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Homotopy Theoretic and Categorical Models of Neural Information Networks

Manin, Yuri I. and Marcolli, Matilde (2020) Homotopy Theoretic and Categorical Models of Neural Information Networks. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210825-184557696

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Abstract

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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2006.15136arXivDiscussion Paper
Additional Information:The second named author is partially supported by NSF grant DMS-1707882, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593, and by FQXi grant FQXi-RFP-1 804.
Funders:
Funding AgencyGrant Number
NSFDMS-1707882
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPIN-2018-04937
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPAS-2018-522593
Foundational Questions Institute (FQXI)RFP-1 804
Record Number:CaltechAUTHORS:20210825-184557696
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210825-184557696
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110542
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:25 Aug 2021 22:18
Last Modified:25 Aug 2021 22:18

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