Research map / 3D vision / Gaussian splatting
HEIR: Learning Graph-Based Motion Hierarchies
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Learns graph-based motion hierarchies end-to-end via differentiable edge-weight learning on a k-NN proximity graph (Gumbel-Softmax parent sampling), decomposing absolute motion into parent-inherited and residual components, and applies it to 1D/2D synthetic motions and dynamic Gaussian splatting deformation.
Problem
Modeling motion hierarchies that decompose complex dynamics into coordinated simpler components, where existing methods rely on manually defined or heuristic hierarchies with fixed motion primitives that do not transfer across tasks.
Approach
Formulates hierarchy inference as differentiable graph learning: a GAT-based encoder learns parent-candidate edge weights on a k-NN proximity graph, Gumbel-Softmax samples a DAG parent assignment, and a Neumann-series decoder reconstructs absolute motion from parent-inherited plus residual relative motion, with a connectivity (algebraic connectivity) regularizer.
Key results
- On the 1D toy hierarchy task, the method recovers a valid three-layer hierarchy in 73% of runs, versus ~5e-7% for a Monte-Carlo random estimate.
- On the planetary system, 100% of hierarchies are reconstructed without noise and 73.6% with Gaussian noise (sigma=0.05).
- On D-NeRF deformation scenes, the method outperforms SC-GS on PSNR, SSIM, CLIP-I and LPIPS across all four scenes (e.g., Excavator PSNR 21.56 vs 19.91, LPIPS 0.0383 vs 0.065).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HEIR instead of Monte-Carlo hierarchy estimation | 1D hierarchical motion reconstruction · 1D hierarchical motion task | accuracy: 5.0 \times 10^{-7} -> 73.0 | Helped |
| Add Gaussian noise (σ=0.05) | HEIR rotational hierarchy reconstruction · Planetary System | hierarchy reconstruction accuracy: 100% -> 73.6% | Hurt |
| Use learned hierarchical deformation instead of SC-GS | D-NeRF scene deformation · Excavator, Hook, Jumpingjacks, and Warrior | PSNR: 21.56 vs 19.91; 18.3 vs 15.7; 21.54 vs 21.12; 16.17 vs 15.29 | Helped |
| Use learned hierarchical deformation instead of SC-GS | D-NeRF scene deformation · Excavator, Hook, Jumpingjacks, and Warrior | SSIM: 0.917 vs 0.88; 0.93 vs 0.92; 0.952 vs 0.944; 0.934 vs 0.926 | Helped |
| Use learned hierarchical deformation instead of SC-GS | D-NeRF scene deformation · Excavator, Hook, Jumpingjacks, and Warrior | CLIP-I: 0.978 vs 0.978; 0.971 vs 0.958; 0.975 vs 0.948; 0.985 vs 0.965 | Mixed |
| Use learned hierarchical deformation instead of SC-GS | D-NeRF scene deformation · Excavator, Hook, Jumpingjacks, and Warrior | LPIPS: 0.0383 vs 0.065; 0.0617 vs 0.0954; 0.0507 vs 0.0748; 0.0567 vs 0.089 | Helped |
Limitations
- Depends on motion being observable in the input; cannot recover parts that stay static in training data.
- Assumes each motion element has a single parent, limiting expressiveness for multi-source influences.
- Uses k-NN proximity graph, which may miss long-range dependencies.
Experimental setup
Datasets: D-NeRF synthetic 1D hierarchical motion synthetic planetary system
Benchmarks: D-NeRF
Metrics: PSNR SSIM CLIP-I LPIPS
Baselines: SC-GS Monte-Carlo estimate
Builds on: graph attention network Gumbel-Softmax 3D Gaussian splatting SC-GS as-rigid-as-possible deformation
Closest papers by meaning
- Motion Decoupled 3D Gaussian Splatting for Dynamic Object Representation (AAAI 2025 · similarity 0.86)
- HIG: Hierarchical Interlacement Graph Approach to Scene Graph Generation in Video Understanding (CVPR 2024 · similarity 0.86)
- HAIF-GS: Hierarchical and Induced Flow-Guided Gaussian Splatting for Dynamic Scene (NeurIPS 2025 · similarity 0.85)
- HiCoM: Hierarchical Coherent Motion for Dynamic Streamable Scenes with 3D Gaussian Splatting (NeurIPS 2024 · similarity 0.85)
- HIMMEL: Hierarchical Interleaved Multi-stream Motion Encoding for Long Video Understanding (NeurIPS 2026 · similarity 0.85)
- Orientation-anchored Hyper-Gaussian for 4D Reconstruction from Casual Videos (NeurIPS 2025 · similarity 0.84)
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