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LieTransformer: Equivariant Self-Attention for Lie Groups
Michael Hutchinson · Charline Le Lan · Sheheryar Zaidi · Emilien Dupont · Yee-Whye Teh · Hyunjik Kim

Tue Jul 20 07:25 AM -- 07:30 AM (PDT) @

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.

Author Information

Michael Hutchinson (University of Oxford)
Charline Le Lan (University of Oxford)
Sheheryar Zaidi (University of Oxford)
Emilien Dupont (University of Oxford)
Yee-Whye Teh (Oxford and DeepMind)
Hyunjik Kim (DeepMind)

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