让神经网络学会处理数据中的对称性破坏，提升小样本训练效率。
Learning Broken Symmetries with Approximate Invariance
- 采用双子网结构，一个受对称性约束，一个不受限。
- 在洛伦兹对称性被破坏的场景中，学习速度媲美约束网络。
- 适合高能物理等对称性不完美但需高效学习的领域。
识别数据中的对称性可显著提升神经网络训练效率，尤其在训练数据有限时尤为重要。然而，在许多情况下，理想数据集中的精确对称性在真实数据中因探测器不对称或动量相关响应分辨率变化而被破坏。标准方法如数据增强或等变网络无法准确表示完整的对称性破缺，导致模型响应过度受限。本文提出一种学习模型，兼顾无约束网络的泛化能力与约束网络的快速学习优势。该模型采用双子网结构：一个子网受对称性约束，另一个不受限，并引入可学习的对称性因子。在一个简化玩具模型中，该方法展示了违反洛伦兹不变性的场景下，学习速度与约束网络相当，同时克服了其性能瓶颈。
原文摘要 · Abstract (English)
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.
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