# Double framed moduli spaces of quiver representations

arXiv: https://arxiv.org/abs/2109.14589 · HTML: https://mlsanity.com/paper/2109.14589/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2021.

## Built on by (most cited first, 3 of 3)

- [Quiver neural networks](https://mlsanity.com/paper/2207.12773/) (2022)
- [Hidden Activations Are Not Enough: A General Approach to Neural Network Predictions](https://mlsanity.com/paper/2409.13163/) (2024)
- [Hidden Activations are not Enough I: Knowledge Matrices as Higher Representations](https://mlsanity.com/paper/2609.34166/) (2026)

## Abstract (arXiv)

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.