Towards One-for-All Robustness Across a Continuum of Threat Levels

Adversarially robust models often overfit to a specific attack budget, necessitating multiple specialized models for diverse and dynamic adversarial environments, a strategy that becomes fundamentally intractable as the threat space grows. This raises an open challenge: can we achieve strong robustness across a continuum of threat levels within a single model? We propose the Threat Conditional Network (TCN), grounded in a representation factorization framework that decomposes representation learning into a threat-invariant shared backbone and a lightweight threat-conditional adaptor. TCN conditions a single model on the perturbation level via Fourier-based embeddings and channel-wise affine modulation, and is trained against a distribution over perturbation budgets, enabling flexible and seamless adaptation across an infinite continuum of threat levels during inference. Extensive experiments on CIFAR-10, CIFAR-100, and Tiny-ImageNet show that TCN matches or surpasses a full ensemble of budget-specialized models with a single set of parameters, generalizes to unseen perturbation budgets, and transfers robustly under mismatched threat conditions, with only 4.6\% parameter overhead. These contributions chart a promising path toward adaptive and generalizable robustness in dynamic and diverse threat environments.