让模型自己发现数据中的对称性，提升预测准确性
LieAugmenter: Equivariant Learning by Discovering Symmetries with Learnable Augmentations
- 用李群理论构建可学习的数据增强，自动发现任务相关对称性
- 在图像分类、分子性质预测等任务上超越现有方法
- 能识别对称性是否存在，结果可解释，适合对物理规律建模的场景
数据增强是等变机器学习中的有力工具，通过训练网络在输入变换下保持输出一致来引入对称性。然而，有效增强通常需要预先指定对称性，当对称性未知或仅近似成立时，会限制泛化能力。为此，我们提出 LieAugmenter，一个端到端框架，通过可学习的增强机制自动发现任务相关的连续对称性。具体而言，增强生成器基于李群理论参数化，并与预测网络联合训练。所学增强具有任务自适应性，实现高效且可解释的对称性发现。我们提供了可辨识性的理论分析，证明该方法能为识别出的群构造尊重对称性的模型。实验表明，LieAugmenter在图像分类、N体动力学预测及分子性质预测任务中均优于基线方法。此外，还能提供可解释的信号以检测对称性的缺失。
原文摘要 · Abstract (English)
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.
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