AT-Field: Rethinking the Games in Adversarial Training

Abstract Adversarial training is often modeled as a two-player zero-sum game, relying on strong assumptions that limit its practical guidance. In this paper, we instead analyze the interactions between training samples and show that even the fundamental objective—minimizing training loss—may not converge. To address this, we propose AT-Field, an adversarial training framework guided by sample-wise game-theoretic relationships. Specifically, we prove that training samples across different batches can form a none-potential game, where gradient descent induces cyclic behaviors, preventing convergence. By strategically searching and grouping these samples within the same batch, AT-Field transforms none-potential games into exact potential games, which are more effectively optimized using gradient-based methods. Experiments demonstrate that AT-Field integrates seamlessly with existing adversarial training techniques, enhancing both accuracy and robustness.