Geometry-Aware Crossover for Effective and Efficient Evolutionary Attacks

Evolutionary algorithms for adversarial attacks leverage population-based search to discover perturbations without gradient information, but suffer from inefficient crossover operations that destroy adversarial properties through discrete interpolation. We introduce Mode Connectivity Evolutionary Attack (MoCo-EA), which replaces traditional crossover with a novel geometry-aware Bézier crossover operator that optimizes perturbations along a continuous Bézier curve between parent perturbations. Our key insight is that adversarial examples lie on connected manifolds where intermediate points maintain, and often enhance attack effectiveness. Our work challenges the traditional view of adversarial examples as isolated points and opens new directions for both attack generation and defense research.