input-convex neural networks

TLDR: We propose the asymmetric certified robustness problem, which requires certified robustness for only one class and reflects real-world adversarial scenarios. This focused setting allows us to introduce feature-convex classifiers, which produce closed-form and deterministic certified radii on the order of milliseconds.

Figure 1. Illustration of feature-convex classifiers and their certification for sensitive-class inputs. This architecture composes a Lipschitz-continuous feature map $\varphi$ with a learned convex function $g$. Since $g$ is convex, it is globally underapproximated by its tangent plane at $\varphi(x)$, yielding certified norm balls in the feature space. Lipschitzness of $\varphi$ then yields appropriately scaled certificates in the original input space.

Despite their widespread usage, deep learning classifiers are acutely vulnerable to adversarial examples: small, human-imperceptible image perturbations that fool machine learning models into misclassifying the modified input. This weakness severely undermines the reliability of safety-critical processes that incorporate machine learning. Many empirical defenses against adversarial perturbations have been proposed—often only to be later defeated by stronger attack strategies. We therefore focus on certifiably robust classifiers, which provide a mathematical guarantee that their prediction will remain constant for an $\ell_p$-norm ball around an input.

Conventional certified robustness methods incur a range of drawbacks, including nondeterminism, slow execution, poor scaling, and certification against only one attack norm. We argue that these issues can be addressed by refining the certified robustness problem to be more aligned with practical adversarial settings.