# How Jellyfish Characterise Alternating Group Equivariant Neural Networks

arXiv: https://arxiv.org/abs/2301.10152 · HTML: https://mlsanity.com/paper/2301.10152/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 12 of 12)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [On the Universality of Invariant Networks](https://mlsanity.com/paper/1901.09342/) (2019)
- [On Learning Sets of Symmetric Elements](https://mlsanity.com/paper/2002.08599/) (2020)
- [Orientation-aware Semantic Segmentation on Icosahedron Spheres](https://mlsanity.com/paper/1907.12849/) (2019)
- [Universal Equivariant Multilayer Perceptrons](https://mlsanity.com/paper/2002.02912/) (2020)
- [What is an equivariant neural network?](https://mlsanity.com/paper/2205.07362/) (2022)
- [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)

## Built on by (most cited first, 5 of 5)

- [Graph Automorphism Group Equivariant Neural Networks](https://mlsanity.com/paper/2307.07810/) (2023)
- [Categorification of Group Equivariant Neural Networks](https://mlsanity.com/paper/2304.14144/) (2023)
- [Revisiting Multi-Permutation Equivariance through the Lens of Irreducible Representations](https://mlsanity.com/paper/2410.06665/) (2024)
- [An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layers](https://mlsanity.com/paper/2304.14165/) (2023)
- [Compact Matrix Quantum Group Equivariant Neural Networks](https://mlsanity.com/paper/2311.06358/) (2023)

## Abstract (arXiv)

We provide a full characterisation of all of the possible alternating group (An) equivariant neural networks whose layers are some tensor power of ℝn. In particular, we find a basis of matrices for the learnable, linear, An-equivariant layer functions between such tensor power spaces in the standard basis of ℝn. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.