Research map / Adversarial robustness and security / Certified and empirical robustness
Orthogonalizing Convolutional Layers with the Cayley Transform
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Parameterize convolutional layers with the Fourier-domain Cayley transform | KWLarge · CIFAR-10 certified robustness (ε=36/255) | certified accuracy: 58.29 -> 59.16 | Helped |
| Parameterize convolutional layers with the Fourier-domain Cayley transform | ResNet9 · CIFAR-10 clean | test accuracy: 80.72 -> 81.70 | Helped |
| Use Cayley convolution layers rather than BCOP | WideResNet10-10 · CIFAR-10 AutoAttack (ε=36/255) | robust accuracy: 71.86 -> 73.16 | Helped |
| Use Cayley convolution layers rather than RKO | KWLarge · CIFAR-10 PGD (ε=36/255) | robust accuracy: 68.32 -> 67.66 | Hurt |
| Use Cayley convolution layers rather than RKO | KWLarge · CIFAR-10 AutoAttack (ε=36/255) | robust accuracy: 66.10 -> 65.13 | Hurt |
| Scale Cayley layers to a Lipschitz upper-bound of 0.85 (ablation) | KWLarge · CIFAR-10 certified robustness (ε=36/255) | certified accuracy: 59.16 -> 59.99 | Helped |
| Scale Cayley layers to a Lipschitz upper-bound of 0.85 (ablation) | KWLarge · CIFAR-10 clean | test accuracy: 75.33 -> 74.35 | Hurt |
| Increase kernel size to 5 (ablation) | Cayley layers in KWLarge · CIFAR-10 | accuracy | Helped |
| Increase kernel size to 7 or 9 (ablation) | Cayley layers in KWLarge · CIFAR-10 | accuracy | Hurt |
| Increase KWLarge width and kernel size to 5 (ablation) | Cayley · CIFAR-10 certified robustness | certified accuracy: 61.13% | Helped |
| Add randomly initialized fixed diagonal scaling matrices (ablation) | Cayley convolution parameterization · CIFAR-10 robustness experiments | performance | No clear effect |
| Use Fixup initialization (ablation) | Cayley residual networks · CIFAR-10 | accuracy | No clear effect |
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