Double framed moduli spaces of quiver representations

2021/09/29 by Armenta, Marco, Brüstle, Thomas, Hassoun, Souheila +1
#14D22 #16G20 #53D30 #68T01 #68T07 #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Neural and Evolutionary Computing (cs.NE) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2109.14589

Abstract

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.

Related

• The Representation Theory of Neural Networks
• Kähler Geometry of Quiver Varieties and Machine Learning
• Moduli of representations of quivers
• Quiver neural networks
• Moduli of Representations I. Projections from Quivers