Double framed moduli spaces of quiver representations

Motivated by problems in the neural networks setting, we study moduli spaces of double framed quiver representations and give both a linear algebra description and a representation theoretic description of these moduli spaces. We define a network category whose isomorphism classes of objects correspond to the orbits of quiver representations, in which neural networks map input data. We then prove that the output of a neural network depends only on the corresponding point in the moduli space. Finally, we present a different perspective on mapping neural networks with a specific activation function, called ReLU, to a moduli space using the symplectic reduction approach to quiver moduli. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

Motivated by problems in the neural networks setting, this study focuses on the moduli spaces of double framed quiver representations and provides both a linear algebra description and a representation theoretic description of these moduli spaces. By defining a network category, it is proven that the output of a neural network depends only on the corresponding point in the moduli space. Finally, a different perspective on mapping neural networks with a specific activation function to a moduli space is presented using the symplectic reduction approach to quiver moduli.