Provable Robustness Against a Union of ${\mathrm{\ell }}_0$ Adversarial Attacks

Sparse or ${\mathrm{\ell }}_0$ adversarial attacks arbitrarily perturb an unknown subset of the features. ${\mathrm{\ell }}_0$ robustness analysis is particularly well-suited for heterogeneous (tabular) data where features have different types or scales. State-of-the-art ${\mathrm{\ell }}_0$ certified defenses are based on randomized smoothing and apply to evasion attacks only. This paper proposes feature partition aggregation (FPA) – a certified defense against the union of ${\mathrm{\ell }}_0$ evasion, backdoor, and poisoning attacks. FPA generates its stronger robustness guarantees via an ensemble whose submodels are trained on disjoint feature sets. Compared to state-of-the-art ${\mathrm{\ell }}_0$ defenses, FPA is up to 3,000$\times$ faster and provides larger median robustness guarantees (e.g., median certificates of 13 pixels over 10 for CIFAR10, 12 pixels over 10 for MNIST, 4 features over 1 for Weather, and 3 features over 1 for Ames), meaning FPA provides the additional dimensions of robustness essentially for free.