Homotopy Theoretic and Categorical Models of Neural Information Networks
Y. Manin, and M. Marcolli. (2020)cite arxiv:2006.15136Comment: 80 pages LaTeX.
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.
Description
[2006.15136] Homotopy Theoretic and Categorical Models of Neural Information Networks
%0 Journal Article
%1 manin2020homotopy
%A Manin, Yuri
%A Marcolli, Matilde
%D 2020
%K category-theory deep-learning information readings
%T Homotopy Theoretic and Categorical Models of Neural Information Networks
%U http://arxiv.org/abs/2006.15136
%X 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.
@article{manin2020homotopy,
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.},
added-at = {2020-06-29T19:08:32.000+0200},
author = {Manin, Yuri and Marcolli, Matilde},
biburl = {https://www.bibsonomy.org/bibtex/2979fbcfde500e36351d414213e5eab38/kirk86},
description = {[2006.15136] Homotopy Theoretic and Categorical Models of Neural Information Networks},
interhash = {4fb964f6173bc567dbd465087f1c3b1a},
intrahash = {979fbcfde500e36351d414213e5eab38},
keywords = {category-theory deep-learning information readings},
note = {cite arxiv:2006.15136Comment: 80 pages LaTeX},
timestamp = {2020-06-29T19:08:32.000+0200},
title = {Homotopy Theoretic and Categorical Models of Neural Information Networks},
url = {http://arxiv.org/abs/2006.15136},
year = 2020
}