# Learning Broken Symmetries with Approximate Invariance

arXiv: https://arxiv.org/abs/2412.18773 · HTML: https://mlsanity.com/paper/2412.18773/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 6 references that are in the map.
- First posted on arXiv 25 Dec 2024.

## Builds on (most cited first, 2 of 2)

- [ConViT: Improving Vision Transformers with Soft Convolutional Inductive Biases](https://mlsanity.com/paper/2103.10697/) (2021)
- [Semi-Equivariant GNN Architectures for Jet Tagging](https://mlsanity.com/paper/2202.06941/) (2022)

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

- [Are We Ready for AI-Driven Discovery? AI Verification Before the Next Fundamental Physics Breakthrough](https://mlsanity.com/paper/2607.10039/) (2026)
- [SEAL - A Symmetry EncourAging Loss for High Energy Physics](https://mlsanity.com/paper/2511.01982/) (2025)

## Abstract (arXiv)

Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized dataset, and is broken in actual data, due to asymmetries in the detector, or varying response resolution as a function of particle momentum. Standard approaches, such as data augmentation or equivariant networks fail to represent the nature of the full, broken symmetry, effectively overconstraining the response of the neural network. We propose a learning model which balances the generality and asymptotic performance of unconstrained networks with the rapid learning of constrained networks. This is achieved through a dual-subnet structure, where one network is constrained by the symmetry and the other is not, along with a learned symmetry factor. In a simplified toy example that demonstrates violation of Lorentz invariance, our model learns as rapidly as symmetry-constrained networks but escapes its performance limitations.