Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 2

Noncommutative geometry of computational models and uniformization for framed quiver varieties

Pages: 731 – 789

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n2.a12

Authors

George Jeffreys (Department of Mathematics and Statistics, Boston University, Boston, Massachusetts, U.S.A.)

Siu-Cheong Lau (Department of Mathematics and Statistics, Boston University, Boston, Massachusetts, U.S.A.)

Abstract

We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of the corresponding framed quiver representations, and find moduli of Euclidean and non-compact types in light of uniformization.

Keywords

noncommutative geometry, near-rings, neural networks, deep learning, representation theory, moduli spaces

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Received 30 May 2022

Received revised 22 February 2023

Accepted 27 February 2023

Published 7 April 2023