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Gauge Equivariant Convolutional Networks and the Icosahedral CNN
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use gauge-equivariant R2R convolutions instead of the S2CNN architecture | IcoMNIST models · IcoMNIST N/R | accuracy: 99.38 -> 69.99 | Mixed |
| Use gauge-equivariant R2R convolutions instead of the S2CNN architecture | IcoMNIST models · IcoMNIST I/R | accuracy: 99.13 -> 66.26 | Mixed |
| Add gauge padding (ablation) | R2R · IcoMNIST N/R | accuracy: 21.4 -> 69.99 | Helped |
| Add kernel expansion (ablation) | R2R · IcoMNIST N/R | accuracy: 17.85 -> 69.99 | Helped |
| Add gauge padding and kernel expansion (ablation) | R2R · IcoMNIST N/R | accuracy: 16.20 -> 69.99 | Helped |
| Preserve regular orientation features through R2R layers instead of using S2S scalar features (ablation) | IcoMNIST · IcoMNIST N/R | accuracy: 55.64 -> 69.99 | Helped |
| Preserve orientation information through R2R layers instead of orientation pooling in S2R (ablation) | IcoMNIST · IcoMNIST N/R | accuracy: 59.76 -> 69.99 | Helped |
| Use R2R instead of S2R convolutions (ablation) | Icosahedral CNN · Climate pattern segmentation | mAP: 0.686 -> 0.759 | Helped |
| Use R2R instead of S2R convolutions (ablation) | Icosahedral CNN · Climate pattern segmentation | Mean accuracy: 97.5 -> 97.7 | Helped |
| Use an icosahedral R2R-U-Net instead of the comparison method | Stanford 2D-3D-S segmentation · Stanford 2D-3D-S | mIoU: 0.383 -> 0.394 | Helped |
| Train with icosahedral symmetry augmentation | Non-equivariant IcoMNIST models · IcoMNIST N/I | accuracy: 25.50 -> 98.52 | Helped |
| Use exact icosahedral equivariance rather than a non-equivariant model | IcoMNIST models · IcoMNIST N/I | accuracy: 25.50 -> 99.43 | Helped |
Closest papers by meaning
- Equivariant Networks for Pixelized Spheres (ICML 2021 · similarity 0.93)
- Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs (ICLR 2021 · similarity 0.90)
- Equivariant Networks for Hierarchical Structures (NeurIPS 2020 · similarity 0.90)
- A Probabilistic Approach to Learning the Degree of Equivariance in Steerable CNNs (ICML 2024 · similarity 0.88)
- Neural Isometries: Taming Transformations for Equivariant ML (NeurIPS 2024 · similarity 0.87)
- A Characterization Theorem for Equivariant Networks with Point-wise Activations (ICLR 2024 · similarity 0.87)
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