The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. The neural correlates of consciousness under the free energy principle From computational correlates to computational explanation Wanja Wiesea (wanja.wiese@rub.de) Karl J. Fristonb (k.friston@ucl.ac.uk) Abstract How can the free energy principle contribute to research on neural correlates of consciousness, and to the scientific study of consciousness more generally? Under the free energy principle, neural correlates should be defined in terms of neural dynamics, not neural states, and should be comple- mented by research on computational correlates of consciousness – defined in terms of probabilities encoded by neural states. We argue that these restrictions brighten the prospects of a computational explanation of con- sciousness, by addressing two central problems. The first is to account for consciousness in the absence of sensory stimulation and behaviour. The second is to allow for the possibility of systems that implement computations associated with consciousness, without being conscious, which re- quires differentiating between computational systems that merely simulate conscious beings and computational systems that are conscious in and of themselves. Given the notion of computation entailed by the free energy principle, we derive constraints on the ascription of consciousness in controversial cases (e.g., in the absence of sensory stimulation and behaviour). We show that this also has implications for what it means to be, as opposed to merely simulate a conscious system. Keywords Active inference ∙ Computational correlates of consciousness ∙ Computational explanation ∙ Consciousness ∙ Free energy principle ∙ Islands of awareness ∙ Minimal unifying model ∙ Neural correlates of consciousness This article is part of a special issue on “The Neural Correlates of Consciousness,” edited by Sascha Benjamin Fink and Ying-Tung Lin. aInstitute of Philosophy II, Ruhr-Universität Bochum bWellcome Centre for Human Neuroimaging, UCL Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://philosophymindscience.org https://orcid.org/0000-0003-3338-7398 https://orcid.org/0000-0001-7984-8909 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 2 1 Introduction The free energy principle (FEP, Friston, 2010) provides an information-theoretic analysis of the concept of existence of self-organising systems (Hohwy, 2020). It entails that self-organising systems at non-equilibrium steady state1 bound the en- tropy of their sensory signals by minimising – on average – a quantity known as variational free energy. As such, FEP is not a theory of consciousness. Con- sequently, it is not obvious that FEP has any relevance to research on neural cor- relates of consciousness (NCCs, see Chalmers, 2000). Furthermore, FEP is a com- putational principle;2 hence, it may seem even less relevant to investigating the neural structures associated with consciousness. Here, we will argue that FEP provides constraints on computational correlates of consciousness (CCCs, see Atkinson et al., 2000; Cleeremans, 2005; Mathis & Mozer, 1996; Reggia et al., 2016, 2019). CCCs specify computational properties instantiated by NCCs, and thereby provide some insights as to why a particular neural structure or type of activity is associated with consciousness. More specifically, we will argue that FEP supports the following three obser- vations with respect to the debate on NCCs and CCCs. (i) According to FEP, NCCs must be defined in terms of neural dynamics, not neural states. (ii) According to FEP, there is a relevant distinction to be made between the probabilities of neu- ral states (or of trajectories) and the probabilities encoded by neural states.3 These distinct families of probability distributions can be regarded as points on statisti- cal manifolds, with corresponding information geometries. In Friston, Wiese, et al. (2020), the information geometries – associated with the probabilities of states and with probabilities encoded by states – are called intrinsic and extrinsic informa- tion geometries, respectively. In line with this distinction, neural dynamics (with NCCs as a special case) pertain to movements on the intrinsic statistical manifold, whereas neural computations (with CCCs as a special case) pertain to movements on the extrinsic manifold. Furthermore, the computations ascribed to movements on the extrinsic manifold can be regarded as inferences or, more poetically, self- evidencing (Hohwy, 2016).4 (iii) Some candidates for CCCs that have been pro- 1A system is at non-equilibrium with its environment if it is in exchange with its environment. It is in steady state if it has characteristic features that remain invariant during this exchange, i.e., if it continues to exist. 2Technically, the FEP is a variational principle of stationary action. The “action” in question here is a path integral of a functional of probabilistic beliefs encoded by the internal states of a system. As such, FEP becomes a computational principle; in that the probabilistic beliefs in question are about something (i.e., the external states of a system). For a discussion of the relationship between FEP, computation, and representation, see Wiese & Friston (2021). 3A general, lucid analysis of the two kinds of information processing associated with probabilities of states (representational vehicles) and with probabilities represented by states (probabilities in represented content), respectively, is provided by Sprevak (2020). For a related, excellent discus- sion with respect to FEP, see Kiefer (2020). 4This is because every point on the extrinsic manifold is equipped with a free energy functional, namely a function of the probabilistic belief corresponding to that point. Crucially, this functional Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 3 posed in the literature are – from the point of view of FEP – just mathematical descriptions of NCCs. (iv) If a goal of research on correlates of consciousness is to infer the presence or absence of consciousness in controversial cases, then one should regard these correlates as necessary (not sufficient) conditions for con- sciousness. In particular, this holds for computational principles entailed by FEP. A key contribution to the debate that follows from these observations is that computational explanations of consciousness (or “explanatory correlates of con- sciousness,” Seth, 2009) must be specified with respect to the extrinsic information geometry. That is, a computational explanation of consciousness requires more than a formal description of neural dynamics. It must also specify computations instantiated by these dynamics. Moreover, FEP has implications for the very idea of a computational explanation of mental phenomena. FEP not only specifies com- putations that have to be performed by self-organising systems at non-equilibrium steady state, but also entails that descriptions of these computations are equivalent to descriptions of physical systems interacting with their environment. Therefore, it provides additional constraints on what it means to be, as opposed to merely sim- ulate a member of a certain class of computational systems.5 This enables a non- trivial role for computational correlates in explanations of consciousness, without having to accept what David Chalmers (2011) calls the thesis of computational suffi- ciency (according to which the right computational structure is sufficient for mind and consciousness). In particular, our account is compatible with the possibility of synthetic phenomenology, but does not entail that every computer that performs the right computations is conscious. Although FEP itself does not provide an explanation of consciousness, it pro- vides a quantitative framework within which models and measures of conscious- ness can be developed. More specifically, process theories conforming to FEP, such as active inference (Friston et al., 2017), can facilitate formulating and testing hy- potheses about necessary computational mechanisms that may underpin different cognitive capacities, or different measures of consciousness. Because of the broad applicability of the framework (for a recent overview, see Costa, Parr, et al., 2020), completely different cognitive or formal properties associated with consciousness can be modelled and analysed. Since all models that conform to FEP describe the phenomena that are modelled as ways of minimising free energy, FEP provides a unifying perspective (Hohwy & Seth, 2020) from which it becomes tractable to determine what necessary computational mechanisms the different phenomena have in common (Wiese, 2018). (function of a function) is an upper bound on surprisal. Equivalently, the negative free energy constitutes a lower bound on model evidence (a.k.a. marginal likelihood) in Bayesian statistics. 5This means FEP not only provides the foundation of a framework for consciousness, but also building blocks for a theory of consciousness. This contrasts with the proposal in Hohwy & Seth (2020), according to which predictive processing (PP) only provides a framework for research on consciousness (and NCCs), without itself being a theory of consciousness. (Although Hohwy and Seth suggest that “aspects of PP may themselves coalesce into a theory of consciousness in its own right,” Hohwy & Seth, 2020, p. 24.) Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 4 The rest of this paper is structured as follows. In section 2, we review the canonical notion of an NCC, as defined by Chalmers (2000). We highlight three challenges for research on neural correlates and suggest that these challenges can be overcome by research on computational correlates of consciousness (CCCs). In section 3, we discuss research on CCCs (section 3.1) and argue that some compu- tational principles associated with consciousness (Cleeremans, 2005) are already entailed by FEP (or by FEP and further, general assumptions; section 3.2). This is one reason why CCCs should be regarded as necessary conditions for conscious- ness (not sufficient conditions; section 3.3). Furthermore, we take up a special case of a challenge identified in section 2, viz. the challenge of “islands of aware- ness” (Bayne et al., 2020). We argue that FEP furnishes a constraint on the as- cription of consciousness in such unusual cases: according to FEP, such systems must minimise the statistical complexity of their internal model (section 3.4). Since empirical evidence suggests that activity in conscious systems has high dynamical complexity, we briefly discuss how these notions relate to one another and suggest that it should be possible to define dynamical complexity in terms of a system’s extrinsic information geometry (section 3.5). The benefit of such a definition is that it would provide not just a fundamental theoretical motivation for associating consciousness with dynamical complexity, but also the basis for a computational explanation of consciousness. The explanatory value of FEP is a matter of contro- versy. Hence, in section 4, we explain what contribution FEP would make to a computational explanation of consciousness. Finally, in section 5, we discuss its potential role in developing a minimal unifying model of consciousness, following a suggestion made in Wiese (2020). 2 From neural correlates to computational corre- lates of consciousness According to the canonical notion of an NCC, as defined by Chalmers (2000), “[a]n NCC is a minimal neural system N such that there is a mapping from states of N to states of consciousness, where a given state of N is sufficient under conditions C, for the corresponding state of consciousness” (Chalmers, 2000, p. 31). A classic example of an NCC is provided by Crick & Koch (1990), who hypothesized that synchronised oscillations (in a range around 40–70 Hz) in parts of visual cortex may underpin visual consciousness. The neural system N would be visual cortex (or parts of it). States of – or, rather, activity in – visual cortex corresponding to visual experiences would be synchronised oscillations within a certain frequency. Note that the definition cited above is a general definition for neural correlates of states of consciousness. That is, it can be applied to neural differences between consciousness and the absence of consciousness, as well as to neural differences between background states, such as wakefulness, dreaming, or hypnosis, or be- tween particular conscious experiences, such as smelling coffee, hearing a voice, Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 5 seeing a face, or seeing a house. In addition to this general notion, Chalmers (2000) proposes a more specific definition for neural correlates of individual contents of consciousness. In what follows, we shall focus on the general definition, because some parts of our discussion mainly apply to neural correlates of global states of consciousness (e.g., being conscious vs. unconscious, being awake vs. dreaming, etc.). We entertain three challenges for Chalmers’ general definition of an NCC. The aim of this discussion is not to argue that the definition is problematic.6 Instead, we wish to highlight the virtues of computational correlates of consciousness (CCCs, Cleeremans, 2005; Reggia et al., 2016). CCCs, as understood here, are not defined in terms of neural structures, but in terms of computational properties that can be instantiated by different substrates. CCCs are thus more general and promise to be more explanatory than NCCs. However, they also pose challenges of their own. 2.1 Challenge 1: Global dynamics The definition of an NCC cited above is meant to pick out core correlates of con- sciousness. An implicit hypothesis is that the difference between neural activity that is associated with consciousness, and neural activity that is not, can be speci- fied in terms of a difference in the neural systems involved, as well as by differences in the type of activity (“states”) instantiated by these systems. This hypothesis is challenged by theoretical considerations, according to which states cannot be mapped to conscious experiences, but only trajectories (Fekete & Edelman, 2011); furthermore, it is in tension with considerations that privilege global (as opposed to local) processes (Mashour et al., 2020; Tononi et al., 2016).7 Recent empirical approaches support such theoretical considerations, by high- lighting global dynamics that are associated with consciousness. Examples include differences in functional connectivity (Huang et al., 2020; Luppi et al., 2019) or in the power spectral density of resting EEG (Colombo et al., 2019; He et al., 2010). A further example is given by research on differences between global neural dy- namics and state transitions during wakefulness and non-REM sleep (Stevner et al., 2019), or global dynamics during wakefulness and different types of unrespon- 6Some of these challenges are explicitly mentioned in Chalmers (2000) already; for discussions of Chalmers’ definition, and NCC research more generally, see Noë & Thompson (2004); Block (2005); Miller (2007); Tononi & Koch (2008); Hohwy (2009); Seth (2009); Aru et al. (2012); Tsuchiya et al. (2015); Koch et al. (2016); Fink (2016); Mashour (2018). 7Chalmers’ definition of an NCC is compatible with this possibility: it may turn out that the min- imal neural system that is sufficient for states of consciousness is the entire brain. However, the possibility also illustrates that NCCs, defined in terms of neural systems, may be less informative if consciousness mainly depends on how neural activity evolves over a certain period of time, and depends less on where in the brain the neural activity takes place. The virtue of computational correlates is that they can be informative regardless of whether they describe properties of the entire brain or of small regions in the brain. Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 6 siveness, such as anaesthesia, unresponsive wakefulness syndrome, or minimally conscious states (Demertzi et al., 2019). Computational correlates are not defined in terms of neural structures, and hence are neutral with respect to the question whether conscious experiences cor- relate with global neural activity or not. Furthermore, they are compatible with the possibility that neural state transitions are more important than the states them- selves. Hence, computational correlates promise progress on the challenge of ac- counting for global dynamics associated with consciousness. 2.2 Challenge 2: Non-arbitrary mappings A further challenge consists in determining why a particular neural structure N is an NCC of consciousness (see Hohwy & Seth, 2020). Chalmers’ (2000) definition only requires that there be a mapping between neural states and states of con- sciousness. This mapping can, as Chalmers himself points out, be “seemingly arbi- trary” (Chalmers, 2000, p. 23). The mapping can be arbitrary in the sense that there seems to be no epistemically necessary connection between certain neural states and states of consciousness; however, such mappings will be non-arbitrary in the sense that the connection must be general and lawful: states of an NCC, as defined by Chalmers, must be sufficient for states of consciousness, given certain general conditions. Finding arbitrary mappings between neural states and conscious expe- riences can help illuminate how consciousness arises in human beings, but it will not lead to a deep understanding of consciousness. Chalmers (2000, p. 23) suggests that a non-arbitrary mapping could be estab- lished if not only neural states themselves are mapped to states of consciousness, but if also relations between neural states are mapped to relations between con- scious states (a recent approach pursuing this idea using category theory is pre- sented in Northoff et al., 2019). Drawing on such a mapping, one can extrapolate from existing NCCs to predict how certain changes in neural activity will change the correlated conscious experience (a similar idea, though not using the notion of an NCC, is explored in Churchland, 2005). CCCs provide another way of increasing explanatory and predictive power. If it is shown that neural activity associated with consciousness implements certain computations, then this provides an explanation of why that activity is associated with consciousness. In principle, this can then be used to predict the presence (or absence) of consciousness in novel (or controversial) cases. This brings us to the final challenge we will consider here. 2.3 Challenge 3: Unusual conditions A problem for research on NCCs consists in specifying the conditions under which a correlation between neural and conscious states exists. Chalmers’ (2000) defini- tion circumvents this problem to some extent, in that his definition only requires Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 7 that the states of an NCC be sufficient for conscious states. It does not require that they be necessary. If, by contrast, a perfect positive correlation between states of an NCC and states of consciousness were required, then states of an NCC would also have to be necessary. However, even a (mere) sufficiency requirement is challenged by unusual cases. Perhaps a certain type of neural activity goes along with consciousness in ordinary cases, but does not when brain functioning is affected by lesions? Chalmers an- ticipates this challenge and restricts the required mapping between neural states and conscious states (i) to ordinary functioning brains in ordinary environments, (ii) with unusual inputs, and (iii) under local brain stimulation. Although this restriction creates a safe methodological footing for research on NCCs, it also comes with a limitation. Ideally, we would like to go beyond usual cases, and make inferences about unusual cases. For instance, we would like to know whether an unresponsive patient is non-conscious, or whether they are just unable to report their conscious experience. Failing to find neural activity that is sufficient for consciousness cannot rule out that the patient is conscious. This would be different if an NCC provided a necessary condition for consciousness. An extreme case of an unusual condition is exemplified by the possibility of consciousness in the complete absence of both sensory stimulation and observ- able behaviour. Bayne et al. (2020) call such cases “islands of awareness” (IOA). The authors define an IOA as a “conscious stream (or system) whose contents are not shaped by sensory input from either the external world or the body and which cannot be expressed via motor output” (Bayne et al., 2020, p. 7). Cases such as dreaming or locked-in syndrome provide an approximation to IOAs (but not com- plete IOAs), in which some connections to the environment (via sensory input or motor output) remain. Genuine IOAs could, as the authors point out, be found in ex cranio brains, hemispherotomy, or cerebral organoids (Bayne et al., 2020, pp. 6–11). An ex cranio brain is a brain that has been extracted from the cranium and is kept alive outside of the body (post-mortem). An example can be found in a study by Vrselja et al. (2019), who extracted pig brains and observed “spontaneous synaptic activity” (Vrselja et al., 2019, p. 336) in them. In hemispherotomy (De Ribaupierre & Delalande, 2008), a cortical hemisphere is more or less disconnected from the rest of the brain, leaving only vascular connectivity intact. A cerebral organoid is a neural structure grown in the lab (Lancaster et al., 2013). How would one determine whether conscious experience is sustained in such isolated systems? NCCs can provide some guideline, at least if activity that has been found to be sufficient for consciousness in ordinary cases is measured in IOAs, as well. However, it would be desirable to have additional criteria for the ascription of consciousness, ideally ones that are also necessary. Bayne et al. (2020) suggest using measures of dynamical complexity, which have been found to be reliable proxies for consciousness (and its absence, respectively), across a variety of conditions (Demertzi et al., 2019; Li & Mashour, 2019; Schartner et al., 2015; Schartner et al., 2017; Sitt et al., 2014). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 8 For this reason, we shall take a closer look at the concept of dynamical com- plexity in the following section. In particular, we will discuss whether it can be regarded as a computational correlate of consciousness. We will also revisit the challenge of IOAs, as this challenge is especially helpful for discussing the rele- vance of FEP to research on NCCs and CCCs: an application of FEP to IOAs seems to suggest that IOAs must minimise complexity, whereas empirical research sug- gests that conscious systems (and hence also IOAs) display high complexity. We shall argue that this apparent tension is resolved upon a closer look; in fact, free energy minimising systems are ipso facto capable of producing activity with dy- namical complexity – and certain kinds of systems are stipulatively defined by their complex dynamics.8 3 Computational correlates of consciousness and the free energy principle A computational correlate of consciousness (CCC) is a set of computational prop- erties that are associated with consciousness. Such properties are specified by computational models. Below we will argue that CCCs should be construed as necessary conditions for consciousness. This constitutes a major departure from the concept of an NCCs, which is usually regarded as a (minimally) sufficient con- dition for consciousness. As we point out below (in section 3.2), this conforms to how the notion of a CCC is construed in the literature. Furthermore, necessary con- ditions for consciousness have some advantages that merely sufficient conditions do not have (in particular, they can be used to infer the absence of consciousness, viz., if a necessary condition is not fulfilled in a given case, see Fink, 2016). Although characterising CCCs in terms of “computational properties associ- ated with consciousness” is relatively general and vague, it already shows that the first two challenges identified above can be overcome by CCCs. A CCC can be specified by a computational model of global neural dynamics, thereby meeting the first challenge. In addition, CCCs are non-arbitrary in the sense that they de- scribe computational functions that are realised by neural activity, which can help explain cognitive capacities associated with consciousness (see section 5 below for more details). The second challenge can therefore also be met by CCCs.9 In order to enrich the general characterisation of a CCC just given, we first review an in- fluential paper by Cleeremans (2005) on CCCs. We then connect some of the ideas presented in that paper to FEP and explain how the notion of a CCC would be conceived from the point of view of FEP. 8There can still be large differences in the level of complexity displayed by different systems. That is, differences in the level of complexity may still account for differences in consciousness. 9Of course, CCCs may still seem arbitrary in the sense that they do not directly address the hard problem (Chalmers, 1995). A complete computational explanation of consciousness, based on CCCs, must therefore also address the meta-problem (Chalmers, 2018). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 9 3.1 CCCs and computational principles Cleeremans (2005) takes the “contrastive approach to consciousness” as a starting point and argues that the study of the correlates of consciousness must go be- yond differences in neural activity, by including differences in computations (and behaviour) that are associated with consciousness (see Cleeremans, 2005, p. 84). Following Mathis & Mozer (1996), he refers to these computations as the compu- tational correlates of consciousness. Based on this idea, Cleeremans suggests two relatively general “computational principles” associated with consciousness. The first principle, “quality of representation,” is defined in terms of a repre- sentation’s “stability in time, strength, and distinctiveness” (Cleeremans, 2005, pp. 91–92). The stability of a representation corresponds to the amount of time for which its contents are available. The strength of a representation is a property of its vehicles and corresponds to the number of “processing units” of which it consists, as well as of their activation strength (Cleeremans, 2005, p. 92). Dis- tinctiveness is primarily a content property, namely its specificity. According to Cleeremans’ second principle, consciousness involves meta-representations. Why are these two computational principles important? One reason is that they refer to properties that can help explain how presumed functions of con- sciousness are realised. The functions mentioned by Cleeremans (2005) include: “flexible, adaptive control over action,” simulating possible actions and their conse- quences, and “error-correcting functions” (Cleeremans, 2005, p. 85). High-quality representations, as characterised by the first principle, are required for control over action and planning, and error correction requires meta-representation (because representations of error are meta-representational, see Shea, 2012b). The benefit of these general computational principles is that they make rela- tively little assumptions about consciousness but can still provide some guidance for specific computational models of consciousness. Furthermore, they can sug- gest why a given type of activity correlates with consciousness: if the neural pop- ulations involved can be interpreted as a representation having the properties de- scribed by the two principles, and if this helps explain a given type of behaviour (a behavioural correlate of consciousness), then we understand (to some extent), why the measured neural activity is associated with consciousness. The generality of these computational principles also has a disadvantage: the properties described by them may be necessary for many types of conscious ex- perience, but probably not sufficient. In particular, stability, strength, and meta- representation may be individually necessary, but it is unclear whether any combi- nation of (individually necessary) CCCs would be sufficient for consciousness. In other words, a complete explanation of consciousness would require more (Cleere- mans et al., 2020). At the same time, it could even be questioned whether the prop- erties are necessary. In order to address this question, we show to what extent, and under what assumptions, some computational principles can be derived from first principles. Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 10 3.2 Deriving computational principles from first principles Here, we shall succinctly summarise the gist of results presented in more detail elsewhere (see especially Friston, 2019b; Friston, Wiese, et al., 2020). This will show that some properties highlighted by the two computational principles given above are already instantiated by a very general class of systems, comprising single-cell organisms, but also more complex systems, such as human beings. This under- scores that the computational principles reviewed above are not sufficient for con- sciousness (unless one is willing to ascribe consciousness to cellular organisms and similarly simple types of system). A general (coarse-grained) form in which a random dynamical system can be described is in terms of Langevin dynamics (Ao, 2008; Seifert, 2012; Sekimoto, 1998): ̇𝑥(𝜏 ) = 𝑓 (𝑥, 𝜏 ) + 𝜔. Here, the state of the system 𝑥(𝜏 ) at time 𝜏 is constituted by slowly-changing macroscopic variables, which are grounded in microscopic variables with faster dy- namics. This is why the result is a stochastic differential equation, comprising not only the state-dependent flow 𝑓, but also a stochastic term 𝜔 (which is a Gaussian stochastic term with mean equal to zero and covariance 2Γ – so Γ is the amplitude of the random fluctuation). The fundamental assumption we shall make here is that things that persist must have measurable properties that remain invariant over a certain amount of time. Formally, this means that the system’s long-term behaviour can be described with reference to a global random attractor (or pullback attractor). Put differently, there is a (random) set of states to which the system will converge. Since the attractor is a random set, it can be described in terms of a density, its non-equilibrium steady- state (NESS) density. The NESS density is a solution to the Fokker-Planck equation (for details, see Friston, 2019b): ̇𝑝(𝑥, 𝜏 ) = ∇ ⋅ (Γ∇ − 𝑓 )𝑝(𝑥, 𝜏 ) The NESS density will be a density 𝑝(𝑥, 𝜏 ) that does not change over time, i.e. ̇𝑝(𝑥, 𝜏 ) = ∇ ⋅ (Γ∇ − 𝑓 )𝑝(𝑥, 𝜏 ) = 0. A solution to the Fokker-Planck equation satisfying ̇𝑝(𝑥, 𝜏 ) = 0 is 𝑝(𝑥, 𝜏 ) = exp(−ℑ(𝑥, 𝜏 )), where ℑ(𝑥) is self-information (or surprisal): ℑ(𝑥) = − ln 𝑝(𝑥). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 11 This means we can express the flow 𝑓 in terms of surprisal (and hence, in terms of the NESS density): 𝑓 (𝑥) = (𝑄(𝑥) − Γ) ⋅ ∇ℑ(𝑥) = (Γ − 𝑄(𝑥)) ⋅ ∇ ln 𝑝(𝑥). Here, 𝑄 denotes solenoidal flow. Furthermore, following a variational principle of least action, the ensuing dynamics are a gradient flow on surprisal. In other words – on average – the dynamics minimise self-information (surprisal) ℑ(𝑥) (Friston, 2019b, pp. 12–13). To recap, anything that exists will have characteristic features that do not change over time. Formally, we express this by assuming that the system is a ran- dom dynamical system in non-equilibrium steady state (NESS). This means that the system is in exchange with its environment and that its dynamics can be de- scribed in terms of its NESS probability density, i.e., a probability distribution that does not change during the time over which the system is said to exist. Such a sys- tem has a random attractor, which can be thought of in two ways: first, it can be considered as the trajectory of systemic states as they evolve over time. Here, the key aspect is that the system will, after sufficient time, revisit particular regions of its state space, i.e., those regions that constitute the attracting set. The second interpretation considers the random attractor as subtending a probability density 𝑝 over the states that the system will be found in, when sampled at random. The density dynamics are described by the Fokker-Planck equation. In nonequilibrium steady state, this density does not change with time. The solution (i.e., setting the equation to zero) shows that there is a lawful relationship between the flow of states 𝑓 and the probability density 𝑝. A further assumption we shall make is that the system possesses a Markov blan- ket. A Markov blanket can be conceived as a boundary between a system and its environment. It is defined as that set of states that statistically separate a system’s internal states from external states: the system’s internal states 𝜇 are conditionally independent of external states 𝜂, given the Markov blanket 𝑏. Here, the Markov blanket 𝑏 = {𝑠, 𝑎} comprises both sensory states 𝑠 (which are not directly influ- enced by internal states) and active states 𝑎 (which are not directly influenced by external states). Note that internal, external, and blanket states jointly constitute the systemic states 𝑥 = {𝜂, 𝑠, 𝑎, 𝜇}. The term “Markov blanket” was originally coined by Pearl (1988), in the context of Bayesian networks, i.e., directed acyclic graphs. However, the notion can also be applied to directed cyclic graphs (i.e., dependency networks) and undirected graphs (i.e., Markov random fields). For examples of applications of the notion, see Clark (2017), Palacios et al. (2017), Parr et al. (2020), Pellet & Elisseeff (2008).10 10In fact, there is an ongoing discussion about how the Markov blanket construct, as used in Friston (2013), Friston (2019b), Friston, Wiese, et al. (2020), and related works, differs from the original definition presented in Pearl (1988). The original definition only considers synchronic properties, Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 12 Here, what matters is that the existence of a Markov blanket has subtle, but pro- found implications. The fact that internal states are conditionally independent of external states, given blanket states, allows us to disentangle the system’s dynamics. In other words, we can write down separate equations of motion for internal states and active states – that only depend on blanket states: 𝑓𝛼(𝜋) = (𝑄𝛼𝛼 − Γ𝛼𝛼)∇𝛼ℑ(𝜋) 𝛼 = {𝑎, 𝜇} (autonomous states) 𝜋 = {𝑠, 𝛼} (particular states) Here, 𝑓𝛼(𝜋) is the flow of internal and active states 𝛼, to which we refer as auto- nomous states. Note that the flow only depends on particular (non-external) states 𝜋 = {𝑠, 𝛼}. This in turn enables us to express the dynamics of internal states in terms of a probability distribution over external states – encoded by internal states. That is, for any blanket state 𝑏, we can map internal states 𝜇 to a probability distribution 𝑞𝜇(𝜂) over external states, given blanket states. Strictly speaking, we can only map expected internal states, because there need not be a unique internal state, associated with a given blanket state. In practice, one must therefore consider averages of internal states (such as average activity of neural populations), which approximate their expected value. If the probability distribution 𝑞𝜇(𝜂) is sufficiently similar to the actual condi- tional distribution 𝑝(𝜂|𝜋) over external states (where 𝑝 is the NESS density), then we can approximate the flow of autonomous states using 𝑞𝜇(𝜂). Equivalently, we can say that the gradient flow of autonomous states can be considered as a gradient flow on variational free energy 𝐹 : 𝑓𝛼(𝜋) ≈ (𝑄𝛼𝛼 − Γ𝛼𝛼)∇𝛼𝐹 (𝜋), with 𝐹 (𝜋) ≜ 𝐸𝑞[ℑ(𝜂, 𝜋)] − 𝐻[𝑞𝜇(𝜂)] = ℑ(𝜋) + 𝐷[𝑞𝜇(𝜂)||𝑝(𝜂|𝜋)] = 𝐸𝑞[ℑ(𝜋|𝜂)] + 𝐷[𝑞𝜇(𝜂)||𝑝(𝜂)] ≥ ℑ(𝜋). According to this way of expressing 𝑓𝛼(𝜋), the system’s autonomous states 𝛼 must change in such a way that the variational free energy 𝐹 (𝜋) is minimised – where variational free energy is a functional of the probability distribution 𝑞𝜇(𝜂) encoded by internal states. Hence, as internal states change, 𝑞𝜇(𝜂) changes, as well; more specifically, it changes in a way that makes it more similar to 𝑝(𝜂|𝜋) (as measured by the Kullback-Leibler divergence 𝐷[𝑞𝜇(𝜂)||𝑝(𝜂|𝜋)]). Changes of internal states therefore go along with changes in the probability distribution encoded by internal states. We can thus map a given internal state whereas its application in the context of FEP involves diachronic properties (i.e., it is meant to formalise dependencies in an action-perception loop). For discussion, see Rosas et al. (2020); see also Friston, Costa, et al. (2020); Friston et al. (2021). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 13 to a point on a statistical manifold, and associate changes of internal states with movement on the statistical manifold. This manifold has an information geometry, which we shall call the extrinsic information geometry (because it is the geometry of probabilistic beliefs about external states). The extrinsic information geometry is thus associated with the probability distributions encoded by internal states. Now note that the NESS density also specifies a probability of internal states. We can regard it as a point on another statistical manifold, which has a geometry we shall call the intrinsic11 information geometry. If we parametrise the density over internal states with time, we can associate the progression of time with a movement on the system’s intrinsic manifold. How- ever, since the NESS is constant, movement on the intrinsic manifold will eventu- ally stop (once the system has reached non-equilibrium steady state). In other words, if – as physicists like to say – we “prepare” the internal states in some initial configuration, and then “push” the probabilistic configuration forwards in time, the internal states pass through a series of probabilistic configurations un- til they reach the point on the intrinsic statistical manifold corresponding to the NESS. Furthermore, if we assume some of the internal states are exchangeable (e.g., one neuron in a neuronal population can be treated as the same as another from the same population), we equip internal states with a statistical mechanics or thermodynamics; i.e., the initial configuration will, over time, converge to the NESS and thermodynamic free energy will fall progressively. In short, the intrinsic geometry underwrites the dynamical complexity and thermodynamics of neuronal populations. Conversely, on the extrinsic manifold, the internal states minimise variational free energy, when conditioned on the blanket states. In other words, whenever the blanket states change, the expected internal state changes and there is movement on the extrinsic manifold that – by construction – can be cast as Bayesian belief updating. This is because the (expected) internal states encode probabilistic (i.e., Bayesian) beliefs about external states. The blanket states here can be construed as the sensory impressions of external states on the Markov blanket that contains the internal states. In short, it may be more useful to consider the system from the point of view of the extrinsic information geometry (probabilities encoded by internal states) than from the point of view of the intrinsic information geometry (probabilities of internal states). We can now relate some of the computational principles of conscious process- ing, as suggested by Cleeremans (2005), to the probability density dynamics just sketched. In particular, we shall consider the “strength” of neural representations (the number of “processing units” that constitute the representational vehicle) and meta-representations. Firstly, recall that only expected internal states can be said 11It is not just intrinsic in the sense that it is about internal states, it is also intrinsic in the sense that it does not depend on the manifold associated with the probabilities encoded by internal states. The extrinsic information geometry, by contrast, presupposes the existence of the manifold associated with probabilities of internal states. Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 14 to encode a probability distribution over external states. If we want to interpret actual neural activity as encoding a probability distribution, we therefore have to consider population averages. Any neural representation will therefore have high “strength”, from the point of view of FEP. Secondly, note that – under Gaussian assumptions about the encoded probabilistic beliefs – minimising variational free energy becomes prediction error minimisation (Friston & Kiebel, 2009). Predic- tion error signals are meta-representational (Shea, 2012b), so the feature of meta- representation is easily fulfilled by many systems.12 We draw the following lessons from these observations. (i) The activity of a large class of systems conforms to at least some of the computational princi- ples that are identified as computational correlates of consciousness in Cleeremans (2005). In particular, this is true for many non-conscious systems (see also Reggia et al., 2016, p. 111). (ii) This suggests, more generally, that computational corre- lates should not be regarded as minimally sufficient conditions for consciousness (in contrast to Chalmers’ NCCs, as presented in his 2000). In particular, compu- tational correlates need not be associated with the difference between conscious and unconscious processing (pace Cleeremans, 2005). (iii) Instead, we should ex- pect computational correlates to specify necessary conditions for consciousness.13 For instance, Reggia et al. (2019) present a model of working memory and propose that CCCs are identified by the “underlying computational mechanisms [that] are critically needed to realize such a model and distinguish it from other contem- porary neural networks in general” (Reggia et al., 2019, pp. 265–266). This is a useful feature, as not fulfilling a necessary condition can license an inference to the absence of consciousness (Fink, 2016). Furthermore, existing evidence for the presence of consciousness in controversial cases can be strengthened, if necessary conditions for consciousness are fulfilled. 3.3 Computational correlates as necessary, sufficient, or necessary and sufficient conditions for consciousness? We noted, almost in passing, that some of the principles identified as computational principles by Cleeremans should be regarded as merely necessary conditions for 12In fact, one could argue that all systems that exist – in the above sense – are meta-representational on this definition. This follows because the gradients of variational free energy can always be ex- pressed as a form of prediction error. One could object that this only entails (meta)representations in an instrumentalist sense, i.e., we can describe internal states of the system as if they were representations (Ramstead et al., 2020). In Wiese & Friston (2021), we argue that at least living organisms that embody a hierarchical generative model are representational systems in a real- ist sense. However, we are aware that this is a controversial claim (see Bruineberg et al., 2018; Downey, 2018; Hutto, 2018; Kirchhoff & Robertson, 2018; Van Es, 2019). 13Some of them may be trivial (e.g., single-cell organisms may fulfill them). A challenge is to find computational correlates that specify non-trivial necessary conditions. One strategy is to focus on computational properties associated with functions of consciousness (see Cleeremans, 2005, and section 5). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 15 consciousness. Even if one agrees with this remark (since, otherwise, one would have to accept that many very simple systems are conscious), one could argue that computational correlates should be sufficient conditions for consciousness. That is, Cleeremans’ principle should then only be regarded as part of a bundle of com- putational principles that (together) yield sufficient conditions for consciousness. In particular, according to this line of reasoning, the search for computational cor- relates of consciousness should consist in searching for necessary and sufficient conditions for consciousness. We disagree. We argue that even finding merely necessary conditions for con- sciousness can be useful and important in the science of consciousness. First of all, necessary conditions for consciousness can complement “minimally sufficient” conditions for consciousness. That is, the search for necessary conditions need not replace the search for minimally sufficient conditions. Secondly, whether suf- ficient or necessary conditions are more useful depends on the domain of applica- tion. For instance, if one already knows that a creature is conscious (e.g., a human being with a normally functioning brain in alert wakefulness), minimally sufficient conditions for consciousness in this type of creature will be most informative. How- ever, if it is unclear whether a creature (or machine) is conscious or not, determin- ing whether necessary conditions for consciousness are fulfilled can be immensely informative. If a necessary conditions is not fulfilled, the question (“Is it conscious or not?”) can even be settled.14 Thirdly, necessary conditions may provide uni- fication. For instance, if CCCs are investigated by modelling different cognitive capacities that are associated with consciousness, necessary computational mech- anisms of these different capacities can reveal what they have in common. (And it is to be expected that they have something in common if they are all enabled, or facilitated, by the same phenomenon, i.e., consciousness. See Birch, 2020, pp. 8–9.) We shall elaborate on this point in section 5 below. 3.4 The challenge of islands of awareness We can now return to a special case of challenge 3 (identified in section 2 above), viz. the possibility of what Bayne et al. (2020) call “islands of awareness” (IOA): conscious experiences that are instantiated in the absence of sensory stimulation and observable behaviour. Most measures of consciousness rely on some kind of neural response to sensory stimulation, which is precluded in the case of IOAs. From the point of view of FEP, the challenge may seem even harder. FEP has 14In a related vein, Fink (2016) discusses four problems with Chalmers’ definition of an NCC, one of which is that sufficient conditions do not enable one to rule out that a system is conscious. Fink argues: “in order to overcome some of the problems of the Chalmers-NCC, it seems that we have to introduce necessity somewhere” (Fink, 2016, p. 9). Fink suggests identifying a feature bundle 𝔽 that is shared by different neural state tokens that are (each) sufficient for the same phenomenal state type. Crucially, 𝔽 must be a necessary condition for consciousness. If the feature bundle consists of neurofunctional and neurocomputational features, then it may also be applicable to many non-human animals, or even machines (Fink, 2016, p. 11). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 16 been developed for systems that sense and act, not for systems that do not receive sensory input and are incapable of producing motor output. In response to this challenge, we will propose to treat IOAs in analogy to brains in altered states of consciousness, such as hallucination or sleep and dreaming. As previously argued (Friston, Wiese, et al., 2020; Hobson & Friston, 2012; Hobson & Friston, 2014), neu- ronal dynamics during sleep minimise the complexity of the brain’s generative model (i.e., by removing redundant model parameters). This can be seen by noting that variational free energy can be expressed as follows: 𝐹 (𝜋) = 𝐸𝑞[ℑ(𝜋|𝜂)] + 𝐷[𝑞𝜇(𝜂)||𝑝(𝜂)]. Here, 𝐷[𝑞𝜇(𝜂)||𝑝(𝜂)] describes the statistical complexity of the internal model (“How much do I have to change my mind to accommodate current changes in sensory signals?”), whereas −𝐸𝑞[ℑ(𝜋|𝜂)] describes accuracy (so minimising free energy entails minimising the difference between accuracy and complexity). Note that accuracy depends on the particular states 𝜋 (comprising blanket states and internal states). During a period of (partial) disconnection from blanket states, such as dreaming, the variational free energy gradient in the following equation will mainly be driven by the complexity part (which does not depend on blanket states): 𝑓𝛼(𝜋) ≈ (𝑄𝛼𝛼 − Γ𝛼𝛼)∇𝛼𝐹 (𝜋). This entails that neural processes can perform the computations required to min- imise free energy, even when the coupling with the environment is temporarily suspended. Using sleep and dreaming as a model, FEP can be applied to IOAs and yields the same result: isolated systems will minimise free energy by reducing the complexity of the generative model. This creates a seeming tension between FEP and the suggestion by Bayne et al. (2020) that high complexity could serve as a proxy for consciousness in IOAs. Mea- sures used to infer the presence of consciousness in altered states (Rohaut et al., 2017; Sarasso et al., 2014; Sarasso et al., 2015) are measures of entropic complexity such as Lempel-Ziv (LZ) complexity (Lempel & Ziv, 1976) that provide an upper bound on algorithmic complexity (Ruffini, 2017) – where the algorithmic complex- ity of a signal is defined as the length of the shortest algorithm that produces the signal. This is exactly the same quantity that underwrites variational free energy. In fact, variational free energy minimization in machine learning was predi- cated on minimizing algorithmic (computational) complexity (MacKay, 1995; Wal- lace & Dowe, 1999), which is the basis of universal computation (Hutter, 2005). Consciousness researchers assume complexity has to be large and yet the imper- atives for universal computation, in general – and the free energy principle, in particular – say exactly the opposite. This apparent paradox can be resolved easily by noting that free energy is a bound on marginal likelihood (a.k.a. model evidence) in the same way that the Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 17 LZ complexity is an upper bound on algorithmic complexity. The logarithm of evidence can always be expressed as accuracy minus complexity. In brief, if con- sciousness entails belief updating (technically, movement on a statistical manifold) then the imperative for this movement is to minimise the difference between ac- curacy and complexity. On this view, complexity provides an incomplete metric for any CCC because it fails to account for accuracy, i.e., the marginal likelihood of the sensorium. In the rhetoric of, e.g., integrated information theory (Tononi et al., 2016) it is the “matching” that matters not the complexity (where matching is scored by model evidence). In a deeply structured world, an accurate account of the sensorium can only be supplied by a complex (Bayesian) belief about the causes of sensations. This means that complexity is always chasing accuracy, so that it will look as if complexity is being maximized. Technically, however, it is the difference between complexity and accuracy that is being minimized. Sleep and related IOA present an interesting scenario. Because there is a tran- sient suspension of exchange with the sensorium (or other parts of the brain) it would appear that there is no accuracy (because there are no inputs to provide an accurate account of). However, these IOA are themselves accountable to a larger context; namely, all the inputs that have been experienced – and will be experi- enced. On this view, it is then no surprise to see that a good model of a complex world will show a high degree of algorithmic or statistical complexity, even when observed in temporary isolation. This perspective provides fundamental constraints on (the utility of) complex- ity measures of consciousness. High complexity (as measured by LZ complexity) is necessary for consciousness in a complex world, but it is not sufficient. Under FEP, the minimisation of free energy constitutes a necessary condition for con- sciousness. This second condition entails the first condition when, and only when, a high degree of complexity is necessary to explain the sensorium. Hence, evi- dence for the presence of consciousness in IOAs can be garnered from at least two sources: First, from measurements of apparent algorithmic complexity (such as LZ complexity). Secondly, from models of IOAs that show such systems minimise free energy when their insular nature disappears. 3.5 Dynamical complexity as a CCC? The proposed solution to the problem posed by potential IOAs is slightly inelegant. While it is pleasing that it does not constitute a problem for FEP per se, it may still seem that FEP can only make a tiny contribution to understanding such cases (or to “measuring consciousness”). This is because measures of dynamical com- plexity (such as LZ complexity of neural time series) may seem to provide much stronger evidence than any criteria derived from FEP: existing empirical results al- ready suggest that dynamical complexity is a correlate of consciousness (Demertzi et al., 2019; Li & Mashour, 2019; Schartner et al., 2015; Schartner et al., 2017; Sitt et Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 18 al., 2014). Hence, it is not unreasonable to extrapolate from this to unusual cases (Bayne et al., 2020), perhaps even without requiring any additional evidence. Let us take a step back and ask: “What is dynamical complexity?” – rather than: “How can it be measured?” In dynamical systems theory, three types of complex behaviour can be distinguished: chaotic itinerancy, heteroclinic cycling, and the switching under multistability (Friston, 2019a). All three types of behaviour in- volve meandering movements between regions that are revisited time and time again, but always following slightly different, unpredictable trajectories. A differ- ence between these types of complex behaviour rests on how they are brought about. Either the system switches between basins of attraction (due to noise, as in multistability, or due to the proximity of basins of attraction, as in chaotic itiner- ancy), or the system’s state space contains a circle of connected saddles with both attracting and repelling manifolds. FEP provides an insight into the conditions under which stochastic dynami- cal systems display behaviour that is characteristic of dynamical complexity (i.e., behaviour such as chaotic itineracy, heteroclinic cycling, or multi-stability and switching). As we saw above, any system with a Markov blanket is trying to min- imise its self-information, i.e. surprisal. One can show that this brings about a tendency to self-organised criticality and dynamical complexity (Friston, 2019a; Friston et al., 2012). At the same time, there is a relation between minimising surprisal of blanket states and minimising statistical (and algorithmic) complex- ity15: the very process by which a system minimises surprisal of blanket states can, equivalently, be described as the process of minimising variational free energy with respect to the internally encoded recognition density. Recall that variational free energy can be described as statistical complexity minus accuracy. Hence, if a system minimises surprisal of blanket states by minimising variational free energy, it will also tend to keep statistical complexity within bounds. Developing a measure of dynamical complexity within the framework of FEP, i.e., a measure that invokes a system’s extrinsic information geometry, would help determine under what conditions systems (that minimise variational free energy) display high dynamical complexity, and under what conditions they display low dynamical complexity. Furthermore, existing measures of dynamical complexity cannot be said to measure computational correlates of consciousness, from the 15The relation between surprisal minimisation and minimising algorithmic complexity (Kol- mogorov complexity) is not straightforward. Heuristically, it can be shown that maximising the posterior probability of external states, given blanket states, 𝑝(𝜂|𝑏), is equivalent to minimising the algorithmic complexity of blanket states (Wallace & Dowe, 1999). Since minimising varia- tional free energy entails that the recognition density 𝑞𝜇(𝜂) approximates the posterior 𝑝(𝜂|𝑏), there is at least an indirect link to algorithmic complexity. Furthermore, in AIXI, a formalism for artificial general intelligence, a reinforcement learning agent optimises its hypotheses about the environment by minimising their algorithmic complexity (Hutter, 2000, 2005). Since active in- ference (which involves minimising expected free energy) subsumes reinforcement learning as a special case (Costa, Sajid, et al., 2020), it should in principle be possible to describe an AIXI agent as an agent that minimises (expected) variational free energy, under a particular set of priors – this remains an important task for future work. Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 19 point of view of FEP. This is because the computations performed by a system that minimises variational free energy are inferences, which correspond to movements on the system’s extrinsic statistical manifold. Existing measures of dynamical com- plexity, however, do not measure complexity in terms of probabilities encoded by neural activity, but in terms of statistical properties of neural activity, that is, prop- erties of the intrinsic statistical manifold. Hence, dynamical complexity, as mea- sured by existing approaches, should be associated with NCCs (at least from the point of view of FEP). Interestingly, FEP suggests an alternative. An FEP-inspired measure of dynami- cal complexity would most naturally be based on the information length of neurally encoded probability distributions (i.e., Bayesian beliefs): instead of considering the statistical properties of a neural time series as such, one would have to consider the probability distributions encoded by this activity – or, equivalently, trajectories on the extrinsic statistical manifold. The information length of a trajectory then sim- ply corresponds to the distance travelled on the manifold (which is measured at any point on the path by the Fisher information metric). Even if a measure based on information length should turn out to be equiva- lent to existing measures of dynamical complexity, it would be advantageous, be- cause it could unify existing approaches under a single overarching principle (i.e., the FEP). Note that, although many existing measures of dynamical complexity are based on LZ complexity (Demertzi et al., 2019; Li & Mashour, 2019; Sitt et al., 2014), some also use amplitude coalition entropy and synchrony coalition entropy (Schartner et al., 2015; Schartner et al., 2017), or the spectral exponent of resting EEG (Colombo et al., 2019) as a proxy. In fact, there is no obviously “correct” way of measuring dynamical complexity. To the extent that proposed measures of dy- namical complexity have empirical validity (as measure of consciousness), they may be regarded as empirically adequate. But it would still be desirable to provide a fundamental justification because this could further support their application to controversial cases. In addition, it could help resolve an uncertainty about whether existing measures of dynamical complexity also track algorithmic complexity. It is well-known that LZ complexity, for instance, constitutes an upper bound on al- gorithmic complexity. However, this entertains the possibility that conscious ac- tivity maximises LZ complexity (and related measures of dynamical complexity), but minimises algorithmic complexity (this hypothesis has been stated by Ruffini, 2017.). Finally, developing a measure of dynamical complexity within FEP could help to provide a computational explanation of consciousness (or “explanatory cor- relates” of consciousness, see Seth, 2009; Seth & Edelman, 2009). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 20 4 From computational correlates to a computa- tional explanation of consciousness Measuring neural activity in conscious creatures yields insights into correlates of consciousness. Here, we shall probe the idea that CCCs, construed as necessary conditions for consciousness, may actually yield a computational explanation of consciousness. Do computational explanations of consciousness imply that implementing the right computations is sufficient for being conscious?16 Or is it possible that some simulations of conscious systems perform all the computations performed by ac- tual conscious systems, without being conscious? Here, we will argue that imple- menting the right computations is not sufficient for instantiating consciousness. But what would then count as a computational explanation of consciousness? We shall argue that the computations must be implemented by the right kind of sys- tem, and that FEP puts constraints on what the right kind of system is. To illustrate, consider the following example.17 A digital assistant (say, a suf- ficiently sophisticated successor of Siri or Alexa) may be able to pass a version of the Turing test, if it implements the right computations. But implementing these computations will not ensure its continued existence. In particular, it may be able to provide sensible answers to any questions it is asked – but it would also continue to exist if it were to respond with nonsensical answers. Such a system computes and may represent the world, but it is not committed to the existence of anything that corresponds to the way it represents the world (Smith, 2019). This is different for systems like us. Our continued existence is systematically related to the way we register (and interact with) the world. Similarly, a digital computer may implement all computations underpinning conscious experience. But it must also (have the potential to18) successfully interact with the world by virtue of these computations, in order to be conscious. We elaborate on this point below (section 4.2). Before that, we discuss a more fundamental problem associated with compu- tational explanations of consciousness (section 4.1) 4.1 The scope of computational explanations Computational explanations seek to explain a target phenomenon characteristic of a system (e.g., a particular type of behaviour) in terms of computations performed by that system. If no computational properties are sufficient for consciousness, then it seems there is something that is left out by computational explanations.19 16This is a special case of what Chalmers (2011) calls the thesis of computational sufficiency. 17This example was brought up in a discussion with Karen Konkoly’s reading group; we are grateful for this suggestion. 18This clause is necessary to accommodate the possibility of islands of awareness. 19Note that this is not simply the explanatory gap (Levine, 1983). An explanatory gap arises if there is no necessary epistemic connection between the explanans and the explanandum. The absence Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 21 Let us consider this problem in a bit more detail. A notorious challenge for com- putational explanations is that they depend on an account of physical computation, i.e., an account of what it means for a concrete, physical system to perform a given computation (Milkowski, 2013; Piccinini, 2015). Such an account should rule out trivial implementations (Sprevak, 2019). For instance, if a computational explana- tion of consciousness specifies internal state transitions that are also instantiated by a rock or a piece of Swiss cheese, then it is doubtful whether describing a system as computing can explain why it is conscious. In other words, if a computational explanation focuses on abstract computational properties (disregarding how they are implemented in the system), then it must be complemented by an account of physical implementation, showing that the same computational properties cannot be instantiated by systems we would not regard as computational. There is, how- ever, no consensus on whether any account of physical computation can avoid trivial implementations (Sprevak, 2019), nor on whether computational properties are intrinsic properties of physical systems (Dewhurst, 2018; Fresco, 2015). For this reason, Schweizer (2019) argues that a computational explanation needs to specify more than just internal state transitions that account for ab- stractly described input-output patterns. Rather, a computational explanation should specify inputs and outputs relative to a particular system. For instance, a computational explanation of mental arithmetic, as performed by actual human beings, would have to specify in which sensory modality and in which format the input is presented to the subject (e.g., whether in terms of verbal questions), as well as how the output is produced (verbally, by way of written response, etc.; see Schweizer, 2019, p. 294). Internal state transitions posited by a computational explanation must then not only be mapped to internal states of the system in question, but these internal states must also be causally connected to the sensory input and behaviour figuring in the description of the input-output patterns that are to be explained. For instance, in a computational explanation of mental arithmetic, as performed by a human being, one would ideally specify neuronal states corresponding to the postulated computational steps, i.e., concrete internal state transitions, which are causally implicated in bringing about behaviour associated with the capacity to perform mental arithmetic (Schweizer, 2019, p. 303). This account of computational explanation is applicable to behavioural explananda. It is not obvious how to apply it to the problem of consciousness.20 of a necessary epistemic connection is compatible with the presence of a necessary ontological connection. For instance, if pain experiences are identical with the firing of certain neural pop- ulations, then there is a necessary ontological connection, but it may still be reasonable to ask why this type of neural activity is identical with pain experiences. By contrast, if all computa- tions performed by a conscious being can be performed by an unconscious computer, then there is not just an epistemic gap, but also an ontological gap between computational properties and consciousness. 20Schweizer makes this point: “The only non-abstract effects that instantiated formalisms are re- quired to preserve are defined in terms of their input/output profiles, and thus internal experi- Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 22 Indeed, it seems it poses a dilemma for computational explanations of conscious- ness. One option is that the computational explanation targets behaviour that is associated with consciousness. But this would always beg the question whether the explanation really explains consciousness – even assuming there are types of behaviour that cannot be performed without consciousness (by human beings at least). On the face of it, such an explanation would only explain behaviour. The other option is that a computational explanation of consciousness targets internal processes in a conscious system (during conscious processing). In fact, given that the first option seemingly only explains behaviour, it seems this is what a computational explanation must account for. However, if one believes that implementing the right kind of computational system is insufficient for instantiating consciousness, then there will be non-conscious systems that still display all the computational properties instantiated by conscious beings. The properties that account for a system’s being conscious must therefore also comprise non-computational properties. Can FEP bring anything more to the table? FEP is not an account of physical computation. However, it can provide con- straints that may complement existing accounts of computation. In other words, if the FEP applies to a given physical process, then that process has to possess certain properties. An account of physical computation specifies what it means to perform a computation (such as variational free-energy minimisation). Furthermore, it is likely that some computing devices will never be conscious, regardless of which computations they perform (e.g., a desktop PC). Such systems might simulate con- sciousness, but will never be conscious. 4.2 Distinguishing simulation from instantiation A fundamental constraint provided by FEP is that it only applies to active sys- tems that engage with their environment (but see the remarks about islands of awareness in section 3 above). A computer simulation of a system that minimises variational free energy may perform computations that are also instantiated by a conscious agent that interacts with its environment. But if these computations are realised by a piece of hardware that cannot be regarded as an agent (e.g., they can- not move or change external states), then they can at most lead to a simulation of consciousness (islands of awareness would constitute a limit case, i.e., they must at least have the potential to interact with the environment, if the causal connec- tion to the environment via sensory and motor systems is restored; see footnote 26 below). Let us unpack this idea. A system in NESS with a Markov blanket comprises internal, external, and blanket states. As shown in section 3, such a system can also be described as per- forming certain computations (inferences), by virtue of causal relations between ences, qua actual events, are in principle omitted” (Schweizer, 2002, p. 144; see also 2019, footnote 11). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 23 internal, external, and blanket states. This is different for a mere simulation.21 To be sure, a simulating system can perform the same computations, and it will per- form them because of causal relations between its parts. However, it will not per- form them because of causal relations between its internal, external, and blanket states. The simulation may instantiate a virtual machine, which may have inter- nal, external, and blanket states, such that its internal states encode a probability distribution over external states, given blanket states. But the internal states of the virtual machine will not be the internal states of the physical machine on which the virtual machine is running. In particular, consider a computer simulation on a von Neumann computer that stores the values of a system’s states in its memory registers. There must be some (indirect) causal links between these memory states, but the interaction between them will always be mediated by the CPU. The causal flow in the virtual machine is thus different from the causal flow in the physical machine. Put differently, not all virtual machines that perform approximate Bayesian in- ference by encoding a probability distribution over external states, given blanket states, are realised by physical machines with the same Markov blanket partition. If we keep this in mind, we can maintain a distinction between simulating and instantiating consciousness, but still retain the hypothesis that the right compu- tational properties are sufficient for consciousness (Chalmers, 2011), if they are instantiated by the right kind of system.22 Moreover, the “right kind of system” is not simply defined in terms of its physical properties (i.e., it is not about silicon- vs. carbon-based systems). Rather, the right kind of system is one in which the internal, external, and blanket states that figure in a computational description of the system are also physical states of the system, such that the system’s internal dynamics can equivalently be described (a) with respect to the system’s NESS den- sity, or (b) with respect to the probability density (i.e., Bayesian beliefs) encoded by internal states.23 One might worry that this constraint still does not suffice to distinguish simula- tion from duplication. A computer simulating a system that performs variational inference over external states must have physical states encoding the probabil- ity distributions over external states that figure in those inferences. Define these physical states as internal. There will then be a unique Markov blanket for these internal states. Hence, the physical system’s internal states will be numerically identical with the internal states that encode the probability distributions figuring in the computational system implemented by the physical system. 21Technically, in dynamical systems theory, this kind of “simulation” corresponds to a skew-product or master-slave system, in which the influence of external states on internal states (mediated vicariously by blanket states) was not complemented by an influence of internal states on external states. In other words, the circular causality – that renders the system autonomous – is precluded. 22In other words, our account is compatible with a slightly modified version of the thesis of com- putational sufficiency. However, it is also compatible with the possibility that computational explanations cannot explain all aspects of consciousness. 23A related argument is presented in Kiefer (2020). Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 24 This consideration overlooks that a system’s Markov blanket must be specified with respect to the system’s dynamics. These dynamics depend on the structure of the system. For instance, the dynamics of a human organism are quite different from the dynamics of a digital computer, even if both have internal states that encode the same probability distributions.24 Moreover, a computer can simulate a vast number of different types of system (with different Markov blankets), but the computer’s Markov blanket will not change when it simulates different systems (or at least it will not change in such a way as to match the Markov blanket of the simulated system). This means the computer’s continued existence does not depend on the computations it performs in simulating another system. Conversely, digital computers with different causal topologies (and different Markov blankets) may be able to simulate the same virtual machine (Gamez, 2014, p. 180). 5 Computational explanations of consciousness and minimal unifying models So far, we have argued that FEP can provide the basis for a computational explana- tion of consciousness. A computational explanation of consciousness must specify computations that are sufficient for at least some features of consciousness, under the assumption that the computations are performed by the right kind of system. If the computations can be described as inferences over external states, then FEP tells us what the right kind of system is: a physical system with internal states that en- code the probability distributions figuring in the computational explanation, such that the physical system’s internal dynamics can equivalently be described a) with respect to the system’s NESS density, or b) with respect to the probability distri- bution encoded by internal states. If correct, this only shows that FEP can provide a framework for computational explanations of consciousness (similarly to the proposal by Hohwy & Seth, 2020). It does not directly provide computational explanations. How should one expect to get to an explanation (or a theory) of consciousness, starting from a framework that itself is not a theory of consciousness (because it applies to basically everything)? The account on offer here is that a computational explanation of consciousness should explain teleological functions of consciousness, i.e., cognitive capacities as- sociated with consciousness (see also Cleeremans, 2005). Explanations of cogni- tive capacities cannot be provided by FEP itself, but by process theories such as active inference (which are theories of how minimising variational free energy is realised). The FEP can fulfil a unificatory role: using FEP as a framework, one can 24A special case of the possibility described in the paragraph above is a computer simulation of an island of awareness. In a mere simulation, blanket states are virtual, not just (temporally) disconnected from internal states; a real artificial island of awareness would have to be able to continue to function (i.e., to continue minimising variational free energy) if it were connected to physical sensors and actuators – not just virtual ones. Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 25 formulate and test hypotheses about necessary computational mechanisms that may underpin different cognitive capacities,25 or different measures of conscious- ness. This could also be used as a defense against the following charge: operational- isations of consciousness employed by consciousness researchers are so hetero- geneous that they do not serve to unequivocally pick out a unique phenomenon (Irvine, 2013, 2017). Hence, it has been argued that the concept of conscious- ness should be eliminated from scientific discourse (Irvine, 2012; Irvine & Sprevak, 2020). As a unifying framework, FEP (and process theories such as active inference) could enable insights into what the phenomena picked out by different measures of consciousness have in common (see also Wiese, 2018). We shall unpack this idea in what follows. Wiese (2020) argues that theoretical work in consciousness research should not focus on creating new theories of consciousness, but on creating a minimal unifying model, which embodies assumptions that existing theories have in com- mon, and are thus more likely to be true than any entire theory. In doing this, only necessary conditions for consciousness are picked out (instead of sufficient conditions) – this is the main sense in which such a model will be minimal (see also Metzinger, 2020). This dovetails with the results presented here, in that CCCs should, from the point of view of FEP, be regarded only as necessary properties of consciousness, not as (minimally) sufficient properties (as suggested by Chalmers’ NCC notion). Minimising variational free energy could count as a minimal unifying model: variational free energy must be minimised by every self-organising system that persists, and hence also by any conscious system. Minimising variational free energy is thus a necessary condition, trivially presupposed by any theory of con- sciousness that does not explicitly reject FEP. Unfortunately, this necessary condi- tion is not really informative, because it is trivial. However, recall that slightly more informative constraints directly follow from FEP. CCCs should be specified in terms of probabilities encoded by internal states, not in terms of probabilities of internal states. Conscious (and unconscious) sys- tems must minimise the difference between accuracy and complexity – and sys- tems with (transiently absent) connection to sensory inputs and motor outputs will tend to minimise complexity. Apart from these implications, more informative minimal unifying models can be developed under the FEP by taking results from consciousness research into account. For instance, a promising approach is to focus on cognitive capacities as- sociated with consciousness, such as trace conditioning, complex types of learning (Birch, 2020; Ginsburg & Jablonka, 2019; Kanai et al., 2019), or perhaps working memory (Reggia et al., 2019). It is unlikely that any particular cognitive capac- ity by itself is sufficient for consciousness (Birch, 2020; Wiese, 2020). Instead, the 25A related idea, put forward by Ginsburg & Jablonka (2019), is that there is a single learning capacitiy that underpins various characteristic features of consciousness. Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Wanja Wiese and Karl J. Friston 26 hypothesis is that consciousness enables a number of different cognitive abilities. Furthermore, if consciousness is a natural kind (Shea, 2012a; Shea & Bayne, 2010), then it is to be expected that there is a single underlying mechanism for these cognitive abilities. Whether consciousness is indeed a natural kind is an empiri- cal question: finding a positive correlation between different cognitive capacities associated with consciousness would support the assumption. FEP-based models can contribute to this approach from a theoretical perspec- tive. For instance, active inference models (Friston et al., 2017) could establish that minimising (expected) variational free energy in deep models is sufficient for a broad range of cognitive capacities associated with consciousness (at least if certain further, to-be-specified conditions are fulfilled; see Wiese, 2018). More specifically, assume there is a cluster of consciousness-linked cognitive capacities 𝑐1, 𝑐2, 𝑐3, … Strong support for the natural-kind hypothesis would be provided if a minimal model of 𝑐1 were ipso facto a minimal model of 𝑐2 (and of 𝑐3, …). This is un- likely, but it may turn out that minimal models of 𝑐1, 𝑐2, 𝑐3, …, respectively, share at least some core structural features (Wiese, 2020) that play a central role in ac- counting for these different cognitive abilities. A model with these core structural features would then point to a common mechanism underlying these capacities. The computational description afforded by such a unifying model would provide an essential part of a computational explanation of consciousness. The explanatory “heavy lifting” would not be done by FEP itself, but by specific models of the respective cognitive capacities (Schlicht & Dołega, 2021). However, finding common core structural features of these models (Fink et al., 2021; Song, 2021) will be facilitated by (or will even be conditional on) expressing the models within a single formal framework, as provided by FEP (and active inference). 6 Conclusion How can research on neural correlates of consciousness (NCCs) contribute to an explanation of consciousness, and what role could the free energy principle (FEP) possibly play in this endeavour? We have suggested that research on neural cor- relates should be complemented by research on computational correlates of con- sciousness (CCCs), in order to yield a computational explanation of consciousness. Moreover, according to FEP, NCCs must be defined in terms of neural dynamics, not neural states, and CCCs should be defined in terms of probabilities encoded by neural states. Consequently, a computational explanation of consciousness requires more than a formal description of neural dynamics. It must also specify computations implemented by these dynamics. A key contribution by FEP is that it provides ad- ditional constraints on what it means to be, as opposed to merely simulate a con- scious system. Put differently, the possibility of a computational explanation of consciousness is compatible with the assumption that some systems instantiate all computational properties associated with consciousness, without being conscious. Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org The neural correlates of consciousness under the free energy principle 27 There are many open problems and questions we have barely mentioned, or even outright ignored, such as the hard problem (Chalmers, 1995), the meta prob- lem (Chalmers, 2018), or the computational explanatory gap (Reggia et al., 2017; Reggia et al., 2014). A computational explanation of consciousness can only be achieved if these problems are addressed as well. Furthermore, the possibility of a computational explanation of consciousness also raises the possibility of machine consciousness (Reggia, 2013), as well as ethical concerns that should be addressed (Agarwal & Edelman, 2020; Metzinger, 2013, 2017, 2021). However, our goal has been more modest. All we hope to have shown is that a computational explana- tion of consciousness is possible, and that the free energy principle can make a significant contribution to this project. Acknowledgments We are extremely grateful to all attendants of a virtual theoretical neurobiology meeting at the Wellcome Centre for Human Neuroimaging, at which an early version of this pa- per was discussed. WW is grateful to Joe Dewhurst and Mark Sprevak for correspon- dence on issues related to ideas presented in this paper, as well as to audiences at the Tokyo Consciousness Club, the Active Inference Lab, the Mathematical Consciousness Science Seminar, and Karen Konkoly’s reading group. We also thank two anonymous re- viewers and Ying-Tung Lin and Sascha Fink for their critical and constructive comments. This research was supported by a Wellcome Trust Principal Research Fellowship (KF; Ref: 088130/Z/09/Z). References Agarwal, A., & Edelman, S. (2020). 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The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. 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Friston 32 Wiese, W., & Friston, K. J. (2021). Examining the continuity between life and mind: Is there a continuity between autopoietic intentionality and representationality? Philosophies, 6(11), 18. https://doi.org/10.3390/philosophies6010018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 Interna- tional License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Wiese, W., & Friston, K. J. (2021). The neural correlates of consciousness under the free energy principle: From computational correlates to computational explanation. Philosophy and the Mind Sciences, 2, 9. https://doi.org/10.33735/phimisci.2021.81 ©The author(s). https://philosophymindscience.org ISSN: 2699-0369 https://doi.org/10.3390/philosophies6010018 https://doi.org/10.33735/phimisci.2021.81 https://creativecommons.org/licenses/by/4.0/ https://philosophymindscience.org Introduction From neural correlates to computational correlates of consciousness Challenge 1: Global dynamics Challenge 2: Non-arbitrary mappings Challenge 3: Unusual conditions Computational correlates of consciousness and the free energy principle CCCs and computational principles Deriving computational principles from first principles Computational correlates as necessary, sufficient, or necessary and sufficient conditions for consciousness? The challenge of islands of awareness Dynamical complexity as a CCC? From computational correlates to a computational explanation of consciousness The scope of computational explanations Distinguishing simulation from instantiation Computational explanations of consciousness and minimal unifying models Conclusion