Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Steerable Partial Differential Operators for Equivariant Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Gaussian-derivative discretization instead of finite differences (ablation) | Regular steerable PDOs · Rotated MNIST | test error [%]: 1.196 ± 0.062 -> 0.795 ± 0.030 (3 × 3); 1.54 ± 0.32 -> 0.750 ± 0.017 (5 × 5) | Helped |
| Use Gaussian-derivative discretization instead of RBF-FD (ablation) | Regular steerable PDOs · Rotated MNIST | test error [%]: 1.313 ± 0.065 -> 0.795 ± 0.030 (3 × 3); 1.475 ± 0.020 -> 0.750 ± 0.017 (5 × 5) | Helped |
| Use Gaussian-derivative discretization instead of finite differences (ablation) | Quotient steerable PDOs · Rotated MNIST | test error [%]: 1.143 ± 0.063 -> 0.825 ± 0.053 (3 × 3); 1.347 ± 0.026 -> 0.744 ± 0.040 (5 × 5) | Helped |
| Use Gaussian-derivative discretization instead of RBF-FD (ablation) | Quotient steerable PDOs · Rotated MNIST | test error [%]: 1.303 ± 0.077 -> 0.825 ± 0.053 (3 × 3); 1.422 ± 0.040 -> 0.744 ± 0.040 (5 × 5) | Helped |
| Use steerable convolution kernels instead of steerable PDOs | Regular and quotient equivariant models · Rotated MNIST | test error [%]: Regular: 0.795 ± 0.030 -> 0.741 ± 0.036 (3 × 3, Gauss vs kernels); 0.750 ± 0.017 -> 0.683 ± 0.021 (5 × 5). Quotient: 0.8 | Helped |
| Increase stencil size from 3 × 3 to 5 × 5 (ablation) | Steerable PDOs with finite differences or RBF-FD · Rotated MNIST | test error [%]: Regular FD: 1.196 ± 0.062 -> 1.54 ± 0.32; regular RBF-FD: 1.313 ± 0.065 -> 1.475 ± 0.020; quotient FD: 1.143 ± 0.063 -> | Mixed |
| Increase stencil size from 3 × 3 to 5 × 5 (ablation) | Steerable PDOs with Gaussian discretization · Rotated MNIST | test error [%]: Regular: 0.795 ± 0.030 -> 0.750 ± 0.017; quotient: 0.825 ± 0.053 -> 0.744 ± 0.040 | Helped |
| Use D4D4D1 instead of D8D4D1 group configuration (ablation) | STL-10 equivariant networks · STL-10 | test error [%]: Kernels: 10.7 ± 0.6 -> 10.2 ± 0.4; FD: 12.1 ± 0.6 -> 12.1 ± 0.7; RBF-FD: 14.3 ± 0.4 -> 14.3 ± 0.4; Gauss: 11.2 ± 0.3 -> | Mixed |
| Add C8 equivariance | Kernel network · Fluid flow prediction | MSE: 3.20 ± 0.22 -> 2.26 ± 0.14 | Helped |
| Add C8 equivariance | PDO network · Fluid flow prediction | MSE: 2.75 ± 0.21 -> 2.32 ± 0.08 | Helped |
| Use equivariant rather than non-equivariant models | Kernel and PDO networks · Fluid flow prediction | MSE: Kernel: 3.20 ± 0.22 -> 2.26 ± 0.14; PDO: 2.75 ± 0.21 -> 2.32 ± 0.08 | Helped |
| Use steerable PDOs rather than steerable kernels | C8-equivariant fluid-flow network · Fluid flow prediction | MSE: 2.26 ± 0.14 vs 2.32 ± 0.08 | No clear effect |
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