Research map / Learning theory and algorithms / Matrix and tensor methods
A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Enforce O(2) equivariance | Neural ODE · Double spring pendulum, 30s rollout | relative rollout error: 0.048 -> 0.019(1) | Helped |
| Enforce SO(2) equivariance | Neural ODE · Double spring pendulum, 30s rollout | relative rollout error: 0.048 -> 0.051(36) | Mixed |
| Enforce D6 equivariance | Neural ODE · Double spring pendulum, 30s rollout | relative rollout error: 0.048 -> 0.036(25) | Helped |
| Enforce O(2) equivariance | Hamiltonian Neural Network · Double spring pendulum, 30s rollout | relative rollout error: 0.028 -> 0.012(2) | Helped |
| Enforce SO(2) equivariance | Hamiltonian Neural Network · Double spring pendulum, 30s rollout | relative rollout error: 0.028 -> 0.015(3) | Helped |
| Enforce D6 equivariance | Hamiltonian Neural Network · Double spring pendulum, 30s rollout | relative rollout error: 0.028 -> 0.013(2) | Helped |
| Use a Hamiltonian Neural Network rather than a Neural ODE | EMLP-O(2) · Double spring pendulum, 30s rollout | relative rollout error: 0.019(1) -> 0.012(2) | Helped |
| Enforce continuous rotation symmetry in the HNN | EMLP-HNN · Double spring pendulum | angular momentum conservation | Helped |
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