Reliable Posterior Support for Long-Tailed Adversarial Robustness

Adversarial training under long-tailed distributions suffers from severe class-wise robustness degradation, especially on tail and worst-performing classes. Existing methods improve long-tailed robustness through rebalancing, distillation, geometric regularization, or posterior-aware supervision, but they largely overlook whether the posterior signal is supported by a reliable local neighborhood. We argue that robust supervision should depend not only on posterior confidence at a training sample, but also on the reliability of the posterior support explored by adversarial perturbations. This issue is most severe for tail classes, whose support is estimated from scarce data and is therefore noisy, high-variance, and easily distorted. We propose a reliable posterior support framework, FEPT(Free Energy-guided Posterior Transport), which constructs free-energy posterior support to down-weight posterior mass in off-support, low-density, or unstable regions, and transports reliable low-free-energy support from related head/medium classes to tail classes. Our analysis formalizes why local margin stability and variance-reducing posterior transport are useful for reliable robust supervision, while extensive experiments show consistent improvements in tail and worst-class performance, balanced robustness, and posterior-support stability.