LieTransformer: Equivariant self-attention for Lie Groups
This work addresses the problem of extending group equivariance to self-attention mechanisms, which is important for researchers developing more generalizable and data-efficient deep learning models.
This paper introduces LieTransformer, a self-attention architecture equivariant to Lie groups and their discrete subgroups. It achieves competitive results across tasks like shape counting on point clouds, molecular property regression, and particle trajectory modeling.
Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly focused on group equivariant convolutions, building on the result that group equivariant linear maps are necessarily convolutions. In this work, we extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups. We demonstrate the generality of our approach by showing experimental results that are competitive to baseline methods on a wide range of tasks: shape counting on point clouds, molecular property regression and modelling particle trajectories under Hamiltonian dynamics.