Probabilistic Adversarial Training

Certified training aims to produce models whose predictions can be formally verified against adversarial perturbations, typically by optimising upper bounds on the worst-case loss over an allowed perturbation set. For neural networks, certified training methods based purely on tight relaxation bounds produce networks that are amenable to certification, but sacrifice standard accuracy. Conversely, adversarial training often yields stronger empirical robustness and standard accuracy, but the resulting models are generally difficult to certify with neural network verifiers. Recently, the literature has shown that better standard-certified accuracy trade-offs can be achieved by combining adversarial training objectives with loose over-approximations based on Interval Bound Propagation (IBP), effectively interpolating between lower and upper bounds of the worst-case loss. Building on this, we introduce AD-CERT, a certified training objective that combines adversarial distillation with an IBP upper bound. We show that distilling adversarial information over the logit space from an empirically robust teacher provides an effective lower bound surrogate for certified training, with AD-CERT achieving state-of-the-art certified performance on several robustness benchmarks. Furthermore, in a unified setup, distilling adversarial information at the logit-level is shown to improve certified accuracy over a robust feature-space distillation objective by up to 5.40 percentage points.

Safety-critical applications require classifiers that are both robust and reliable. Adversarial training is a widely adopted defense for improving robustness in deep neural networks; however, its effect on the reliability of predictive uncertainty remains underexplored. We investigate this gap through the lens of selective classification, which has rarely been systematically analyzed alongside adversarial robustness. We introduce a unified benchmark for the robustness-uncertainty trade-off. It standardizes architectures, augmentations, threat models, and evaluation metrics across clean, adversarial, and common-corruption settings. Across a wide range of state-of-the-art adversarial training methods, we uncover a recurring failure mode: several approaches improve robust accuracy while degrading uncertainty ranking, leading to poorer selective behavior. To address this, we propose Evidential Adversarial Training (EV-AT), which models uncertainty through a Dirichlet distribution and combines (i) an evidence-based loss promoting clean accuracy and reliable uncertainty with (ii) a robust evidence-alignment loss matching clean and adversarial predictions in log Dirichlet-parameter space. Extensive experiments show that EV-AT shifts the Pareto frontier of robustness-uncertainty trade-offs beyond prior state-of-the-art adversarial training methods. Our source code is publicly available at https://github.com/NicolasSournac/Robustness_Meets_Uncertainty.EV-AT.

Adversarial Training (AT) is one of the most effective methods for developing robust deep neural networks (DNNs). However, AT faces a trade-off problem between clean accuracy and adversarial robustness. In this work, we reveal a surprising phenomenon for the first time: Varying input perturbation intensities for training samples near decision boundaries in AT have minimal impact on model robustness. This finding directly exposes the inconsistency between accuracy and robustness score fluctuations, leading us to identify the misalignment between input and latent spaces as a critical driver of the robustness-accuracy trade-off. To mitigate this misalignment for harmonizing accuracy and robustness, we define Robust Alignment as a new AT target, encouraging the model perception to change with input perturbations provided the final label prediction remains unchanged, which can be achieved via two novel ideas. First, we suggest a reduced and fixed perturbation intensity for those boundary samples, which facilitates the model to utilize the perturbations as learnable patterns, instead of noises that complicate decision boundaries meaninglessly. Second, we propose a Domain Interpolation Consistency Adversarial Regularization (DICAR), based on rigorous theoretical derivations, which explicitly introduces semantic alignment between input and latent spaces into AT. Based on these two ideas, we end up with a new Robust Alignment Adversarial Training (RAAT) method, effectively harmonizing accuracy and robustness. Extensive experiments on CIFAR-10, CIFAR-100, and Tiny-ImageNet with ResNet-18, PreActResNet-18, and WideResNet-28-10 demonstrate the effectiveness of RAAT in improving the trade-off beyond four common baselines and a total of 14 related state-of-the-art (SOTA) works.