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Poster
Automatic Symmetry Discovery with Lie Algebra Convolutional Network
Nima Dehmamy · Robin Walters · Yanchen Liu · Dashun Wang · Rose Yu

Thu Dec 09 08:30 AM -- 10:00 AM (PST) @
in Poster Session 6 »

Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra convolutional network (L-conv) can automatically discover symmetries and does not require discretization of the group. We show that L-conv can serve as a building block to construct any group equivariant feedforward architecture. Both CNNs and Graph Convolutional Networks can be expressed as L-conv with appropriate groups. We discover direct connections between L-conv and physics: (1) group invariant loss generalizes field theory (2) Euler-Lagrange equation measures the robustness, and (3) equivariance leads to conservation laws and Noether current. These connections open up new avenues for designing more general equivariant networks and applying them to important problems in physical sciences.

Keywords: Theory · Deep Learning · Machine Learning · Robustness · Graph Learning

Author Information

Nima Dehmamy (Northwestern University)

I obtained my PhD in physics on complex systems from Boston University in 2016. I did postdoc at Northeastern University working on 3D embedded graphs and graph neural networks. My current research is on physics-informed machine learning and computational social science.

Robin Walters (Northeastern University)
Yanchen Liu (Northeastern University)
Dashun Wang (Northwestern University)
Rose Yu (Northeastern University)

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