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Equivariance with Learned Canonicalization Functions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Learn the canonicalization function end-to-end instead of using PCA | CNN on Rotated-MNIST · Rotated-MNIST | error %: 3.35 ± 0.21 -> 1.99 ± 0.10 | Helped |
| Learn canonicalization instead of freezing its weights (ablation) | CN-GNN · N-body dynamics prediction | MSE: 0.0085 ± 0.0002 -> 0.0043 ± 0.0001 | Helped |
| Use centroid translation canonicalization and learn only O(3) canonicalization (ablation) | CN-GNN · N-body dynamics prediction | MSE: 0.0043 ± 0.0001 -> 0.0045 ± 0.0001 | No clear effect |
| Learn canonicalization before retraining the prediction network, then freeze the canonicalizer (ablation) | CNN on Rotated-MNIST · Rotated-MNIST | error %: 3.30 ± 0.20 -> 2.05 ± 0.15 | Helped |
| Use a higher rotation order in the canonicalization network (ablation) | CN-CNN · Rotated-MNIST | error %: 2.41 ± 0.11 -> 1.99 ± 0.10 | Helped |
| Add canonicalization rather than modifying the backbone with Vector Neurons | PointNet inference · ModelNet40 classification test split | inference time (seconds): 30s -> 20s | Helped |
| Add canonicalization rather than modifying the backbone with Vector Neurons | DGCNN inference · ModelNet40 classification test split | inference time (seconds): 39s -> 25s | Helped |
| Use one versus three canonicalization layers (ablation) | CN-CNN p4 · Rotated-MNIST p4 | error %: 2.52 ± 0.12 -> 2.41 ± 0.11 | Helped |
| Use one versus three canonicalization layers (ablation) | CN-CNN p64 · Rotated-MNIST p64 | error %: 2.01 ± 0.09 -> 1.99 ± 0.10 | No clear effect |
Closest papers by meaning
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