Research map / Graph learning / GNN architectures
Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use anisotropic gauge-equivariant filters instead of isotropic graph kernels | GEM-CNN · MNIST flat geometry | test error: 19.80±3.43% -> 0.60±0.05% | Helped |
| Add radial-distance dependence to the neighbor kernel (ablation) | GEM-CNN · Mesh experiments | performance | No clear effect |
| Break gauge symmetry in the final 1×1 layers (ablation) | GEM-CNN · FAUST | shape correspondence performance | Helped |
| Add RegularNonlinearity samples (ablation) | GEM-CNN · FAUST | time / epoch: 21.2 (none), 21.9 (1), 21.6 (5), 21.5 (10), 22.0 (20), 21.7 (50) | No clear effect |
| Add more RegularNonlinearity samples (ablation) | GEM-CNN · FAUST | memory: 1.22 (none) -> 1.35 (50) | Hurt |
| Replace anisotropic gauge-equivariant kernels with isotropic graph kernels (ablation) | GEM-CNN · FAUST | shape correspondence performance | Hurt |
Closest papers by meaning
- Gauge Equivariant Convolutional Networks and the Icosahedral CNN (ICML 2019 · similarity 0.90)
- Modeling Dynamics over Meshes with Gauge Equivariant Nonlinear Message Passing (NeurIPS 2023 · similarity 0.89)
- Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs (ICML 2023 · similarity 0.88)
- Isometric Transformation Invariant and Equivariant Graph Convolutional Networks (ICLR 2021 · similarity 0.88)
- GIST: Gauge-Invariant Spectral Transformers for Scalable Graph Neural Operators (NeurIPS 2026 · similarity 0.85)
- Universally Invariant Learning in Equivariant GNNs (NeurIPS 2025 · similarity 0.85)
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