# Symmetry From Scratch: Group Equivariance as a Supervised Learning Task

arXiv: https://arxiv.org/abs/2410.03989 · HTML: https://mlsanity.com/paper/2410.03989/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Stealing Machine Learning Models via Prediction APIs](https://mlsanity.com/paper/1609.02943/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Sequence Tutor: Conservative Fine-Tuning of Sequence Generation Models with KL-control](https://mlsanity.com/paper/1611.02796/) (2016)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Revisiting Spatial Invariance with Low-Rank Local Connectivity](https://mlsanity.com/paper/2002.02959/) (2020)
- [Learning Probabilistic Symmetrization for Architecture Agnostic Equivariance](https://mlsanity.com/paper/2306.02866/) (2023)

## Abstract (arXiv)

In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest. However, this process becomes increasingly over-engineered as models are geared towards specific symmetries/asymmetries hardwired of a particular set of equivariant basis functions. In this work, we introduce symmetry-cloning, a method for inducing equivariance in machine learning models. We show that general machine learning architectures (i.e., MLPs) can learn symmetries directly as a supervised learning task from group equivariant architectures and retain/break the learned symmetry for downstream tasks. This simple formulation enables machine learning models with group-agnostic architectures to capture the inductive bias of group-equivariant architectures.