🤖 AI Summary
This work investigates how to automatically uncover low-dimensional constraint structures induced by symmetries and conservation laws from high-dimensional physical data in the absence of explicit prior knowledge. To this end, we propose an unsupervised representation learning framework based on variational autoencoders that eschews conventional designs relying on explicit symmetry embeddings. Instead, our approach leverages the information bottleneck principle to drive the latent space to self-organize and reveal the dimensionality reduction inherent to underlying symmetries. Evaluated on geometric systems and particle physics datasets, the method successfully recovers theoretically expected symmetry structures and systematically delineates the theoretical limits and practical challenges of symmetry inference under minimal inductive bias.
📝 Abstract
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.