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Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace trivial equivariance with SE(2) equivariance (ablation) | LieConv · RotMNIST | classification error (%): 1.58 -> 1.24 | Helped |
| use SO(2) × R* rather than SE(2) equivariance (ablation) | LieConv · RotMNIST | classification error (%): 1.24 -> 1.27 | Hurt |
| replace trivial equivariance with SE(3) equivariance (ablation) | LieConv · QM9 HOMO | MAE (meV): 31.7 -> 26.8 | Helped |
| replace trivial equivariance with T(3) equivariance (ablation) | LieConv · QM9 HOMO | MAE (meV): 31.7 -> 29.6 | Helped |
| replace trivial equivariance with SO(3) equivariance (ablation) | LieConv · QM9 HOMO | MAE (meV): 31.7 -> 65.4 | Hurt |
Closest papers by meaning
- Lie Group Decompositions for Equivariant Neural Networks (ICLR 2024 · similarity 0.92)
- Group Equivariant Conditional Neural Processes (ICLR 2021 · similarity 0.91)
- On Making $SE(2)$-Invariant Networks Optimal (NeurIPS 2026 · similarity 0.90)
- Variational Partial Group Convolutions for Input-Aware Partial Equivariance of Rotations and Color-Shifts (ICML 2024 · similarity 0.90)
- Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions (NeurIPS 2025 · similarity 0.89)
- Affine Equivariant Networks Based on Differential Invariants (CVPR 2024 · similarity 0.89)
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