Predictive Set Theory is introduced, a formal generative framework that reconstructs cognitive architecture from first principles that offers novel resolutions to classical problems such as Russell's paradox, the cognitive status of G\"{o}delian incompleteness, the grounding of negative feedback, and the comprehension of film editing.
Abstract
Predictive processing theories portray the brain as a hierarchical prediction engine that minimizes prediction error, yet they lack operational definitions for the structure of a"prediction,"the standardized response to a prediction error, and the mechanism that maintains consistency across successive updates. Bayesian cognitive science attempts to subsume all uncertainty under probabilistic belief updating, but it presupposes a closed hypothesis space and provides no generative account of how the objects over which probabilities are distributed become discrete, identifiable referents in the first place. This paper introduces Predictive Set Theory (PST), a formal generative framework that reconstructs cognitive architecture from first principles. PST anchors cognition in a minimal set of operations---a sensor formalized as an identity function, set-theoretic state refresh, and three fundamental forms of reference chains (reference, counter-reference, and semi-reference)---and rigorously derives core cognitive functions including state sequences, demand, comparison, efficiency, and finite-horizon probabilistic planning. Rather than modeling neural mechanisms, PST constitutes a design specification for any system that must maintain internal consistency while acting under incomplete information and irreversible risk. The framework offers novel resolutions to classical problems such as Russell's paradox, the cognitive status of G\"{o}delian incompleteness, the grounding of negative feedback, and the comprehension of film editing. The primary purpose of this paper is to establish, through the public academic record, the originality and completeness of the Predictive Set Theory framework.
Predictive Processing (PP) is commonly described as a mechanism sketch—an incomplete, primarily mechanistic representation of cognitive processes. While this characterization rightly emphasizes PP’s structural and causal explanatory aspects, I argue that it tends to overlook important functional and normative dimensions that are essential for a comprehensive account of cognitive processes. In response, I claim that PP, while providing mechanism sketches in the standard sense, simultaneously performs a second, normative-functional epistemic role. This expanded view on PP preserves the value of its mechanistic explanation while clarifying the essential role of functional constraints in shaping predictive models. Specifically, I show how PP models postulate explanatory constraints—formal, structural, and functional—that are inherently normative, as they specify the conditions viable mechanisms must satisfy to be biologically plausible and adaptive. Drawing on Levenstein et al. (2023), I situate this account within a pragmatic framework that recognizes the legitimacy of mechanistic, normative, and descriptive theories without reducing one to another. This pluralistic approach enables genuine integration across explanatory levels and points toward more adequate future models in cognitive neuroscience.
Predictive processing casts perception, action, and learning as probabilistic inference. This paper asks when a Bayesian description identifies a mechanism. I distinguish computational description, algorithm, and physical implementation. Mechanism requires a causal mapping from physical transitions to inferential roles; behavioural fit cannot establish it. Priors range over model-supplied alternatives; observation does not reveal the organism’s individuation. Bayesian algorithms may be high-dimensional, continuous, nonparametric, and representation-growing. Every specified model has a fixed reachable closure; neither closure nor size decides mechanism. The question is which differences a proposed controller state treats as irrelevant. If histories assigned to that state respond differently to intervention because of timing, phase, contact, or field structure, the mapping omits part of the mechanism. A prospectively richer Bayesian or hybrid account may include those differences. High-dimensional systems and flexible model families often resist binary falsification when an experiment’s projection loses distinctions required by the claim. I therefore propose convergent tests of specified internal, coupled, and hybrid mappings. Results reject only a mapping within a declared task, scale, horizon, and margin; post-hoc revision creates a new hypothesis. The resource-bounded coupling hypothesis predicts that human-level transfer on contact-rich tasks depends on distinctions retained in organism–environment relations. An adaptive internal controller counts against it when transfer has no preregistered resource disadvantage, relational-history effects vanish in state-collision tests, the relational block adds no meaningful intervention-predictive value, and internal-realiser interventions have distinctive predicted effects. Existing evidence has not established a Bayesian mechanism for unconstrained embodied behaviour.
Human-centered adaptive systems require behavioral models that are both psychologically interpretable and mathematically analyzable. Many existing predictors either operate as black-box input-output mappings or provide limited access to latent internal dynamics. This paper addresses this gap by modeling behavior as a perception-cognition-decision pipeline. We propose a modular state-space model in which attentional selection, predictive inference, cognitive-state evolution, intention formation, and action selection are represented by coupled mathematical mappings. The model links sensory inputs to observable behavior through latent internal states while retaining interpretable connections to neuro-cognitive mechanisms. We establish sufficient conditions for boundedness, Lipschitz regularity, forward invariance, contraction of perceptual inference under constant input, and input-to-state stability of the cognitive state dynamics. Numerical sensitivity analyses show that the model yields interpretable changes in perceptual tracking, cognitive amplification, intention expression, and action decisiveness. We further demonstrate a closed-loop rehabilitation case study in which a receding-horizon controller uses the model to adapt movement difficulty from partial feedback. In this proof-of-concept setting, the model-based controller sustains simulated task participation and achieves lower realized cumulative cost than target-following and random baselines. Overall, the framework provides a white-box dynamical structure for estimation, validation, and model-based control in human-centered settings.
Sven Schoonebeek, C. Cenedese, A. Jamshidnejad· arXiv.org· 0 citations
Predictive coding offers a powerful theory of cortical computation, but corresponding scalable algorithmic implementations for artificial intelligence have remained elusive. This paper introduces the Bayesian reflex, a computational framework that directly instantiates predictive coding through three pillars: belief maintenance via hierarchical generative models, sequential Bayesian updating via prediction-error minimization, and uncertainty-driven action via active inference. We show that recent breakthroughs---ellipsoidal decomposition for exact $i.i.d.$ sampling, recursive Gaussian processes for deep hierarchical inference, and derivative-aware Bayesian optimization---provide the missing algorithmic ingredients. The resulting framework enables mathematically principled, scalable, and brain-inspired continual learning, perception, and decision-making. We illustrate its versatility through applications ranging from climate model evaluation to prime number discovery, offering a blueprint for truly adaptive artificial intelligence.
Under the free energy principle, a predictive system does not observe reality directly; it maintains a generative model of the world and experiences that model's best current hypothesis. Can a synthetic environment be made consistent enough that a predictive system's own inference machinery adopts it as this default hypothesis, permanently displacing the environment that first shaped it? We call this state ontological inversion. Because inducing and monitoring such a transition in a nervous system is neither ethical nor technically feasible, we study the underlying computational problem through a controlled proxy: a convolutional variational autoencoder paired with a recurrent latent predictor, whose evidence lower bound objective is mathematically identical, up to sign, to variational free energy itself. The network is trained first on a baseline visual domain, then on a mixed stream in which a swept rehearsal ratio r controls how much baseline content persists during transition to a target domain. Representational capacity, what the latent space can discriminate, is tracked separately from default behavior, what the system generates when left unconstrained. Across a full sweep of 90 runs, the two diverge sharply: representational accuracy stays near ceiling, 0.97 to 0.998, regardless of r, while default behavior spans nearly the system's entire range depending on r alone, a decoupling of learning from acceptance. More strikingly, at intermediate r the system's default output rises toward the target domain, then partially reverts toward the baseline while training continues unchanged, a structural failure we term cognitive relapse. Resistance to reality-adoption is not reducible to learning speed; it is a structural property with its own distinct failure modes, established here as a computational existence proof and nothing further.
The neural mechanisms underlying conscious perception remain contested, with global neuronal workspace theory (GNWT) and integrated information theory (IIT) offering divergent predictions about the spatiotemporal dynamics of conscious processing. The Cogitate Consortium (2025) recently conducted a large-scale adversarial collaboration to arbitrate between GNWT and IIT; however, some of their analyses yielded mixed findings. As the original study relied on functional connectivity, it could not assess the directed neural influences required to directly test the mechanistic claims of these theories. Here, we re-examined the Cogitate Consortium’s MEG dataset (N = 100) using dynamic causal modelling (DCM) to test the effective connectivity profiles predicted by each theory during task-irrelevant face perception. We adopted a split discovery-validation procedure and an expanding time-window approach to track the temporal evolution of prototypical networks for each theory. Specifically, we evaluated GNWT’s prediction of phasic prefrontal “ignition” by testing the necessity of PFC feedback to category-selective areas at stimulus onset and offset, and then tested IIT’s prediction of sustained posterior integration by testing extrinsic feedback and intrinsic connectivity within content-specific regions. We found support for both GNWT predictions of prefrontal ignition at stimulus onset and offset; noting that the latter was not previously observed in the original Cogitate analyses. For IIT, whilst feedback connectivity between the fusiform gyrus and primary visual cortex was not sustained throughout the stimulus duration, intrinsic fusiform gyrus connectivity was broadly consistent with IIT’s prediction of sustained processing within a content-specific substrate. However, a post-hoc validation analysis comparing face- and object-specific DCM networks did not yield strong evidence for face selectivity at any time window (pp< 0.95), warranting a conservative interpretation of the IIT findings in particular.
Kavindu Bandara, Elise G. Rowe, Marta I. Garrido· bioRxiv· 0 citations
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