2023/02/01 by Jianke Yang, Robin Walters, Yang, Jianke +5 · 7 citations
Computer Science · Materials Science · #Computational Physics and Python Applications #FOS: Computer and information sciences #Image Processing and 3D Reconstruction #Machine Learning (cs.LG) #Machine Learning in Materials Science
paper · pdf · doi:10.48550/arxiv.2302.00236
openalex publication_date 2023/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the wrong symmetry could even hurt the performance. In this paper, we propose a framework, LieGAN, to automatically discover equivariances from a dataset using a paradigm akin to generative adversarial training. Specifically, a generator learns a group of transformations applied to the data, which preserve the original distribution and fool the discriminator. LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries such as the rotation group SO(n), restricted Lorentz group SO(1,3)+ in trajectory prediction and top-quark tagging tasks. The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.