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Isometric Transformation Invariant and Equivariant Graph Convolutional Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use IsoGCN instead of SE(3)-Transformer | Differential operator prediction, scalar-to-gradient · Differential operator dataset, 0→1 | MSE (× 10⁻⁵): 1.79 ± 0.02 -> 2.67 ± 0.02 | Hurt |
| Use IsoGCN instead of SE(3)-Transformer | Differential operator prediction, scalar-to-Hessian · Differential operator dataset, 0→2 | MSE (× 10⁻⁶): 3.50 ± 0.04 -> 6.37 ± 0.07 | Hurt |
| Use IsoGCN instead of SE(3)-Transformer | Differential operator prediction, gradient-to-Laplacian · Differential operator dataset, 1→0 | MSE (× 10⁻⁶): 2.52 ± 0.02 -> 7.18 ± 0.06 | Hurt |
| Use IsoGCN instead of SE(3)-Transformer | Differential operator prediction, gradient-to-Hessian · Differential operator dataset, 1→2 | MSE (× 10⁻⁶): No numeric baseline reported; IsoGCN: 1.44 ± 0.02, SE(3)-Transformer: OOM | Helped |
| Increase IsoGCN hop count from 2 to 5 (ablation) | IsoGCN · Differential operator dataset, 0→1 | MSE (× 10⁻⁵): 2.67 ± 0.02 -> 14.19 ± 0.10 | Hurt |
| Increase IsoGCN hop count from 2 to 5 (ablation) | IsoGCN · Differential operator dataset, 0→2 | MSE (× 10⁻⁶): 6.37 ± 0.07 -> 21.72 ± 0.25 | Hurt |
| Increase IsoGCN hop count from 2 to 5 (ablation) | IsoGCN · Differential operator dataset, 1→0 | MSE (× 10⁻⁶): 7.18 ± 0.06 -> 34.09 ± 0.19 | Hurt |
| Increase IsoGCN hop count from 2 to 5 (ablation) | IsoGCN · Differential operator dataset, 1→2 | MSE (× 10⁻⁶): 1.44 ± 0.02 -> 8.32 ± 0.09 | Hurt |
| Increase IsoGCN hop count from 2 to 5 (ablation) | IsoGCN · Anisotropic nonlinear heat equation dataset | MSE (× 10⁻³): 4.674 ± 0.014 -> 2.470 ± 0.008 | Helped |
| Use IsoGCN instead of SGCN | Anisotropic nonlinear heat equation prediction · Anisotropic nonlinear heat equation dataset | MSE (× 10⁻³): 6.426 ± 0.018 -> 2.470 ± 0.008 | Helped |
| Use IsoGCN instead of FrontISTR (Δt = 0.5) | Heat equation inference at 21,289 vertices · Anisotropic nonlinear heat equation, 21,289 vertices | inference time (s): 30.5 -> 7.4 | Helped |
| Use IsoGCN instead of FrontISTR (Δt = 0.5) | Heat equation inference at 155,019 vertices · Anisotropic nonlinear heat equation, 155,019 vertices | inference time (s): 288.0 -> 84.1 | Helped |
Closest papers by meaning
- Universally Invariant Learning in Equivariant GNNs (NeurIPS 2025 · similarity 0.87)
- On Explaining Equivariant Graph Networks via Improved Relevance Propagation (ICML 2025 · similarity 0.86)
- Equivariant Machine Learning on Graphs with Nonlinear Spectral Filters (NeurIPS 2024 · similarity 0.86)
- Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks? (NeurIPS 2024 · similarity 0.86)
- A Characterization Theorem for Equivariant Networks with Point-wise Activations (ICLR 2024 · similarity 0.86)
- Neural Isometries: Taming Transformations for Equivariant ML (NeurIPS 2024 · similarity 0.85)
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