# LieAugmenter: Equivariant Learning by Discovering Symmetries with Learnable Augmentations

arXiv: https://arxiv.org/abs/2506.03914 · HTML: https://mlsanity.com/paper/2506.03914/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2025.

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

- [Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks](https://mlsanity.com/paper/2509.24886/) (2025)
- [How Do Transformers Learn to Represent Symmetries?](https://mlsanity.com/paper/2610.10305/) (2026)

## Abstract (arXiv)

Data augmentation is a powerful mechanism in equivariant machine learning, encouraging symmetry by training networks to produce consistent outputs under transformed inputs. Yet, effective augmentation typically requires the underlying symmetry to be specified a priori, which can limit generalization when symmetries are unknown or only approximately valid. To address this, we introduce LieAugmenter, an end-to-end framework that discovers task-relevant continuous symmetries through learnable augmentations. Specifically, the augmentation generator is parameterized using the theory of Lie groups and trained jointly with the prediction network using the augmented views. The learned augmentations are task-adaptive, enabling effective and interpretable symmetry discovery. We provide a theoretical analysis of identifiability and show that our method yields symmetry-respecting models for the identified groups. Empirically, LieAugmenter outperforms baselines on image classification, as well as on the prediction of N-body dynamics and molecular properties. In addition, it can also provide an interpretable signature for detecting the absence of symmetries.