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.
Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021 |
Editors | Marc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan |
Publisher | Neural information processing systems foundation |
Pages | 2503-2515 |
Number of pages | 13 |
ISBN (Electronic) | 9781713845393 |
State | Published - 2021 |
Event | 35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online Duration: Dec 6 2021 → Dec 14 2021 |
Publication series
Name | Advances in Neural Information Processing Systems |
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Volume | 4 |
ISSN (Print) | 1049-5258 |
Conference
Conference | 35th Conference on Neural Information Processing Systems, NeurIPS 2021 |
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City | Virtual, Online |
Period | 12/6/21 → 12/14/21 |
Funding
R. Walters is supported by a Postdoctoral Fellowship from the Roux Institute and NSF grants #2107256 and #2134178. This work was supported in part by the U. S. Army Research Office under Grant W911NF-20-1-0334, DOE ASCR 2493 and NSF Grant #2134274. N. Dehmamy and D. Wang were supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0354.
ASJC Scopus subject areas
- Computer Networks and Communications
- Information Systems
- Signal Processing