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This research proposes a mathematical framework using convex cone algebras to model how neuron populations actively process information, moving beyond passive transmission theories. By demonstrating that these biological structures perform operations like dimensionality reduction and prediction through matrix embeddings, the study suggests new pathways for extending representational capacity in artificial intelligence systems. The work bridges mechanistic neuroscience with advanced AI concepts, offering potential insights into hierarchical concept formation that vector-based models currently struggle to achieve.
Information Processing by Neuron Populations in the Central Nervous System: A Theory of the Mathematical Structure of Data and Operations
arXiv:2309.02332v3 Announce Type: replace-cross Abstract: In the mammalian central nervous system, neurons are organized into populations communicating by spike trains propagating along axonal bundles. How such populations encode and transform information is only partially understood. In this study we introduce a mathematical framework derived from a mechanistic model of a single plastic neuron. Within this framework, an algebra of convex cones can rigorously characterize population-level activity. This algebra provides a natural language describing information representation and processing. Neuron populations are thereby interpreted not as passive transmitters but as operators acting within this algebraic structure. When interconnected, such populations realize compact algebraic expressions whose functional repertoire includes specialization, generalization, novelty detection, dimensionality reduction, inverse modeling, prediction, and associative memory. Finally, the approach highlights the role of matrix embeddings in extending representational capacity beyond that afforded by vector-based models. In particular, such embeddings support hierarchical concept formation and structured information processing, with potential implications for both cognitive neuroscience and artificial intelligence. This paper assumes familiarity with elementary functional analysis and algebras of operators.
Abstract:In the mammalian central nervous system, neurons are organized into populations communicating by spike trains propagating along axonal bundles. How such populations encode and transform information is only partially understood. In this study we introduce a mathematical framework derived from a mechanistic model of a single plastic neuron. Within this framework, an algebra of convex cones can rigorously characterize population-level activity. This algebra provides a natural language describing information representation and processing. Neuron populations are thereby interpreted not as passive transmitters but as operators acting within this algebraic structure. When interconnected, such populations realize compact algebraic expressions whose functional repertoire includes specialization, generalization, novelty detection, dimensionality reduction, inverse modeling, prediction, and associative memory. Finally, the approach highlights the role of matrix embeddings in extending representational capacity beyond that afforded by vector-based models. In particular, such embeddings support hierarchical concept formation and structured information processing, with potential implications for both cognitive neuroscience and artificial intelligence. This paper assumes familiarity with elementary functional analysis and algebras of operators.
60 pages, 12 figures. Major revision. The neuron model is shown to perform online projected-gradient optimization for NNLS. New results connect neuron-local learning to conic projection and rejection through sparse, activity-selected mappings, strengthen the cone algebra with Moreau-based proofs, and characterize approximate invariance under sparse embeddings. Adds a sensorimotor application
Neurons and Cognition (q-bio.NC); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE)
F.1.1; J.3; I.2.4
arXiv:2309.02332 [q-bio.NC]
(or arXiv:2309.02332v3 [q-bio.NC] for this version)
From: Martin N. P. Nilsson PhD [view email] [v1] Tue, 5 Sep 2023 15:52:45 UTC (3,208 KB) [v2] Sat, 30 Dec 2023 21:11:44 UTC (520 KB) [v3] Fri, 31 Jul 2026 17:49:39 UTC (467 KB)
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