Symmetry Discovery for Different Data Types
This addresses the challenge of incorporating symmetries into neural networks for tasks like physics simulations and particle tagging, offering a more efficient alternative to existing methods.
The paper tackles the problem of constructing equivariant neural networks without prior knowledge of symmetries by proposing LieSD, a method that discovers symmetries using trained neural networks, Lie algebra, and gradients, achieving accurate determination of Lie algebra bases and performance on non-uniform datasets where GAN-based methods fail.
Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically requires prior knowledge of data types and symmetries, which is difficult to achieve in most tasks. In this paper, we propose LieSD, a method for discovering symmetries via trained neural networks which approximate the input-output mappings of the tasks. It characterizes equivariance and invariance (a special case of equivariance) of continuous groups using Lie algebra and directly solves the Lie algebra space through the inputs, outputs, and gradients of the trained neural network. Then, we extend the method to make it applicable to multi-channel data and tensor data, respectively. We validate the performance of LieSD on tasks with symmetries such as the two-body problem, the moment of inertia matrix prediction, and top quark tagging. Compared with the baseline, LieSD can accurately determine the number of Lie algebra bases without the need for expensive group sampling. Furthermore, LieSD can perform well on non-uniform datasets, whereas methods based on GANs fail.