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Implicit Convolutional Kernels for Steerable CNNs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SO(2) symmetry instead of O(3) equivariance | N-body model · N-body, stiffness 1000 | MSE: 0.1313 -> 0.0162 | Helped |
| Use SO(2) symmetry instead of O(3) equivariance | N-body model · N-body, stiffness 0 | MSE: 0.0009 -> 0.0010 | Mixed |
| Replace standard steerable kernels with implicit kernels (ablation) | Steerable CNN · QM9 ε_HOMO | MAE | Helped |
| Condition implicit kernels on bond attributes (ablation) | Steerable CNN · QM9 ε_HOMO | MAE | Helped |
| Condition implicit kernels on atom types as well as edge type (ablation) | Steerable CNN · QM9 ε_HOMO | MAE | Helped |
| Batch-normalize the polynomial representation of relative positions (ablation) | Implicit kernel MLP · ModelNet-40 and QM9 | performance | Helped |
| Increase the implicit-kernel MLP depth beyond 3 layers (ablation) | Implicit kernel MLP · Experiments across tasks | training stability | Hurt |
| Use a larger O(3) symmetry for the symmetry-broken N-body system | N-body model · N-body with plane-string forces | MSE | Hurt |
| Use implicit kernels instead of group-restricted standard kernels (ablation) | Steerable CNN · ModelNet-40, subgroup comparison | test accuracy | Mixed |
| Use the tailored SO(3) kernel basis rather than implicit kernels (ablation) | ModelNet-40 SO(3) model · ModelNet-40, SO(3) | test accuracy | Helped |
| Use the narrower, deeper configuration (W=16, L=30) instead of W=24, L=15 (ablation) | Implicit-kernel Steerable CNN · QM9 ε_HOMO | MAE: 24.1 -> 22.8 | Helped |
Closest papers by meaning
- A Program to Build E(N)-Equivariant Steerable CNNs (ICLR 2022 · similarity 0.92)
- General E(2)-Equivariant Steerable CNNs (NeurIPS 2019 · similarity 0.92)
- Clifford-Steerable Convolutional Neural Networks (ICML 2024 · similarity 0.89)
- A Probabilistic Approach to Learning the Degree of Equivariance in Steerable CNNs (ICML 2024 · similarity 0.87)
- Equivariant Neural Tangent Kernels (ICML 2025 · similarity 0.86)
- Variational Partial Group Convolutions for Input-Aware Partial Equivariance of Rotations and Color-Shifts (ICML 2024 · similarity 0.86)
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