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Efficient Generalized Spherical CNNs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed MST-based generalized spherical CNN instead of the strongest prior spherical CNN | Rotated MNIST on the Sphere · NR/R | test accuracy: 99.08 -> 99.34 | Helped |
| Use the proposed MST-based generalized spherical CNN instead of the strongest prior method | QM7 · QM7 | RMS error: 5.96 -> 3.16 | Helped |
| Use the proposed model instead of the strongest prior method | SHREC'17 retrieval · perturbed micro-all | F1@N: 0.701 -> 0.708 | Helped |
| Use the proposed model instead of the strongest prior method | SHREC'17 retrieval · perturbed micro-all | R@N: 0.737 -> 0.710 | Hurt |
| Replace MST mixing sets with RMST mixing sets (ablation) | Efficient generalized spherical CNN · Rotated MNIST on the Sphere, R/R | test accuracy: 99.38 -> 99.17 | Hurt |
| Replace MST mixing sets with RMST mixing sets (ablation) | Efficient generalized spherical CNN · QM7 | RMS error: 3.16 -> 3.46 | Hurt |
| Use full mixing sets instead of MST mixing sets (ablation) | Efficient generalized spherical CNN · Rotated MNIST on the Sphere, R/R | test accuracy: 99.38 -> 99.39 | No clear effect |
| Oversample the signal by 2× before pointwise ReLU (ablation) | Spherical pointwise ReLU · Sphere equivariance test | mean relative equivariance error: 3.4 \times 10^{-1} -> 8.9 \times 10^{-2} | Helped |
| Oversample the signal by 8× before pointwise ReLU (ablation) | Rotation-group pointwise ReLU · SO(3) equivariance test | mean relative equivariance error: 3.7 \times 10^{-1} -> 9.6 \times 10^{-3} | Helped |
| Use tensor-product activation followed by generalized convolution instead of pointwise ReLU | Equivariant spherical layers · Layer equivariance tests | mean relative equivariance error: 3.4 \times 10^{-1} -> 5.0 \times 10^{-7} | Helped |
Closest papers by meaning
- Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutions (ICLR 2023 · similarity 0.93)
- Spin-Weighted Spherical CNNs (NeurIPS 2020 · similarity 0.92)
- Spherical CNNs (ICLR 2018 · similarity 0.92)
- DeepSphere: a graph-based spherical CNN (ICLR 2020 · similarity 0.92)
- O$n$ Learning Deep O($n$)-Equivariant Hyperspheres (ICML 2024 · similarity 0.88)
- Attention on the Sphere (NeurIPS 2025 · similarity 0.87)
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