Generative Adversarial Symmetry Discovery
This addresses the challenge for researchers and practitioners in scientific applications who need to incorporate symmetries into neural networks without prior knowledge, offering a novel automated approach.
The paper tackles the problem of automatically discovering symmetry groups from data, as manually choosing them can be difficult and harmful to performance, and introduces LieGAN, a framework that uses generative adversarial training to learn interpretable symmetries like rotation groups, improving accuracy and generalization in tasks such as trajectory prediction and top-quark tagging.
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 $\mathrm{SO}(n)$, restricted Lorentz group $\mathrm{SO}(1,3)^+$ 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.