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Memory-Scalable and Simplified Functional Map Learning
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Proposes a memory-scalable GPU computation of soft pointwise maps for functional map learning (via KeOps), a differentiable ZoomOut refinement layer, and a single-branch unsupervised network that avoids differentiating through a linear system.
Problem
Deep functional map methods that enforce properness via dense soft pointwise maps scale quadratically in memory with vertex count, and dual-branch designs rely on unstable differentiation through a linear system solver.
Approach
Compute the product of the soft pointwise map with the Laplacian basis directly via block-wise kernel reductions (KeOps) so the dense n2×n1 matrix is never stored; use a differentiable GPU ZoomOut whose refined map is enforced consistent with the initial functional map through a principal-submatrix loss, replacing the spectral branch.
Key results
- On FAUST/SCAPE/SHREC19 (Table 1), the method reaches comparable errors to state-of-the-art, e.g. F+S train F 1.9 and S19 3.6 versus ConsistentFMaps 2.2 and 4.3.
- On DT4D-H inter-class, error 4.1 versus ConsistentFMaps 6.1 and ULRSSM 4.4 (intra-class 1.8 vs ULRSSM 0.9).
- On 100k-vertex meshes, GPU ZoomOut and differentiable ZoomOut run out of memory, while the scalable version takes 5 s and the approximation-based variant takes 0.4 s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed single-branch pipeline instead of the strongest listed baseline | Functional map learning · FAUST/SCAPE/SHREC19, all train-test combinations in Table 1 | mean geodesic error (×100): 1.5 -> 1.9; 2.2 -> 2.4; 3.8 -> 4.2; 1.6 -> 1.9; 1.8 -> 2.4; 4.5 -> 6.9; 1.5 -> 1.9; 2.0 -> 2.3; 4.3 -> 3.6 | Mixed |
| Use the proposed single-branch pipeline instead of ULRSSM | Functional map learning · DT4D-H intra-class | mean geodesic error (×100): 0.9 -> 1.8 | Hurt |
| Use the proposed single-branch pipeline instead of ULRSSM | Functional map learning · DT4D-H inter-class | mean geodesic error (×100): 4.4 -> 4.1 | Helped |
| Add the ZoomOut consistency loss (ablation) | Proposed feature-learning pipeline · SHREC19 feature functions after training on SCAPE | feature smoothness | Helped |
Surprising findings
- The refinement consistency loss, without any spectral branch, also yields smoother learned features than without it.
- AttentiveFMaps runs out of 24GB GPU memory beyond about 11k vertices.
Limitations
- Depends on computing the Laplacian spectrum of input shapes, which can be slow for large shapes.
- ZoomOut is prone to failure under highly non-isometric deformations or partiality, making the consistency loss unsuitable there.
Experimental setup
Datasets: FAUST SCAPE SHREC19 DT4D-H
Benchmarks: FAUST SCAPE SHREC19 DT4D-H
Metrics: mean geodesic error GPU memory usage processing time
Baselines: GeomFmaps DUO-FMNet DeepShells NeuroMorph AttentiveFMaps ConsistentFMaps UDMSM ULRSSM
Builds on: functional maps ZoomOut GeomFmaps ConsistentFMaps DiffusionNet
Closest papers by meaning
- Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching (CVPR 2024 · similarity 0.89)
- Locality Preserving Refinement for Shape Matching with Functional Maps (AAAI 2024 · similarity 0.89)
- Denoising Functional Maps: Diffusion Models for Shape Correspondence (CVPR 2025 · similarity 0.88)
- Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning (CVPR 2024 · similarity 0.88)
- Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation (CVPR 2024 · similarity 0.88)
- Latent Functional Maps: a spectral framework for representation alignment (NeurIPS 2024 · similarity 0.86)
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