Research map / Adversarial robustness and security / Certified and empirical robustness
Generalised Lipschitz Regularisation Equals Distributional Robustness
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Gaussian-kernel Lipschitz regularisation (GLIP) instead of Parseval ReLU | Kernel classifiers · MNIST, Fashion-MNIST, and CIFAR10; PGD with C&W loss, ℓ2 and ℓ∞ attacks | test accuracy | Helped |
| Use Gaussian-kernel Lipschitz regularisation (GLIP) instead of Parseval MaxMin | Kernel classifiers · MNIST, Fashion-MNIST, and CIFAR10; PGD with C&W loss, ℓ2 and ℓ∞ attacks | test accuracy | Helped |
| Use inverse-kernel Lipschitz regularisation (ILIP) instead of Parseval ReLU | Kernel classifiers · MNIST, Fashion-MNIST, and CIFAR10; PGD attacks | test accuracy | No clear effect |
| Use Parseval MaxMin instead of Parseval ReLU | Parseval networks · ℓ2 PGD attacks | test accuracy | Helped |
| Use Parseval MaxMin instead of Parseval ReLU | Parseval networks · ℓ∞ PGD attacks | test accuracy | Helped |
| Use Gaussian-kernel Lipschitz regularisation (GLIP) instead of Parseval MaxMin | Kernel classifiers · MNIST, Fashion-MNIST, and CIFAR10; cross-entropy PGD attacks, ℓ2 and ℓ∞ | test accuracy | Helped |
| Use coordinate-wise Nyström approximation instead of holistic Nyström approximation | Gaussian-kernel Lipschitz regularisation · Product-kernel Lipschitz-constant approximation | number of samples required | Helped |
| Select landmark points greedily using L-BFGS rather than relying on random sampling | GLIP and ILIP · Kernel Lipschitz-constraint training | number of samples required: by an order of magnitude | Helped |
| Replace the RKHS-norm Lipschitz surrogate with λmax(GᵀG) | Kernel classifiers · Lipschitz-constant approximation | approximation tightness | Helped |
| Increase the Gaussian-kernel bandwidth | Kernel classifiers · Lipschitz-constant approximation | approximation gap | Helped |
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- Distributional Robustness with IPMs and links to Regularization and GANs (NeurIPS 2020 · similarity 0.89)
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