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Pose-Transformed Equivariant Network for 3D Point Trajectory Prediction
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Proposes PT-EvNet, an SE(3)-equivariant 3D point trajectory predictor that PCA-normalizes point clouds and then predicts motion over learnable pose-transformed copies with a global-local motion estimation layer.
Problem
Predicting future 3D point trajectories equivariantly under SE(3) transformations, balancing equivariance guarantees against accuracy and computational cost in existing equivariant models.
Approach
Combines a unique PCA-based pose normalization (with sign disambiguation) with learnable SE(3) pose transformations instead of fixed frame-averaging group elements, and decomposes motion into global and local displacements estimated iteratively and aggregated over the transformed poses.
Key results
- On CMU Walking, PT-EvNet reaches MSE 4.8 (x10^-2) versus 5.8 for EqMotion, the prior best, and 18.7 on Running versus 20.3.
- On MD17 Benzene, MSE drops from 48.12 to 26.25 (x10^-2), and PT-EvNet is best on six of eight molecules.
- On the Simulation dataset, PT-EvNet achieves the lowest error on all single systems and most multiple systems, with the (10,10) multiple system as the exception.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the PT-EvNet architecture | 3D point trajectory prediction · CMU Walking | MSE (×10−2): 5.8 -> 4.8 | Helped |
| add the PT-EvNet architecture | 3D point trajectory prediction · CMU Running | MSE (×10−2): 20.3 -> 18.7 | Helped |
| add the PT-EvNet architecture | 3D point trajectory prediction · MD17 Benzene | MSE (×10−2): 48.12 -> 26.25 | Helped |
| add the PT-EvNet architecture | 3D point trajectory prediction · MD17 Malonaldehyde | MSE (×10−2): 12.82 -> 13.22 | Hurt |
| add the PT-EvNet architecture | 3D point trajectory prediction · Simulation multiple (10,10) | MSE (×10−2): 13.11 -> 14.25 | Hurt |
| use one prediction block instead of three (ablation) | PT-EvNet · CMU Walking | MSE (×10−2): 4.8 -> 5.6 | Hurt |
| use one prediction block instead of three (ablation) | PT-EvNet · MD17 Aspirin | MSE (×10−2): 6.63 -> 7.64 | Hurt |
| replace learned pose transformations with frame averaging (ablation) | PT-EvNet · CMU Walking | MSE (×10−2): 4.82 -> 4.83 | Hurt |
| replace learned pose transformations with random rotations (ablation) | PT-EvNet · CMU Walking | MSE (×10−2): 4.82 -> 10.04 | Hurt |
| replace the global-local motion estimation layer with a local-only branch (ablation) | PT-EvNet · CMU Walking | MSE (×10−2): 4.83 -> 6.89 | Hurt |
| replace the global-local motion estimation layer with a local-only branch (ablation) | PT-EvNet · MD17 Aspirin | MSE (×10−2): 6.63 -> 7.27 | Hurt |
| increase the number of pose transformations from zero to a positive number (ablation) | PT-EvNet · CMU Walking | MSE (×10−2): 5.36 -> 4.83 | Helped |
Surprising findings
- Random pose transformations (RT) perform worse than frame averaging on some subsets, with Benzene MSE 48.47 for RT versus 72.88 for FA, but the learned PT transformations beat both on most subsets.
Limitations
- Evaluated only on non-sequential, frame-pair trajectory prediction; the authors plan sequential prediction as future work.
- Parameter count (4.88e5) and memory (8.18 MB) are higher than several baselines, and the paper describes the cost as tolerable rather than low.
- Results on the Simulation (10,10) multiple-system setting are not best.
Experimental setup
Datasets: CMU Motion Capture Database MD17 Simulation Dataset (EGHN)
Benchmarks: CMU Motion Capture (Walking, Running) MD17 (8 molecules) Simulation dataset
Metrics: MSE
Baselines: RF MPNN TFN SE(3)-Transformer EGNN GMN EGHN EqMotion FA-GNN LieConv
Builds on: frame averaging EGNN EGHN GMN EqMotion
Closest papers by meaning
- Leveraging Equivariant Features for Absolute Pose Regression (CVPR 2022 · similarity 0.89)
- E2PN: Efficient SE(3)-Equivariant Point Network (CVPR 2023 · similarity 0.88)
- 3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction (NeurIPS 2024 · similarity 0.86)
- Approximately Piecewise E(3) Equivariant Point Networks (ICLR 2024 · similarity 0.85)
- An Intuitive Multi-Frequency Feature Representation for SO(3)-Equivariant Networks (ICLR 2024 · similarity 0.85)
- Fast, Expressive $\mathrm{SE}(n)$ Equivariant Networks through Weight-Sharing in Position-Orientation Space (ICLR 2024 · similarity 0.84)
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