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.

翻译：数据增强是等变机器学习中一种强大的机制，它通过训练网络在输入变换下产生一致输出，从而鼓励对称性。然而，有效的增强通常需要预先指定基础对称性，当对称性未知或仅近似成立时，这会限制泛化能力。为解决此问题，我们提出了LieAugmenter，一种通过可学习增强发现任务相关连续对称性的端到端框架。具体而言，增强生成器利用李群理论进行参数化，并与预测网络使用增强视图进行联合训练。所学习的增强具有任务自适应性，能够实现有效且可解释的对称性发现。我们提供了可识别性的理论分析，并证明我们的方法能为所识别的群产生尊重对称性的模型。实验表明，LieAugmenter在图像分类、N体动力学预测以及分子性质预测任务上均优于基线方法。此外，它还能为检测对称性缺失提供可解释的特征标识。