Equivariant Machine Learning Structured Like Classical Physics
summary
Provides a concrete, dimension-agnostic parameterization: inner products as complete invariants for O(d) and Minkowski variants, and any O(d)-equivariant vector output is a linear combination of inputs — equivariant outputs lie in input span — with scalar coefficients that are invariant functions (polynomial choices give universality). Implements this for rotations, parity, boosts and tests on springed double pendulum, where Hamiltonian-equivariant models beat prior EMLP baselines and give smaller long-term errors; notes n^2 features are avoidable and links to FMM for scaling.
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chapters (16)
- 0:00Introduction
- 1:10Motivation
- 2:05Graph Neural Networks
- 3:55Recap
- 4:35Invariant
- 6:00Spectral Methods
- 7:00Community Detection
- 19:40Graph Neural Networks Expressivity
- 23:02Equivariant Machine Learning
- 29:03Output
- 29:40Fundamental Theorem
- 38:36Translation equivalence
- 39:59General groups
- 42:58Numerical examples
- 47:31Conclusion
- 48:26Questions
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