Homotopy theoretic and categorical models of neural information networks

Manin, Yuri; Marcolli, Matilde

doi:10.46298/compositionality-6-4

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学術論文

Homotopy theoretic and categorical models of neural information networks

MPS-Authors

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Manin, Yuri
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.48550/arXiv.2006.15136
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https://doi.org/10.46298/compositionality-6-4
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Manin-Marcolli_Homotopy theoretic and categorical models of neural information networks_2024.pdf
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引用

Manin, Y., & Marcolli, M. (2024). Homotopy theoretic and categorical models of neural information networks. Compositionality, 6:. doi:10.46298/compositionality-6-4.

引用: https://hdl.handle.net/21.11116/0000-000F-F076-D

要旨

In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The starting point for this construction is the notion of summing functors and of Segal's Gamma-spaces in homotopy theory. The main results in this paper include functorial assignments of concurrent/distributed computing architectures and associated binary codes to networks and their subsystems, a categorical form of the Hopfield network dynamics, which recovers the usual Hopfield equations when applied to a suitable category of weighted codes, a functorial assignment to networks of corresponding information structures and information cohomology, and a cohomological version of integrated information.