Robustness Meets Uncertainty: Evidential Adversarial Training for Robust Selective Classification

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.

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.

A prediction that is both confident and wrong is a critical reliability failure because it can bypass abstention and human review precisely when the model is mistaken. Empirical risk minimization (ERM) controls average loss but not this failure directly, while calibration, uncertainty estimation, conformal risk control, and selective prediction methods target related reliability properties rather than bounding the joint failure event during training. We propose ReliableNet, which constrains the Joint Confident-Wrong (JCW) probability, the probability that a prediction is simultaneously confident and incorrect, below a user-specified risk budget $α\in(0,1)$. We formulate this as a chance-constrained ERM problem, use a conservative smooth inner approximation whose population feasibility implies the original JCW constraint. Across four tabular and two image datasets, ReliableNet is the only method certified within the JCW budget for every dataset and seed in distribution, when compared against baselines spanning ERM, post-hoc calibration, conformal risk control, and selective prediction. Under demographic, ambiguity, spurious-correlation, novel-class, and covariate shifts, it achieves the lowest empirical JCW among the compared methods while remaining very competitive in accuracy, coverage, calibration, and selective prediction. Risk-coverage results further indicate that ReliableNet achieves better selective ranking than the benchmark methods on most datasets. Overall, ReliableNet provides a principled approach to trustworthy classification.