# Categorification of Group Equivariant Neural Networks

arXiv: https://arxiv.org/abs/2304.14144 · HTML: https://mlsanity.com/paper/2304.14144/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Category Theory in Machine Learning](https://mlsanity.com/paper/2106.07032/) (2021)
- [Brauer's Group Equivariant Neural Networks](https://mlsanity.com/paper/2212.08630/) (2022)
- [Connecting Permutation Equivariant Neural Networks and Partition Diagrams](https://mlsanity.com/paper/2212.08648/) (2022)
- [Fast computation of permutation equivariant layers with the partition algebra](https://mlsanity.com/paper/2303.06208/) (2023)
- [How Jellyfish Characterise Alternating Group Equivariant Neural Networks](https://mlsanity.com/paper/2301.10152/) (2023)

## Built on by (most cited first, 2 of 2)

- [Enriching Disentanglement: From Logical Definitions to Quantitative Metrics](https://mlsanity.com/paper/2305.11512/) (2023)
- [Compact Matrix Quantum Group Equivariant Neural Networks](https://mlsanity.com/paper/2311.06358/) (2023)

## Abstract (arXiv)

We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power space of ℝn for the groups Sn, O(n), Sp(n), and SO(n). By using category theoretic constructions, we build a richer structure that is not seen in the original formulation of these neural networks, leading to new insights. In particular, we outline the development of an algorithm for quickly computing the result of a vector that is passed through an equivariant, linear layer for each group in question. The success of our approach suggests that category theory could be beneficial for other areas of deep learning.