Information Processing by Neuron Populations in the Central Nervous System: Mathematical Structure of Data and Operations

TL;DR

This paper models neuron populations in the central nervous system using an algebra of convex cones, revealing their computational capabilities and potential applications in AI and cognitive science.

Contribution

It introduces a novel mathematical framework linking neuron populations to algebraic structures, enabling diverse information processing operations.

Findings

Neuron populations act as operators in a convex cone algebra.

Networks can implement operations like prediction and memory.

Matrix embeddings enhance concept processing in AI.

Abstract

In the intricate architecture of the mammalian central nervous system, neurons form populations. Axonal bundles communicate between these clusters using spike trains. However, these neuron populations' precise encoding and operations have yet to be discovered. In our analysis, the starting point is a state-of-the-art mechanistic model of a generic neuron endowed with plasticity. From this simple framework emerges a subtle mathematical construct: The representation and manipulation of information can be precisely characterized by an algebra of convex cones. Furthermore, these neuron populations are not merely passive transmitters. They act as operators within this algebraic structure, mirroring the functionality of a low-level programming language. When these populations interconnect, they embody succinct yet potent algebraic expressions. These networks allow them to implement many operations, such as specialization, generalization, novelty detection, dimensionality reduction, inverse modeling, prediction, and associative memory. In broader terms, this work illuminates the potential of matrix embeddings in advancing our understanding in fields like cognitive science and AI. These embeddings enhance the capacity for concept processing and hierarchical description over their vector counterparts.