O'Reilly-Shah's State Space Theory and Computational Dynamic Monism

Anesthesiologist and consciousness scientist Vikas N. O'Reilly-Shah's State Space Theory (SST) proposes that phenomenal consciousness arises from hierarchical delay coordinate embedding (DCE) in plastic recurrent neural networks. He says this is a mathematically precise proposal that the brain reconstructs the dynamical history of its own states and its environment through recurrent feedback in plastic neural networks. The accompanying metaphysical framework, Computational Dynamic Monism (CDM), identifies consciousness with the temporally extended computational process itself, not with any static neural state, functional role, or intrinsic property of matter. The claim is that this dissolves the hard problem through identity rather than explanation (O’Reilly-Shah, 2025, 2026a). The structured, temporally thick experience that constitutes subjective awareness is the instantiation of such a processing trajectory.

The Mechanism: Delay Coordinate Embedding in Neural Networks

SST's central claim is mechanistic. Delay coordinate embedding is an established technique from nonlinear dynamical systems theory, grounded in Takens' embedding theorem (Takens, 1981), by which time-delayed copies of a single observable variable are used to reconstruct the full state space of a dynamical system. O'Reilly-Shah proposes that biological recurrent neural networks implement this process naturally: recurrent feedback connections create the time delays. Through this mechanism, a recurrent network processes its current input in combination with prior inputs to create an embedding. On Takens, this reconstructs a topologically faithful image of the dynamical history that produced the input.

The arrangement of these 'DCE engines' is hierarchical. Lower-level networks embed sensory dynamics; higher-level networks embed the dynamics of lower-level networks, creating a nested hierarchy of increasingly abstract dynamical reconstructions. At the highest levels of this hierarchy, the system embeds its own embedding activity. O'Reilly-Shah argues that this hierarchical self-referential DCE structure is the computational signature of phenomenal consciousness in biological cortex. The system does not just model the world; it models itself modeling the world. This modeling is the internal perspective that is experienced as subjectivity (O’Reilly-Shah, 2026b).

Candidate Mechanisms and Converging Evidence

O’Reilly-Shah says that several independent lines of mathematical and empirical work support the hypothesis that recurrent neural networks perform operations with the formal properties SST predicts. From reservoir computing: Hart and colleagues mathematically proved that a contracting recurrent network driven by structured input develops a synchronization function that embeds the input dynamics into the network's state space: the theory of generalized synchronization (A. Hart et al., 2020; A. G. Hart, 2025). Uribarri and Mindlin (2022) observed that trained recurrent neural networks develop internal representations with the geometric signature of time-delay embeddings, and Ostrow, Eisen, and Fiete (2024) extended this analysis to modern neural sequence models. These converging results suggest that delay coordinate embedding may be a generic computational property of recurrent neural networks rather than an architectural idiosyncrasy.

Treating reservoirs as a candidate mechanism with established mathematical principles, O'Reilly-Shah and Selvitella formalize the connection between Hart's theorems and perception (O’Reilly-Shah & Selvitella, 2026). Contracting recurrent networks driven by regular dynamics generically implement smooth embeddings via generalized synchronization. Many perceptual domains involve environmental dynamics representable on low-dimensional regular attractors; for example, both bats and rodents represent three-dimensional space on a topological torus (Finkelstein et al., 2015; Gardner et al., 2022). This work provides a rigorous mathematical bridge from recurrent network dynamics to topology-preserving representation.

Plasticity, Process, and the Deflection of Substitution Arguments

O'Reilly-Shah emphasizes plasticity and process as critical features distinguishing SST from static computational theories. While computing, a static neural network traverses state space; a plastic recurrent network traverses function space. The function the network computes at time t₁need not be the function it computes at time t₂, because plasticity continuously reshapes the network's parameters. This means the system's computational identity is not a snapshot but a trajectory: consciousness is constituted by the ongoing, history-dependent evolution of the embedding process, computationally modulated by ongoing interaction with environmental input.

This has formal consequences. O'Reilly-Shah, Selvitella, and Schurger demonstrate that no static feedforward network can maintain equivalence with a plastic recurrent network over unbounded time, because the recurrent system's future behavior depends on continuing self-modification that a fixed architecture cannot track (O’Reilly-Shah et al., 2025). Any system that does track it indefinitely must itself implement equivalent plasticity and environmental coupling, at which point it shares the original's process organization rather than constituting a genuinely different system. This is a key computational point that has also been made in the multiple realizability literature: that putative cases of multiple realizability frequently dissolve under closer examination of causal-mechanistic detail (Polger & Shapiro, 2016; Shapiro, 2000).

This result deflects the unfolding argument (Doerig et al., 2019) and its Turing Completeness generalization (Herzog et al., 2022): the claim that any computable function can be re-implemented on any Turing-complete system with different causal structure. The claim is formally valid, O'Reilly-Shah maintains, when read as a statement about input-output functions, but its force diminishes as the required level of computational equivalence rises. A system matching a plastic recurrent network's behavior indefinitely must preserve its temporal organization, plasticity, and environmental coupling—and at that point, the Turing Completeness result supports multiple realizability of the same process organization across substrates, not the substitutability of a different process organization. On SST, O'Reilly-Shah argues that a system with identical plastic and processual trajectory would indeed have phenomenal consciousness; however, such precise equivalence is extraordinarily unlikely in practice due to unpredictable environmental input and, in chaotic regimes, sensitivity to initial conditions.

The interactive Turing machine framework further clarifies that systems engaged in ongoing environmental exchange perform something that is not a function in the Church-Turing sense yet not hypercomputational. In an open-ended interactive process, the inputs cannot be pre-specified because they have not yet occurred (Goldin & Wegner, 2008; Martin et al., 2023; van Leeuwen & Wiedermann, 2001). Computationally, this means that ongoing environmental interaction also lends resistance to the unfolding argument and Turing Completeness generalization.

Quality Spaces: Where Representational Geometry Meets Phenomenal Structure

SST also offers a candidate computational mechanism for the structured representational spaces—quality spaces—that the structuralist program in consciousness science posits as the basis of phenomenal content. When a recurrent network reconstructs the dynamics of its sensory input through DCE, the geometry of the resulting embedding preserves the relational organization of the environment it tracks: stimuli that are dynamically similar (that lead to similar futures) are represented nearby in the network's state space, while stimuli that are dynamically distinct are represented far apart. The theory predicts that this representational geometry should distort in characteristic ways: compressing where prediction is poor, collapsing where physically distinct inputs have indistinguishable future consequences, and sharpening where the system's predictive accuracy is highest. These distortion patterns map onto known perceptual phenomena: metamers (physically distinct stimuli experienced as identical), categorical perception (sharpened boundaries between frequently encountered categories), and discrimination thresholds (principled limits on perceptual resolution). On this account, the imperfections in conscious perception are not noise but the predictable signature of a topology-preserving embedding operating under finite predictive resources.

Computational Dynamic Monism: Dissolving the Hard Problem

The metaphysical framework accompanying SST, Computational Dynamic Monism, holds that consciousness is identical to the temporally extended computational process, not produced by it, not correlated with it, and not emergent from it in any sense that would leave an explanatory gap. Just as lightning is identical to atmospheric electrical discharge (not caused by it, not correlated with it), phenomenal experience is identical to hierarchical self-referential DCE in plastic recurrent networks. The apparent gap between mechanism and phenomenology is epistemological, not ontological. It arises from the difference between third-person description and first-person instantiation (O’Reilly-Shah, 2026a). Thus, according to O'Reilly-Shah, CDM is a process monism: a single ontological category (physical process) underwrites both the objective description available to science and the subjective character available to the system itself. These characteristics of CDM, he claims, dissolve the hard problem as a category error and explain the privacy of qualia. Qualia are private not because they are ontologically separate from physical process, but because instantiating a process and describing it are irreducibly different epistemic relations to the same phenomenon.

References

Doerig, A., Schurger, A., Hess, A., & Herzog, M. H. (2019). The unfolding argument: Why IIT and other causal structure theories cannot explain consciousness. Consciousness and Cognition, 72, 49–59.

Finkelstein, A., Derdikman, D., Rubin, A., Foerster, J. N., Las, L., & Ulanovsky, N. (2015). Three-dimensional head-direction coding in the bat brain. Nature, 517(7533), 159–164. https://doi.org/10.1038/nature14031

Gardner, R. J., Hermansen, E., Pachitariu, M., Burak, Y., Baas, N. A., Dunn, B. A., Moser, M.-B., & Moser, E. I. (2022). Toroidal topology of population activity in grid cells. Nature, 602(7895), 123–128. https://doi.org/10.1038/s41586-021-04268-7

Goldin, D., & Wegner, P. (2008). The Interactive Nature of Computing: Refuting the Strong Church--Turing Thesis. Minds and Machines, 18(1), 17–38.

Hart, A. G. (2025). Generic and isometric embeddings in reservoir computers. Chaos (Woodbury, N.Y.), 35(11), 111103. https://doi.org/10.1063/5.0301957

Hart, A., Hook, J., & Dawes, J. (2020). Embedding and approximation theorems for echo state networks. Neural Networks: The Official Journal of the International Neural Network Society, 128, 234–247. https://doi.org/10.1016/j.neunet.2020.05.013

Herzog, M. H., Schurger, A., & Doerig, A. (2022). First-person experience cannot rescue causal structure theories from the unfolding argument. Consciousness and Cognition, 98, 103274.

Martin, A., Magnaudet, M., & Conversy, S. (2023). Computers as Interactive Machines: Can We Build an Explanatory Abstraction? Minds and Machines, 33(1), 83–112.

O’Reilly-Shah, V. N. (2025). Delay coordinate embedding as neuronally implemented information processing: The state space theory of consciousness. Journal of Consciousness Studies, 32(1--2), 132–164.

O’Reilly-Shah, V. N. (2026a). Computational dynamic monism: Process metaphysics for the state space theory of consciousness. In SSRN Electron. J. https://doi.org/10.2139/ssrn.6042716

O’Reilly-Shah, V. N. (2026b). State Space Theory as a Unifying Framework for Consciousness. Nonlinear Dynamics, Psychology, and Life Sciences.

O’Reilly-Shah, V. N., & Selvitella, A. M. (2026). Smooth embeddings in contracting recurrent networks driven by regular dynamics: A synthesis for neural representation. In arXiv [q-bio.NC]. arXiv. https://doi.org/10.48550/arXiv.2601.19019

O’Reilly-Shah, V. N., Selvitella, A., & Schurger, A. (2025). A caveat regarding the unfolding argument: Implications of plasticity for computational theories of consciousness. In bioRxiv (p. 2025.11.04.686457). https://doi.org/10.1101/2025.11.04.686457

Ostrow, M., Eisen, A., & Fiete, I. (2024). Delay embedding theory of neural sequence models. In arXiv [cs.LG]. arXiv. http://arxiv.org/abs/2406.11993

Polger, T. W., & Shapiro, L. A. (2016). The Multiple Realization Book (L. A. Shapiro (ed.)). Oxford University Press UK.

Shapiro, L. A. (2000). Multiple Realizations. Journal of Philosophy, 97(12), 635–654.

Takens, F. (1981). Detecting strange attractors in turbulence. In Lecture Notes in Mathematics, Berlin Springer Verlag (Vol. 898, p. 366). https://doi.org/10.1007/BFb0091924

Uribarri, G., & Mindlin, G. B. (2022). Dynamical time series embeddings in recurrent neural networks. Chaos, Solitons, and Fractals, 154(111612), 111612. https://doi.org/10.1016/j.chaos.2021.111612

van Leeuwen, J., & Wiedermann, J. (2001). The Turing Machine Paradigm in Contemporary Computing. In B. Engquist & W. Schmid (Eds.), Mathematics Unlimited---2001 and Beyond (pp. 1139–1155). Springer.