Integrated World Modeling Theory (IWMT) Expanded: Implications for Theories of Consciousness and Artificial Intelligence

Adam Safron* 1,2,3 1 Center for Psychedelic and Consciousness Research, Johns Hopkins University School of Medicine, Baltimore, MD 21218, USA 2 Kinsey Institute, Indiana University, Bloomington, IN 47405, USA 3 Cognitive Science Program, Indiana University, Bloomington, IN 47405, USA * [email protected]

Abstract Integrated World Modeling Theory (IWMT) is a synthetic theory of consciousness that uses the Free Energy Principle and Active Inference (FEP-AI) framework to combine insights from Integrated Information Theory (IIT) and Global Neuronal Workspace Theory (GNWT). Here, I first review philosophical principles and neural systems contributing to IWMT’s integrative perspective. I then go on to describe predictive processing models of brains and their connections to machine learning architectures, with particular emphasis on autoencoders (perceptual and active inference), turbo- codes (establishment of shared latent spaces for multi-modal integration and inferential synergy), and graph neural networks (spatial and somatic modeling and control). Particular emphasis is placed on the hippocampal/entorhinal system, which may provide a source of high-level reasoning via predictive contrasting and generalized navigation, so affording multiple kinds of conscious access. Future directions for IIT and GNWT are considered by exploring ways in which modules and workspaces may be evaluated as both complexes of integrated information and arenas for iterated Bayesian model selection. Based on these considerations, I suggest novel ways in which integrated information might be estimated using concepts from probabilistic graphical models, flow networks, and game theory. Mechanistic and computational principles are also considered with respect to the ongoing debate between IIT and GNWT regarding the physical substrates of different kinds of conscious and unconscious phenomena. I further explore how these ideas might relate to the “Bayesian blur problem”, or how it is that a seemingly discrete experience can be generated from probabilistic modeling, with some consideration of analogies from quantum mechanics as potentially revealing different varieties of inferential dynamics. Finally, I go on to describe parallels between FEP-AI and theories of universal intelligence, including with respect to implications for the future of artificially intelligent systems. Particular emphasis is given to recurrent computation and its relationships with feedforward processing, including potential means of addressing critiques of causal structure theories based on network unfolding,

and the seeming absurdity of conscious expander graphs (without cybernetic symbol grounding). While not quite solving the Hard problem, this article expands on IWMT as a unifying model of consciousness and the potential future evolution of minds.

Keywords: Consciousness, Integrated Information Theory (IIT), Global Neuronal Workspace Theory (GNWT), Free Energy Principle and Active Inference (FEP-AI) framework, predictive turbo autoencoding, expander graphs, shared latent spaces, graph neural networks

Portions of this manuscript were originally published in the preprint “Integrated World Modeling Theory (IWMT) Revisited.” (Safron, 2020; PsyArXiv).

Contents

FACING UP TO THE ENDURING PROBLEMS OF CONSCIOUSNESS WITH INTEGRATED WORLD MODELING THEORY (IWMT) 4

PRECONDITIONS FOR EXPERIENCE: SPACE, TIME, CAUSE, SELF, AGENCY 7

NEURAL SYSTEMS FOR COHERENT WORLD MODELING 9

MACHINE LEARNING ARCHITECTURES AND PREDICTIVE PROCESSING MODELS OF BRAIN AND MIND 13

Cortex as folded disentangled variational autoencoder heterarchy 16

The hippocampal/entorhinal system (H/E-S) as gateway to high-level cognition 22

The conscious turbo-code 25

FUTURE DIRECTIONS FOR IIT AND GNWT? 27

A review of IIT terminology 27

Modules and workspaces as complexes of integrated information; potential physical substrates of consciousness 29

Cognitive cycles and fluctuating substrates of consciousness? 31

Bayesian blur problems and solutions; quasi-quantum consciousness? 34

Mechanisms for integration and workspace dynamics 36

Towards new methods of estimating integrated information 39

Beyond integrated information? 42

IWMT AND UNIVERSAL INTELLIGENCE 43

FEP-AI and AIXI: Intelligence as Prediction/Compression 43

Recurrent networks, universal computation, generalized predictive coding, unfolding, and (potentially conscious) self-world modeling 45

Kinds of world models 52

Kinds of minds: bringing forth worlds of experience 54

Machine consciousness? 56

CONCLUSIONS 58

REFERENCES 59

Facing up to the enduring problems of consciousness with Integrated World Modeling Theory (IWMT)

The Hard problem of consciousness asks, how can it be that there is “something that it is like” to be a physical system (Chalmers, 1995; Nagel, 1974)? The “meta- problem” of consciousness refers to the (potentially more tractable) challenge of addressing why it is that opinions and intuitions vary greatly with respect to what it would take to meaningfully answer this question (Chalmers, 2018). The “real problem” of consciousness refers to the further challenge of addressing why it is that different biophysical and computational phenomena correspond to different qualities of experience (Seth, 2016). IWMT attempts to address these unsolved problems about the nature(s) of consciousness by combining Integrated Information Theory (IIT) and Global Neuronal Workspace Theory (GNWT) with the Free Energy Principle and Active Inference framework (FEP-AI). IIT speaks to the Hard problem by beginning from phenomenological axioms, and then goes on to postulate mechanisms that could realize such properties, ultimately coming to the conclusion that consciousness is “what physics feels like from the inside” (Koch, 2012). GNWT speaks to the real problem by focusing on the properties of computational systems that could realize the functions of consciousness as a means of globally integrating and broadcasting information from mental systems. FEP-AI has been used to address all these problems in a variety of ways, with IWMT representing one such attempt (Figure 1).

Figure 1. Intersections between FEP-AI, IIT, GNWT, and IWMT. (Reprinted with permission from Safron, 2020a.) The Free Energy Principle (FEP) constitutes a general means of analyzing systems based on the preconditions for their continued existence via implicit models. Integrated Information Theory (IIT) provides another general systems theory, focused on what it means for a system to exist from an intrinsic perspective. The extremely broad scope of FEP-AI and IIT suggests (and requires for the sake of conceptual consistency) substantial opportunities for their integration as models of systems and their emergent properties. Within the FEP (and potentially within the scope of IIT), a normative functional-computational account of these modeling processes is suggested in Active Inference (AI). Hierarchical predictive processing (HPP) provides an algorithmic and implementational description of means by which systems may minimize prediction error (i.e., free energy) via Bayesian model selection in accordance with FEP-AI. Particular (potentially consciousness-entailing) implementations of HPP have been suggested that involve multi-level modeling via the kinds of architectures suggested by Global Neuronal Workspace Theory (GNWT). The concentric circles depicted above are intended to express increasingly specific modeling approaches with increasingly restricted scopes. (Note: These nesting relations ought not be over-interpreted, as it could be argued that HPP does not require accepting the claims of FEP-AI.) This kind of generative synthesis may potentially be facilitated by developing an additional version of IIT, specifically optimized for analyzing systems without concern for their conscious status, possibly with modified axioms and postulates: IIT- Consciousness (i.e., current theory) and IIT-Emergence (e.g., alternative formulations that utilize semi-overlapping conceptual-analytic methods). Integrated World Modeling Theory (IWMT) distinguishes between phenomenal consciousness (i.e., subjective experience) and conscious access (i.e., higher-order awareness of the contents of consciousness). Non-overlap between the circle containing GNWT and the circle containing IIT-Consciousness is meant to indicate the conceivability of subjectivity-lacking systems that are nonetheless capable of realizing the functional properties of conscious access via workspace architectures. IWMT is agnostic as to whether such systems are actually realizable, either in principle or in practice.

In attempting to explain how there could be “something that it is like” to be a physical system, it is worth noting that this question is often phrased as “something that it feels like”. The nature of embodied perception and affective states lie at the heart of what it would take to provide a satisfying solution to the Hard problem. Further, the Hard problem could be viewed as containing an implicit begged question (that also begs to be answered): “something that it feels like, for whom?” While some may want to separate consciousness from sensations or selfhood (Tononi et al., 2016), it may also be the case that addressing the Hard problem requires understanding the nature of selves, and as Dennett (2018) has argued, “free will.” Along these lines, IWMT specifically places somatic experiences and agentic selfhood at the core of consciousness, and consciousness at the core of agency. IWMT specifically argues that integrated information and global workspaces only entail consciousness when applied to systems capable of functioning as Bayesian belief networks and cybernetic controllers for embodied agents (Safron, 2019a, 2019b; Seth, 2014). That is, IWMT agrees with IIT and GNWT with respect to the integration

and widespread availability of information as necessary preconditions for consciousness, but disagrees that these are sufficient enabling conditions for subjective experience. [Note: GNWT’s more specific claim is that workspaces help to select particular interpretations of events, which is highly compatible with IWMT, especially with more recent Bayesian interpretations of workspace dynamics (Mashour et al., 2020; Safron, 2020a; Whyte & Smith, 2020).] Rather, IWMT argues that consciousness is what integrated world-modeling is like, when generative processes are capable of jointly integrating information into models with coherence with respect to space (i.e., relative degrees of locality), time (i.e., relative changes within space), and cause (i.e., regularities with respect to these changes) for systems and their relationships with their environments. These coherence- making properties are stipulated to be required for situating modeled entities relative to each other with specific features, without which there would be no means of generating an experienceable world. Consciousness-entailing nervous systems (functioning as generative models) are stipulated to provide these sources of coherence via particular organizational features, as well as by having actual semantic content by virtue of evolving through interactions with a coherently structured (and so semi-predictable) world. IWMT further introduces a mechanism for generating complexes of integrated information and global workspaces via self-organizing harmonic modes (SOHMs), wherein synchrony both emerges from and facilitates “communication-through-coherence” (Atasoy et al., 2018; Buzsáki & Watson, 2012; Deco & Kringelbach, 2016; Fries, 2015). SOHMs are proposed to both require and allow for high degrees of meaningful integrated information, where meaning is understood as differences that make a difference to the ability of systems to pursue their goals, including the goal of modeling the world for the sake of prediction and control. To summarize, IWMT’s primary claims are as follows: (1) Basic phenomenal consciousness is what it is like to be the functioning of a probabilistic generative model for the sensorium of an embodied-embedded agent. (2) Higher order and access consciousness are made possible when this information can be integrated into a world model with spatial, temporal, and causal coherence. Here, coherence is broadly understood as sufficient consistency to enable functional closure and semiotics/sense-making. That is, for there to be the experience of a world, the things which constitute that world must be able to be situated and contrasted with other things in some kind of space, with relative changes constituting time, and with regularities of change constituting cause. These may also be preconditions for basic phenomenality (#1), especially if consciousness (as subjectivity) requires an experiencing subject with a point of view on the world. (3) Conscious access—and possibly phenomenal consciousness—likely requires generative processes capable of counterfactual modeling with respect to selfhood and self- generated actions. Below I explore the nature of these claims in greater depth than in the original publication, and also consider additional considerations and future directions

for understanding the nature of experience in biological, and potentially artificial systems.

Preconditions for experience: space, time, cause, self, agency

By emphasizing the properties by which coherent world-modeling is made possible, the philosophical foundations of IWMT can be most strongly tied to the thought of Kant and Helmholtz. The core claims of the theory are particularly informed by Kant’s stipulation of synthetic a priori categories (i.e., complex concepts possessed in advance of experience) as preconditions for judgement. IWMT further argues that these preconditions for coherent knowledge are also preconditions for coherent experience, and focuses on the categories of space (i.e., relative localization of entities), time (i.e., relative transformations of entities in space), and cause (i.e., regularity with respect to transformations). Without spatial, temporal, and causal coherence, there can be no means of situating entities relative to each other with specific properties, and so there would be no means of generating an experienceable world. This position is consistent with both the axioms of IIT (e.g. composition), the kind of informational synergy emphasized by GNWT, and also the constructive epistemology of FEP-AI (Swanson, 2016). IWMT goes further in emphasizing the importance of selfhood, consistent with Kant’s notion of the transcendental unity of apperception in which spatiotemporal and causal information are bound together into a unified manifold via a unified experiencing subject (Northoff, 2012). In the following discussions we will explore the question: how much of these forms of coherence must be present in which ways in order to enable different forms of consciousness? Helmholtz extended Kant's project in a more empirical direction, arguing that the experience of selfhood and freedom in willing are preconditions for deriving conceptions of space, time, and cause (De Kock, 2016). According to Helmholtz, a self/world distinction and sense of agency are both required for making sense of experience, including with respect to constructing these categories of experience. This more empirically focused perspective is contrasted with Liebnizian (Sleigh, 2003) notions of “pre-established harmony” as an explanation for how minds come to be equipped with precisely the intuitions required for making sense of the world. In this way, Helmholtz rejected the a priori status of Kantian categories as part of his general project of deflating mysticism, which elsewhere involved critiquing the vitalist posit of a supernatural force animating living things (i.e., élan vital). IWMT was developed in the same spirit as Helmholtz’s naturalization of mind and nature, although with somewhat greater sympathies to notions of pre-established harmonies, since evolution by natural selection represents a means by which mental systems could come to non-

mystically resonate with essential properties of the world (Badcock et al., 2019; Ramstead et al., 2017; Zador, 2019). Helmholtz’s argument for selfhood and agency as foundational cognitive capacities is fully compatible with IWMT and FEP-AI. The necessity of autonomy for coherent modeling is emphasized in FEP-AI, in which expected free energy (i.e., precision-weighted cumulative prediction errors with respect to preferred states) is minimized via action/policy selection over predictive models for future (counterfactual) goal realization (K. J. Friston, 2018; K. J. Friston, FitzGerald, et al., 2017). In these ways, IWMT supports both Kantian and Helmholtzian views on the preconditions and origins of mind. IWMT also agrees with Kant’s view in that the process of bootstrapping minds (Gentner, 2010; Safron, 2019b; Tenenbaum et al., 2011) likely requires some pre- established modes of cognitive organization (Spelke & Kinzler, 2007). For example the place/grid cells of the hippocampal/entorhinal system (H/E-S) could contribute initial structuring of experience according to space and time (Buzsáki & Tingley, 2018; Moser et al., 2008)—although these response-properties may substantially depend on experience for their emergence (Kaplan & Friston, 2018; Kropff & Treves, 2008)—with a general capacity for tracking time-varying sequences being a potentially ubiquitous feature of cortex (Hawkins & Blakeslee, 2004). Implicit objective functions from innate salience mechanisms—e.g. maximizing information gain and empowerment (de Abril & Kanai, 2018; Redgrave et al., 2008)—and neuroplasticity rules such as spike-timing dependent plasticity (Hayek, 1952; Markram et al., 2011) could both be thought of as “evolutionary priors” that further help to organize experience according to likely patterns of causal influence (e.g. causes ought to precede effects). However, Helmholtz’s criticism of Kant’s intuitions may also highlight important differences between initial inductive biases and later constructive modeling of space (Terekhov & O’Regan, 2016), time (Buonomano, 2017; Wittmann, 2017), and cause (Buchsbaum et al., 2012). It may be misleading to refer to largely innate mechanisms for structuring experience as “intuitions”, as these capacities may lack experiential content by not (yet) affording sufficient coherence for the generation of an experienceable world. Finally, agency-related knowledge may be particularly complex, diverse in its forms, and dependent upon experience for its development (Chernyak et al., 2019; Kushnir, 2018; Kushnir et al., 2015). Some open questions for future research: • To what extent are our intuitions of space and time elaborated by our intuitions regarding causal unfoldings that depend on the agentic self as a point of view on the world (De Kock, 2016; Ismael, 2016)? • If coherence-making is bidirectional in this way, would this imply a kind of mutual bootstrapping in learning of self, agency, and space/time/cause over the course of development?

• If sense-making involves this kind of bidirectionally, or capacity for inferential positive feedback, could the mutual dependency of subjective categories of experience partially explain non-linear shifts in psychological development (Isler et al., 2018)? • Do different categories and intuitions asymmetrically drive different parts of development at different points in time?

Neural systems for coherent world modeling

As hopefully is made clear by the preceding discussion, philosophical considerations may be invaluable for helping to identify fundamental properties enabling conscious experience. Whether considered as synthetic a priori categories or experience-dependent constructed intuitions, the foundations of mind suggest that a primary task for cognitive science should be characterizing these properties on functional, algorithmic, and implementational levels of description. While such an analysis is beyond the scope of a single article, here I will suggest neural systems that could contribute to some of these foundational capacities. IWMT identifies two main sources of consciousness for space: 1) a sense of locality based on body-centric coordinates (Terekhov & O’Regan, 2013), and 2) introspectable 2D maps (Haun & Tononi, 2019) organized according to quasi-Cartesian coordinates with irregular spacings biased by salience and ‘navigation’ potential. Body- centric spatial senses would likely primarily be found in superior and inferior parietal cortices based on convergence of the dorsal visual stream and upper levels of the somatosensory hierarchy. 2D spatial maps can be found throughout the brain, but consciously-accessible mappings are likely primarily localized to the precuneus at the brain’s posterior midline. These precuneus-based maps may couple with the more well- known spatial maps of the hippocampal/entorhinal system (H/E-S) (Faul et al., 2020; Moser et al., 2008), so allowing for ‘navigating’ (Kaplan & Friston, 2018) through visualized domains. IWMT suggests that H/E-S representations are unlikely to themselves be directly introspectable, as deep spatiotemporal hierarchies and grounding within sensory modalities are likely required for coherent conscious experience. Precuneus-based maps may also be aligned with dynamics in the dorsomedial prefrontal cortex (another midline structure) (Faul et al., 2020; Hassabis et al., 2014; Li et al., 2018), which is here interpreted as sources of “attention schemas” (Graziano, 2019), upper levels of action hierarchies, and—perhaps most saliently with respect to conscious awareness—as an additional level of hierarchical control over the pre-supplementary eye fields. With precise sequencing shaped by striatal-thalamic- cerebellar loops (Gao et al., 2018), these frontal representations may provide a source of

coherent vectors for directing the “mind’s eye”, so influencing what is likely to be ‘projected’ onto the precuneus as a kind of inner ‘theater’ (Figure 2). Mechanistically, these action-oriented influences on perception may further depend on pulvinar- mediated synchrony for their realization (Hu et al., 2019; O’Reilly et al., 2017).

Figure 2. Precuneus as shared latent (work)space and source of visuospatial phenomenology. The precuneus may be particularly central for integrated world modeling. This posterior-medial structure is depicted as a kind of “Cartesian theater” that provides a basis for visuospatial modeling and phenomenal experience. In IWMT, “self-organizing harmonic modes” (SOHMs) are introduced as mechanisms in which synchronous complexes provide enhanced communication-through-coherence, entailing the calculation of joint marginal probability distributions for the subnetworks over which they form. In the left panel, small and fast beta- synchronized SOHMs close to primary modalities infer estimates of the causes of sensations in terms of low-level stimulus features. In the middle panel, these features are combined within the synchronization manifold provided by somewhat larger and slower forming beta SOHMs, so providing a source of more abstract and potentially more behaviorally meaningful object-like modeling. In the right panel, SOHMs evolving at alpha/beta-frequencies aggregate information for precuneus-centered models in which complex features are bound together into an even larger visual field with specific composition and integrated information content. IWMT suggests that this is the level of deep temporal modeling at which visuospatial consciousness is achieved, and also explicit re(-)presentations. While not depicted, a similar 3-level hierarchy may be involved with the generation of somatospatial awareness from lateral parietal cortices. These shared latent (work)spaces for autoencoding hierarchies are suggested to be structured according to the principles of geometric deep learning as kind of graph neural networks. Taken together, the “mind’s eye” and “lived body” (whose coupling may potentially be mediated by an additional graph-mesh neural network for attention/intention schemas) would constitute the physical and computational substrates for phenomenal consciousness, functioning as an integrated generative world model and cybernetic controller for embodied-embedded agents. Perhaps strangely,

experience may be exclusively realized via visuospatial and somatospatial awareness, including with respect to seemingly non-spatial/somatic modalities such as hearing and olfaction.

IWMT suggests that we ought to expect all phenomenal content to involve spatial aspects, potentially requiring multi-level processes of spatialization. Recent evidence suggests that we parse complex features by performing a kind of multidimensional scaling (Hout et al., 2013) in which features are mapped onto 2D spaces. The H/E-S may be particularly important for establishing these mappings (J. L. Bellmund et al., 2016; J. L. S. Bellmund et al., 2018; Nau et al., 2018), and potentially for establishing the routes by which we are able to make sense of these complex domains by performing (generalized) ‘navigation’ through their spatialized representations. For example, it has recently been demonstrated that entorhinal grid cells are used to spatially organize reward-related representations in the ventromedial prefrontal cortex (another midline structure), with spatialization of task structure having behavioral significance for reinforcement learning problems (Baram et al., 2019). The nature of time perception may be somewhat more complicated compared to space, and may even be conceptually derived from initially spatial understanding (Levin, 1992; Levin et al., 1978). While the entire brain (or at least much of the neocortex) may be sensitive to temporally varying sequences (Hawkins & Blakeslee, 2004), there seems to be no singular clock for time perception. One candidate clock-like mechanism potentially influencing conscious time perception includes the formation of “global emotional moments” via the insular salience hierarchy (Craig, 2009), with a greater density of salient events corresponding to relatively slower experienced (but not necessarily remembered) temporal unfoldings. Speculatively, dopaminergic influences on time perception (Buonomano, 2017; Soares et al., 2016) may suggest that the ability to both track and simulate (and track via simulations) causal sequences via actions may provide another factor influencing time perception, with a greater frequency of actions corresponding to elongated subjective timelines. Non-mutually-exclusively, relationships between dopamine and time perception could be H/E-S mediated (Mannella et al., 2013; McNamara & Dupret, 2017). These influences could include multiple factors, such as the frequency with which events are encoded as new memories, or through the mapping of timelines onto (2D) spatial trajectories with place/grid cells. Indeed, the ability of the H/E-S to construct maps and routes for navigation (broadly construed) may be a primary means by which space and time come together in brain and mind. Such simultaneous localization and mapping mechanisms may provide a basis for both the spatialization of time as well as the temporalization of space, as these two modes of quantization are fundamentally linked (and mutually defined) in terms of velocity, which may be physiologically linked via locomotion- dependent cholinergic midbrain nuclei (Lee et al., 2014). Velocity estimation both

requires and enables the ability to track changing relative spatial locations, with speed being time-varying displacement within space. Speculatively, similar relationships between time and space might also be mediated by mapping events onto body maps, both in terms of using bodily representations as a kind of space (within which things can change at varying speeds), as well as via potential magnitude estimation via the intensity of proprioceptive and interoceptive sensations. Finally, for linguistic beings such as humans, it may be difficult to overstate the importance of analogical/metaphorical construction processes for tying together and expanding these fundamental categories (Jaynes, 1976; Lakoff & Johnson, 1999; Safron, 2019a). Causal understandings may be more difficult to map unto neural systems than time and space. As previously mentioned, some proto-causal understanding may derive from mechanisms such as the ability of spike-timing dependent plasticity to arrange events into likely time-varying sequences (Hayek, 1952; Markram et al., 2011)—wherein causes can be expected to precede events—or via salience mechanisms such as modulation of midbrain dopamine by whether events are likely to have been internally or externally generated (de Abril & Kanai, 2018; Redgrave et al., 2008). However, understanding causation requires more than these proto-intuitions, and in particular the ability to generate counterfactual scenarios involving simulated interventions, potentially providing an implementation of the “do-operator” introduced by Judea Pearl for causal inference with graphical models (Pearl & Mackenzie, 2018). While it is unclear whether anything like the graphical representations underlying Pearlean analysis are used by brains and minds, the ability to simulate a variety of actions/interventions could provide a basis for similar kinds of causal reasoning. However, this ability to generate counterfactual scenarios likely required the advent of internal dynamics that can be decoupled from immediate engagement with the environment. Intriguingly, such adaptations may have arisen relatively straightforwardly with increasing degrees of cortical expansion, some of which may have provided a difference in kind with respect to expanded association cortices and a more freely operating default mode network (Buckner & Krienen, 2013; Sormaz et al., 2018). Finally, while the potential complexities of selfhood are inexhaustible, a very minimal sense of self and agency could potentially be derived from the reliable ability of embodied brains to learn that bodies depend on particular sensors by which they can perceive and effectors by which they can act. Since sensors and effectors are located on and in the body—and not elsewhere—the fact that bodily states are uniquely perceivable and controllable may provide a relatively straightforward means of construing models in which an agentic self exists as a separate entity from the rest of the (less immediately perceivable/controllable) world. While a broad range of neural systems may contribute to self-consciousness in diverse ways, IWMT focuses on body

maps and visuospatial models for scaffolding inferences about selves and the (life)worlds in which they find themselves embedded.

Machine learning architectures and predictive processing models of brain and mind

IWMT suggests that many of the processes and systems underlying consciousness may also be describable in terms of computational principles from machine learning. It may seem rather implausible that present technologies could reveal deep principles about the nature of mind, with potentially cautionary tales to be found in previous metaphorizations based on the technology of the day. Is this just another case of naïve arrogance of overgeneralizing from the familiar and fashionable, akin to previous claims that minds could be understood in terms of the accumulation and release of pressures, or when nervous systems were suggested to function according to the logical operations found in computers (McCulloch & Pitts, 1943)? Metaphors in which brains are understood as computers and even steam engines are both consistent with IWMT and the Free Energy Principle and Active Inference (FEP-AI) framework. Not only is there necessarily a sense in which brains compute information, but the serial operation of conscious access may even be thought of as a kind of (neural) Turing machine (Dehaene, 2014; Graves et al., 2014). Even more, if neural systems minimize (informational) free energy, then this may not only provide computational justification for pressure-based analogies (Carhart-Harris & Friston, 2010), but potentially even models inspired by the causal powers of engines as systems that perform thermodynamic work cycles (Safron, 2019b, 2020a). Thus, these previous attempts to analogize the nature of mind with existing technologies may have been surprisingly prescient. Considering that FEP-AI has foundations in the free-energy objective functions used to train Helmholtz machines and autoencoders (Dayan et al., 1995), the rise of deep learning may have afforded conceptual progress for understanding not just minds, but all dynamical systems (viewed as generative models). The idea that deep learning could potentially inform neuroscience ought to be relatively unsurprising (Hassabis et al., 2017; Richards et al., 2019), in that artificial neural networks were designed to try to capture relevant aspects of nervous systems, albeit with limited physiological detail and some biologically implausible functionalities (e.g. training by backpropagation). IWMT goes further in arguing that not only can useful computational principles be derived from machine learning, but some architectures may have close correspondences with the neural processes contributing to consciousness via coherent world modeling. Below I will review a few of these relevant technologies and the ways functionally equivalent processes might be realized in biological systems (Figure 3). I will then go on to consider the implications of these

suggested computational mappings for informing IWMT and associated theories. Then, I will consider intersections between these ideas and other notable frameworks for intelligence (Hutter, 2000; J. Schmidhuber, 2020, 2021), including with respect to implications for the future of AI.

Figure 3. Depiction of the human brain in terms of phenomenological correspondences, as well as computational (or functional), algorithmic, and implementational levels of analysis. (Reprinted from Safron, 2021b.) Depiction of the human brain in terms of entailed aspects of experience (i.e., phenomenology), as well as computational (or functional), algorithmic, and implementational levels of analysis (1983; Safron, 2020b). A phenomenological level is specified to provide mappings between consciousness and these complementary/supervenient levels of analysis. Modal depictions connotate the radically embodied nature of mind, but not all images are meant to indicate conscious experiences. Phenomenal consciousness may solely be generated by hierarchies centered on posterior medial cortex, supramarginal gyrus, and angular gyrus as respective visuospatial (cf. consciousness as projective geometric modeling) (Rudrauf et al., 2017; Williford et al., 2018), somatic (cf. grounded cognition and intermediate level theory) (Barsalou, 2010; Prinz, 2017; Varela et al., 1992), and intentional/attentional phenomenology (cf. Attention Schema Theory) (Graziano, 2019). Computationally, various brain functions are identified according to particular modal aspects, either with respect to generating perception (both unconscious and conscious) or action (both unconscious and potentially conscious, via posterior generative models). [Note: Action selection can also occur via affordance competition in posterior cortices (Cisek, 2007), and frontal generative models could be interpreted as a kind of forward-looking (unconscious) perception, made conscious as imaginings via parameterizing the inversion of posterior generative models.] On the algorithmic level, these functions are mapped onto variants of machine learning architectures—e.g. autoencoders and generative adversarial networks, graph neural networks (GNNs), recurrent reservoirs and liquid state machines—organized according to

potential realization by neural systems. GNN-structured latent spaces are suggested as a potentially important architectural principle (Zhou et al., 2019), largely due to efficiency for emulating physical processes (Bapst et al., 2020; Battaglia et al., 2018; Cranmer et al., 2020). Hexagonally-organized grid graph GNNs are depicted in posterior medial cortices as contributing to quasi-Cartesian spatial modeling (and potentially experience) (Haun, 2020; Haun & Tononi, 2019), as well as in dorsomedial, and ventromedial prefrontal cortices for agentic control. With respect to AI systems, such representations could be used to implement not just modeling of external spaces, but of consciousness as internal space (or blackboard), which could potentially be leveraged for reasoning processes with correspondences to category theory, analogy making via structured representations, and possibly causal inference. Neuroimaging evidence suggests these grids may be dynamically coupled in various ways (Faul et al., 2020), contributing to higher-order cognition as a kind of navigation/search process through generalized space (Çatal et al., 2021; Hills et al., 2010; Kaplan & Friston, 2018). A further GNN is speculatively adduced to reside in supramarginal gyrus as a mesh grid placed on top of a transformed representation of the primary sensorimotor homunculus (cf. body image/schema for the sake of efficient motor control/inference). This quasi-homuncular GNN may have some scaled correspondence to embodiment as felt from within, potentially morphed/re-represented to better correspond with externally viewed embodiments (potentially both resulting from and enabling “mirroring” with other agents for coordination and inference) (Rochat, 2010). Speculatively, this partial translation into a quasi-Cartesian reference frame may provide more effective couplings (or information-sharing) with semi-topographically organized representations in posterior medial cortices. Angular gyrus is depicted as containing a ring-shaped GNN to reflect a further level of abstraction and hierarchical control over action-oriented body schemas—which may potentially mediate coherent functional couplings between the “lived body” and the “mind’s eye”—functionally entailing vectors/tensors over attentional (and potentially intentional) processes (Graziano, 2018). Frontal homologues to posterior GNNs are also depicted, which may provide a variety of higher-order modeling abilities, including epistemic access for extended/distributed self-processes and intentional control mechanisms. These higher-order functionalities may be achieved via frontal cortices being more capable of temporally-extended generative modeling (Parr, Rikhye, et al., 2019), and potentially also by virtue of being located further from primary sensory cortices, so affording (“counterfactually rich”) dynamics that are more decoupled from immediate sensorimotor contingencies. Further, these frontal control hierarchies afford multi-scale goal-oriented behavior via bidirectional effective connectivity with the basal ganglia (i.e., winner-take-all dynamics and facilitation of sequential operations) and canalization via diffuse neuro-modulator nuclei of the brainstem (i.e., implicit policies and value signals) (Dabney et al., 2020; Houk et al., 2007; Humphries & Prescott, 2010; Morrens et al., 2020; Stephenson-Jones et al., 2011). Finally, the frontal pole is described as a highly non-linear recurrent system capable of shaping overall activity via bifurcating capacities (Tani, 2016; J. X. Wang et al., 2018)—with potentially astronomical combinatorics—providing sources of novelty and rapid adaptation via situation-specific attractor dynamics. While the modal character of prefrontal computation is depicted at the phenomenological level of analysis, IWMT proposes frontal cortices might only indirectly contribute to consciousness via influencing dynamics in posterior cortices. Speculatively, functional analogues for ring-shaped GNN salience/relevance maps may potentially be found in the central complexes of insects and the tectums of all vertebrates (Honkanen et al., 2019), although it is unclear whether those structures would be associated with any kind of subjective experience. Even more speculatively, if these functional mappings were realized in a human-mimetic, neuromorphic AI, then it may have both flexible

general intelligence and consciousness. In this way, this figure is a sort of pseudocode for (partially human-interpretable) AGI with “System 2” capacities (Bengio, 2017; Thomas et al., 2018), and possibly also phenomenal consciousness. [Note: The language of predictive processing provides bridges between implementational and computational (and also phenomenological) levels, but descriptions such as vector fields and attracting manifolds could have alternatively been used to remain agnostic as to which implicit algorithms might be entailed by physical dynamics.] On the implementational level, biological realizations of algorithmic processes are depicted as corresponding to flows of activity and interactions between neuronal populations, canalized by the formation of metastable synchronous complexes (i.e., “self-organizing harmonic modes” (Safron, 2020a)). [Note: The other models discussed in this manuscript do not depend on the accuracy of these putative mappings, nor the hypothesized mechanisms of centralized homunculi and “Cartesian theaters” with semi-topographic correspondences with phenomenology.]

Cortex as folded disentangled variational autoencoder heterarchy

Autoencoders use encoder networks to compress higher-dimensionality data into lower-dimensionality feature representations (Kramer, 1991), which are then used by generative decoders to reconstruct likely patterns of higher-dimensional data. These generative models are typically trained by minimizing the reconstruction loss between initial input layers of encoders and output layers of generative decoders. Autoencoders allow richer feature descriptions to be generated from highly compressed or noisy inputs, and can also be used to infer missing data (e.g. filling pixels for occluded sensors). Variational autoencoders separate the low-dimensionality output of encoders into separate vectors for means and variances, from which sample vectors are derived as inputs to generative decoders, so allowing data to be generated with novel feature combinations (Kingma and Welling, 2014; Doersch, 2016). Training proceeds by simultaneously minimizing both the reconstruction loss (as with non-variational autoencoders), as well as the KL-divergence between the posterior distributions and priors—often a unit Gaussian—so preventing overfitting of observed data and inducing more evenly distributed models of latent feature spaces with more interpretable features (Hanson, 1990). Disentangled variational autoencoders have a precision- weighting term applied to the KL-divergence—equivalent to Kalman-gain in Bayesian filtering—increasing or decreasing the degree to which different (combinations of) feature dimensions are weighted, so allowing more reliable/useful information to be more heavily leveraged during training and inference. A predictive coding model of cortex may be approximated by folding a disentangled variational autoencoder over at the low-dimensional bottleneck such that levels align in encoders and generative decoders, respectively implemented via hierarchies of superficial and deep pyramidal neurons (Figure 4). To implement predictive coding, descending messages from generative decoder networks would

continuously suppress (or “explain away”) ascending messages from encoders. In this coding scheme, only failed predictions from generative decoders get passed upwards through encoders, with these prediction errors continuing to rise up hierarchical levels until they can be successfully suppressed by the descending stream. These descending predictions are generated on multiple levels, both locally via recurrent dynamics, as well as on a more global basis, potentially accompanied by unique architectural features and discrete updating of integrative models (K. J. Friston, Parr, et al., 2017; Parr & Friston, 2018b). Viewed as folded autoencoders, these higher-level predictions would constitute a parameterization of generative decoder networks by samples from reduced-dimensionality latent feature spaces. As training proceeds, such an architecture should form increasingly predictive and sparse representations, so maximizing inferential power, while also minimizing the number of messages that need to be passed. This training for prediction and sparsification would correspond to the development of models of increasing accuracy, efficiency, and robust generalizability (Ahmad & Scheinkman, 2019; N. Srivastava et al., 2014). A predictive coding model of cortex would correspond to not just a single (folded) autoencoder hierarchy, but a heterarchy composed of multiple intersecting hierarchies, so enabling cortical learning systems to obtain inferential synergy through multi-modal sensory integration (Eguchi et al., 2020; McGurk & MacDonald, 1976). In terms of machine learning principles, high-bandwidth connections between association cortices could correspond to the chaining of low-dimensionality bottlenecks from multiple autoencoders, so forming an auto-associative network capable of supporting loopy belief propagation (the potential functional significance of which will be explored below) (Figure 5). Neuroanatomically speaking, these highly connected areas would correspond to the brain’s “rich club” networks (Heuvel et al., 2012), including the 2D grid structures described above (Figure 3), which could contribute to spatiotemporal modeling (Haun & Tononi, 2019) in both concrete physical and abstract (via spatialization) domains. Theoretically, these subnetworks (entailing shared latent space) may be well-modelled as graph neural networks (GNNs) (Safron, 2020b; Zhou et al., 2019), which are gaining increasing popularity as a means of efficiently modelling a broad range of processes. Further, the regulation of neuronal dynamics by diffuse neuromodulator systems could be computationally understood as parameterizing inference and learning with respect to the formation of partially disentangled features in perception, as well as through the selecting and sculpting of particular policies for enaction (e.g. dopamine as precision weighting, or Kalman gain) (Parr & Friston, 2018a). To the degree diffuse neuromodulator systems both influence and are influenced by overall levels of message passing, these chemicals could be used to adaptively optimize generative models with context sensitivity.

Figure 4. Sparse folded variational autoencoders with recurrent dynamics via self-organizing harmonic modes (SOHMs). (Reprinted with permission from Safron, 2020a.) (i) Autoencoder. An autoencoder is a type of artificial neural network that learns efficient representations of data, potentially including a capacity for generating more complete data from less complete sources. The encoder compresses input data over stages of hierarchical feature extraction, passes it through a dimensionality-reducing bottleneck and into a decoder. The decoder attempts to generate a representation of the input data from these reduced-dimensionality latent representations. Through backpropagation of error signals, connections contributing to a more inaccurate representation are less heavily weighted. With training, the decoder learns how to generate increasingly high-fidelity data by utilizing the compressed (and potentially interpretable) feature representations encoded in the latent space of the bottleneck portion of the network. In the more detailed view on the left, black arrows on the encoder side represent connections contributing to relatively high marginal likelihoods for particular latent feature space representations, given connection weights and data. Red arrows on the decoder side represent connections with relatively high marginal likelihoods for those reconstructed features, given connection weights and latent space feature hypotheses. While these autoencoders are fully connected dense networks, particular connections are depicted (and associated probabilities discussed) because of their relevance for predictive processing. Note: Although the language of probability theory is being used here to connect with neurobiologically-inspired implementations, this probabilistic interpretation—and links to brain functioning—is more commonly associated with variational autoencoders, which divide latent spaces into mean and variance distributions parameterized by stochastic sampling operations in generating likely

patterns of data, given experience. (ii) Folded autoencoder implementing predictive processing. In this implementation of predictive processing, autoencoders are ‘folded' at their low- dimensionality bottlenecks—such that corresponding encoding and decoding layers are aligned—with decoding hierarchies (purple circles) depicted as positioned underneath encoding hierarchies (gray circles). Within a brain, these decoding and encoding hierarchies may correspond to respective populations of deep and superficial pyramidal neurons (Bastos et al., 2012). In the figure, individual nodes represent either units in an artificial network—or groups of units; e.g., capsule networks (Kosiorek et al., 2019)—or neurons (or neuronal groups; e.g., cortical minicolumns) in a brain. Predictions (red arrows) suppress input signals when successfully predicted, and are depicted as traveling downwards from representational bottlenecks (corresponding to latent spaces) along which autoencoding networks are folded. Prediction errors, or observations for a given level (black arrows) continue to travel upwards through encoders unless they are successfully predicted, and so “explained away.” Data observations (i.e., prediction errors) are depicted as being sparser relative to high-weight connections in the (non- folded) encoding network presented above, where sparsity is induced via predictive suppression of ascending signals. This information flow may also be viewed as Bayesian belief propagation or (marginal) message passing (Friston et al., 2017; Parr et al., 2019). In contrast to variational autoencoders in which training proceeds via backpropagation with separable forward and backward passes—where cost functions both minimize reconstruction loss and deviations between posterior latent distributions and priors (usually taking the form of a unit Gaussian)— training is suggested to occur (largely) continuously in predictive processing (via folded autoencoders), similarly to recent proposals of target propagation (Hinton, 2017; Lillicrap et al., 2020). Note: Folded autoencoders could potentially be elaborated to include attention mechanisms, wherein higher-level nodes may increase the information gain on ascending prediction-errors, corresponding to precision-weighting (i.e., inverse variance over implicit Bayesian beliefs) over selected feature representations. (iii) Folded autoencoder with information flows orchestrated via recurrent dynamics. This row shows a folded autoencoder model of a cortical hierarchy, wherein neuronal oscillations mediate predictions—potentially orchestrated by deep pyramidal neurons and thalamic (and striatal) relays—here characterized as self-organizing harmonic modes (SOHMs). This paper introduces SOHMs as mechanisms realizing synchronization manifolds for coupling neural systems (Palacios et al., 2019), and sources of coherent neuronal oscillations and evidence accumulation for predictive processing. Depending on the level of granularity being considered, these predictive oscillations could either be viewed as traveling or standing waves (i.e., harmonics). SOHM-based predictions are shown as beta oscillations forming multiple spatial and temporal scales. These predictive waves may be particularly likely to originate from hierarchically higher levels—corresponding to latent spaces of representational bottlenecks— potentially due to a relatively greater amount of internal reciprocal connectivity, consistent information due to information aggregation, or both. SOHMs may also occur at hierarchically lower levels due to a critical mass of model evidence accumulation allowing for the generation of coherent local predictions, or potentially on account of semi-stochastic synchronization. Faster and smaller beta complexes are depicted as nested within a larger and slower beta complex, all of which are nested within a relatively larger and slower alpha complex. Note: In contrast to standard machine learning implementations, for this proposal of predictive processing via folded autoencoders (and SOHMs), latent space is depicted as having unclear boundaries due to its realization via recurrent dynamics. Further, inverse relationships between the spatial extent and

speed of formation for SOHMs are suggested due to the relative difficulties of converging on synchronous dynamics within systems of various sizes; theoretically, this mechanism could allow for hierarchical modeling of events in the world for which smaller dynamics would be expected to change more quickly, and where larger dynamics would be expected to change more slowly.

Figure 5. Cortical turbo codes. (Reprinted with permission from Safron, 2020a.) (i) Turbo coding between autoencoders. Turbo coding allows signals to be transmitted over noisy channels with high fidelity, approaching the theoretical optimum of the Shannon limit. Data bits are distributed across two encoders, which compress signals as they are passed through a dimensionality reducing bottleneck—constituting a noisy channel—and are then passed through decoders to be reconstructed. To represent the original data source from compressed signals, bottlenecks communicate information about their respective (noisy) bits via loopy message passing.

Bottleneck z1 calculates a posterior over its input data, which is now passed to Bottleneck z2 as a prior for inferring a likely reconstruction (or posterior) over its data. This posterior is then passed back in the other direction (Bottleneck z2 to Bottleneck z1) as a new prior over its input data, which will then be used to infer a new posterior distribution. This iterative Bayesian updating repeats multiple times until bottlenecks converge on stable joint posteriors over their respective (now less noisy) bits. IWMT proposes that this operation corresponds to the formation of synchronous complexes as self-organizing harmonic modes (SOHMs), entailing marginalization over synchronized subnetworks—and/or precision-weighting of effectively connected representations—with some SOHM-formation events corresponding to conscious “ignition” as described in Global Neuronal Workspace Theory (Dehaene, 2014). However, this process is proposed to provide a means of efficiently realizing (discretely updated) multi-modal sensory integration, regardless of whether “global availability” is involved. Theoretically, this setup could allow for greater data efficiency with respect to achieving inferential synergy and minimizing reconstruction loss during training in both biological and artificial systems. In terms of concepts from variational autoencoders, this loopy message passing over bottlenecks is proposed to entail discrete updating and maximal a posteriori (MAP) estimates, which are used to parameterize semi-stochastic sampling operations by decoders, so enabling the iterative generation of likely patterns of data, given past experience (i.e., training) and present context (i.e., recent data preceding turbo coding). Note: In turbo coding as used in industrial applications such as enhanced telecommunications, loopy message passing usually proceeds between interlaced decoder networks; within cortex, turbo coding could potentially occur with multiple (potentially nested) intermediate stages in deep cortical hierarchies. (ii) Turbo coding between folded autoencoders. This panel shows turbo coding between two folded autoencoders connected by a shared latent space. Each folded autoencoder sends predictions downwards from its bottleneck (entailing reduced-dimensionality latent spaces), and sends prediction errors upwards from its inputs. These coupled folded autoencoders constitute a turbo code by engaging in loopy message passing, which when realized via coupled representational bottlenecks is depicted as instantiating a shared latent space via high-bandwidth effective connectivity. Latent spaces are depicted as having unclear boundaries—indicated by shaded gradients—due to their semi- stochastic realization via the recurrent dynamics. A synchronous beta complex is depicted as centered on the bottleneck latent space—along which encoding and decoding networks are folded—and spreading into autoencoding hierarchies. In neural systems, this spreading belief propagation (or message-passing) may take the form of traveling waves of predictions, which are here understood as self-organizing harmonic modes (SOHMs) when coarse-grained as standing waves and synchronization manifolds for coupling neural systems. Relatively smaller and faster beta complexes are depicted as nested within—and potentially cross-frequency phase coupled by—this larger and slower beta complex. This kind of nesting may potentially afford multi-scale representational hierarchies of varying degrees of spatial and temporal granularity for modeling multi-scale world dynamics. An isolated (small and fast) beta complex is depicted as emerging outside of the larger (and slower) beta complex originating from hierarchically higher subnetworks (hosting shared latent space). All SOHMs may be understood as instances of turbo coding, parameterizing generative hierarchies via marginal maximum a posteriori (MAP) estimates from the subnetworks within their scope. However, unless these smaller SOHMs are functionally nested within larger SOHMs, they will be limited in their ability to both inform and be informed by larger zones of integration (as probabilistic inference). (iii) Multiplexed multi-scale turbo coding between folded autoencoders.

This panel shows turbo coding between four folded autoencoders. These folded autoencoders are depicted as engaging in turbo coding via loopy message passing, instantiated by self-organizing harmonic modes (SOHMs) (as beta complexes, in pink), so forming shared latent spaces. Turbo coding is further depicted as taking place between all four folded autoencoders (via an alpha complex, in blue), so instantiating further (hierarchical) turbo coding and thereby a larger shared latent space, so enabling predictive modeling of causes that achieve coherence via larger (and more slowly forming) modes of informational integration. This shared latent space is illustrated as containing an embedded graph neural network (GNN) (Liu et al., 2019; Steppa and Holch, 2019), depicted as a hexagonal grid, as a means of integrating information via structured representations, where resulting predictions can then be propagated downward to individual folded autoencoders. Variable shading within the hexagonal grid-space of the GNN is meant to indicate degrees of recurrent activity—potentially implementing further turbo coding—and red arrows over this grid are meant to indicate sequences of activation, and potentially representations of trajectories through feature spaces. These graph-grid structured representational spaces may also afford reference frames at various levels of abstraction; e.g., space proper, degrees of locality with respect to semantic distance, abductive connections between symbols, causal relations, etc. If these (alpha- and beta-synchronized) structured representational dynamics and associated predictions afford world models with spatial, temporal, and causal coherence, these processes may entail phenomenal consciousness. Even larger integrative SOHMs may tend to center on long-distance white matter bundles establishing a core subnetwork of neuronal hubs with rich-club connectivity (Heuvel and Sporns, 2011). If hippocampal-parietal synchronization is established (typically at theta frequencies), then bidirectional pointers between neocortex and the entorhinal system may allow decoders to generate likely patterns of data according to trajectories of the overall system through space and time, potentially enabling episodic memory and imagination. If frontal-parietal synchronization is established (potentially involving theta-, alpha-, and beta- synchrony), these larger SOHMs may also correspond to “ignition” events as normally understood in Global Neuronal Workspace Theory, potentially entailing access consciousness and volitional control.

The hippocampal/entorhinal system (H/E-S) as gateway to high-level cognition

In this view of the brain in terms of machine learning architectures, the hippocampal/entorhinal system (H/E-S) could be thought of as the top of the cortical heterarchy (Baldassano et al., 2017; Çatal et al., 2021; Hawkins & Blakeslee, 2004) and spatiotemporally-organized memory register (Figure 6). As IWMT suggests, this spatial and temporal organization may be essential for coherent world modeling. With respect to place/grid cells of the H/E-S (Moser et al., 2008), this organization appears to take the form of 2D trajectories through space, wherein organisms situate themselves according to a kind of simultaneous localization and mapping via Kalman filtering. Anatomically speaking, this dynamic (and volatile) memory system has particularly strong bi- directional linkages with deeper portions of cortical generative models (i.e., reduced- dimensionality latent feature spaces), so being capable of both storing information and shaping activity for these core auto-associative networks. Because of the predictive

coding setup—and biasing via neuromodulatory value signals (Mannella et al., 2013; McNamara & Dupret, 2017)—only maximally informative, novel, unexplained observations will tend to be stored in this spatiotemporally organized memory register. Indeed, this may be one of the primary functions of the H/E-S: temporarily storing information that could not be predicted elsewhere, and then using replay to train relevant subnetworks to be more successfully predictive of likely observations. As the H/E-S replays trajectories of the organism through space, pointers to prediction errors will be replayed in sequences, with the generative model inferring a more complete sensorium based on its training from a lifetime of experience. Computationally speaking, this setup could be thought of as a Kalman variational auto- encoder (Fraccaro et al., 2017). Experientially speaking, this integration of organismic spatiotemporal trajectories with auto-associative filling-in could provide not just a basis for forming episodic memories, but also the imagination of novel scenarios (Hassabis & Maguire, 2009). Importantly, memories and imaginings can be generated by cortex on its own—given a lifetime of experience with a functioning H/E-S—but medial temporal lobe involvement appears to be required for these dynamics to be shaped in novel directions that break free of past experience (Canolty & Knight, 2010; Hills, 2019; MacKay, 2019; Sarel et al., 2017).

Figure 6. Hippocampally-orchestrated imaginative planning and action selection via generalized navigation/search. This illustration depicts memory and planning (as inference) via predictive processing, orchestrated via the spatiotemporal trajectories of the hippocampal/entorhinal system (H/E-S). In this model, precision-weighting/gain-amplification takes place via “big loop recurrence” with the frontal lobes (Koster et al., 2018), with the more specific suggestion that selection/biasing of policies over forward models cause efference copies to be projected to posterior generative models. In line with recent proposals (Barron et al., 2020), the hippocampus can operate with either “predictive-suppressive” or “fictive prediction error” modes, which are here suggested to correspond to degree of coupling with respective posterior or frontal cortices, with the former corresponding to direct suppression of observations, and the latter facilitating the ‘reinstatement’ of memories, and novel imaginings for the sake of planning and causal reasoning (Faul et al.,

2020; Pearl & Mackenzie, 2018). This frontal coupling is hypothesized to be a source of “successor representations” (i.e., population vectors forming predictive anticipatory sweeps of where the organism is likely to go next) via integration of likely policies and action models (via dorsal prefrontal cortex) and evaluations of likely outcomes (via ventral prefrontal cortex). In this model of generalized navigation, the hippocampal system iteratively contrasts predictive representations with (either sensory-coupled or imaginative) present state-estimates (from coupling with posterior cortices), where prediction-errors both modify future paths, and also allow for encoding of novel information within likely (generalized) spatiotemporal trajectories, given the meta-prior (or inductive bias) that organisms are likely to be pursuing valued goals as they navigate/forage-through physical and conceptual spaces. This alternation may occur at different phases of theta oscillations (Kay et al., 2020), so affording iterative contrasting of desired and current-estimated states, so canalizing neural activity for goal realization (Dohmatob et al., 2020), potentially including the formation of complex action sequences (either physical or virtual) via (conscious) back-chaining from potential desired states (i.e., goals) to presently-inferred realities (Safron, 2019b). Theoretically, this kind of iterated contrasting mechanism may also provide a source of high-level analogical (and potentially causal) reasoning (Crouse et al., 2020; Hill et al., 2019; Pearl & Mackenzie, 2018; Safron, 2019a). By orchestrating alternating counterfactual simulations (Kunz et al., 2019), the H/E-S may allow for evaluation of possible futures, biased on a moment-to-moment basis by integrated (spatialized) value representations from ventromedial prefrontal cortex (Baram et al., 2019), and also via “as-if-body loops” with interoceptive hierarchies (Damasio, 2012; Livneh et al., 2020). In this view of thought as generalized navigation, alternating exploration/sampling of counterfactuals could also be understood as implementing Markov chain Monte Carlo tree search over policy/value space for planning (Dohmatob et al., 2020; Parascandolo et al., 2020). Theoretically, similar processes could be involved in generating particular actions, if visualization of acts is accompanied by a critical mass of model-evidence (as recurrent activity) accumulating in interoceptive/salience hierarchies (Rueter et al., 2018). Speculatively, this threshold crossing (or phase transition) may represent a source of readiness potentials (Park et al., 2020; Travers et al., 2020; Verleger et al., 2016), potentially understood as a kind of “ignition” event and driver of workspace dynamics (understood as high-level Bayesian model selection), corresponding to explosive percolation, triggered by the accumulation of recurrent-activity/model-evidence within upper levels of frontoparietal control hierarchies for enacting/inferring a particular (virtual or physical) proprioceptive state, or pose (Adams et al., 2013).

The conscious turbo-code

Turbo-codes are used for reliably sending data over noisy channels (Berrou et al., 1993; Berrou & Glavieux, 1996), with efficiency approaching the Shannon limit, suggesting near optimality. These codes were independently discovered by the cryptography community and Judea Pearl (1982) as methods for approximate Bayesian inference via loopy belief propagation (McEliece et al., 1998). This method of extracting information from noisy signals has found a wide range of uses, including with respect to wireless communication standards. Perhaps these codes were also discovered by natural selection?

IWMT proposes that turbo-coding may be implemented by reciprocal effective connectivity between auto-associated cortical hierarchies, entailing shared reduced- dimensionality latent feature spaces among coupled autoencoders (Figure 5). Mechanistically, this would be realized by the formation of large-scale synchronous complexes as self-organizing harmonic modes (SOHMs) over connectivity backbones, some of which may entail action-oriented body maps (i.e., lateral parietal cortices) and visuospatial modeling (i.e., posterior medial cortices). Algorithmically, this would correspond to the calculation of approximate joint posteriors—and maximally likely (MAP) estimates derived thereof—via loopy belief propagation. Functionally, this would correspond to a series of estimated world states of sufficient reliability to form bases for action selection (Vul et al., 2014). Experientially, this would correspond to the stream of consciousness. (Note: While all synchronous complexes could potentially be interpreted as engaging in turbo-coding on some level of abstraction, IWMT suggests that only turbo-codes spanning multiple modalities are likely to be capable of generating conscious experiences.) The high-bandwidth message passing required for conscious turbo-coding may be enabled by the brain's rich-club, which consumes up to 50% of cortical metabolism (Heuvel et al., 2012). Theoretically, this metabolic expense may be (evolutionarily) justified by reducing the overall number of (noisy) neuronal signal transactions required to achieve adequately reliable perceptual inference, so increasing overall efficiency, and perhaps more importantly, decreasing latencies with respect to action selection. Perhaps even more importantly, turbo-coding over fronto-parietal networks may enable the inferential synergy required for consciously accessible experiences, and potentially the imagination of counterfactual scenarios (Buchsbaum et al., 2012; Pearl & Mackenzie, 2018; J. Schmidhuber, 2012), so facilitating a) causal reasoning, b) planning, and c) ‘offline’ learning (e.g. self-supervised training via imaginative self-play). Different rhythmic frequency bands may entail different kinds of information with respect to conscious turbo-codes. When beta complexes are cross-frequency phase coupled within alpha rhythms in posterior cortices, this may correspond to cross-modal message passing across the entire sensorium of the organism, organized within egocentric spatial reference frames, entailing consciousness (i.e., an experienced world) (Figure 3). When these alpha and beta complexes are further orchestrated by theta rhythms from the H/E-S and its “big loop recurrence” with frontal cortices (Koster et al., 2018), this may correspond to action-driven perception (including simulated actions), and reflective access via comparisons amongst conscious states. Thus, turbo-coding may help to explain some of the mechanisms enabling consciousness. However, these modeling efforts may themselves have a further (circular) causal significance in that they may help to facilitate the conditions that enable them. Under normal circumstances, only coherent and well-evidenced world

models are likely to enable loopy message passing to converge upon (approximate) posteriors, which in turn allow consciously experienced world models to arise. Developmentally, this kind of circular bootstrapping suggests that modeling capacity may increase non-linearly, potentially resulting in relatively abrupt (or punctuated) phase transitions for the evolution of consciousness (Isler et al., 2018). In this view, consciousness emerges from an auto-associative network of coupled generative decoders, connected together to constitute a turbo-code. When message passing is forced to converge via synchrony—and where synchrony emerges from convergent message passing—this may entail maximal a posteriori estimates as coherent/discrete vectors with maximal control in governing overall system evolution, sampled from probabilistic spatial-temporal-causal world models. Thus, consciousness (as turbo-code) may not only govern perception as Bayesian model selection, but also action selection (broadly construed to include thought as covert 'behavior').

Future directions for IIT and GNWT?

IWMT proposes that FEP-AI can be used as a framework for synergistically combining leading theories of consciousness, specifically focusing on IIT and GNWT. Below we will discuss some of the ways in which our understandings of the physical and computational bases of consciousness may be advanced through this synthesis, and then move on to discuss how these principles may also lead to potential advances in artificial intelligence.

A review of IIT terminology

The IIT formalism begins by choosing a candidate system—as substrate for consciousness or maximal complex with irreducible cause-effect power over itself—and then identifying the intrinsic cause-effect structure of that (proto-)system as a set of elements. The cause-effect structure for (and definition of) a system is composed of all maximally irreducible cause-effect distinctions (i.e., “concepts”, or “MICE” repertoires), which in recent developments within IIT have been extended to include relations between concepts/distinctions (Haun and Tononi, 2019). In this way, each and every intrinsically existing system is defined by a single (maximally irreducible) cause-effect structure, composed of at least one and possibly many distinctions/concepts/MICEs. The cause-effect structure and corresponding Phi value can be computed for any candidate system, but only candidates that maximize integrated information (as Phi, or self-cause-effect power) exclusively qualify as intrinsically existing systems. These maximal complexes (of experience) are referred to as MICS in IIT 3.0, and are hypothesized to correspond to the physical substrates of consciousness.

In this way, the interrelationships between the conceptual entities of IIT for analyzing potentially conscious systems may be summarized as follows: 1. Elements: Physical constituents of a system that can be manipulated and observed, which may or may not contribute to a system’s cause-effect structure. 2. Mechanisms: Individual elements or sets of elements that have irreducible cause- effect power by virtue of constraining both past and future states of other elements within a candidate system. 3. Cause-effect repertoire: Probability distributions over both past and future states for a mechanism, given its present state. 4. Concepts/distinctions: Mechanisms and their associated phi values and the intrinsic information (as distinctions) specified over their purviews with respect to repertoires of causes and effects within a candidate system, understood as an ability to maximally (irreducibly) constrain past and future states, given present states (i.e., MICE, or maximally irreducible cause effect repertoires). 5. Cause-effect structure: The set of all concepts/distinctions for all mechanisms within a system. 6. Conceptual structure: All cause-effect repertoires within a candidate system (which may potentially be reducible to simpler systems), so including all the intrinsic (cause-effect) information from the mechanisms of which a system is composed. 7. Complex: Candidate system with maximal Phi across all possible system definitions, existing for itself intrinsically, corresponding to the physical substrate of consciousness. 8. MICS: The maximally irreducible cause-effect structure entailed by a complex, corresponding to “what it is like” to be that intrinsically existing set of mechanisms, composed of MICE repertories, which correspond to the individual phenomenal distinctions within experience. In this way, IIT begins from axioms regarding the nature of consciousness, postulates corresponding mechanisms with those properties, and then formally analyzes candidate systems from a system-internal perspective in order to identify sets of mechanisms with maximal claim to intrinsic existence as nexuses of self-cause-effect- power (i.e., integrated information). A maximal complex is suggested to constitute a physical substrate of consciousness, entailing a MICS as the totality of experience (as concept) unfolding at a particular temporal and spatial grain, within which particular qualitative distinctions can be identified (i.e., MICE repertoires). IWMT supports this process for identifying maximally explanatory systems and even physical substrates of consciousness, except a MICS would entail subjectivity if (and only if) it corresponded to a joint probability distribution (or maximal estimate derived thereof) from a generative model with spatial, temporal, and causal coherence

for system and world. In this Bayesian/FEP-AI interpretation of IIT, MICE repertoires would correspond to particular factorizations of generative models, which would have phenomenal content by virtue of reflecting sensorimotor states for embodied-embedded agents. That is, the reason there may be “something that it is like” to be such a generative model, is because neural dynamics are coupled to (or entrained with) sensors and effectors (which are in turn coupled to system-world dynamics), so providing means of modeling spatiotemporally (and causally) coherent patterns in system and world. In this way, spatiotemporal (and causal) coherence for both system and world allows for the possibility of phenomenal consciousness through the alignment/representation of (or generalized synchrony between) those coherences.

Modules and workspaces as complexes of integrated information; potential physical substrates of consciousness

GNWT describes how global workspaces allow otherwise isolated specialist modules to exchange information. However, the dynamics by which local modules and global workspaces interact remain poorly understood. IIT describes how complexes of effective connectivity can have varying degrees of cause-effect power upon themselves. However, the functional relationships between complexes of integrated information remain poorly understood. With FEP-AI as an integrative framework, it may be possible to combine GNWT’s emphasis on function and IIT’s emphasis on dynamics in mutually informative ways. A potentially promising avenue is to apply IIT’s analytic approaches to modules and workspaces as complexes with varying degrees of irreducible self-cause-effect power, including with respect to the ways integrated information varies over the course of cognitive cycles. Some justification for this approach can be found by evaluating local modules and global workspaces in terms of the axioms of IIT: 1. Intrinsic existence a. Modules have cause-effect power upon themselves; modules depend upon workspaces in order to have cause-effect power upon each other. b. Workspaces have cause-effect power upon themselves and the modules with which they couple. That is, workspaces emerge via processes of self- organization involving reentrant signaling (Edelman et al., 2011). 2. Composition a. Modules have internal structure by which they exert cause-effect power on themselves, as well as other modules via workspaces. b. Workspaces have internal structures by which they exert cause-effect power upon themselves, the compositions of which depend on the modules with which they couple. That is, workspaces have particular

compositions, so allowing them to possess information about other structured phenomena, such as the compositions of the world (Whyte and Smith, 2020). 3. Information a. Modules have particular cause-effect structures that differentiate their specific compositions from other possible configurations; modules depend on workspaces to share this intrinsic information with each other. b. Workspaces have particular cause-effect structures that specify particular large-scale state compositions, which inform and are informed by the modules with which they couple in the context of cognitive cycles of perception and action selection, so acting as large-scale systemic causes (Madl et al., 2011). 4. Integration a. Modules specify unified cause-effect structures that are irreducible to sub- components. b. Workspaces specify unified cause-effect structures that are irreducible to sub-components, including information from the modules with which they couple. That is, workspaces are wholes that are greater than the sum of their parts (Chang et al., 2019). 5. Exclusion a. Modules specify particular cause-effect structures whose degree of intrinsic irreducibility evolves over particular spatial and temporal grains, depending on their ability to couple with each other and workspaces. b. Workspaces specify particular cause-effect structures whose degree of intrinsic irreducibility evolves over particular spatial and temporal scales, with particular community structures depending on both internal and external dynamics (Betzel et al., 2016).

Thus, both local modules and global workspaces can be viewed as constituting complexes of integrated information with varying amounts of irreducible self-cause- effect power (phi). The extent to which modules have more or less phi would specifically depend on the phase of cognitive cycles. Specifically, if “ignition” events correspond to the breakdown of local modularity via the formation of larger complexes of effective connectivity, then we would expect the relative phi for local modules and global workspaces to vary in an inverse fashion. IIT might view this changing modularity as trading off consciousness level between modules and workspaces, with separate modules entailing consciousness when they represent phi maxima, but with these consciousnesses being replaced with a single consciousness when workspace

dynamics are present. IWMT and GNWT, in contrast, would only view large-scale workspaces as being capable of supporting conscious experiences. IIT, in contrast to GNWT, does not view consciousness as corresponding to a global workspace, but only a posterior “hot zone” as constituting a phi maximum (Boly et al., 2017). The involvement of frontal cortices may be important for instantiating workspace dynamics of a more global nature in terms of widespread availability of information, but according to IIT, these systems would not themselves represent physical substrates of consciousness. IWMT agrees with IIT that basic phenomenality likely centers on posterior cortices, and also agrees with GNWT that frontal cortices are likely crucial for enabling conscious access and autonoetic awareness. However, IWMT disagrees with IIT that a given module would necessarily be conscious if it constitutes a complex that maximize integrated information (Phi). Rather, modules may be conscious only if they entail integrated models with spatial, temporal, and causal coherence for embodied systems and their relationships to environments in which they are embedded. Given the previously discussed properties of posterior medial cortices, synchronous activity within posterior hot zones could represent an instance of a (large) module being conscious when not participating in global workspace dynamics via the frontal lobes. However, this could also be viewed as a primarily semantic argument, as complexes capable of synergistically integrating information across occipital, temporal, and parietal cortices could reasonably be said to be functioning as ‘global’ workspaces. Perhaps some disputes between GNWT and IIT may be partially resolved by attempting to be more precise about how widespread integration must be to ‘count’ as global.

Cognitive cycles and fluctuating substrates of consciousness?

In mammals, “posterior hot zones” (Boly et al., 2017) may be both necessary and sufficient for generating consciousness (as integrated world modeling process), and these (both competitive and cooperative) attractor-formation processes may tend to be strictly dominated by dynamics within posterior association cortices. However, by coupling with posterior cortices, frontal cortices could help influence the specific compositions of maximal complexes on their timescales of formation. Frontal cortices may be able to influence posterior attracting networks before maximal coherence/integration is achieved, so defining spatial and temporal grains for qualia generation, enabling intentional control of attention, working memory, and action selection. When this effective coupling involves driving of frontal cortices by posterior complexes, this information may also be made more globally available for the sake of higher-order modeling. In these ways, IWMT is also in agreement with GNWT regarding the importance of frontal network hubs, although this may be the case for

conscious access, rather than the more posterior-located processes that may be responsible for generating coherent streams of experience. These hypotheses could potentially be tested via transcranial magnetic stimulation applied at different phases of cognitive cycles (Madl et al., 2011; Sasai et al., 2016) in which (possibly theta-coupled) alpha rhythms may alternate across frontal and posterior cortices, assessing whether intervention influences different kinds of either implicit (e.g. via perturbation complexity index (PCI) methods) or explicit modeling (Schartner et al., 2017). Alternatively, evoked complexity could be time-stamped to endogenous potentials as a measure of different kinds of integrative complexity. While PCI measures can potentially be explained without appealing to IIT, they can nonetheless be used as proxies for integrated information. If GNWT and IIT are compatible in the ways suggested by IWMT, then PCI should be higher during periods where workspace dynamics are present. This could potentially be tested by timing the TMS pulse to coincide with ignition events during which large scale integration occurs, or evaluating Lempel-Ziv complexity after putative ignition events such as the p300 (Mashour et al., 2020; Riggins & Scott, 2020). If integrative complexity measures were not found to be higher accompanying workspace dynamics, this could potentially falsify IWMT. Perhaps relatedly, an unresolved issue within IWMT is whether consciousness (as experience) corresponds to a series of discrete “snapshots” (Crick & Koch, 2003; Herzog et al., 2016; Madl et al., 2011), like a flipbook or sequential frames in a cartoon/comic (Ha & Schmidhuber, 2018). Alternatively, such discretization could reflect a process of consciously accessing—or sampling from, as in inference via Markov chain Monte Carlo (Dohmatob et al., 2020; S. J. Gershman, 2019)—an otherwise continuous stream of experience. IWMT’s account of synchronous complexes as entailing turbo-coding between coupled autoencoders suggests that consciousness could either be understood as flows of inference via traveling waves on a fine-grained level, or as self-organizing harmonic modes (SOHMs) when coarse-grained according to the scales at which various forms of functional closure are achieved (Chang et al., 2019; Joslyn, 2000), including those which would allow for the kinds of higher-order cognition involved in conscious access, self-awareness, forms of meta-awareness, acting with awareness, and planning. In terms of the machine learning models described above, ignition events could potentially be viewed as semi-stochastic sampling from latent spaces, used by variational auto-encoders to parameterize generative models in creating novel combinations of features. If these samples are biased according to histories of reward learning, then these events/samples could correspond to neural dynamics (including those entailing consciousness) being driven in directions that are most likely to realize organismic value, given the data of experience. In this way, it could be the case that ignition events themselves generate consciousness as a series of

“snapshots,” or maximal a posteriori (MAP) estimates from nervous systems viewed as generative models. Alternatively, it could be the case that ignition events correspond to a source of vectors that parameterize generative models that evolve through more continuous updating. The seemingly continuous nature of the stream of experience could be illusory, actually corresponding to a series of MAP estimates realized by the turbo coding of ignition events, corresponding to a parameterization of sampling operations, with cortical hierarchies functionally understood as coupled variational autoencoders. Or, iteratively forming these largescale attracting-states may instead be a highly efficient (and potentially optimal) means of realizing globally coherent/integrated inference, where organizing behavior based on a series of estimates has been demonstrated to also be highly efficient from a decision-theoretic perspective (Vul et al., 2014). All of these perspectives may be accurate, except with respect to different aspects of experience unfolding on different scales. While frontal-mediated conscious access may be discrete, posterior-generated basic phenomenal consciousness may truly be more like a continuous stream of entangled inferences, whose—potentially shockingly limited (Chater, 2018)—richness overflows awareness. IWMT currently does not have a definitive prediction as to whether the prefrontal cortices ever represent a physical substrate for consciousness as suggested by GNWT. While a “posterior hot zone” may provide both necessary and sufficient conditions for generating experience as suggested by IIT, it is unclear that frontal cortices ought to be considered as separate from these generative processes, particularly during ignition events in which large-scale frontoparietal complexes are observed. Alternatively, it may be the case that frontal cortices are incapable of significantly driving the heavily entangled internal dynamics of posterior cortices on the timescales at which integration occurs, where posterior-centered inter-relations may have enough causal density to establish functional closure with respect to the processes generating coherent (and so experienceable) world models. Considerations of developmental necessity may also be relevant to debates between IIT and GNWT regarding the neural substrates of consciousness. Frontal cortices may potentially be necessary for the initial development of basic phenomenal consciousness, but not for its continued realization after sufficient experience. That is, frontal cortices may be essential for bootstrapping phenomenal consciousness via the construction of coherent world models, but once developed, these experience-generating capacities—but probably not conscious access, contrary evidence notwithstanding (Bor et al., 2017)—may be preserved even with complete disruption of these initially necessary enabling conditions. Yet another possibility is that frontal cortices may themselves have enough integrative capacity over requisite sources of information that they represent sufficient substrates of consciousness on their own, potentially offering a source of predictions for

what posterior cortices are likely to experience in the future (Ha & Schmidhuber, 2018; Knight & Grabowecky, 1995; J. X. Wang et al., 2018). This hypothesis of forward-looking PFCs would be consistent with their roles in action selection and motor control through predicting the sensory consequences of movement (Adams et al., 2013). However, for frontal cortices to themselves generate experience, IWMT would require sufficiency with respect to establishing perspectival reference frames with spatiotemporal and causal coherence. Regardless of whether or not frontal cortices are considered to be directly part of subnetworks generating consciousness, the nature of subjective experience will likely heavily depend on their involvement as emphasized by GNWT and higher order theories (Brown et al., 2019; Shea & Frith, 2019). While (very difficult to test) dissociations may be expected with respect to phenomenal consciousness being possible without conscious access, the qualities of experience will depend on their multi-scale interactions with higher order cognitive processes. For example, the act of introspecting will substantially change the nature of what is (a)perceived (e.g. attention; Sperling phenomena) (Manning et al., 2012).

Bayesian blur problems and solutions; quasi-quantum consciousness?

While the brain probably does not support the kinds of large-scale coherence required for quantum computation (Schmidhuber, 2000; Tegmark, 2000), it may nonetheless be the case that neuronal dynamics can be viewed as emulating quantum- like computations (e.g. annealing) by classical means (Borders et al., 2019; Coyle et al., 2019; Guillet et al., 2019). Machine learning algorithms play a central role in IWMT, and quantum implementations of autoencoders (e.g. as used in error-correcting codes) may be relevant for making further advances in developing functional analogues for the computational properties of brains. Very speculatively, it may even be the case that dynamic reconfigurations of neuronal microtubules could emulate quantum-like computation in orchestrating signaling (e.g. via transportation rates for neurotransmitter containing vesicles) and memory (via synaptic modifications and synaptogenesis), while not themselves involving sustained quantum coherence (cf. Orch OR theories) (McKemmish et al., 2009). Indeed, quantum mechanics inspired models could have potential relevance to solving the “Bayesian blur problem” (Clark, 2018). That is, how can a probabilistic model generate seemingly unified experience (cf. the intuition underlying the exclusion axiom from IIT) composed of discrete perceptual experiences, rather than a superposition of possibilities? Functionally speaking, it may be desirable for the brain to provide discrete estimates of—or highly precise distributions over—world states for the sake coherent action selection. However, a “Bayesian blur solution” could also be proposed, in that it may also be desirable to maintain full probability distributions with

multiple possibilities kept in play for the sake of adaptation and exploration. In considering workspace dynamics as implementing Bayesian model selection, it may be the case that brains obtain the best of both discrete and probabilistic modeling by “dividing and conquering” across different phases of cognitive cycles, or possibly across brain areas (Gazzaniga, 2018; McGilchrist, 2019). Alternating workspace modes— potentially reflected by the formation/dissolution of mesoscale connectomic modularity (Betzel et al., 2016)—could allow periods where multiple competing and cooperating hypotheses can remain in play, followed by winner-take-all dynamics when this information is integrated into larger scale networks and models (Cheung et al., 2019), and then “broadcasted” back to modules as they re-form. Stanislas Dehaene intriguingly (2014) suggested that the formation of workspaces via ignition events could be understood as a kind of phase change akin to those observed in physical systems. Intriguingly, he goes onto propose that a potentially productive analogy could be found in models of wave function collapse in quantum physics, where a superposition of possibilities is reduced to a determinate classical world. IWMT considers this to be a promising avenue for future investigation. It may be similarly productive to explore whether multiple interpretations of quantum mechanics apply to varying degrees as abstract descriptions of varying informational modes within minds, understood in terms of varieties of Bayesian model selection and inferential dynamics. That is, conceptualizations from multiple quantum interpretations (Schmidhuber, 2000; Tegmark, 2014; Carroll, 2016) could potentially apply to different aspects of integrative world modeling. Could entanglement be used to model changes in the precision of probabilistic densities as a result of coupling sub-systems? Could more precise distributions (or estimates derived thereof) due to re-entrant signaling from prefrontal cortices (PFCs) be used to implement a kind of Copenhagen-style observer-dependent selection of classical phenomena? Could marginalization via self- organizing synchronous complexes be modeled in a similar manner to spontaneous wave function collapse (and quantum Darwinian interpretations)? Could periods of high modularity/segregation for functional connectomes be productively analogized with branching many worlds? Could relationships between fine-grained neuronal message passing and standing wave descriptions exhibit abstract similarities with Bohmian pilot waves (e.g. chained gamma complexes as quantized prediction errors and solitons)? To be clear, these are all (very) highly speculative analogies for information dynamics, and quantum physical phenomena are likely not directly relevant to the brain's computational abilities in any meaningful sense, given the hot and crowded nature of biological systems (Tegmark, 2000). Nonetheless, such metaphors/models may potentially afford insights into the nature of neuronal information processing and its connections to different aspects of consciousness.

Regarding “consciousness as collapsing agent” theories (to continue with the analogical extension of quantum mechanics described above): If PFC involvement is important for establishing synchronous coherence in posterior cortices, then this process of dimensionality reduction over dynamics may potentially be likened to wave function collapse by a (potentially unconscious) PFC ‘observer.’ That is, the operation/action of conscious access via PFC re-entry may be required for transforming a continuous sea of probabilities into a discrete stream of experience—as the iterated generation of particular qualia. If the “Bayesian blur” problem is overcome in this manner, then experience may not be solely generated by posterior cortices as described above, potentially favoring GNWT’s suggestion that frontal lobes are part of the physical substrates of consciousness. However, this functionality could potentially be achieved at different stages of cognitive cycles, so excluding PFCs from stages where consciousness is generated (cf. dual phase evolution) (Paperin et al., 2011). Alternatively, another possibility would involve basic phenomenal consciousness being more diffuse/probabilistic without PFC-involvement, but where conscious access is more particular/discrete. But if this kind of PFC-independent modeling lacks sufficient organization with respect to space, time, and cause, then there may be insufficient coherence to result in the appearance of an experienced world. If this were the case, then it would challenge the distinction between phenomenal and access consciousness, and may potentially support some theories emphasizing higher order cognition (LeDoux and Brown, 2017). The evolving adversarial collaboration between IIT and GNWT theorists may potentially provide evidence that could disambiguate some of these matters.

Mechanisms for integration and workspace dynamics

IWMT views ignition events in terms of the formation of self-organizing harmonic modes (SOHMs), entailing message passing in nervous systems understood as Bayesian belief networks. In this way, the formation of any meta-stable synchronous complex is viewed as both an ignition event and establishment of a kind of workspace, regardless of whether or not the frontal lobes and ‘global’ access is achieved. In all cases, SOHMs are hypothesized to entail loopy belief propagation and marginalization over effectively connected subnetworks. In the case of small ensembles synchronized at fast gamma frequencies, SOHMs may contribute to the communication of prediction errors up cortical hierarchies (Bastos et al., 2012; Scheeringa & Fries, 2019) via quantized packets of information (as sufficient/summary statistics), so establishing marginal message passing regimes (Parr, Markovic, et al., 2019). In the case of large ensembles synchronized at beta, alpha, and theta frequencies, SOHMs may allow for large-scale

updating of beliefs and sources of integrative predictions from deeper portions of generative models. Considering their potential central role for driving neural evolution, it is worth considering in detail the dynamics by which synchronous complexes form. Some recent promising work in this direction can be found in models of synchronous dynamics emerging through collaborative inference among interacting oscillators (Palacios et al., 2019). This kind of coordination in the Free Energy Principle and Active Inference (FEP- AI) framework is often described in terms of the near ubiquitous phenomenon whereby systems minimize free energy through generalized synchrony (Strogatz, 2012; Kachman et al., 2017), as first demonstrated by Huygens with respect to pendulum clocks (Oliveira and Melo, 2015; Willms et al.). Here, I will provide an informal sketch of how SOHM-formation might proceed and the potential functional consequences that may result from these processes: 1. Let us consider a set of neuronal oscillators that are initially maximally desynchronized, but which gradually acquire a shared absorbing rhythm. 2. If neuronal oscillators happen to interact while phase-aligned, then they will be more likely to be able to drive activity due to stimulation happening within windows wherein temporal summation is possible. 3. If reciprocal connectivity is present between phase-aligned neuronal oscillators, then there is a potential for positive feedback and self-sustaining rhythmic activity. 4. In this way, initial locally synchronized ensembles may be able to spread synchronous organization as the stability of their rhythmic activity provides opportunities for additional phase-aligned oscillators to become entrained to the absorbing rhythm. 5. However, this potential for positive feedback must be accompanied by negative feedback mechanisms (e.g. GABAergic interneurons) to maintain adaptive exploration of state spaces (Friston et al., 2012), and also to avoid the kinds of explosive percolation events observed in clinical conditions like epilepsy (Bartolomei and Naccache, 2011; D’Souza and Nagler, 2015; Safron, 2016; Kinouchi et al., 2019). 6. During periods of minimal synchronization, we may expect synchronizing ensembles to be maximally sensitive to signals at any phase (Lahav et al., 2018), but with minimal abilities to drive coupling systems. 7. During periods of maximum synchronization, we may expect synchronizing ensembles to be maximally sensitive to phase-aligned signals—as well as minimally sensitive to non-phase-aligned signals—and with maximal abilities to drive coupling systems.

8. During intermediate periods where synchronization dynamics are accumulating, we may expect sensitivity to a greater diversity of signals, with a potential capacity for mutual influence between coupling systems during this bifurcation window. With respect to belief propagation in Bayesian networks, all of this could potentially be understood as a means of enabling and constraining belief propagation, influencing which messages will be likely to be exchanged on what timescales. In terms of mesoscale and macroscale neuronal dynamics, we might expect large- scale SOHMs to be particularly likely to form in proximity to rich-club hubs of the brain with their high degrees of reciprocal connectivity. These core networks have been found to provide backbones of effective connectivity and robust sources of synchronizing dynamics (Castro et al., 2020). Within these highly interconnected systems, signals may be particularly likely to undergo positive feedback amplification, where this explosive signal transduction may be able to temporarily form synchronous complexes capable of integrating information from across the brain and then propagating (or “broadcasting”) this information to the rest of the network as Bayesian beliefs (or priors in predictive coding). In terms of generalized synchrony, direction of entraining influence may potentially switch between peripheral and core networks before and after critical ignition events. Theoretically, peripheral sensory hierarchies may asymmetrically entrain deeper levels with core connectivity, seeding them with ascending prediction errors, communicated via driving inputs at gamma frequencies. In this way, Bayesian model selection would be driven via a process of differential seeding of core states via competition (and cooperation) amongst neuronal coalitions entailing hypotheses regarding latent causes of sensory observations. Then, these discretely updated core states from deep in the heterarchy could be used to asymmetrically drive peripheral networks. According to IWMT, these core inferences would be communicated at beta frequencies for specific predictions, alpha frequencies for predictions integrated within egocentric reference frames, and theta frequencies for predictions shaped by particular actions (broadly construed to include mental acts such as attentional fixations (Parr, Corcoran, et al., 2019; Safron, 2019b)). Thus, SOHMs and the processes by which they form may function as complexes of integrated information and sources of workspace dynamics, so implementing Bayesian model selection on multiple levels. This multi- level selection—which may also be understood in terms of neural Darwinism and dual- phase evolution (Paperin et al., 2011)—may proceed simultaneously over multiple scales, with both global serial and local parallel integration being implemented by SOHMs of varying spatial (and temporal) extents. It is worth noting that this proposal does not depend on any given account of predictive processing being accurate. For example, it may be the case that descending

modulatory inputs at slower frequencies do not necessarily involve predictive explaining away, but could instead be used to allow sensory observations to ascend with more feedforward driving (George et al., 2020; Heeger, 2017)— which would not be incompatible with an interpretation of attending based on precision weighting (i.e., Kalman gain)—as may be the case with respect to theta-gamma cross-frequency phase coupling (Buzsáki & Watson, 2012; Canolty et al., 2010). It may be the case that slower frequencies could be used to either inhibit or promote the relative contributions of different sensory observations—communicated at faster gamma frequencies—to iterative rounds of Bayesian model selection. This kind of adaptive enhancement of prediction errors may help to reconcile predictive processing with findings that consciousness level and phenomenal binding have been associated with increases in gamma power and inter-electrode gamma coherence (Singer, 2001, 2007), potentially realized by mechanisms involving zero-lag phase synchronization (Gollo et al., 2014). Alternatively, it may merely be the case that more precise predictions tend to be accompanied by increased prediction errors, without observations being specifically enhanced through attentional selection mechanisms. In either case, predictive processing diverges with some more well-known ideas in suggesting that gamma-band activity may not itself generate consciousness, but instead indirectly modulates the updating of beliefs forming at slower frequencies.

Towards new methods of estimating integrated information

According to IWMT, IIT’s maximal complexes and GNWT’s workspaces are emergent eigenmodes of effective connectivity (Friston et al., 2014; Atasoy et al., 2018), or self-organizing harmonic modes (SOHMs) (Safron, 2020). Considering the network properties of brains (Heuvel and Sporns, 2011), these SOHMs are likely to be centered around deep portions of hierarchical generative models which may enable (via turbo- coding) convergence upon approximate posteriors (and empirical priors for subsequent rounds of Bayesian model selection). If this integrative view is accurate, then it may provide new means of evaluating phi estimation methods (Tegmark, 2016), with significance for both basic research and clinical practice. Reliable means of estimating phi are necessary for practical applications, as the formally-prescribed calculations are NP-hard (Mayner et al., 2018; Toker and Sommer, 2019), and so require simplifying assumptions for even modestly-sized causal networks. Nature, in contrast may implicitly perform such calculations nearly ‘for free’ via Hamilton’s principle of least action. Unfortunately, Seth and colleagues (2019) have found radically different integrated information estimates can be derived with seemingly reasonable modeling assumptions. If IWMT’s proposal is correct—that phi corresponds to self-model- evidence; a claim which has recently received endorsement from the primary architect

of FEP-AI (2020)—then applying different integration estimation methods to Bayesian networks may provide a ground truth for adjudicating between different estimation approaches. If IWMT’s proposal is correct in suggesting a complex with maximally irreducible cause-effect power (i.e., a MICS) is also a maximally informative subgraph, then this correspondence could provide further means of estimating integrated information (phi). [Note: IWMT does not necessarily ascribe to the particular definition of phi provided by IIT 3.0, as a case could be made for meaningful informational synergy being better reflected in other ways in different circumstances.] According to FEP-AI, neural dynamics can be viewed as implementing approximate Bayesian inference, where activation cascades constitute a message passing regime (Friston et al., 2017; Parr et al., 2019). Theoretically, differential rates of message passing may automatically discover maximally connected subnetworks (Mišić et al., 2015), and in doing so, converge on processes of variable elimination (Koller and Friedman, 2009). In variable elimination, marginal information from factors are progressively integrated into an induced graph—or maximal clique—thereby providing a maximally likely a posterior (MAP) estimate from the overall belief network. If maximal complexes tend to be centered on these maximal cliques (or are equivalent to them) these internally- directed cause-effect structures could have actual semantic content by virtue of containing (or entailing) MAP estimates over hidden causes that define self and world for embodied-embedded agents. It is unclear whether these specific correspondences between probabilistic graphical modeling techniques and concepts from IIT will be found to be valid. However, if IWMT is accurate in claiming that self-cause-effect power in IIT corresponds with self-model-evidence in FEP-AI, then relative merits for different phi estimation techniques could be evaluated based on their abilities to track the inferential properties of Bayesian networks. Specifically, metrics of quality for phi estimates could be indicated by quicker convergence times for loopy message passing, more precise posterior distributions and accurate MAP estimates, and enhanced learning rate or inferential power more generally (Koller and Friedman, 2009). IWMT’s synthesis could also potentially lead to novel phi estimation methods based on modeling processes by which complexes of integrated information emerge via self-organization (i.e., SOHMs). Although a detailed handling is beyond the scope of the present discussion, useful means of estimating phi and modeling SOHM/complex formation may potentially be found in flow networks (cf. max-flow-min-cut theorem) (Dantzig and Fulkerson, 1955; Garg et al., 1996; Hoffman, 2003) and other kinds of physical systems. Further, game theoretically informed constructs such as Shapley centrality have been used in the study of dynamic networks (Chen and Teng, 2017; Ghorbani and Zou, 2020), and such measures may be relevant for modeling processes

by which complexes of cause-effect power emerge. Estimation techniques inspired by these kinds of analogies may potentially be more computationally tractable than other phi estimation methods, and may also provide further bridges between IIT and FEP-AI (and thereby GNWT when workspace dynamics are considered to represent Bayesian model selection). Speculatively, it appears that there may be potentially fruitful correspondences between maximal complexes in IIT and the identification of the kernel (and/or nucleolus) of the core of a game (Schmeidler, 1969; Maschler et al., 1979; Maschler, 1992). But with respect to the core of a cooperative game, integrated information as cause-effect power would refer to a nexus of bargaining influence amongst players in a coalition. Below, I provide an informal sketch of how such an analysis might proceed: 1. Persisting neuronal dynamics may be modeled as quasi-agents, with patterns constituted by implicit models for their continued existence (i.e., preserving their Markov blankets). 2. For these quasi-agents, utility would be defined in terms of generating self- model-evidence, and cost would be defined in terms of prediction error—within a generalized Darwinian framework, these implicit utility functions would also be fitness functions (Safron, 2019a). 3. Hamilton’s principle of least action implies that each dynamical pattern will always choose its best response for minimizing free energy (Kaila and Annila, 2008; Friston, 2019). 4. In this self-prediction game, stable coalitions (as cores) would correspond to Nash equilibrium solutions, wherein competing and cooperating neuronal quasi- agents are not incentivized to leave the grand coalition, because doing so would increase free energy. 5. When stable game theoretic equilibria can be found, the center of gravity for these geometries would also represent Shapley values (Maschler et al., 1979), or solutions that balance the respective utilities and bargaining power for participating quasi-agents. 6. If the game being played entails hypotheses regarding latent causes, and if bargaining power is a function of predictive ability, then this Shapley value may also represent a precision-weighted probabilistic model of world states, or maximal (MAP) estimate derived thereof. While admittedly speculative and underdeveloped, such a game theoretic derivation of complexes of integrated information—functioning as workspaces—could help provide a further cybernetic-computational grounding for IIT (and GNWT), answering the question of why there may be “something that it is like” to be a maximal complex, or workspace, or any physical system. That is, if the formation processes of workspaces and complexes entail ‘calculation’ of probabilistic estimates of system-environment

states, then for an embodied-embedded agent this could correspond to a “lived” world. Alternatively (and very speculatively), similar analyses (and implications) may potentially be derived by modeling neural dynamics as entailing a kind of prediction market (Conitzer, 2012), with estimated prices representing probabilities for the sufficient statistics for world models. These kinds of handlings of integrative processes may render notions of “neuronal coalitions” (Crick and Koch, 2003) as something more than a mere metaphor, and could also give new meaning to Edelman’s (2011) description of consciousness as being realized by a “dynamic core” (Safron, 2019b).

Beyond integrated information?

IIT has evolved as a theory over two decades of concerted effort, and further refinements and elaborations of the theory are currently being developed. This ongoing evolution has caused some people to question whether IIT’s postulated mechanisms are truly grounded in axiomatic principles of phenomenology (Bayne, 2018), and whether its methods may contain questionable modeling assumptions. Indeed, many of the most practically useful (and highly face valid) phi estimation techniques rely on previous versions of the theory, such as estimating integrated information based on causal density (Barrett & Seth, 2011; Seth et al., 2011). Much skepticism regarding IIT has resulted from demonstrations of high phi values being associated with systems for which there are strong a priori reasons to suspect a lack of consciousness, such as the kinds of 2D grids used in expander graphs (Aaronson, 2014). Yet such objections to IIT’s validity can be readily handled by considering integrated information to be necessary, but not sufficient for consciousness without the cybernetic grounding suggested by IWMT. However, the potential modeling capacity of even a single 2D grid should not be underestimated (T. Wang & Roychowdhury, 2019). With respect to the particular example of the dubious consciousness of expander graphs, it should be noted that such systems have many of the properties which may contribute to the computational power of brains, including small-world connectivity (Takagi, 2018), sparseness (Ahmad & Scheinkman, 2019), and ability to support error-correcting codes (Liu & Poulin, 2019). Theoretically, an arrangement of hierarchically-organized expander graphs could be used to implement predictive processing and may be functionally equivalent to the kinds of turbo coding adduced by IWMT. Nonetheless IWMT states that such systems will not be conscious unless their functionality enables coherently-integrated world modeling, which may be afforded in mammalian brains by posterior medial cortices (Figure 2) with respect to visual phenomenology and a sense of quasi-Cartesian space (Sutterer et al., 2021). Others have questioned the merit of emphasizing a single measure for the informational dynamics of complex systems (Mediano et al., 2019). This work has

challenged the assumption of pairwise causal interactions in networks, instead focusing on dynamical complexity in terms of the decomposition of integrated information into potentially coexisting modes of informational flows. These novel measures reveal that integration processes can be understood as aggregates of multiple heterogeneous phenomena such as informational storage, copy, transfer, erasure, downward causation, and upward causation. Promisingly, these decomposed measures of integrated information could allow for the creation of novel methods for assessing informational dynamics, which may be superior in some use cases. IWMT agrees with Mediano and colleagues that integrated information is not the only valuable way to look at consciousness or complex systems more generally. Nonetheless, aggregations of heterogeneous phenomena can produce wholes that are greater than the sum of their parts. Mind and life are two such phenomena, and this kind of functional synergy may also apply to informational constructs (including mind and life). If integrated information corresponds to self-model-evidence as described by FEP-AI, then this would be a very special measure of dynamical complexity, potentially indicating the ability of whole systems to be both stable, adaptive, and even autonomous (Albantakis, 2017). Indeed, connections between integrated information and self-organized criticality further suggests that we may be dealing with a measure that applies to all systems capable of not just persisting, but evolving (Arsiwalla et al., 2017; Arsiwalla & Verschure, 2016; Hoffmann & Payton, 2018; Takagi, 2018).

IWMT and Universal Intelligence

Many of the ideas described above have extensive correspondences with the work of Juergen Schmidhuber (2020, 2021). This pioneering researcher’s intellectual contributions include early developments in unsupervised machine learning, characterization of fundamental principles of intelligence, discovery of means of realizing scalable deep learning, designing world models of the kinds emphasized by IWMT, and more (J. Schmidhuber, 1990, 1991, 1992, 2000, 2007a, 2007b, 2012, 2015, 2018, 2002b). While this body of work cannot be adequately described in a single article, below I will explore how the principles of universal intelligence and algorithmic information theory may shed light on the nature(s) of consciousness.

FEP-AI and AIXI: Intelligence as Prediction/Compression

IWMT was developed within the unifying framework of FEP-AI as a formally- grounded model of intelligent behavior, with rich connections to both empirical phenomena and advances in machine learning. In this view, consciousness and cognition more generally is understood as a process of learning how to better predict

the world for the sake of adaptive control. However, these ideas could have been similarly expressed in the language of algorithmic information theory (Kolmogorov, 1963; J. Schmidhuber, 2002a), wherein complexity is quantified according to the length of programs capable of generating patterns of data (rather than the number of parameters for a generative model). From this point of view, intelligence is understood in terms of abilities to effectively compress information with algorithms of minimal complexity. These two perspectives can be understood as mutually supporting, in that predictability entails compressibility. If one is able to develop a predictive model of a system, then one also has access to some kind of code (even if only implicitly) capable of describing relevant information in a more compressed fashion. Similarly, if compression allows information to be represented with greater efficiency, then this compressed knowledge could be used as a basis for modeling future likely events, given past and present data. This understanding of intelligence as compression was given a formal description in AIXI, a provably-optimal model of intelligent behavior that combines algorithmic and sequential decision theories (Hutter, 2000). Solomonoff induction provides a Bayesian derivation of Occam’s razor (Solomonoff, 2009), in selecting models that minimize the Kolmogorov complexity of associated programs. AIXI agents use this principle in selecting programs that generate actions expected to maximize expected reward over some time horizon for an agent. This parsimony-constraint also constitutes a highly adaptive inductive bias and meta-prior in that we should indeed expect to be more likely to encounter simpler processes in the worlds we encounter (Campbell, 2016; Feynman, 1965; Kaila & Annila, 2008; J. Schmidhuber, 2000; Vanchurin, 2020), all else being equal. Similarly, FEP-AI agents select policies (as Bayesian model selection over predictions) expected to maximize model evidence for realizing adaptive system-world states. However, this expectation is evaluated according to a free energy functional that prioritizes inferences based on their ability to fit data (the enthalpy term), penalized by the degree to which updates of generative models diverge from priors (the entropy term), so preventing overfitting and facilitating knowledge generalization (Hanson, 1990). While thoroughly exploring connections between FEP-AI and AIXI is beyond the scope of this paper, their parallels are striking in that both frameworks prescribe choice behavior as the model-based realization of preferences under conditions of uncertainty, where governing models are privileged according to parsimony. Further, both FEP-AI and AIXI agents operate according to curiosity motivations, in which choices are selected not only to realize particular outcomes, but to explore for the sake of acquiring novel information in the service of model evolution (K. J. Friston, Lin, et al., 2017; Orseau et al., 2013). Both AIXI and FEP-AI confront the challenge of not being able to evaluate the full distribution of hypotheses required for normative program/model

selection, instead relying on approximate inferred distributions. Further, both frameworks also attempt to overcome potentially complicated issues around ergodic exploration of state spaces with various forms of sophisticated planning (Aslanides et al., 2017; K. Friston et al., 2020). Taken together, the combination of these frameworks may provide a provably-optimal, formally-grounded theory for studying intelligent behavior in both biological and artificial systems. Further conceptual and functional integration between AIXI and FEP-AI could potentially be achievable through the study of generative modeling based on probabilistic programs (Lake et al., 2015; Lázaro- Gredilla et al., 2019; Ullman & Tenenbaum, 2020). With relevance to IWMT, consciousness may be understood as kind of lingua franca (or semi-interpretable shared latent space) for more efficiently converting between heterogeneous programs for the sake of promoting functional synergy (Safron, 2020a, 2020b; VanRullen & Kanai, 2021). Although AIXI and FEP-AI both specify optimality criteria, both frameworks require the further specification of process theories and heuristic implementations in order to realize these principles in actual systems (Hesp et al., 2020; Veness et al., 2010). Below I will focus on some of the work of Schmidhuber (2020, 2021) and colleagues, in which principles of universal computation have been used to inform the creation of artificial systems with many of the hallmarks of biological intelligences. Understanding the design of these systems may be informative for understanding not only computational properties of nervous systems, but also their ability to generate integrative world models for the sake of adaptively controlling behavior.

Recurrent networks, universal computation, generalized predictive coding, unfolding, and (potentially conscious) self-world modeling

In describing brain function in terms of generative modeling, IWMT attempts to model different aspects of nervous systems in terms of principles from machine learning. Autoencoders are identified as a particularly promising framework for understanding cortical generative models due to their architectural structures reflecting core principles of FEP-AI (and also AIXI). By training systems to reconstruct data while filtering (or compressing) information through dimensionality-reducing bottlenecks, this process induces the discovery of both accurate and parsimonious models of data in the service of the adaptive control of behavior (Lange & Riedmiller, 2010). IWMT’s description of the cortical hierarchies as consisting of “folded” autoencoders was proposed to provide a bridge between machine learning and predictive-coding models of cortical functioning. Encouraging convergence may be found in that these autoencoder-inspired models were developed without knowledge of similar proposals by others (Jiang et al., 2019; Kanai et al., 2019; Lillicrap et al., 2020; Lotter et al., 2016; Y. Wu et al., 2018).

However, these computational principles have an older lineage predating “The Helmholtz machine” and its later elaboration in the form of variational autoencoders (Dayan et al., 1995; Kingma & Welling, 2014). These “Neural Sequence Chunkers” (NSCs) instantiate nearly every functional aspect of IWMT’s proposed architecture for integrated world modeling (J. Schmidhuber, 1991). NSCs consist of recurrent neural networks (RNNs) organized into a predictive hierarchy, where each RNN attempts to predict data from the level below, and where only unpredicted information is passed upwards. These predictions are realized in the form of recurrent dynamics (Candadai & Izquierdo, 2020; Lu & Bassett, 2020), whose unfolding entails a kind of search processes via competitive/cooperative attractor formation over states capable of most efficiently responding to—or resonating with (Rumelhart & McClelland, 1987; Safron, 2020b)— ascending data streams. In this way, much as in FEP-AI, predictive abilities come nearly “for free” via Hamilton’s principle of least action (Ali et al., 2021; K. J. Friston, 2019; Kachman et al., 2017; Kaila & Annila, 2008), as dynamical systems automatically minimize thermodynamic (and informational) free energy by virtue of greater flux becoming more likely to be channeled through efficient and unobstructed flow paths (Bejan & Lorente, 2010). RNNs are Turing complete in that they are theoretically capable of performing any computational operation, partially by virtue of the fact that small clusters of signaling neurons may entail the logical operations such as NAND gates (McCulloch & Pitts, 1943). Further, considering that faster forming attractors are more likely to dominate subsequent dynamics, such systems could be considered to reflect the “Speed prior”, whereby the search for more parsimonious models is heuristically realized by the selection of faster running programs (J. Schmidhuber, 2002b). Attracting states dependent upon communication along fewer synaptic connections can be thought of as minimal length descriptions, given data. In this way, each RNN constitutes an autoencoder, which when hierarchically organized constitute an even larger autoencoding system (Safron, 2020b). Thus, predictive coding via “folded” (or stacked) autoencoders can be first identified in the form of NSCs as the first working deep learning system. Even more, given the recurrent message passing of NSCs (or “stacked” autoencoders), the system as a whole can be considered to be an RNN, the significance of which will be described below. RNN-based NSCs exhibited all of the virtues of predictive coding and more in forming increasingly predictive and sparse representations via predictive suppression of ascending signals (Ahmad & Scheinkman, 2019; Hanson, 1990; N. Srivastava et al., 2014). However, such systems have even greater power than strictly suppressive predictive coding architectures (Bastos et al., 2012; Mumford, 1991; Rao & Ballard, 1999), in that auto-associative matching/resonance allows for microcolumn-like ensemble inference as well as differential prioritization and flexible recombination of

information (George et al., 2020; Greff et al., 2020; Grossberg, 2017; Heeger, 2017). The auto-associative properties of RNNs afford an efficient (free-energy-minimizing) basis for generative modeling in being capable of filling-in likely patterns of data, given experience. Further, the dynamic nature of RNN-based computation is naturally well- suited for instantiating sequential representation of temporally-extended processes, which IWMT stipulates to be a necessary coherence-enabling condition for conscious world modeling. Even more, the kinds of hierarchically-organized RNNs embodied in NSCs naturally provide a basis for representing extended unfoldings via nested hierarchy of recurrent dynamics evolving over various timescales, so affording generative modeling with temporal depth (K. J. Friston, Rosch, et al., 2017), and potentially counterfactual richness (K. J. Friston, 2018; Pearl & Mackenzie, 2018; Seth, 2014). Some of these temporally-extended unfoldings include agent-information as sources of relatively invariant—but nonetheless dynamic—structure across a broad range of tasks. Given these invariances, the predictive coding emerging from NSCs will nearly automatically discover efficient encodings of structure for self and other (J. Schmidhuber, 2020), potentially facilitating meta-learning and knowledge-transfer across training epochs, including explicit self-modeling for the sake of reasoning, planning, and selecting actions (J. Schmidhuber, 2015). In contrast to feedforward neural networks (FNNs), RNNs allow for multiple forms of open-ended learning (J. Schmidhuber, 2007a, 2012; R. Wang et al., 2020), in that attractor dynamics may continually evolve until they discover configurations capable of predicting/compressing likely patterns of data. FNNs can be used to approximate any function (Csáji, 2001), but this capacity for universal computation may often be more of a theoretical variety that may be difficult to achieve in practice (Malach & Shalev- Shwartz, 2019), even with the enhanced processing efficiency afforded by adding layers for hierarchical pattern abstraction (Lin et al., 2017; R. K. Srivastava et al., 2015). The potential limitations of FNNs can potentially be understood in light of their relationship with recurrent networks. RNNs can be translated into feedforward systems through “unrolling” (Hochreiter & Schmidhuber, 1997; Sherstinsky, 2020), wherein the evolution of dynamics across time points can be represented as subsequent layers in an FNN hierarchy, and vice versa. Some of the success of very deep FNNs such as “Resnets” could potentially be explainable in terms of entailing RNNs whose dynamics are allowed to unfold over longer timescales in searching for efficient encodings. However, FNN systems are still limited relative to their RNN brethren in that the former are limited to exploring inferential spaces over a curtailed length of time, while the latter can explore without these limitations and come to represent arbitrarily extended sequences. On a higher level of abstraction, such open-endedness allows for one of the holy grails of AI in terms of enabling transfer and meta-learning across the entire lifetime of a system (J. Schmidhuber, 2018; J. X. Wang et al., 2018).

However, this capacity for open-ended evolution is also a potential liability of RNNs, in that they may become difficult to train with backpropagation, partially due to potential non-linearities in recurrent dynamics. More specifically, training signals may either become exponentially amplified or diminished via feedback loops—or via the number of layers involved in very deep FNNs—resulting in either exploding or vanishing gradients, so rendering credit assignment intractable. These potential problems for RNNs were largely solved by the advent of “long short-term memories” (LSTMs) (Hochreiter & Schmidhuber, 1997), wherein recurrent networks are provided flexible routing capacities for controlling information-flow. This functionality is achieved via an architecture in which RNN nodes contain nested (trainable) gate-RNNs that allow information to either be ignored, held onto for a period of time, or forgotten. Notably, LSTMs not only overcame a major challenge in the deployment of RNN systems, but they also bear striking resemblances to descriptions of attention in global workspace theories (Dehaene, 2014; VanRullen & Kanai, 2021). Limited-capacity workspaces may ignore insufficiently precise/salient data (i.e., unconscious or subliminal processing), or may instead hold onto it for a period of time (i.e., active attending, working memory, and imagination) before releasing (or forgetting) these short-term memories so that new information can be processed. Although beyond the scope of the present discussion, LSTMs may represent a multiscale, universal computational framework for realizing adaptive autoencoding/compression. With respect to consciousness, a notable feature of deep FNNs is that their performance may be greatly enhanced via the addition of layer-skipping connections, which can be thought of as entailing RNNs with small-world connectivity (Watts & Strogatz, 1998), so allowing for a synergistic combination of integrating both local and global informational dependencies. Such deep learning systems are even more effective if these skip connections are adaptively configurable (R. K. Srivastava et al., 2015), so providing an even closer correspondence to the processes of dynamic evolution underlying the intelligence of RNNs (Jarman et al., 2017; Rentzeperis et al., 2021), including nervous systems (Gal et al., 2017; Goekoop & de Kleijn, 2021; Massobrio et al., 2015; Takagi, 2018). The flexible small-worldness of these “highway nets”—and their entailed recurrent processing—has potentially strong functional correspondences with aspects of brains thought to enable workspace architectures via connectomic “rich clubs,” which may be capable of supporting “dynamic cores” of re-entrant signaling, so allowing for synergistic processing via balanced integrated and segregated processing (Cohen & D’Esposito, 2016; Mohr et al., 2016; J. Shine, 2019; Sporns, 2013). Notably, such balanced integration and segregation via small-worldness is also a property of systems capable of both maximizing integrated information and supporting self-organized critical dynamics (Badcock et al., 2019; Safron, 2020a), the one regime in which (generalized) evolution is possible (Bak & Sneppen, 1993; Campbell, 2016; Edelman et

al., 2011; Kaila & Annila, 2008; Paperin et al., 2011). As previously described with respect to the critique of Aaronson’s critique of IIT, small-world networks can also be used for error-correction via expander graphs (or low-density parity checking codes), which enable systems to approach the Shannon limit with respect to handling noisy, lossily—and irreversibly (Smith, 2014)—compressed data. Speculatively, all efficiently functioning recurrent systems might instantiate turbo codes in evolving towards regimes where they may come to efficiently resonate with (and thereby predict/compress) information from other systems in the world. Given this generalized predictive coding, there may be a kind of implicit intelligence at play across all persisting dynamical systems (K. J. Friston, 2019; K. J. Friston et al., 2020; J. Schmidhuber, 2000; Vanchurin, 2020; Wolfram, 2002). However, according to IWMT, consciousness will only be associated with systems capable of coherently modeling themselves and their interactions with the world. This is not to say that recurrence is necessarily required for the functionalities associated with consciousness (Doerig et al., 2019). However, recurrent architectures may be a practical requirement, as supra-astronomical resources may be necessary for unrolling a network the size of the human brain across even the 100s of msec over which workspace dynamics unfold. Further, the supposed equivalence of feedforward and feedback processes are only demonstrated when unrolled systems are returned to initial conditions and allowed to evolve under identical circumstances (Marshall et al., 2017). These feedforward “zombie” systems will tend to diverge from the functionality of their recurrent counterparts when intervened upon and will be unable to repair their structure when modified. This lack of robustness and context-sensitivity means that unrolling loses one of the primary advantages of consciousness as dynamic core and temporally-extended adaptive (modeling) process, where such (integrated world) models allow organisms to flexibly handle novel situations. Further, while workspace- like processing may be achievable by feedforward systems, largescale neuronal workspaces heavily depend on recurrent dynamics unfolding over multiple scales. Perhaps we could model a single inversion of a generative model corresponding to one quale state, given a sufficiently large computational device, even if this structure might not fit within the observable universe. However, such computations would lack functional closure across moments of experience (Chang et al., 2019; Joslyn, 2000), which would prevent consciousness from being able to evolve as a temporally-extended process of iterative Bayesian model selection. Perhaps more fundamentally, one of the primary functions of workspaces and their realization by dynamic cores of effective connectivity may be the ability to flexibly bind information in different combinations in order to realize functional synergies (Baars et al., 2013; Greff et al., 2020; Singer, 2001). While an FNN could theoretically achieve adaptive binding with respect to a single state estimate, this would divorce the

integrating processes from its environmental couplings and historicity as an iterative process of generating inferences regarding the contents of experience, comparing these predictions against sense data, and then updating these prior expectations into posterior beliefs as priors for subsequent rounds of predictive modeling. Further, the unfolding argument does not address the issue of how it is that a network may come to be perfectly configured to reflect the temporally-extended search process by which recurrent systems come to encode (or resonate with) symmetries/harmonies of the world. Such objections notwithstanding, the issue remains unresolved as to whether an FNN-based generative model could generate experience when inverted. This issue also speaks to the ontological status of “self-organizing harmonic modes” (SOHMs), which IWMT claims provide a functional bridge between biophysics and phenomenology. Harmonic functions are places where solutions to the Laplacian are 0, indicating no net flux, which could be defined intrinsically with respect to the temporal and spatial scales over which dynamics achieve functional closure in forming self-generating resonant modes (Atasoy et al., 2016). (Note: These autopoietic self- resonating/forming attractors are more commonly referred to as “nonequilibrium steady state distributions” in the FEP literature (K. J. Friston, 2019), which are derived using different—but possibly related (L. Wu & Zhang, 2006)—maths.) However, such recursively self-interacting processes would not evolve in isolation, but would rather be influenced by other proto-system dynamics, coarse-graining themselves and each other as they form renormalization groups in negotiating the course of overall evolution within and without. Are standing wave descriptions ‘real,’ or is everything just a swirling flux of traveling waves? Or, are traveling waves real, or is there ‘really’ just an evolving set of differential equations over a vector field description for the underlying particles? Or are underlying particles real, or are there only the coherent eigenmodes of an underlying topology? Even if such an eliminative reductionism bottoms out with some true atomism, from an outside point of view we could still operate according to a form of subjective realism (Carroll, 2016), in that once we identify phenomena of interest, then maximally efficient/explanatory partitioning into kinds might be identifiable (Albantakis et al., 2017; E. P. Hoel, 2017; E. P. Hoel et al., 2016). Yet even then, different phenomena will be of differential ‘interest’ to other phenomena in different contexts evolving over different timescales. While the preceding discussion may seem needlessly abstract, it speaks to the question as to whether we may be begging fundamental questions in trying to identify sufficient physical substrates of consciousness, and also speaks to the boundary problem of which systems can and cannot be considered to entail subjective experience. More concretely, do unrolled SOHMs also entail joint marginals over synchronized subnetworks, some of which IWMT claims to be the computational substrate of consciousness? Based on the inter-translatability of RNNs and FNNs described above,

this question appears to be necessarily answered in the affirmative. However, if the functional closure underlying these synchronization manifolds require temporally- extended processes that recursively alter themselves (Rocha, 2000; Rudrauf et al., 2003), then it may be the case that this kind of autopoietic ouroboros cannot be represented via geometries lacking such entanglement. Speculatively (and well-beyond the technical expertise of this author), SOHMs might necessarily represent “time crystals” (Chen et al., 2020; Everhardt et al., 2019; Fruchart et al., 2021), whose symmetry-breaking might provide a principled reason to privilege recurrent systems as physical and computational substrates for consciousness. If this were found to be the case, then we may find yet another reason to describe consciousness as a kind of “strange loop” (Hofstadter, 1979, 2007; Lloyd, 2012), above and beyond the seeming and actual paradoxes involved in explicit self-reference. This kind of self-entanglement would render SOHMs opaque to external systems lacking the cypher of the self-generative processes realizing those particular topologies (Rocha, 2000). Hence, we may have another way of understanding marginalization/renormalization with respect to inter-SOHM information flows as they exchange messages in the form of sufficient statistics (Parr, Markovic, et al., 2019), while also maintaining degrees of independent evolution (cf. mean field approximation) over the course of cognitive cycles (Madl et al., 2011). These self-generating entanglements could further speak to interpretations of IIT in which quale states correspond to maximal compressions of experience (Maguire & Maguire, 2010). In evaluating the integrated information of systems according to past and future combinatorics entailed by minimally impactful graph cuts (Tegmark, 2016), we may be describing systems capable of encoding data with maximal efficiency (Maguire et al., 2016), in terms of possessing maximum capacities for information-processing via supporting “differences that make a difference.” Indeed, adaptively configurable skip connections in FNNs could potentially be understood as entailing a search process for discovering these maximally efficient codes via the entanglements provided by combining both short- and long-range informational dependencies in a small-world (and self-organized-critical) regime of compression/inference. A system experiencing maximal alterations in the face of minimal perturbations would have maximal impenetrability when observed from without, yet accompanied by maximal informational sensitivity when viewed from within. If we think of minds as systems of interacting SOHMs, then this lack of epistemic penetration could potentially be related to notions phenomenal transparency (via opacity) (Limanowski & Friston, 2018; Metzinger, 2009), and perhaps “user interface” theories of consciousness (Hoffman & Prakash, 2014). Intriguingly, maximal compressions have also been used as conceptualizations of the event horizons of black holes, for which corresponding holographic principles have been adduced in terms of

internal information being projected onto 2D topologies. With respect to the FEP, it is also notable that singularities and Markov blankets have been interpreted as both points of epistemic boundaries as well as maximal thermal reservoirs (Kirchhoff et al., 2018). Even more speculatively, such holography could even help explain how 3D perception could be derived from 2D sensory arrays, and perhaps also experienced this way in the form of the precuneus acting as a basis for visuospatial awareness and kind of “Cartesian theater” (D. Dennett, 1992; Haun & Tononi, 2019; Sutterer et al., 2021). As described above, this structure may constitute a kind of graph neural network (GNN), utilizing the locality of recurrent message passing over grid-like representational geometries for generating sufficiently informative projections on timescales proportional to the closure of action-perception cycles (Safron, 2020b, 2020b). However, in exploring the potential conscious status of recurrent systems, we would still do well to consider the higher-level functional desiderata for consciousness as a process of integrated world modeling. More specifically, if particular forms of coherence are required for generating experience, then we may require hybrid architectures with specialized subsystems capable of supporting particular kinds of learning. It is to this issue that we will turn towards next.

Kinds of world models

World models are becoming an increasingly central topic in machine learning due to their ability to support knowledge synthesis for self-supervised learning, especially for agents governed by objective functions (potentially implicit and meta- learned) involving intrinsic sources of value such as curiosity and empowerment (de Abril & Kanai, 2018; Hafner, Lillicrap, et al., 2020; Hafner, Ortega, et al., 2020; J. Schmidhuber, 2007a, 2012, 2020, 2021; R. Wang et al., 2020). IWMT emphasizes consciousness as an entailment of integrated world modeling (Safron, 2020a), and attempts to specify which brain systems and machine learning principles may be important for realizing different aspects of this function (Safron, 2020b). According to IWMT (Figure 3), posterior cortices represent generative models over the sensorium for an embodied agent, whose inversion allows for the generation of likely patterns of sense data (given past experience), entailing the stream of consciousness. Cortical perceptual hierarchies are modelled as “folded” variational autoencoders (VAEs), but this could similarly be described as hierarchically-organized LSTMs (Hochreiter & Schmidhuber, 1997; J. Schmidhuber, 1991), or perhaps (generalized) transformer hierarchies (Lee-Thorp et al., 2021; Ramsauer et al., 2021; Schlag et al., 2021; Tay et al., 2021). There is a sense in which this posterior-located autoencoding heterarchy is itself a world model by not only containing information regarding the spatially-organized structure of environments, but also temporal coherence via the capacity of recurrent

systems—and complex dendritic processing (Hawkins & Ahmad, 2016)—to support sequence memory, whose coherent state transitions could be understood as entailing causal dependencies. However, this world modeling achieves much greater temporal depth and counterfactual richness with the addition of the hippocampal-entorhinal system (H/E-S) and frontal lobes (Faul et al., 2020; Knight & Grabowecky, 1995; Koster et al., 2018), which together may generate likely-future (or counterfactual/postdicted- past) state transitions for the sensorium of the embodied agent. Further, the involvement of subcortical structures such as the basal ganglia allow actions—broadly construed to include forms of attentional selection and imaginative mental acts—to be selected and policies to be updated based on by histories of reward learning (Mannella et al., 2013). This involvement of value-canalized control structures provides functional closure in realizing action-perception cycles, which are preconditions for any kind of coherent world modeling to be achieved via active inference (K. J. Friston, 2018; K. J. Friston, FitzGerald, et al., 2017). These sorts of functions have been realized in artificial systems for decades (J. Schmidhuber, 1990, 1991), with recent advances exhibiting remarkable convergence with the neurocomputational account of world modeling described by IWMT. One particularly notable world modeling system was developed by Ha and Schmidhuber (2018), in which a VAE is used to compress sense data into reduced-dimensionality latent vectors, which are then predicted by a lower parameter RNN, whose outputs are then used as bases for policy selection by a much lower parameter controller trained with evolutionary strategies. The ensuing actions from this control system are then used as a basis for further predictive modeling and policy selection, so completing action- perception cycles for further inference and learning. The dimensionality-reducing capacities of VAEs not only allow for greater efficiency in providing compressions for subsequent computation, but moving from pixel space to latent space—with associated principle components of data variation—allows for more tractable training regimes. The use of evolutionary optimization is capable of handling challenging credit-assignment problems (e.g. non-differentiable free energy landscapes) via utilizing the final cumulative reward over a behavioral epoch, rather than requiring evaluation of the entire history of performance and attempting to determine which actions contributed to which outcomes to which degrees. (Speculatively, this could be understood as one interpretation of hippocampal ripples contributing to phasic dopamine signals in conjunction with remapping events (Rusu & Pennartz, 2020; Sanders et al., 2020).) This architecture was able to achieve unprecedented performance on car racing, first-person shooter video games, and challenging locomotion problems requiring the avoidance of local minima. Further, by feeding the signals from the controller directly back into latent space (rather than issuing commands for over actions), this architecture was able to achieve even greater functionality by allowing training with policy rollouts in

simulated (or “imagined”) environments. Even more, incorporation of a temperature (or uncertainty) parameter into this imaginative training was able to avoid patterns of self-adversarial/degenerate policy selection from leveraging exploits of internal world model, so enhancing transfer learning from simulations to real-world situations. Theoretically, this could provide one interpretation of the behavioral significance of dreaming (E. Hoel, 2021), and possibly also aspects of serotonin systems (Boureau & Dayan, 2011). Limitations of this world modeling system include the problem of isolated VAE optimization resulting in the encoding task-irrelevant observations, but with task-based training potentially undermining transfer learning. An additional challenge involves issues of catastrophic forgetting as the encoding of new data interferes with prior memories. Ha and Schmidhuber (2018) suggested that these challenges could be respectively overcome with governance by intrinsic drives for artificial curiosity— which could be thought of as a kind of adaptive-adversarial learning (J. Schmidhuber, 2020, 2021)—as well as the incorporation of external memory modules for exploring more complicated worlds. Intriguingly, both of these properties seem to be a feature of the H/E-S (Çatal et al., 2021; Hassabis & Maguire, 2009; Safron, 2020b) (Figure 6), which possesses high centrality and effective connectivity with value-estimation networks such as ventral prefrontal cortices and basal ganglia (Mannella et al., 2013). An additional means of enhancing the performance of world modeling architectures is the incorporation of separate “teacher” and “student” networks, whose particular functional details may shed light on not just the conditions for optimal learning, but for the particular nature(s) of conscious experience, as will be explored next.

Kinds of minds: bringing forth worlds of experience

One of Schmidhuber’s (1991) more intriguing contributions involves a two-tier unsupervised machine learning architecture operating according to principles of predictive coding. The lower level consists of a fast “subconscious automatiser RNN” that attempts to compress (or predict) action sequences, so learning to efficiently encode histories of actions and associated observations. This subsystem will automatically create abstraction hierarchies with similar features to those found in receptive fields of the mammalian neocortical ventral visual stream. In this way, the automatiser identifies symmetries across data structures and generates prototypical features that can be used to efficiently represent particular instances by only indicating deviations from these eigenmode basis functions. Surprising information not predicted by this lower level is passed up to a more slowly operating “conscious chunker RNN,” so becoming the object of attention for more elaborative processing (J. Schmidhuber, 2015). The automatiser continuously attempts to encode subsequent streams of information in

compressed forms, eventually rendering them as subconscious in terms of not requiring the more complex (expensive, and relatively slow) modeling of the conscious chunker. This setup can also be understood as a “teacher” network being imitated by a “student” network, and through this knowledge distillation process, high-level policy selection becomes “cloned” such that it can be realized by fast and efficient lower-level processes. With the “Neural History Compressor” (J. Schmidhuber, 2018; J. H. Schmidhuber et al., 1993), this architecture was augmented with the additional functionality of having the strength of updates for the conscious chunker be modulated by the magnitude of surprises for the subconscious automatiser. In terms of brain functioning, we would expect predictive processing mechanisms to cause information to be predicted in a way that is increasingly sparse and pushed closer to primary modalities with time and experience. Because these areas lack access to the kind of rich club connectivity found in deeper portions of the cortical heterarchy, this information would be less likely to be taken up into workspace dynamics and contribute to alpha/beta-synchronized large-scale “ignition” events, which IWMT interprets as Bayesian model selection over the sensorium of an embodied-embedded agent, entailing iterative estimation of system-world states. In this way, initially conscious patterns of action selection involving workspace dynamics would constitute “teacher” networks, but which with experience will tend to become automatic/habitual/unconscious as they are increasingly realized by distributed fast/small ensembles coordinated by cerebellar-mediated forward models (J. M. Shine, 2021), functioning as “student” networks. In terms of some of the architectures associated with FEP-AI, this could be thought of as information being processed in the lower level of Forney factor graphs with continuous (as opposed to discrete) updating and less clearly symbolic functionality (K. J. Friston, Parr, et al., 2017; Parr & Friston, 2018b). In more standard machine learning terms, this could be thought as moving from more “model-based” to more “model-free” control, or “amortized inference” with respect to policy selection (S. Gershman & Goodman, 2014; Mannella et al., 2013). However, when these more unconscious forms of inference fail, associated prediction errors will ascend until they can receive more elaborative handling by conscious systems, whose degree of activity may be modulated by overall surprisal (Holroyd & Verguts, 2021; Safron, 2020b; Sales et al., 2019; Shea & Frith, 2019; J. Shine, 2019). To return to artificial neural history compressors (J. Schmidhuber, 2018; J. H. Schmidhuber et al., 1993), these systems are capable of discovering a wide range of invariances across actions and associated observations, with one of the most enduring of these symmetries being constituted by the agent itself as a relatively constant feature. With RNN-realized predictive coding mechanisms combined with reinforcement learning, the system learns to efficiently represent itself, with these symbols becoming activated in the context of planning and through active self-exploration, so exhibiting a

basic form of self-modeling, including with respect to counterfactual imaginings. Based on the realization of these functionalities, Schmidhuber (2020, 2021) has controversially claimed that “we have had simple, conscious, self-aware, emotional, artificial agents for 3 decades.” IWMT has previously focused on the neurocomputational processes that may realize phenomenal consciousness, but functionally speaking (albeit potentially not experientially), this statement is consistent with the computational principles identified for integrated world modeling. These functional and mechanistic accounts have strong correspondences aspects of Hiedeggerian phenomenology (Dreyfus, 2007). A “ready-to-hand” situation of effortless mastery of sensorimotor contingencies could correspond to maximally sparse/compressed patterns of neural activity, pushed down close to primary cortices, with the system coupling with the world in continuously evolving unconscious action- perception cycles, without requiring explicit representation of information. In such a situation of nearly effortless (and largely unconscious) mastery of sensorimotor contingencies, dithering would be prevented as the changing affordance landscape results in rapid selection of appropriate grips (Cisek, 2007; Kiverstein et al., 2019; Safron, 2019b; Seth, 2014; Tani, 2016), with coordination largely occurring via reflexes and morphological constraints. However, a present-at-hand situation of reflective evaluation could correspond to prediction errors making their way up to upper levels of cortical heterarchies, where largescale ignition events become more likely due to closer proximity to the rich-club connectivity core. In such a situation of coupling with a simulated world model, agents could draw upon counterfactual considerations for causal reasoning and planning, so requiring flexibly (and consciously) accessible re- presentations and various forms of self-referential modeling. Convergence between these machine learning architectures, neural systems, and phenomenology is compelling, but does this mean that Schmidhuberian world-modeling agents and similar systems possess phenomenal consciousness? This is the final issue that we will consider before concluding this expansion of IWMT.

Machine consciousness?

More recent work from Schmidhuber’s group has explored the preconditions for human-like abilities to generalize knowledge beyond direct experience (Greff et al., 2020). They suggest that such capable systems require capacities to flexibly bind distributed information in novel combinations, and where this binding problem requires capacities for compositional and symbolization of world structure for systematic and predictable knowledge synthesis. They further describe a unifying framework involving the formation of meaningful internal structure from unstructured sense data (segregation), the maintenance of this segregated data at an abstract level

(representation), and the ability to construct new inferences through novel combinations of these representations (composition). Similarly to IIT’s preconditions for subjective experience, this framework describes a protocol for producing data structures with intrinsic existence (realization via entangled connections), composition (possessing meaningful structure), information (distinguishability from alternatives), and integration (constituting wholes that are greater than the sum of their parts). This is further compatible with GNWT’s description of architectures for dynamically combining information in synergistic ways. Even more, the particular architectural principles identified by this framework as promising research directions are the same as those previously suggested by IWMT: geometric deep learning and graph neural networks (GNNs). However, this proposal for solving binding problems for neural networks also suggests utilizing a generalization of GNNs in the form of graph nets (Battaglia et al., 2018). This is likely a place where IWMT ought to be updated, in that rather than hippocampal system being understood as hosting graph-grid GNNs for spatial mapping, graph nets may be a more apt description of this system on algorithmic and functional levels of analysis (Çatal et al., 2021; Gothoskar et al., 2019; Peer et al., 2021). These technical details notwithstanding, there are striking parallels between the functionalities described by this framework for functional binding and the machine learning description of neural systems suggested by IWMT (Figures 2 and 3). More specifically, autoencoding/compressing hierarchies provide segregation, with GNN-structured latent spaces providing explicit representation (and potentially conscious experiences), and a further level of higher abstraction providing novel representational combinations for creative cognition (i.e., hippocampal place fields as flexibly configurable graph net). If such an architecture were to be artificially realized, would it possess ‘consciousness?’ GNWT would likely answer this question in the affirmative with respect to conscious access (Dehaene, 2014), and IIT would provide a tentative affirmation for phenomenal consciousness (Tononi & Koch, 2015), given realization on neuromorphic hardware capable of generating high phi for the physical system (rather than for an entailed virtual machine). IWMT is agnostic on this issue, yet may side with IIT in terms of matters of practical realization. Something like current developments with specialized graph processors might be required for these systems to achieve sufficient efficiency (Ortiz et al., 2020) for engaging in iterative estimation of system- world states with sufficient rapidity that such estimates could both form and be informed by perceivable action-perception cycles. If such a system were constructed as a controller for an embodied-embedded agent, then it may be the case that it could not only generate “System 2” abilities (Bengio, 2017; Kahneman, 2011), but also phenomenal consciousness, and everything that entails.

Conclusions In attempting to expand on IWMT, opinions will surely vary as to whether we have made substantial progress on contributing to a satisfying solution to the Hard problem of consciousness, or the meta-issue as to whether this is even a real problem (Chalmers, 2018; Seth, 2016). Regardless of whether the Hard problem can be felt to be (dis)solved, we have only begun to explore the nature of conscious experiences. Some directions for future work: • What are the different forms and enabling mechanisms for self-consciousness? • To what degree are different forms of consciousness constructed via social pressures on evolutionary and developmental timescales? • What questions are we not asking right now, but ought to be?

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