# Neural Discovery of Permutation Subgroups

arXiv: https://arxiv.org/abs/2309.05352 · HTML: https://mlsanity.com/paper/2309.05352/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [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)
- [Equivariance Through Parameter-Sharing](https://mlsanity.com/paper/1702.08389/) (2017)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [Automatic Symmetry Discovery with Lie Algebra Convolutional Network](https://mlsanity.com/paper/2109.07103/) (2021)
- [Meta-Learning Symmetries by Reparameterization](https://mlsanity.com/paper/2007.02933/) (2020)
- [Universal Equivariant Multilayer Perceptrons](https://mlsanity.com/paper/2002.02912/) (2020)
- [Theoretical Aspects of Group Equivariant Neural Networks](https://mlsanity.com/paper/2004.05154/) (2020)
- [Learning to Infer Structures of Network Games](https://mlsanity.com/paper/2206.08119/) (2022)

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

- [Grokking Group Multiplication with Cosets](https://mlsanity.com/paper/2312.06581/) (2023)
- [Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures](https://mlsanity.com/paper/2411.16260/) (2024)

## Abstract (arXiv)

We consider the problem of discovering subgroup H of permutation group Sn. Unlike the traditional H-invariant networks wherein H is assumed to be known, we present a method to discover the underlying subgroup, given that it satisfies certain conditions. Our results show that one could discover any subgroup of type Sk (k ≤ n) by learning an Sn-invariant function and a linear transformation. We also prove similar results for cyclic and dihedral subgroups. Finally, we provide a general theorem that can be extended to discover other subgroups of Sn. We also demonstrate the applicability of our results through numerical experiments on image-digit sum and symmetric polynomial regression tasks.