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 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. We demonstrate three findings: (1) Successful adversarial perturbations exhibit mode connectivity; (2) Intermediate points along optimized paths achieve higher transferability than endpoints; (3) Bézier crossover dramatically outperforms discrete genetic operations while reducing convergence time and query requirements. By exploiting the geometric structure of adversarial space through path optimization, MoCo-EA provides an efficient and reliable method. Our work challenges the traditional view of adversarial examples as isolated points and opens new directions for both attack generation and defense research.
Adversarial Training (AT) is a leading defense against adversarial examples but often suffers from Catastrophic Overfitting (CO) in efficient single-step variants, where robustness to multi-step attacks collapses despite high single-step performance. We address this failure mode with two contributions. First, we formalize Epsilon Overfitting (EO), a perspective in which fixed perturbation magnitudes and directions exacerbate CO, and show that introducing perturbation variability significantly improves robust generalization across different architectures and datasets. Second, we propose PertAlign (Perturbation Alignment), a theoretically grounded, computationally negligible metric that predicts CO onset by measuring gradient alignment across attack stages. Leveraging these insights, we introduce SORA, an adaptive step-size AT method that dynamically adjusts perturbations based on loss surface geometry. SORA consistently prevents CO, achieves state-of-the-art robustness and clean accuracy, and generalizes across datasets and architectures using a single fixed set of hyperparameters, which is essential for applicability in fast AT. Extensive experiments on diverse datasets and architectures show that SORA matches or surpasses the robustness of prior methods while delivering higher clean accuracy and superior efficiency. Code is available at https://github.com/SecondOrderAT/SORA.
Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we study CBO in the context of closed-box adversarial attacks, which are imperceptible input perturbations that aim to fool a classifier, without accessing its gradient. Our contribution is to establish a connection between the so-called consensus hopping as introduced by Riedl et al. and natural evolution strategies (NES) commonly applied in the context of adversarial attacks and to rigorously relate both methods to gradient-based optimization schemes. Beyond that, we provide a comprehensive experimental study that shows that despite the conceptual similarities, CBO can outperform NES and other evolutionary strategies in certain scenarios.
Transfer-based adversarial attacks craft adversarial examples using surrogate models to mislead black-box victim models. Beyond perturbation generation, transferability is fundamentally governed by the coupling of initialization, surrogate adaptation, and gradient dynamics. We revisit this challenge from a bilevel-minimax perspective and propose BMAT (Bilevel-Minimax Adversarial Transfer). The bilevel formulation captures the dependency between initialization and perturbation, while the inner minimax problem promotes surrogate robustness for cross-architecture generalization. Algorithmically, we develop an integrated bottom-up solver that combines a Soft Weight Modulator and an Implicit Gradient Approximator to enable ternary coupling among initialization, surrogate adaptation, and perturbation optimization. We further provide theoretical insights into the optimization dynamics of the proposed bilevel-minimax framework. Extensive experiments on classification and segmentation benchmarks show that BMAT outperforms more than 10 strong baselines across more than 30 victim models, improving both intra- and cross-architecture transfer and yielding up to a 2x reduction in mIoU. Code is available at https://github.com/callous-youth/BMAT.