Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a remarkable ability to extract low-dimensional structure from high-dimensional data through representation learning. This review examines the interplay between these two perspectives, focusing on the extent to which symmetry-induced constraints can be identified, encoded, or diagnosed using machine learning techniques. Rather than emphasizing architectures that enforce known symmetries by construction, we concentrate on data-driven approaches and latent representation learning, with particular attention to variational autoencoders. We discuss how symmetries and conservation laws reduce the intrinsic dimensionality of physical datasets, and how this reduction may manifest itself through self-organization of latent spaces in generative models trained to balance reconstruction and compression. We review recent results, including case studies from simple geometric systems and particle physics processes, and analyze the theoretical and practical limitations of inferring symmetry structure without explicit inductive bias.

翻译：对称性在物理学中扮演着核心角色，它组织动力学、约束相互作用并决定物理自由度的有效数量。与此同时，现代人工智能方法通过表示学习，已展现出从高维数据中提取低维结构的卓越能力。本综述审视了这两种视角之间的相互作用，重点关注利用机器学习技术识别、编码或诊断对称性诱导约束的程度。我们并非强调通过构造强制已知对称性的架构，而是集中于数据驱动方法和潜在表示学习，尤其关注变分自编码器。我们讨论了对称性和守恒定律如何降低物理数据集的固有维度，以及这种降维如何通过生成模型的潜在空间自组织显现——这些模型经过训练以平衡重构与压缩。我们回顾了最新研究成果，包括来自简单几何系统和粒子物理过程的案例研究，并分析了在没有显式归纳偏置的情况下推断对称性结构的理论与实际局限性。