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In the intricate architecture of the mammalian central nervous system,neurons form populations. Axonal bundles communicate between these clustersusing spike trains. However, these neuron populations' precise encoding andoperations have yet to be discovered. In our analysis, the starting point is astate-of-the-art mechanistic model of a generic neuron endowed with plasticity.From this simple framework emerges a subtle mathematical construct: Therepresentation and manipulation of information can be precisely characterizedby an algebra of convex cones. Furthermore, these neuron populations are notmerely passive transmitters. They act as operators within this algebraicstructure, mirroring the functionality of a low-level programming language.When these populations interconnect, they embody succinct yet potent algebraicexpressions. These networks allow them to implement many operations, such asspecialization, generalization, novelty detection, dimensionality reduction,inverse modeling, prediction, and associative memory. In broader terms, thiswork illuminates the potential of matrix embeddings in advancing ourunderstanding in fields like cognitive science and AI. These embeddings enhancethe capacity for concept processing and hierarchical description over theirvector counterparts.

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