Pomi2025TopoNC

Title

Topological Neural Coding
View PDF | Save PDF

Authors

Andrés Pomi

Affiliations

Andrés Pomi, Sección Biofísica y Biología de Sistemas, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay.

Abstract

Understanding the neural representation of complex cognitive activities, such as processing algebraic or topological structures like graphs, groups, and knots, is a fundamental challenge in cognitive neuroscience. This study explores how associative matrix memories, as mesoscopic models, bridge symbolic data processing with dynamic neuronal activity. We demonstrate that these memories naturally represent graphs of associations between concepts and extend this framework to encode finite groups via their Cayley graphs and knots through tensor product representations. For knots, we propose a context-dependent associative memory matrix that captures crossing states in knot diagrams, linking Gauss codes to Seifert circles and aiding knot classification. These representations provide a unified neural framework for encoding diverse topological objects, offering insights into the brain's ability to process abstract mathematical structures.

KeyPhrases

Associative memories, representation models, tensor products, graphs, groups, knots.

Dates

Created 2025-05-01, presented 2025-06-02, published 2025-07-16.

Citation

Brainiacs Journal 2025 Volume 6 Issue 1 Edoc T43E35E87
DOI: 10.48085/T43E35E87
PDP: Nexus/Brainiacs/Pomi2025TopoNC
URL: BrainiacsJournal.org/arc/pub/Pomi2025TopoNC