BayesAT: Bayes-Guided Progressive Distillation for Semi-Supervised Adversarial Training

Existing semi-supervised adversarial training (SSAT) methods typically employ a teacher-student framework where a teacher model provides supervisory signals for unlabeled data. However, they rely on static supervision---either hard pseudo-labels or soft labels with fixed temperature---which maintains constant learning difficulty throughout training. This rigidity fails to accommodate the student's evolving capability, especially when the teacher's performance plateaus. To address this, we reframe SSAT as knowledge distillation from a Bayes teacher and formalize a stage-dependent bias-variance tradeoff. This analysis reveals the existence of an optimal temperature: low temperatures reduce bias, while higher temperatures control the variance term in the robust generalization bound. Guided by this insight, we propose BayesAT, a Bayes-guided progressive distillation framework that jointly employs a low-to-high temperature warming schedule and confidence-adaptive sample reweighting. BayesAT allows the student to first learn from sharp, high-confidence supervision to establish reliable decision boundaries, then progressively from smoother distributions that encourage exploration of inter-class relationships. Extensive experiments on CIFAR-10, CIFAR-100, and ImageNet-200 demonstrate that BayesAT consistently improves robust accuracy while maintaining natural accuracy over existing SSAT methods, highlighting the importance of dynamic, theory-driven supervision for effective knowledge transfer in semi-supervised adversarial training.