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Rethinking Human Motion Prediction with Symplectic Integral
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Proposes SINN, a symplectic-integral-inspired human motion prediction framework that encodes poses as Hamiltonian trajectories (velocity-based, per-joint, per-axis) and performs long-term prediction by splitting into short-term steps with a pre-trained GRU operator fine-tuned with a GAN critic.
Problem
Long-horizon human motion prediction suffers sharp accuracy degradation as the horizon grows, attributed to noisy high-dimensional pose data (numerical instability) and unstable long-range sequence modeling (modeling instability).
Approach
Represent each joint as a Hamiltonian-style trajectory (location plus velocity magnitude and direction angles), predict low-dimensional per-axis velocity controls, and aggregate multiple pre-trained short-term symplectic operator predictions via temporal splitting with a GAN-based fine-tuning stage.
Key results
- Reports 20.1% long-term improvement over SOTA on Human3.6M (e.g., 80.1 vs 107.0 average at 1000 ms per the text), 16.7% on CMU Mocap, and 10.2% on 3DPW.
- Symplectic operator plus STA ablation on Human3.6M reduces 1000 ms error for eating from 65.1 (SRE only) to 52.2 (full model).
- Plugging SINN into existing methods (e.g., FDU&FAU, res-GRU) lowers errors at most horizons in Table 5.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add SINN instead of FDU&FAU | Human motion prediction · Human3.6M average, 1,000 ms | MPJPE: 107.0 -> 80.1 | Helped |
| Add SINN instead of FDU&FAU | Human motion prediction · CMU Mocap average, 1,000 ms | MPJPE: 75.4 -> 62.8 | Helped |
| Add SINN instead of FDU&FAU | Human motion prediction · 3DPW average, 1,000 ms | MPJPE: 94.5 -> 88.2 | Helped |
| Add Symplectic Temporal Aggregation (STA) (ablation) | SINN with SRE · Human3.6M Eating, 1,000 ms | MPJPE: 65.1 -> 52.2 | Helped |
| Add Symplectic Representation Encoder (SRE) (ablation) | SINN with STA · Human3.6M Eating, 1,000 ms | MPJPE: 80.5 -> 52.2 | Helped |
| Add Symplectic Temporal Aggregation (STA) (ablation) | SINN with SRE · CMU Mocap Basketball, 1,000 ms | MPJPE: 95.1 -> 88.1 | Helped |
| Add Symplectic Representation Encoder (SRE) (ablation) | SINN with STA · CMU Mocap Basketball, 1,000 ms | MPJPE: 108.5 -> 88.1 | Helped |
Surprising findings
- Adding SINN to res-GRU slightly worsens 400 ms error in some reported numbers relative to the table's own trends is not claimed; instead, the paper notes existing methods converge to static poses on stochastic actions like smoking.
Limitations
- Symplectic framing is largely heuristic; the 'symplectic' guarantees are not formally analyzed
- Operator is a simple multi-GRU model and training is done separately per dataset and action
- Gains are reported mainly against MPJPE with a single-run evaluation setup
Experimental setup
Datasets: Human3.6M CMU Mocap 3DPW
Benchmarks: Human3.6M CMU Mocap 3DPW
Metrics: MPJPE
Baselines: res-GRU HPGAN BiGAN HMR LTD DMGNN HRI MSR-GCN FDU&FAU
Builds on: res-GRU generative adversarial networks Euler integrator
Closest papers by meaning
- Existence Is Chaos: Enhancing 3D Human Motion Prediction with Uncertainty Consideration (AAAI 2024 · similarity 0.84)
- SimpliHuMoN: Simplifying Human Motion Prediction (NeurIPS 2026 · similarity 0.84)
- Motion Diversification Networks (CVPR 2024 · similarity 0.84)
- SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model (CVPR 2024 · similarity 0.84)
- Multi-agent Long-term 3D Human Pose Forecasting via Interaction-aware Trajectory Conditioning (CVPR 2024 · similarity 0.84)
- Optimal-state Dynamics Estimation for Physics-based Human Motion Capture from Videos (NeurIPS 2024 · similarity 0.83)
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