Automatic Symmetry Discovery with Lie Algebra Convolutional Network | Nima Dehmamy

Abstract: 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

Authors: Nima Dehmamy, Robin Walters, Yanchen Liu, Dashun Wang, Rose Yu

~

00:00 - Intro
00:18 - Speaker Intro
01:54 - Symmetry in Physics
03:29 - Encoding Symmetries
10:57 - Need for Improvement
17:02 - Symmetry Groups
38:48 - Lie groups and Lie Algebras
43:10 - Group Action and Equivariance
50:15 - Group Convolution and Lie algebras
1:03:40 - Lie algebra Convolution
1:07:51 - Universal Approximation of Equivarient NN
1:10:07 - L-Conv Implemented as GCN
1:13:31 - Example: 2D Rotations
1:17:14 - Test Results
1:25:12 - Relation to Physics

[ggman]

QFT method applied in ML, this is genius. Waiting for GR method applied in Tensor network!