Noncommutative Geometry of Computational Models and Uniformization for Framed Quiver Varieties

TL;DR

This paper develops a mathematical framework for neural networks using noncommutative geometry, exploring moduli spaces of quiver representations and their uniformization, inspired by quantum automata.

Contribution

It introduces a novel noncommutative geometric approach to modeling neural networks and analyzes the moduli spaces of quiver representations with uniformization techniques.

Findings

Identification of Euclidean and non-compact moduli spaces

Application of noncommutative algebras to neural network models

Insights into the geometric structure of quantum-inspired automata

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.