Research map / Adversarial robustness and security / Certified and empirical robustness
Beyond the Universal Law of Robustness: Sharper Laws for Random Features and Neural Tangent Kernels
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use random features with nonzero Gaussian-mean activation derivative, rather than relying on greater over-parameterization | Random features ERM · Stated high-dimensional data and activation assumptions | sensitivity: \Omega \left( \sqrt[6]{N} \right) | Hurt |
| Increase the number of random-feature parameters | Random features ERM · Synthetic data, MNIST, and CIFAR-10 | sensitivity | Mixed |
| Use an even activation, such as x^2, instead of a non-even activation such as tanh (ablation) | NTK regression · Synthetic data, MNIST, and CIFAR-10 | sensitivity | Helped |
| Use an even activation and scale k super-linearly in N | NTK regression · Stated data and model assumptions | sensitivity: \bigO{\log k \left( 1 + \sqrt{\frac{N}{k}} \right) \sqrt{\frac{N}{k}}} | Helped |
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