Unified Model of Neural Encoding and Decoding of Stimuli: Predicate-Coding from Applied Category Theory

This paper presents a mathematical model, grounded in category theory, which unifies neural encoding and decoding across scales and modalities and gives rise to equations incorporating individual neural codes into a unified picture. The model introduces three fundamental categories, one representing stimuli, another representing single-neurons and one representing neural networks; with functors representing encoding and decoding. At the neuronal scale, a unified coding equation represents a neuron’s code as a normalized convex mixture of component codes (such as rate code, latency code...) inputted through a nonlinearity function. At the neuronal scale, a unified coding equation represents a network’s code and combines the vector of single-neuron codes with network-level codes (such as population code, correlation code...) through convex weights. Noise is modelled as discrepancies between encoding and decoding. Moreover, through an encoding functor within the categorical framework, neurons are modelled as encoding a given many-valued logical predicate (whose output is in [0,1]) applied to a given stimulus. Networks, however, are modelled as encoding a given vector of such predicates. Predicate coding thus parallels the "feature detector neuron" conception, but strengthens it as logical predicates can be made from any well-formed formula containing a free variable (and can thus even model a disjunction of multiple other predicates). Hence, predicate-coding, its underlying categorical architecture as well as unified equations, provide a mathematically rigorous and experimentally implementable unification of neural encoding and decoding from the cellular scale to large-scale neural networks.