	38	mixed	mixed	ADJ
bracis-33567	332	39	-	-	PUNCT
bracis-33567	332	40	integer	integer	NOUN
bracis-33567	332	41	linear	linear	PROPN
bracis-33567	332	42	programming	programming	NOUN
bracis-33567	332	43	.	.	PUNCT
bracis-33567	333	1	math	math	NOUN
bracis-33567	333	2	.	.	PUNCT
bracis-33567	334	1	program	program	NOUN
bracis-33567	334	2	.	.	PUNCT
bracis-33567	335	1	1	1	NUM
bracis-33567	335	2	,	,	PUNCT
bracis-33567	335	3	76–94	76–94	NUM
bracis-33567	335	4	(	(	PUNCT
bracis-33567	335	5	1971	1971	NUM
bracis-33567	335	6	)	)	PUNCT
bracis-33567	335	7	article	article	NOUN
bracis-33567	335	8	  	  	SPACE
bracis-33567	335	9	mathscinet	mathscinet	NOUN
bracis-33567	335	10	  	  	SPACE
bracis-33567	335	11	math	math	NOUN
bracis-33567	335	12	  	  	SPACE
bracis-33567	335	13	google	google	PROPN
bracis-33567	335	14	scholar	scholar	NOUN
bracis-33567	335	15	  	  	SPACE
bracis-33567	335	16	bonami	bonami	NOUN
bracis-33567	335	17	,	,	PUNCT
bracis-33567	335	18	p.	p.	NOUN
bracis-33567	335	19	,	,	PUNCT
bracis-33567	335	20	lodi	lodi	PROPN
bracis-33567	335	21	,	,	PUNCT
bracis-33567	335	22	a.	a.	NOUN
bracis-33567	335	23	,	,	PUNCT
bracis-33567	335	24	tramontani	tramontani	VERB
bracis-33567	335	25	,	,	PUNCT
bracis-33567	335	26	a.	a.	NOUN
bracis-33567	335	27	,	,	PUNCT
bracis-33567	335	28	wiese	wiese	PROPN
bracis-33567	335	29	,	,	PUNCT
bracis-33567	335	30	s.	s.	PROPN
bracis-33567	335	31	:	:	PUNCT
bracis-33567	335	32	on	on	ADP
bracis-33567	335	33	mathematical	mathematical	ADJ
bracis-33567	335	34	programming	programming	NOUN
bracis-33567	335	35	with	with	ADP
bracis-33567	335	36	indicator	indicator	NOUN
bracis-33567	335	37	constraints	constraint	NOUN
bracis-33567	335	38	.	.	PUNCT
bracis-33567	336	1	math	math	NOUN
bracis-33567	336	2	.	.	PUNCT
bracis-33567	337	1	program	program	NOUN
bracis-33567	337	2	.	.	PUNCT
bracis-33567	338	1	151(1	151(1	NUM
bracis-33567	338	2	)	)	PUNCT
bracis-33567	338	3	,	,	PUNCT
bracis-33567	338	4	191–223	191–223	NUM
bracis-33567	338	5	(	(	PUNCT
bracis-33567	338	6	2015	2015	NUM
bracis-33567	338	7	)	)	PUNCT
bracis-33567	338	8	.	.	PUNCT
bracis-33567	339	1	https://doi.org/10.1007/s10107-015-0891-4	https://doi.org/10.1007/s10107-015-0891-4	NUM
bracis-33567	339	2	article	article	NOUN
bracis-33567	339	3	  	  	SPACE
bracis-33567	339	4	mathscinet	mathscinet	NOUN
bracis-33567	339	5	  	  	SPACE
bracis-33567	339	6	math	math	NOUN
bracis-33567	339	7	  	  	SPACE
bracis-33567	339	8	google	google	PROPN
bracis-33567	339	9	scholar	scholar	NOUN
bracis-33567	339	10	  	  	SPACE
bracis-33567	339	11	choi	choi	NOUN
bracis-33567	339	12	,	,	PUNCT
bracis-33567	339	13	a.	a.	NOUN
bracis-33567	339	14	,	,	PUNCT
bracis-33567	339	15	shih	shih	NOUN
bracis-33567	339	16	,	,	PUNCT
bracis-33567	339	17	a.	a.	NOUN
bracis-33567	339	18	,	,	PUNCT
bracis-33567	339	19	goyanka	goyanka	PROPN
bracis-33567	339	20	,	,	PUNCT
bracis-33567	339	21	a.	a.	NOUN
bracis-33567	339	22	,	,	PUNCT
bracis-33567	339	23	darwiche	darwiche	NOUN
bracis-33567	339	24	,	,	PUNCT
bracis-33567	339	25	a.	a.	NOUN
bracis-33567	339	26	:	:	PUNCT
bracis-33567	339	27	on	on	ADP
bracis-33567	339	28	symbolically	symbolically	ADV
bracis-33567	339	29	encoding	encode	VERB
bracis-33567	339	30	the	the	DET
bracis-33567	339	31	behavior	behavior	NOUN
bracis-33567	339	32	of	of	ADP
bracis-33567	339	33	random	random	ADJ
bracis-33567	339	34	forests	forest	NOUN
bracis-33567	339	35	.	.	PUNCT
bracis-33567	340	1	in	in	ADP
bracis-33567	340	2	:	:	PUNCT
bracis-33567	340	3	3rd	3rd	ADJ
bracis-33567	340	4	fomlas	fomla	NOUN
bracis-33567	340	5	(	(	PUNCT
bracis-33567	340	6	2020	2020	NUM
bracis-33567	340	7	)	)	PUNCT
bracis-33567	340	8	google	google	PROPN
bracis-33567	340	9	scholar	scholar	NOUN
bracis-33567	340	10	  	  	SPACE
bracis-33567	340	11	fischetti	fischetti	ADJ
bracis-33567	340	12	,	,	PUNCT
bracis-33567	340	13	m.	m.	NOUN
bracis-33567	340	14	,	,	PUNCT
bracis-33567	340	15	jo	jo	PROPN
bracis-33567	340	16	,	,	PUNCT
bracis-33567	340	17	j.	j.	PROPN
bracis-33567	340	18	:	:	PUNCT
bracis-33567	340	19	deep	deep	ADJ
bracis-33567	340	20	neural	neural	ADJ
bracis-33567	340	21	networks	network	NOUN
bracis-33567	340	22	and	and	CCONJ
bracis-33567	340	23	mixed	mixed	ADJ
bracis-33567	340	24	integer	integer	NOUN
bracis-33567	340	25	linear	linear	PROPN
bracis-33567	340	26	optimization	optimization	NOUN
bracis-33567	340	27	.	.	PUNCT
bracis-33567	341	1	constraints	constraint	NOUN
bracis-33567	341	2	23(3	23(3	NUM
bracis-33567	341	3	)	)	PUNCT
bracis-33567	341	4	,	,	PUNCT
bracis-33567	341	5	296–309	296–309	NUM
bracis-33567	341	6	(	(	PUNCT
bracis-33567	341	7	2018	2018	NUM
bracis-33567	341	8	)	)	PUNCT
bracis-33567	341	9	.	.	PUNCT
bracis-33567	342	1	https://doi.org/10.1007/s10601-018-9285-6	https://doi.org/10.1007/s10601-018-9285-6	NUM
bracis-33567	342	2	article	article	NOUN
bracis-33567	342	3	  	  	SPACE
bracis-33567	342	4	mathscinet	mathscinet	NOUN
bracis-33567	342	5	  	  	SPACE
bracis-33567	342	6	math	math	NOUN
bracis-33567	342	7	  	  	SPACE
bracis-33567	342	8	google	google	PROPN
bracis-33567	342	9	scholar	scholar	NOUN
bracis-33567	342	10	  	  	SPACE
bracis-33567	342	11	goodfellow	goodfellow	PROPN
bracis-33567	342	12	,	,	PUNCT
bracis-33567	342	13	i.j	i.j	PROPN
bracis-33567	342	14	.	.	PROPN
bracis-33567	342	15	,	,	PUNCT
bracis-33567	342	16	shlens	shlens	PROPN
bracis-33567	342	17	,	,	PUNCT
bracis-33567	342	18	j.	j.	PROPN
bracis-33567	342	19	,	,	PUNCT
bracis-33567	342	20	szegedy	szegedy	PROPN
bracis-33567	342	21	,	,	PUNCT
bracis-33567	342	22	c.	c.	NOUN
bracis-33567	342	23	:	:	PUNCT
bracis-33567	342	24	explaining	explain	VERB
bracis-33567	342	25	and	and	CCONJ
bracis-33567	342	26	harnessing	harness	VERB
bracis-33567	342	27	adversarial	adversarial	ADJ
bracis-33567	342	28	examples	example	NOUN
bracis-33567	342	29	.	.	PUNCT
bracis-33567	343	1	in	in	ADP
bracis-33567	343	2	:	:	PUNCT
bracis-33567	343	3	3rd	3rd	ADJ
bracis-33567	343	4	iclr	iclr	NOUN
bracis-33567	343	5	(	(	PUNCT
bracis-33567	343	6	2015	2015	NUM
bracis-33567	343	7	)	)	PUNCT
bracis-33567	343	8	google	google	PROPN
bracis-33567	343	9	scholar	scholar	NOUN
bracis-33567	343	10	  	  	SPACE
bracis-33567	343	11	gorji	gorji	NOUN
bracis-33567	343	12	,	,	PUNCT
bracis-33567	343	13	n.	n.	PROPN
bracis-33567	343	14	,	,	PUNCT
bracis-33567	343	15	rubin	rubin	PROPN
bracis-33567	343	16	,	,	PUNCT
bracis-33567	343	17	s.	s.	PROPN
bracis-33567	343	18	:	:	PUNCT
bracis-33567	343	19	sufficient	sufficient	ADJ
bracis-33567	343	20	reasons	reason	NOUN
bracis-33567	343	21	for	for	ADP
bracis-33567	343	22	classifier	classifier	NOUN
bracis-33567	343	23	decisions	decision	NOUN
bracis-33567	343	24	in	in	ADP
bracis-33567	343	25	the	the	DET
bracis-33567	343	26	presence	presence	NOUN
bracis-33567	343	27	of	of	ADP
bracis-33567	343	28	domain	domain	NOUN
bracis-33567	343	29	constraints	constraint	NOUN
bracis-33567	343	30	.	.	PUNCT
bracis-33567	344	1	in	in	ADP
bracis-33567	344	2	:	:	PUNCT
bracis-33567	344	3	36th	36th	ADJ
bracis-33567	344	4	aaai	aaai	PROPN
bracis-33567	344	5	(	(	PUNCT
bracis-33567	344	6	2022	2022	NUM
bracis-33567	344	7	)	)	PUNCT
bracis-33567	344	8	google	google	PROPN
bracis-33567	344	9	scholar	scholar	NOUN
bracis-33567	344	10	  	  	SPACE
bracis-33567	344	11	ignatiev	ignatiev	NOUN
bracis-33567	344	12	,	,	PUNCT
bracis-33567	344	13	a.	a.	NOUN
bracis-33567	344	14	,	,	PUNCT
bracis-33567	344	15	narodytska	narodytska	PROPN
bracis-33567	344	16	,	,	PUNCT
bracis-33567	344	17	n.	n.	NOUN
bracis-33567	344	18	,	,	PUNCT
bracis-33567	344	19	marques	marques	PROPN
bracis-33567	344	20	-	-	NOUN
bracis-33567	344	21	silva	silva	PROPN
bracis-33567	344	22	,	,	PUNCT
bracis-33567	344	23	j.	j.	PROPN
bracis-33567	344	24	:	:	PUNCT
bracis-33567	344	25	abduction	abduction	NOUN
bracis-33567	344	26	-	-	PUNCT
bracis-33567	344	27	based	base	VERB
bracis-33567	344	28	explanations	explanation	NOUN
bracis-33567	344	29	for	for	ADP
bracis-33567	344	30	machine	machine	NOUN
bracis-33567	344	31	learning	learning	NOUN
bracis-33567	344	32	models	model	NOUN
bracis-33567	344	33	.	.	PUNCT
bracis-33567	345	1	in	in	ADP
bracis-33567	345	2	:	:	PUNCT
bracis-33567	345	3	33rd	33rd	PROPN
bracis-33567	345	4	aaai	aaai	PROPN
bracis-33567	345	5	(	(	PUNCT
bracis-33567	345	6	2019	2019	NUM
bracis-33567	345	7	)	)	PUNCT
bracis-33567	345	8	google	google	PROPN
bracis-33567	345	9	scholar	scholar	NOUN
bracis-33567	345	10	  	  	SPACE
bracis-33567	345	11	katz	katz	PROPN
bracis-33567	345	12	,	,	PUNCT
bracis-33567	345	13	g.	g.	PROPN
bracis-33567	345	14	,	,	PUNCT
bracis-33567	345	15	barrett	barrett	PROPN
bracis-33567	345	16	,	,	PUNCT
bracis-33567	345	17	c.	c.	PROPN
bracis-33567	345	18	,	,	PUNCT
bracis-33567	345	19	dill	dill	NOUN
bracis-33567	345	20	,	,	PUNCT
bracis-33567	345	21	d.l	d.l	PROPN
bracis-33567	345	22	.	.	PROPN
bracis-33567	345	23	,	,	PUNCT
bracis-33567	345	24	julian	julian	PROPN
bracis-33567	345	25	,	,	PUNCT
bracis-33567	345	26	k.	k.	PROPN
bracis-33567	345	27	,	,	PUNCT
bracis-33567	345	28	kochenderfer	kochenderfer	NOUN
bracis-33567	345	29	,	,	PUNCT
bracis-33567	345	30	m.j	m.j	PROPN
bracis-33567	345	31	.	.	PROPN
bracis-33567	345	32	:	:	PUNCT
bracis-33567	346	1	reluplex	reluplex	NOUN
bracis-33567	346	2	:	:	PUNCT
bracis-33567	346	3	an	an	DET
bracis-33567	346	4	efficient	efficient	ADJ
bracis-33567	346	5	smt	smt	PROPN
bracis-33567	346	6	solver	solver	VERB
bracis-33567	346	7	for	for	ADP
bracis-33567	346	8	verifying	verify	VERB
bracis-33567	346	9	deep	deep	ADJ
bracis-33567	346	10	neural	neural	ADJ
bracis-33567	346	11	networks	network	NOUN
bracis-33567	346	12	.	.	PUNCT
bracis-33567	347	1	in	in	ADP
bracis-33567	347	2	:	:	PUNCT
bracis-33567	347	3	majumdar	majumdar	PROPN
bracis-33567	347	4	,	,	PUNCT
bracis-33567	347	5	r.	r.	PROPN
bracis-33567	347	6	,	,	PUNCT
bracis-33567	347	7	kunčak	kunčak	NOUN
bracis-33567	347	8	,	,	PUNCT
bracis-33567	347	9	v.	v.	PROPN
bracis-33567	347	10	(	(	PUNCT
bracis-33567	347	11	eds	ed	NOUN
bracis-33567	347	12	.	.	PUNCT
bracis-33567	347	13	)	)	PUNCT
bracis-33567	347	14	computer	computer	NOUN
bracis-33567	347	15	aided	aid	VERB
bracis-33567	347	16	verification	verification	NOUN
bracis-33567	347	17	:	:	PUNCT
bracis-33567	347	18	29th	29th	ADJ
bracis-33567	347	19	international	international	ADJ
bracis-33567	347	20	conference	conference	NOUN
bracis-33567	347	21	,	,	PUNCT
bracis-33567	347	22	cav	cav	NOUN
bracis-33567	347	23	2017	2017	NUM
bracis-33567	347	24	,	,	PUNCT
bracis-33567	347	25	heidelberg	heidelberg	PROPN
bracis-33567	347	26	,	,	PUNCT
bracis-33567	347	27	germany	germany	PROPN
bracis-33567	347	28	,	,	PUNCT
bracis-33567	347	29	july	july	PROPN
bracis-33567	347	30	24	24	NUM
bracis-33567	347	31	-	-	SYM
bracis-33567	347	32	28	28	NUM
bracis-33567	347	33	,	,	PUNCT
bracis-33567	347	34	2017	2017	NUM
bracis-33567	347	35	,	,	PUNCT
bracis-33567	347	36	proceedings	proceeding	NOUN
bracis-33567	347	37	,	,	PUNCT
bracis-33567	347	38	part	part	NOUN
bracis-33567	347	39	i	i	PRON
bracis-33567	347	40	,	,	PUNCT
bracis-33567	347	41	pp	pp	ADJ
bracis-33567	347	42	.	.	PUNCT
bracis-33567	348	1	97–117	97–117	NUM
bracis-33567	348	2	.	.	PUNCT
bracis-33567	349	1	springer	springer	NOUN
bracis-33567	349	2	international	international	ADJ
bracis-33567	349	3	publishing	publishing	NOUN
bracis-33567	349	4	,	,	PUNCT
bracis-33567	349	5	cham	cham	PROPN
bracis-33567	349	6	(	(	PUNCT
bracis-33567	349	7	2017	2017	NUM
bracis-33567	349	8	)	)	PUNCT
bracis-33567	349	9	.	.	PUNCT
bracis-33567	350	1	https://doi.org/10.1007/978-3-319-63387-9_5	https://doi.org/10.1007/978-3-319-63387-9_5	PROPN
bracis-33567	350	2	chapter	chapter	NOUN
bracis-33567	350	3	  	  	SPACE
bracis-33567	350	4	math	math	NOUN
bracis-33567	350	5	  	  	SPACE
bracis-33567	350	6	google	google	PROPN
bracis-33567	350	7	scholar	scholar	NOUN
bracis-33567	350	8	  	  	SPACE
bracis-33567	350	9	katz	katz	PROPN
bracis-33567	350	10	,	,	PUNCT
bracis-33567	350	11	g.	g.	PROPN
bracis-33567	350	12	,	,	PUNCT
bracis-33567	350	13	et	et	PROPN
bracis-33567	350	14	al	al	PROPN
bracis-33567	350	15	.	.	PROPN
bracis-33567	350	16	:	:	PUNCT
bracis-33567	351	1	the	the	DET
bracis-33567	351	2	marabou	marabou	NOUN
bracis-33567	351	3	framework	framework	NOUN
bracis-33567	351	4	for	for	ADP
bracis-33567	351	5	verification	verification	NOUN
bracis-33567	351	6	and	and	CCONJ
bracis-33567	351	7	analysis	analysis	NOUN
bracis-33567	351	8	of	of	ADP
bracis-33567	351	9	deep	deep	ADJ
bracis-33567	351	10	neural	neural	ADJ
bracis-33567	351	11	networks	network	NOUN
bracis-33567	351	12	.	.	PUNCT
bracis-33567	352	1	in	in	ADP
bracis-33567	352	2	:	:	PUNCT
bracis-33567	352	3	31st	31st	PROPN
bracis-33567	352	4	cav	cav	NOUN
bracis-33567	352	5	(	(	PUNCT
bracis-33567	352	6	2019	2019	NUM
bracis-33567	352	7	)	)	PUNCT
bracis-33567	352	8	google	google	NOUN
bracis-33567	352	9	scholar	scholar	NOUN
bracis-33567	352	10	  	  	SPACE
bracis-33567	352	11	kroening	kroening	NOUN
bracis-33567	352	12	,	,	PUNCT
bracis-33567	352	13	d.	d.	PROPN
bracis-33567	352	14	,	,	PUNCT
bracis-33567	352	15	strichman	strichman	NOUN
bracis-33567	352	16	,	,	PUNCT
bracis-33567	352	17	o.	o.	NOUN
bracis-33567	352	18	:	:	PUNCT
bracis-33567	352	19	decision	decision	NOUN
bracis-33567	352	20	procedures	procedure	NOUN
bracis-33567	352	21	:	:	PUNCT
bracis-33567	352	22	an	an	DET
bracis-33567	352	23	algorithmic	algorithmic	ADJ
bracis-33567	352	24	point	point	NOUN
bracis-33567	352	25	of	of	ADP
bracis-33567	352	26	view	view	NOUN
bracis-33567	352	27	.	.	PUNCT
bracis-33567	353	1	springer	springer	NOUN
bracis-33567	353	2	,	,	PUNCT
bracis-33567	353	3	berlin	berlin	PROPN
bracis-33567	353	4	,	,	PUNCT
bracis-33567	353	5	heidelberg	heidelberg	PROPN
bracis-33567	353	6	(	(	PUNCT
bracis-33567	353	7	2016	2016	NUM
bracis-33567	353	8	)	)	PUNCT
bracis-33567	353	9	.	.	PUNCT
bracis-33567	354	1	https://doi.org/10.1007/978-3-662-50497-0	https://doi.org/10.1007/978-3-662-50497-0	PROPN
bracis-33567	354	2	book	book	NOUN
bracis-33567	354	3	  	  	SPACE
bracis-33567	354	4	math	math	NOUN
bracis-33567	354	5	  	  	SPACE
bracis-33567	354	6	google	google	PROPN
bracis-33567	354	7	scholar	scholar	NOUN
bracis-33567	354	8	  	  	SPACE
bracis-33567	354	9	lahav	lahav	NOUN
bracis-33567	354	10	,	,	PUNCT
bracis-33567	354	11	o.	o.	PROPN
bracis-33567	354	12	,	,	PUNCT
bracis-33567	354	13	katz	katz	PROPN
bracis-33567	354	14	,	,	PUNCT
bracis-33567	354	15	g.	g.	PROPN
bracis-33567	354	16	:	:	PUNCT
bracis-33567	354	17	pruning	prune	VERB
bracis-33567	354	18	and	and	CCONJ
bracis-33567	354	19	slicing	slice	VERB
bracis-33567	354	20	neural	neural	ADJ
bracis-33567	354	21	networks	network	NOUN
bracis-33567	354	22	using	use	VERB
bracis-33567	354	23	formal	formal	ADJ
bracis-33567	354	24	verification	verification	NOUN
bracis-33567	354	25	.	.	PUNCT
bracis-33567	355	1	in	in	ADP
bracis-33567	355	2	:	:	PUNCT
bracis-33567	355	3	21st	21st	ADJ
bracis-33567	355	4	fmcad	fmcad	X
bracis-33567	355	5	(	(	PUNCT
bracis-33567	355	6	2021	2021	NUM
bracis-33567	355	7	)	)	PUNCT
bracis-33567	355	8	google	google	PROPN
bracis-33567	355	9	scholar	scholar	NOUN
bracis-33567	355	10	  	  	SPACE
bracis-33567	355	11	liu	liu	PROPN
bracis-33567	355	12	,	,	PUNCT
bracis-33567	355	13	w.	w.	PROPN
bracis-33567	355	14	,	,	PUNCT
bracis-33567	355	15	wang	wang	PROPN
bracis-33567	355	16	,	,	PUNCT
bracis-33567	355	17	z.	z.	PROPN
bracis-33567	355	18	,	,	PUNCT
bracis-33567	355	19	liu	liu	PROPN
bracis-33567	355	20	,	,	PUNCT
bracis-33567	355	21	x.	x.	PROPN
bracis-33567	355	22	,	,	PUNCT
bracis-33567	355	23	zeng	zeng	PROPN
bracis-33567	355	24	,	,	PUNCT
bracis-33567	355	25	n.	n.	PROPN
bracis-33567	355	26	,	,	PUNCT
bracis-33567	355	27	liu	liu	PROPN
bracis-33567	355	28	,	,	PUNCT
bracis-33567	355	29	y.	y.	PROPN
bracis-33567	355	30	,	,	PUNCT
bracis-33567	355	31	alsaadi	alsaadi	NOUN
bracis-33567	355	32	,	,	PUNCT
bracis-33567	355	33	f.e	f.e	PROPN
bracis-33567	355	34	.	.	PROPN
bracis-33567	355	35	:	:	PUNCT
bracis-33567	356	1	a	a	DET
bracis-33567	356	2	survey	survey	NOUN
bracis-33567	356	3	of	of	ADP
bracis-33567	356	4	deep	deep	ADJ
bracis-33567	356	5	neural	neural	ADJ
bracis-33567	356	6	network	network	NOUN
bracis-33567	356	7	architectures	architecture	NOUN
bracis-33567	356	8	and	and	CCONJ
bracis-33567	356	9	their	their	PRON
bracis-33567	356	10	applications	application	NOUN
bracis-33567	356	11	.	.	PUNCT
bracis-33567	357	1	neurocomputing	neurocompute	VERB
bracis-33567	357	2	234	234	NUM
bracis-33567	357	3	,	,	PUNCT
bracis-33567	357	4	11–26	11–26	NUM
bracis-33567	357	5	(	(	PUNCT
bracis-33567	357	6	2017	2017	NUM
bracis-33567	357	7	)	)	PUNCT
bracis-33567	357	8	article	article	NOUN
bracis-33567	357	9	  	  	SPACE
bracis-33567	357	10	math	math	NOUN
bracis-33567	357	11	  	  	SPACE
bracis-33567	357	12	google	google	PROPN
bracis-33567	357	13	scholar	scholar	NOUN
bracis-33567	357	14	  	  	SPACE
bracis-33567	357	15	ribeiro	ribeiro	PROPN
bracis-33567	357	16	,	,	PUNCT
bracis-33567	357	17	m.t	m.t	PROPN
bracis-33567	357	18	.	.	PROPN
bracis-33567	357	19	,	,	PUNCT
bracis-33567	357	20	singh	singh	PROPN
bracis-33567	357	21	,	,	PUNCT
bracis-33567	357	22	s.	s.	PROPN
bracis-33567	357	23	,	,	PUNCT
bracis-33567	357	24	guestrin	guestrin	NOUN
bracis-33567	357	25	,	,	PUNCT
bracis-33567	357	26	c.	c.	PROPN
bracis-33567	357	27	:	:	PUNCT
bracis-33567	357	28	why	why	SCONJ
bracis-33567	357	29	should	should	AUX
bracis-33567	357	30	i	i	PRON
bracis-33567	357	31	trust	trust	VERB
bracis-33567	357	32	you	you	PRON
bracis-33567	357	33	?	?	PUNCT
bracis-33567	357	34	:	:	PUNCT
bracis-33567	357	35	explaining	explain	VERB
bracis-33567	357	36	the	the	DET
bracis-33567	357	37	predictions	prediction	NOUN
bracis-33567	357	38	of	of	ADP
bracis-33567	357	39	any	any	DET
bracis-33567	357	40	classifier	classifier	NOUN
bracis-33567	357	41	.	.	PUNCT
bracis-33567	358	1	in	in	ADP
bracis-33567	358	2	:	:	PUNCT
bracis-33567	358	3	22nd	22nd	PROPN
bracis-33567	358	4	kdd	kdd	PROPN
bracis-33567	358	5	(	(	PUNCT
bracis-33567	358	6	2016	2016	NUM
bracis-33567	358	7	)	)	PUNCT
bracis-33567	358	8	google	google	PROPN
bracis-33567	358	9	scholar	scholar	NOUN
bracis-33567	358	10	  	  	SPACE
bracis-33567	358	11	ribeiro	ribeiro	PROPN
bracis-33567	358	12	,	,	PUNCT
bracis-33567	358	13	m.t	m.t	PROPN
bracis-33567	358	14	.	.	PROPN
bracis-33567	358	15	,	,	PUNCT
bracis-33567	358	16	singh	singh	PROPN
bracis-33567	358	17	,	,	PUNCT
bracis-33567	358	18	s.	s.	PROPN
bracis-33567	358	19	,	,	PUNCT
bracis-33567	358	20	guestrin	guestrin	NOUN
bracis-33567	358	21	,	,	PUNCT
bracis-33567	358	22	c.	c.	PROPN
bracis-33567	358	23	:	:	PUNCT
bracis-33567	358	24	anchors	anchor	NOUN
bracis-33567	358	25	:	:	PUNCT
bracis-33567	358	26	high	high	ADJ
bracis-33567	358	27	-	-	PUNCT
bracis-33567	358	28	precision	precision	NOUN
bracis-33567	358	29	model	model	NOUN
bracis-33567	358	30	-	-	ADJ
bracis-33567	358	31	agnostic	agnostic	ADJ
bracis-33567	358	32	explanations	explanation	NOUN
bracis-33567	358	33	.	.	PUNCT
bracis-33567	359	1	in	in	ADP
bracis-33567	359	2	:	:	PUNCT
bracis-33567	359	3	32th	32th	ADJ
bracis-33567	359	4	aaai	aaai	PROPN
bracis-33567	359	5	(	(	PUNCT
bracis-33567	359	6	2018	2018	NUM
bracis-33567	359	7	)	)	PUNCT
bracis-33567	359	8	google	google	PROPN
bracis-33567	359	9	scholar	scholar	NOUN
bracis-33567	359	10	  	  	SPACE
bracis-33567	359	11	shih	shih	NOUN
bracis-33567	359	12	,	,	PUNCT
bracis-33567	359	13	a.	a.	NOUN
bracis-33567	359	14	,	,	PUNCT
bracis-33567	359	15	choi	choi	NOUN
bracis-33567	359	16	,	,	PUNCT
bracis-33567	359	17	a.	a.	NOUN
bracis-33567	359	18	,	,	PUNCT
bracis-33567	359	19	darwiche	darwiche	NOUN
bracis-33567	359	20	,	,	PUNCT
bracis-33567	359	21	a.	a.	NOUN
bracis-33567	359	22	:	:	PUNCT
bracis-33567	359	23	a	a	DET
bracis-33567	359	24	symbolic	symbolic	ADJ
bracis-33567	359	25	approach	approach	NOUN
bracis-33567	359	26	to	to	ADP
bracis-33567	359	27	explaining	explain	VERB
bracis-33567	359	28	bayesian	bayesian	NOUN
bracis-33567	359	29	network	network	NOUN
bracis-33567	359	30	classifiers	classifier	NOUN
bracis-33567	359	31	.	.	PUNCT
bracis-33567	360	1	in	in	ADP
bracis-33567	360	2	:	:	PUNCT
bracis-33567	360	3	27th	27th	ADJ
bracis-33567	360	4	ijcai	ijcai	NOUN
bracis-33567	360	5	(	(	PUNCT
bracis-33567	360	6	2018	2018	NUM
bracis-33567	360	7	)	)	PUNCT
bracis-33567	360	8	google	google	PROPN
bracis-33567	360	9	scholar	scholar	NOUN
bracis-33567	360	10	  	  	SPACE
bracis-33567	360	11	tjeng	tjeng	NOUN
bracis-33567	360	12	,	,	PUNCT
bracis-33567	360	13	v.	v.	PROPN
bracis-33567	360	14	,	,	PUNCT
bracis-33567	360	15	xiao	xiao	PROPN
bracis-33567	360	16	,	,	PUNCT
bracis-33567	360	17	k.y	k.y	PROPN
bracis-33567	360	18	.	.	PROPN
bracis-33567	360	19	,	,	PUNCT
bracis-33567	360	20	tedrake	tedrake	PROPN
bracis-33567	360	21	,	,	PUNCT
bracis-33567	360	22	r.	r.	PROPN
bracis-33567	360	23	:	:	PUNCT
bracis-33567	360	24	evaluating	evaluate	VERB
bracis-33567	360	25	robustness	robustness	NOUN
bracis-33567	360	26	of	of	ADP
bracis-33567	360	27	neural	neural	ADJ
bracis-33567	360	28	networks	network	NOUN
bracis-33567	360	29	with	with	ADP
bracis-33567	360	30	mixed	mixed	ADJ
bracis-33567	360	31	integer	integer	NOUN
bracis-33567	360	32	programming	programming	NOUN
bracis-33567	360	33	.	.	PUNCT
bracis-33567	361	1	in	in	ADP
bracis-33567	361	2	:	:	PUNCT
bracis-33567	361	3	7th	7th	ADJ
bracis-33567	361	4	iclr	iclr	NOUN
bracis-33567	361	5	(	(	PUNCT
bracis-33567	361	6	2019	2019	NUM
bracis-33567	361	7	)	)	PUNCT
bracis-33567	361	8	google	google	PROPN
bracis-33567	361	9	scholar	scholar	NOUN
bracis-33567	361	10	  	  	SPACE
bracis-33567	361	11	wu	wu	PROPN
bracis-33567	361	12	,	,	PUNCT
bracis-33567	361	13	m.	m.	NOUN
bracis-33567	361	14	,	,	PUNCT
bracis-33567	361	15	wu	wu	PROPN
bracis-33567	361	16	,	,	PUNCT
bracis-33567	361	17	h.	h.	PROPN
bracis-33567	361	18	,	,	PUNCT
bracis-33567	361	19	barrett	barrett	PROPN
bracis-33567	361	20	,	,	PUNCT
bracis-33567	361	21	c.	c.	PROPN
bracis-33567	361	22	:	:	PUNCT
bracis-33567	361	23	verix	verix	PROPN
bracis-33567	361	24	:	:	PUNCT
bracis-33567	361	25	towards	towards	ADP
bracis-33567	361	26	verified	verify	VERB
bracis-33567	361	27	explainability	explainability	NOUN
bracis-33567	361	28	of	of	ADP
bracis-33567	361	29	deep	deep	ADJ
bracis-33567	361	30	neural	neural	ADJ
bracis-33567	361	31	networks	network	NOUN
bracis-33567	361	32	.	.	PUNCT
bracis-33567	362	1	in	in	ADP
bracis-33567	362	2	:	:	PUNCT
bracis-33567	362	3	37th	37th	ADJ
bracis-33567	362	4	neurips	neurip	NOUN
bracis-33567	362	5	(	(	PUNCT
bracis-33567	362	6	2023	2023	NUM
bracis-33567	362	7	)	)	PUNCT
bracis-33567	362	8	google	google	NOUN
bracis-33567	362	9	scholar	scholar	NOUN
bracis-33567	362	10	  	  	SPACE
bracis-33567	362	11	download	download	NOUN
bracis-33567	362	12	references	reference	NOUN
bracis-33567	362	13	author	author	NOUN
bracis-33567	362	14	information	information	NOUN
bracis-33567	362	15	authors	author	NOUN
bracis-33567	362	16	and	and	CCONJ
bracis-33567	362	17	affiliations	affiliation	NOUN
bracis-33567	362	18	instituto	instituto	PROPN
bracis-33567	362	19	federal	federal	PROPN
bracis-33567	362	20	do	do	AUX
bracis-33567	362	21	ceará	ceará	NOUN
bracis-33567	362	22	(	(	PUNCT
bracis-33567	362	23	ifce	ifce	PROPN
bracis-33567	362	24	)	)	PUNCT
bracis-33567	362	25	,	,	PUNCT
bracis-33567	362	26	fortaleza	fortaleza	PROPN
bracis-33567	362	27	,	,	PUNCT
bracis-33567	362	28	brazil	brazil	PROPN
bracis-33567	362	29	levi	levi	PROPN
bracis-33567	362	30	cordeiro	cordeiro	PROPN
bracis-33567	362	31	carvalho	carvalho	PROPN
bracis-33567	362	32	,	,	PUNCT
bracis-33567	362	33	 	 	SPACE
bracis-33567	362	34	saulo	saulo	PROPN
bracis-33567	362	35	a.	a.	PROPN
bracis-33567	362	36	f.	f.	PROPN
bracis-33567	362	37	oliveira	oliveira	PROPN
bracis-33567	362	38	 	 	SPACE
bracis-33567	362	39	&	&	CCONJ
bracis-33567	362	40	 	 	SPACE
bracis-33567	362	41	thiago	thiago	PROPN
bracis-33567	362	42	alves	alves	PROPN
bracis-33567	362	43	rocha	rocha	PROPN
bracis-33567	362	44	authors	author	NOUN
bracis-33567	362	45	levi	levi	PROPN
bracis-33567	362	46	cordeiro	cordeiro	PROPN
bracis-33567	362	47	carvalhoview	carvalhoview	PROPN
bracis-33567	362	48	author	author	NOUN
bracis-33567	362	49	publications	publication	NOUN
bracis-33567	362	50	search	search	NOUN
bracis-33567	362	51	author	author	NOUN
bracis-33567	362	52	on	on	ADP
bracis-33567	362	53	:	:	PUNCT
bracis-33567	362	54	pubmed	pubmed	PROPN
bracis-33567	362	55	 	 	SPACE
bracis-33567	362	56	google	google	PROPN
bracis-33567	362	57	scholar	scholar	PROPN
bracis-33567	362	58	saulo	saulo	PROPN
bracis-33567	362	59	a.	a.	PROPN
bracis-33567	362	60	f.	f.	PROPN
bracis-33567	362	61	oliveiraview	oliveiraview	PROPN
bracis-33567	362	62	author	author	NOUN
bracis-33567	362	63	publications	publication	NOUN
bracis-33567	362	64	search	search	NOUN
bracis-33567	362	65	author	author	NOUN
bracis-33567	362	66	on	on	ADP
bracis-33567	362	67	:	:	PUNCT
bracis-33567	362	68	pubmed	pubmed	PROPN
bracis-33567	362	69	 	 	SPACE
bracis-33567	362	70	google	google	PROPN
bracis-33567	362	71	scholar	scholar	NOUN
bracis-33567	362	72	thiago	thiago	PROPN
bracis-33567	362	73	alves	alves	PROPN
bracis-33567	362	74	rochaview	rochaview	PROPN
bracis-33567	362	75	author	author	NOUN
bracis-33567	362	76	publications	publication	NOUN
bracis-33567	362	77	search	search	NOUN
bracis-33567	362	78	author	author	NOUN
bracis-33567	362	79	on	on	ADP
bracis-33567	362	80	:	:	PUNCT
bracis-33567	362	81	pubmed	pubmed	PROPN
bracis-33567	362	82	 	 	SPACE
bracis-33567	362	83	google	google	PROPN
bracis-33567	362	84	scholar	scholar	NOUN
bracis-33567	362	85	corresponding	correspond	VERB
bracis-33567	362	86	author	author	NOUN
bracis-33567	362	87	correspondence	correspondence	NOUN
bracis-33567	362	88	to	to	ADP
bracis-33567	362	89	thiago	thiago	PROPN
bracis-33567	362	90	alves	alves	PROPN
bracis-33567	362	91	rocha	rocha	PROPN
bracis-33567	362	92	.	.	PUNCT
bracis-33567	363	1	editor	editor	NOUN
bracis-33567	363	2	information	information	NOUN
bracis-33567	363	3	editors	editor	NOUN
bracis-33567	363	4	and	and	CCONJ
bracis-33567	363	5	affiliations	affiliation	NOUN
bracis-33567	363	6	universidade	universidade	VERB
bracis-33567	363	7	federal	federal	PROPN
bracis-33567	363	8	fluminense	fluminense	PROPN
bracis-33567	363	9	,	,	PUNCT
bracis-33567	363	10	niterói	niterói	PROPN
bracis-33567	363	11	,	,	PUNCT
bracis-33567	363	12	brazil	brazil	PROPN
bracis-33567	363	13	aline	aline	PROPN
bracis-33567	363	14	paes	paes	PROPN
bracis-33567	363	15	instituto	instituto	PROPN
bracis-33567	363	16	tecnológico	tecnológico	PROPN
bracis-33567	363	17	de	de	PROPN
bracis-33567	363	18	aeronáutica	aeronáutica	PROPN
bracis-33567	363	19	,	,	PUNCT
bracis-33567	363	20	são	são	PROPN
bracis-33567	363	21	josé	josé	PROPN
bracis-33567	363	22	dos	dos	PROPN
bracis-33567	363	23	campos	campos	PROPN
bracis-33567	363	24	,	,	PUNCT
bracis-33567	363	25	brazil	brazil	PROPN
bracis-33567	363	26	filipe	filipe	PROPN
bracis-33567	363	27	a.	a.	PROPN
bracis-33567	363	28	n.	n.	PROPN
bracis-33567	363	29	verri	verri	PROPN
bracis-33567	363	30	rights	right	NOUN
bracis-33567	363	31	and	and	CCONJ
bracis-33567	363	32	permissions	permission	NOUN
bracis-33567	363	33	reprints	reprint	NOUN
bracis-33567	363	34	and	and	CCONJ
bracis-33567	363	35	permissions	permission	VERB
bracis-33567	363	36	copyright	copyright	NOUN
bracis-33567	363	37	information	information	NOUN
bracis-33567	363	38	©	©	ADP
bracis-33567	363	39	2025	2025	NUM
bracis-33567	363	40	the	the	DET
bracis-33567	363	41	author(s	author(s	NOUN
bracis-33567	363	42	)	)	PUNCT
bracis-33567	363	43	,	,	PUNCT
bracis-33567	363	44	under	under	ADP
bracis-33567	363	45	exclusive	exclusive	ADJ
bracis-33567	363	46	license	license	NOUN
bracis-33567	363	47	to	to	ADP
bracis-33567	363	48	springer	springer	NOUN
bracis-33567	363	49	nature	nature	PROPN
bracis-33567	363	50	switzerland	switzerland	PROPN
bracis-33567	363	51	ag	ag	PROPN
bracis-33567	363	52	about	about	ADP
bracis-33567	363	53	this	this	DET
bracis-33567	363	54	paper	paper	NOUN
bracis-33567	363	55	cite	cite	VERB
bracis-33567	363	56	this	this	DET
bracis-33567	363	57	paper	paper	NOUN
bracis-33567	363	58	carvalho	carvalho	NOUN
bracis-33567	363	59	,	,	PUNCT
bracis-33567	363	60	l.c	l.c	PROPN
bracis-33567	363	61	.	.	PROPN
bracis-33567	363	62	,	,	PUNCT
bracis-33567	363	63	oliveira	oliveira	PROPN
bracis-33567	363	64	,	,	PUNCT
bracis-33567	363	65	s.a.f	s.a.f	PROPN
bracis-33567	363	66	.	.	PROPN
bracis-33567	363	67	,	,	PUNCT
bracis-33567	363	68	rocha	rocha	PROPN
bracis-33567	363	69	,	,	PUNCT
bracis-33567	363	70	t.a	t.a	PROPN
bracis-33567	363	71	.	.	PROPN
bracis-33567	363	72	(	(	PUNCT
bracis-33567	363	73	2025	2025	NUM
bracis-33567	363	74	)	)	PUNCT
bracis-33567	363	75	.	.	PUNCT
bracis-33567	364	1	comparing	compare	VERB
bracis-33567	364	2	neural	neural	ADJ
bracis-33567	364	3	network	network	NOUN
bracis-33567	364	4	encodings	encoding	NOUN
bracis-33567	364	5	for	for	ADP
bracis-33567	364	6	 	 	SPACE
bracis-33567	364	7	logic	logic	NOUN
bracis-33567	364	8	-	-	PUNCT
bracis-33567	364	9	based	base	VERB
bracis-33567	364	10	explainability	explainability	NOUN
bracis-33567	364	11	.	.	PUNCT
bracis-33567	365	1	in	in	ADP
bracis-33567	365	2	:	:	PUNCT
bracis-33567	365	3	paes	paes	PROPN
bracis-33567	365	4	,	,	PUNCT
bracis-33567	365	5	a.	a.	PROPN
bracis-33567	365	6	,	,	PUNCT
bracis-33567	365	7	verri	verri	NOUN
bracis-33567	365	8	,	,	PUNCT
bracis-33567	365	9	f.a.n	f.a.n	ADJ
bracis-33567	365	10	.	.	PUNCT
bracis-33567	365	11	(	(	PUNCT
bracis-33567	365	12	eds	ed	NOUN
bracis-33567	365	13	)	)	PUNCT
bracis-33567	365	14	intelligent	intelligent	ADJ
bracis-33567	365	15	systems	system	NOUN
bracis-33567	365	16	.	.	PUNCT
bracis-33567	365	17	bracis	bracis	PROPN
bracis-33567	365	18	2024	2024	NUM
bracis-33567	365	19	.	.	PUNCT
bracis-33567	366	1	lecture	lecture	NOUN
bracis-33567	366	2	notes	note	NOUN
bracis-33567	366	3	in	in	ADP
bracis-33567	366	4	computer	computer	NOUN
bracis-33567	366	5	science	science	NOUN
bracis-33567	366	6	(	(	PUNCT
bracis-33567	366	7	)	)	PUNCT
bracis-33567	366	8	,	,	PUNCT
bracis-33567	366	9	vol	vol	NOUN
bracis-33567	366	10	15412	15412	NUM
bracis-33567	366	11	.	.	PUNCT
bracis-33567	367	1	springer	springer	NOUN
bracis-33567	367	2	,	,	PUNCT
bracis-33567	367	3	cham	cham	PROPN
bracis-33567	367	4	.	.	PUNCT
bracis-33567	368	1	https://doi.org/10.1007/978-3-031-79029-4_20	https://doi.org/10.1007/978-3-031-79029-4_20	PROPN
bracis-33567	368	2	download	download	NOUN
bracis-33567	368	3	citation	citation	NOUN
bracis-33567	368	4	.ris	.ris	PUNCT
bracis-33567	368	5	.enw	.enw	PROPN
bracis-33567	368	6	.bib	.bib	PUNCT
bracis-33567	369	1	doi	doi	PROPN
bracis-33567	369	2	:	:	PUNCT
bracis-33567	369	3	https://doi.org/10.1007/978-3-031-79029-4_20	https://doi.org/10.1007/978-3-031-79029-4_20	PROPN
bracis-33567	369	4	published	publish	VERB
bracis-33567	369	5	:	:	PUNCT
bracis-33567	369	6	30	30	NUM
bracis-33567	369	7	january	january	PROPN
bracis-33567	369	8	2025	2025	NUM
bracis-33567	369	9	publisher	publisher	NOUN
bracis-33567	369	10	name	name	NOUN
bracis-33567	369	11	:	:	PUNCT
bracis-33567	369	12	springer	springer	NOUN
bracis-33567	369	13	,	,	PUNCT
bracis-33567	369	14	cham	cham	PROPN
bracis-33567	369	15	print	print	PROPN
bracis-33567	369	16	isbn	isbn	PROPN
bracis-33567	369	17	:	:	PUNCT
bracis-33567	369	18	978	978	NUM
bracis-33567	369	19	-	-	SYM
bracis-33567	369	20	3	3	NUM
bracis-33567	369	21	-	-	PUNCT
bracis-33567	369	22	031	031	NUM
bracis-33567	369	23	-	-	PUNCT
bracis-33567	369	24	79028	79028	NUM
bracis-33567	369	25	-	-	SYM
bracis-33567	369	26	7	7	NUM
bracis-33567	369	27	online	online	ADJ
bracis-33567	369	28	isbn	isbn	NOUN
bracis-33567	369	29	:	:	PUNCT
bracis-33567	369	30	978	978	NUM
bracis-33567	369	31	-	-	SYM
bracis-33567	369	32	3	3	NUM
bracis-33567	369	33	-	-	PUNCT
bracis-33567	369	34	031	031	NUM
bracis-33567	369	35	-	-	PUNCT
bracis-33567	369	36	79029	79029	NUM
bracis-33567	369	37	-	-	SYM
bracis-33567	369	38	4	4	NUM
bracis-33567	369	39	ebook	ebook	NOUN
bracis-33567	369	40	packages	package	NOUN
bracis-33567	369	41	:	:	PUNCT
bracis-33567	369	42	computer	computer	NOUN
bracis-33567	369	43	sciencecomputer	sciencecomputer	NOUN
bracis-33567	369	44	science	science	NOUN
bracis-33567	369	45	(	(	PUNCT
bracis-33567	369	46	r0	r0	NOUN
bracis-33567	369	47	)	)	PUNCT
bracis-33567	369	48	share	share	VERB
bracis-33567	369	49	this	this	DET
bracis-33567	369	50	paper	paper	NOUN
bracis-33567	369	51	anyone	anyone	PRON
bracis-33567	369	52	you	you	PRON
bracis-33567	369	53	share	share	VERB
bracis-33567	369	54	the	the	DET
bracis-33567	369	55	following	follow	VERB
bracis-33567	369	56	link	link	NOUN
bracis-33567	369	57	with	with	ADP
bracis-33567	369	58	will	will	AUX
bracis-33567	369	59	be	be	AUX
bracis-33567	369	60	able	able	ADJ
bracis-33567	369	61	to	to	PART
bracis-33567	369	62	read	read	VERB
bracis-33567	369	63	this	this	DET
bracis-33567	369	64	content	content	NOUN
bracis-33567	369	65	:	:	PUNCT
bracis-33567	369	66	get	get	VERB
bracis-33567	369	67	shareable	shareable	ADJ
bracis-33567	369	68	linksorry	linksorry	NOUN
bracis-33567	369	69	,	,	PUNCT
bracis-33567	369	70	a	a	DET
bracis-33567	369	71	shareable	shareable	ADJ
bracis-33567	369	72	link	link	NOUN
bracis-33567	369	73	is	be	AUX
bracis-33567	369	74	not	not	PART
bracis-33567	369	75	currently	currently	ADV
bracis-33567	369	76	available	available	ADJ
bracis-33567	369	77	for	for	ADP
bracis-33567	369	78	this	this	DET
bracis-33567	369	79	article	article	NOUN
bracis-33567	369	80	.	.	PUNCT
bracis-33567	370	1	copy	copy	VERB
bracis-33567	370	2	shareable	shareable	ADJ
bracis-33567	370	3	link	link	NOUN
bracis-33567	370	4	to	to	PART
bracis-33567	370	5	clipboard	clipboard	NOUN
bracis-33567	370	6	provided	provide	VERB
bracis-33567	370	7	by	by	ADP
bracis-33567	370	8	the	the	DET
bracis-33567	370	9	springer	springer	NOUN
bracis-33567	370	10	nature	nature	PROPN
bracis-33567	370	11	sharedit	sharedit	PROPN
bracis-33567	370	12	content	content	NOUN
bracis-33567	370	13	-	-	PUNCT
bracis-33567	370	14	sharing	share	VERB
bracis-33567	370	15	initiative	initiative	NOUN
bracis-33567	370	16	keywords	keyword	VERB
bracis-33567	370	17	artificial	artificial	ADJ
bracis-33567	370	18	neural	neural	ADJ
bracis-33567	370	19	networks	network	NOUN
bracis-33567	370	20	explainable	explainable	ADJ
bracis-33567	370	21	artificial	artificial	ADJ
bracis-33567	370	22	intelligence	intelligence	NOUN
bracis-33567	370	23	logic	logic	NOUN
bracis-33567	370	24	-	-	PUNCT
bracis-33567	370	25	based	base	VERB
bracis-33567	370	26	explainable	explainable	ADJ
bracis-33567	370	27	ai	ai	NOUN
bracis-33567	370	28	publish	publish	NOUN
bracis-33567	370	29	with	with	ADP
bracis-33567	370	30	us	us	PROPN
bracis-33567	370	31	policies	policy	NOUN
bracis-33567	370	32	and	and	CCONJ
bracis-33567	370	33	ethics	ethic	NOUN
bracis-33567	370	34	profiles	profile	NOUN
bracis-33567	370	35	saulo	saulo	PROPN
bracis-33567	370	36	a.	a.	PROPN
bracis-33567	370	37	f.	f.	PROPN
bracis-33567	370	38	oliveira	oliveira	PROPN
bracis-33567	370	39	view	view	PROPN
bracis-33567	370	40	author	author	NOUN
bracis-33567	370	41	profile	profile	NOUN
bracis-33567	370	42	search	search	NOUN
bracis-33567	370	43	search	search	NOUN
bracis-33567	370	44	by	by	ADP
bracis-33567	370	45	keyword	keyword	NOUN
bracis-33567	370	46	or	or	CCONJ
bracis-33567	370	47	author	author	NOUN
bracis-33567	370	48	search	search	NOUN
bracis-33567	370	49	navigation	navigation	NOUN
bracis-33567	370	50	find	find	VERB
bracis-33567	370	51	a	a	DET
bracis-33567	370	52	journal	journal	NOUN
bracis-33567	370	53	publish	publish	VERB
bracis-33567	370	54	with	with	ADP
bracis-33567	370	55	us	we	PRON
bracis-33567	370	56	track	track	VERB
bracis-33567	370	57	your	your	PRON
bracis-33567	370	58	research	research	NOUN
bracis-33567	370	59	discover	discover	VERB
bracis-33567	370	60	content	content	NOUN
bracis-33567	370	61	journals	journal	NOUN
bracis-33567	370	62	a	a	DET
bracis-33567	370	63	-	-	PUNCT
bracis-33567	370	64	z	z	NOUN
bracis-33567	370	65	books	book	NOUN
bracis-33567	370	66	a	a	DET
bracis-33567	370	67	-	-	PUNCT
bracis-33567	370	68	z	z	NOUN
bracis-33567	370	69	publish	publish	NOUN
bracis-33567	370	70	with	with	ADP
bracis-33567	370	71	us	us	PROPN
bracis-33567	370	72	journal	journal	PROPN
bracis-33567	370	73	finder	finder	PROPN
bracis-33567	370	74	publish	publish	VERB
bracis-33567	370	75	your	your	PRON
bracis-33567	370	76	research	research	NOUN
bracis-33567	370	77	language	language	NOUN
bracis-33567	370	78	editing	edit	VERB
bracis-33567	370	79	open	open	ADJ
bracis-33567	370	80	access	access	NOUN
bracis-33567	370	81	publishing	publishing	NOUN
bracis-33567	370	82	products	product	NOUN
bracis-33567	370	83	and	and	CCONJ
bracis-33567	370	84	services	service	NOUN
bracis-33567	370	85	our	our	PRON
bracis-33567	370	86	products	product	NOUN
bracis-33567	370	87	librarians	librarian	VERB
bracis-33567	370	88	societies	society	NOUN
bracis-33567	370	89	partners	partner	NOUN
bracis-33567	370	90	and	and	CCONJ
bracis-33567	370	91	advertisers	advertiser	NOUN
bracis-33567	370	92	our	our	PRON
bracis-33567	370	93	brands	brand	NOUN
bracis-33567	370	94	springer	springer	NOUN
bracis-33567	370	95	nature	nature	PROPN
bracis-33567	370	96	portfolio	portfolio	PROPN
bracis-33567	370	97	bmc	bmc	PROPN
bracis-33567	370	98	palgrave	palgrave	PROPN
bracis-33567	370	99	macmillan	macmillan	PROPN
bracis-33567	370	100	apress	apress	PROPN
bracis-33567	370	101	discover	discover	VERB
bracis-33567	370	102	your	your	PRON
bracis-33567	370	103	privacy	privacy	NOUN
bracis-33567	370	104	choices	choice	NOUN
bracis-33567	370	105	/	/	SYM
bracis-33567	370	106	manage	manage	NOUN
bracis-33567	370	107	cookies	cookie	NOUN
bracis-33567	370	108	your	your	PRON
bracis-33567	370	109	us	us	PROPN
bracis-33567	371	1	state	state	NOUN
bracis-33567	371	2	privacy	privacy	NOUN
bracis-33567	371	3	rights	right	NOUN
bracis-33567	371	4	accessibility	accessibility	NOUN
bracis-33567	371	5	statement	statement	NOUN
bracis-33567	371	6	terms	term	NOUN
bracis-33567	371	7	and	and	CCONJ
bracis-33567	371	8	conditions	condition	NOUN
bracis-33567	371	9	privacy	privacy	NOUN
bracis-33567	371	10	policy	policy	NOUN
bracis-33567	371	11	help	help	NOUN
bracis-33567	371	12	and	and	CCONJ
bracis-33567	371	13	support	support	VERB
bracis-33567	371	14	legal	legal	ADJ
bracis-33567	371	15	notice	notice	NOUN
bracis-33567	371	16	cancel	cancel	VERB
bracis-33567	371	17	contracts	contract	NOUN
bracis-33567	371	18	here	here	ADV
bracis-33567	371	19	129.74.145.123	129.74.145.123	NUM
bracis-33567	371	20	hesburgh	hesburgh	PROPN
bracis-33567	371	21	library	library	PROPN
bracis-33567	371	22	er	er	INTJ
bracis-33567	371	23	unit	unit	NOUN
bracis-33567	371	24	(	(	PUNCT
bracis-33567	371	25	3005732405	3005732405	NUM
bracis-33567	371	26	)	)	PUNCT
bracis-33567	371	27	northeast	northeast	ADJ
bracis-33567	371	28	research	research	NOUN
bracis-33567	371	29	libraries	library	NOUN
bracis-33567	371	30	(	(	PUNCT
bracis-33567	371	31	nerl	nerl	PROPN
bracis-33567	371	32	)	)	PUNCT
bracis-33567	371	33	(	(	PUNCT
bracis-33567	371	34	8200828607	8200828607	NUM
bracis-33567	371	35	)	)	PUNCT
bracis-33567	371	36	nerl	nerl	VERB
bracis-33567	371	37	ta	ta	X
bracis-33567	371	38	account	account	NOUN
bracis-33567	371	39	(	(	PUNCT
bracis-33567	371	40	3006206169	3006206169	NUM
bracis-33567	371	41	)	)	PUNCT
bracis-33567	371	42	university	university	NOUN
bracis-33567	371	43	of	of	ADP
bracis-33567	371	44	notre	notre	PROPN
bracis-33567	371	45	dame	dame	PROPN
bracis-33567	371	46	hesburgh	hesburgh	PROPN
bracis-33567	371	47	library	library	NOUN
bracis-33567	371	48	(	(	PUNCT
bracis-33567	371	49	3000184373	3000184373	NUM
bracis-33567	371	50	)	)	PUNCT
bracis-33567	372	1	©	©	ADP
bracis-33567	372	2	2025	2025	NUM
bracis-33567	372	3	springer	springer	NOUN
bracis-33567	372	4	nature	nature	NOUN