Double framed moduli spaces of quiver representations
This work addresses theoretical foundations for neural networks, offering a novel mathematical framework, but it appears incremental as it builds on existing quiver representation theory without demonstrating practical applications or performance gains.
The paper tackles the problem of understanding neural networks by studying moduli spaces of double framed quiver representations, providing linear algebra and representation theoretic descriptions, and proving that neural network outputs correspond to points in these moduli spaces.
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.