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From Entropy Dynamics of Neuronal Coherence to Valenced Percepts: A Topos-Theoretic Construction

Authors: Cacioppo, Robert;

From Entropy Dynamics of Neuronal Coherence to Valenced Percepts: A Topos-Theoretic Construction

Abstract

We develop a theory of neural organization in which percepts are modeled as probabilistic structures on directed acyclic graphs of time-stamped subthreshold oscillatory states, and affective valence is defined by entropy dynamics on these structures. Each graph is assigned two pattern functors: a bound functor, whose elements are Bayesian networks compatible with the graph's causal organization, and an unbound functor, whose elements are arbitrary distributions on the corresponding vertex-state spaces. These functors are organized in a set-valued presheaf topos over the category of directed acyclic graphs with ancestral inclusions, so that restriction corresponds to marginalization. Within this setting, percept-types are subfunctors, percepts are compatible families of local distributions, and the entropic valence determines a time-dependent Grothendieck topology governing which local patterns count as admissible for perceptual integration. The resulting internal intuitionistic logic provides a formal language for describing local endorsement, obstruction, and amalgamation of perceptual structure. We argue that this framework gives a principled account of how perceptual coherence and affective valence may jointly arise from mesoscopic cortical field dynamics.

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