# Equivariance and generalization in neural networks

arXiv: https://arxiv.org/abs/2112.12493 · HTML: https://mlsanity.com/paper/2112.12493/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 9 references that are in the map.
- First posted on arXiv 23 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)

## Built on by (most cited first, 3 of 3)

- [SIDDA: SInkhorn Dynamic Domain Adaptation for Image Classification with Equivariant Neural Networks](https://mlsanity.com/paper/2501.14048/) (2025)
- [Equivariant symmetry-aware head pose estimation for fetal MRI](https://mlsanity.com/paper/2512.04890/) (2025)
- [Representation Gap: Explaining the Unreasonable Effectiveness of Neural Networks from a Geometric Perspective](https://mlsanity.com/paper/2605.21692/) (2026)

## Abstract (arXiv)

The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under consideration. In these proceedings, we focus on the consequences of incorporating translational equivariance among the network properties, particularly in terms of performance and generalization. The benefits of equivariant networks are exemplified by studying a complex scalar field theory, on which various regression and classification tasks are examined. For a meaningful comparison, promising equivariant and non-equivariant architectures are identified by means of a systematic search. The results indicate that in most of the tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies not only to physical parameters beyond those represented in the training set, but also to different lattice sizes.