Vikas O'Reilly-Shah

The free energy principle casts perception as variational inference, but its biological implementation remains underspecified. In particular, the generalized-coordinate formalism should not be read as a literal claim that neurons compute arbitrary Taylor expansions. This paper argues that generalized synchronization provides the missing bottom-up mechanism. A contractive recurrent circuit driven by structured sensory input can synchronize to the driving dynamics. Under generic embedding conditions developed in the reservoir-computing literature, the resulting synchronization map can embed the low-dimensional sensory manifold into neural state space. Thus, the geometry predicted by the free energy principle need not be imposed from above by an explicitly Bayesian neural calculus; it can arise from ordinary recurrent dynamics driven by the world. I then propose a developmental extension. Hebbian plasticity acting on the correlations generated by sensory-driven synchronization may crystallize the embedded manifold into recurrent connectivity, yielding an autonomous continuous attractor network when the required fixed point exists. On this view, mature head-direction, grid-cell, and stimulus-driven visual manifolds are not genetically prespecified templates, but developmental products of three interacting processes: dynamical contraction, generalized synchronization, and correlation-based plasticity. The synthesis links the free energy principle, reservoir-computing embedding theorems, and contraction-theoretic models of Hebbian recurrent networks. It also yields testable predictions about dimensional thresholds for topological recovery, developmental sensitivity to plasticity, and the dependence of attractor geometry on input statistics. The central open problem is whether the Hebbian fixed point exists and preserves the embedding quality of the synchronization manifold.

Temporal structure contains geometric structure. When a recurrent neural network is driven by structured sensory input, delay coordinate embedding theory shows that its internal state develops a geometry preserving the relational organization of the environment it tracks. The mechanism mathematically specifies not only where this geometry is faithful but where it must distort. Prediction error and environmental separability together set a resolution floor that maps onto metamers, categorical perception, and discrimination thresholds. This paper develops DCE as a candidate computational mechanism for structuralist quality spaces, addressing exploitation criteria, Shea's misrepresentation requirement, and Kleiner and Hoel's lenient dependency. The results are conditional on an empirical hypothesis about cortical implementation; nine failure-mode predictions test both the hypothesis and the structuralist implications simultaneously. The implications for the Newman problem and for process ontology are developed. The invariance condition that generates the geometry is identical to the equation that defines the system's predictive function; this raises questions about the separation of structure from function presupposed by both structuralist and functionalist programs.

Searle's response to the Systems Reply, the internalization argument, and contemporary unfolding-based objections to AI consciousness share a premise that neither literature has made explicit: that the computationally relevant organization of a temporally extended process can be preserved under static re-specification. I call this the re-realizability premise and show that internalizability, static-rulebook re-realizability, and unfoldability coincide under the strong reading of internalization relevant here. The premise holds for any system whose transition law is time-invariant. It fails for systems whose transition law is modified by their own processing history: systems with plasticity. A formal result establishes that no single static architecture maintains temporal functional equivalence with a plastic recurrent network whose learning rule produces non-trivial changes in the implemented function. The augmented-state representation of such systems provides stepwise simulation but not re-realization: the weight parameters play a constitutive role in the original system and a bookkeeping role in the simulation, a distinction visible under intervention. A second, independent obstruction arises from open-ended interaction, which resists finite feedforward surrogacy for structural rather than parametric reasons. These results motivate a four-level taxonomy of computational architectures organized by transition-law stationarity and endogenous constitutive modification. The taxonomy is applied to three positions in the current AI consciousness debate: Hoel's proximity argument is reinterpreted, Cerullo's internal-consistency critique is given positive theoretical content, and Buonomano's continuous-time argument is shown to address a structural dimension independent of plasticity. For agentic systems coupling frozen models with dynamic environments, the re-realizability question is genuinely open and boundary-sensitive. The framework does not establish that any AI system is conscious; it identifies which architectural properties determine whether a major class of arguments against computational consciousness is even applicable.

Neural population activity in sensory cortex is organized on low-dimensional manifolds, but it is unclear why such manifolds should arise and what determines their geometry. We address this sensory representation problem by modeling cortical populations as recurrent circuits driven by low-dimensional, regular sensory dynamics (e.g. motion on a circle, head direction, multi-frequency tones on tori). By combining tools from generalized synchronization and delay-embedding theory, specialized to this quasiperiodic regime, we show that contracting recurrent networks generically develop smooth internal manifolds that embed the sensory dynamics. The dimensional requirement is modest and depends only on the intrinsic dimension d of the effective sensory manifold, not on the complexity of the external world: a hidden dimension N>2d suffices (e.g. N≥3 for a circle, N≥5 for a two-frequency torus; bounds compatible with Whitney and Takens' embedding theorems). We then prove a prediction–separation result that links representational geometry directly to predictive performance, without assuming knowledge of contraction rates: if the circuit can predict future sensory inputs with small error, then states with different futures must be separated in neural state space, up to a resolution set by the prediction error. The resulting scale-limited embeddings naturally give rise to categorical boundaries, metameric equivalence of distinct stimuli, and discrimination thresholds. Numerical experiments with trained tanh recurrent networks driven by head-direction-like and multi-frequency signals recover ring- and torus-shaped hidden manifolds with the expected topology; state separation improves sharply when N crosses the 2d+1 threshold. Training typically pushes the networks beyond the strict contraction regime where the theory guarantees faithful embedding, yet convergence consistent with generalized synchronization and manifold recovery persist, indicating that our conditions are sufficient but not necessary. Together, these results provide a mechanistic account of why low-dimensional sensory manifolds emerge in recurrent circuits and how prediction constrains their resolution, grounded in dynamical systems embedding theory and consistent with empirical findings on cortical population dynamics.

This paper introduces the state space theory of consciousness, positing that the cortex processes information through delay coordinate embedding operationalized by recurrent neural network engines. This leverages the power of Takens’ theorem, giving rise to representations of reality as points within state space. Consciousness is posited to arise at the highest order engines amongst hierarchical and parallel engine pathways. Consciousness is cast as a dynamic process rather than as a neuronal state, reconciling dualist intuitions with a monist perspective. Neuronal representations develop uniquely in each individual due to history-dependent training of these engines, accounting for the privacy of qualia while also addressing cortical plasticity and the heuristic nature of cortical processing. Posited engines exhibit non-linear dynamics that are sensitive to initial conditions, explaining phenomena such as ambiguous figure interpretation and offering a pathway to explaining free will. The state space theory aligns with and expands upon major theories (e.g.higher-order theories, global workspace theories, integrated information theory), essentially providing a computational mechanism that unifies elements of these theories. Future work will explore neural mechanisms and validate predictions.

The unfolding argument in the neuroscience of consciousness posits that causal structure cannot account for consciousness because any recurrent neural network (RNN) can be “unfolded” into a functionally equivalent feedforward neural network (FNN) with identical input-output behavior. Subsequent debate has focused on dynamical properties and philosophy of science critiques. We examine a novel caveat to the unfolding argument for RNN systems with rapid plasticity in their connection weights. We demonstrate through rigorous mathematical proofs that plasticity negates the functional equivalence between RNN and FNN. Our proofs address history-dependent plasticity, dynamical systems analysis, information-theoretic considerations, perturbational stability, complexity growth, and resource limitations. We demonstrate that neuronal systems that possess properties such as plasticity, history-dependence, and complex temporal information encoding have features that cannot be captured by a static FNN. Our findings delineate limitations of the unfolding argument that apply if consciousness arises from temporally extended dynamic neural processes rather than static input-output mappings. This work has implications for theories of consciousness, and for the fields of computational neuroscience and philosophy of mind more generally, providing new constraints for theories of consciousness.

Consciousness science has generated diverse theoretical frameworks, each offering insights into different aspects of conscious experience. However, this diversity has created a fractured landscape: theories operate at different explanatory levels, and a principled account of how conscious phenomena arise from specific neural computations remains largely absent. This work argues that State Space Theory (SST) can serve as a unifying mechanistic framework for consciousness science. SST proposes that consciousness arises from hierarchical delay coordinate embedding (DCE) - the reconstruction of dynamical system structure from time-delayed signals - implemented through recurrent cortical circuits ('DCE engines'), with gain modulation determining which reconstructions achieve system-wide influence. SST identifies these dynamics with consciousness itself, not merely as correlates. We draw on recent empirical and theoretical work to demonstrate the feasibility of this proposal, including empirical demonstrations that recurrent networks learn via embedding and mathematical results linking recurrent dynamics to embedding theory. We identify how major cognitive theories map onto this architecture mechanistically: parallel DCE engines correspond to Dennett's competing "drafts," global broadcasting reflects gain-amplified propagation, recurrent processing enables the temporal integration DCE requires, and the attention schema emerges as a higher-order reconstruction of gain modulation dynamics. SST's fundamentally process-based character provides immunity to the unfolding argument and resolves the temporal paradox facing causal structure theories. The framework generates a number of falsifiable predictions related to topological structure of perceptual dynamics, temporal vulnerability windows, and selective disruption of recurrent timing. SST thus offers a computational foundation for consciousness research that grounds existing theories mechanistically while generating empirical commitments.

Contemporary theories of consciousness often treat experience as a state, property, or representational structure instantiated at a time. This paper argues that this shared assumption underlies persistent explanatory problems, including the Hard Problem, the explanatory gap, and functionalist equivalence objections such as the unfolding argument. It proposes instead Computational Dynamic Monism (CDM), a process-metaphysical framework according to which phenomenal consciousness is constituted by temporally extended, hierarchically self-referential delay coordinate embedding (DCE) in plastic recurrent neural networks. The experiential and the dynamical are not two things requiring a bridge, but one thing accessed via different epistemic routes. CDM departs from standard type-B physicalism by reconceiving consciousness as a process rather than a property: a reconception that dissolves the Hard Problem by denying the separation between process and phenomenal character that the snapshot view presupposes. The paper defends CDM against the explanatory gap objection, the conceivability argument, and the knowledge argument; establishes through converging arguments that consciousness requires temporal extension; and shows how CDM survives the unfolding argument that threatens static structural theories. The threshold problem - which processes are conscious - is addressed through a self-reference criterion for subjectivity. Building on the State Space Theory of Consciousness, the account integrates insights from dynamical systems theory, neuroscience, and process philosophy. It distinguishes the metaphysical framework (CDM) from the specific mechanism (DCE), and yields principled constraints on artificial systems capable of conscious experience.

This paper introduces the state space theory of consciousness, positing that the cortex processes information through delay coordinate embedding operationalized by recurrent neural network engines. This leverages the power of Takens' theorem, giving rise to representations of reality as points within state space. Consciousness is posited to arise at the highest order engines amongst hierarchical and parallel engine pathways. Consciousness is cast as a dynamic process rather than as a neuronal state, reconciling dualist intuitions with a monist perspective. Neuronal representations develop uniquely in each individual due to history-dependent training of these engines, accounting for the privacy of qualia while also addressing cortical plasticity and the heuristic nature of cortical processing. Posited engines exhibit non-linear dynamics that are sensitive to initial conditions, explaining phenomena such as ambiguous figure interpretation and offering a pathway to explaining free will. The state space theory aligns with and expands upon major theories (e.g.higher-order theories, global workspace theories, integrated information theory), essentially providing a computational mechanism that unifies elements of these theories. Future work will explore neural mechanisms and validate predictions.