Robust Evidential Learning Through Latent Consistency

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.

Evidential Deep Learning (EDL) has emerged as an efficient, sampling-free strategy for uncertainty estimation. A series of EDL variants have been proposed to address specific limitations of the original framework, achieving notable success. However, the underlying theoretical structure of EDL and the relationships among these variants have received limited systematic investigation. In this work, we establish a principled theoretical foundation for EDL by interpreting it within a generalized Bayesian framework that includes prior specification, posterior update, and training objective. We further characterize evidential uncertainty from a Bayesian distributional uncertainty viewpoint, established via asymptotic analysis. Building on this perspective, we further propose Generalized Evidential Deep Learning (GEDL), a unified and extensible framework that explicitly disentangles the roles of individual components and systematically relates GEDL to existing variants. Extensive experiments demonstrate that GEDL yields comparable results on classification, uncertainty estimation and OOD detections, with theoretical grounding.

While Deep Neural Networks (DNNs) achieve remarkable performance, their tendency to produce overconfident predictions. Evidential Deep Learning (EDL) mitigates this by formulating predictions as a Dirichlet distribution over class probabilities to explicitly quantify epistemic uncertainty. However, we found that the conventional EDL suffers from two fundamental limitations: a Kullback-Leibler (KL) penalty that only suppresses the evidence of negative classes, producing excessively high evidence therefore decreasing the model's ability to quantify uncertainty, and an absence in theoretical guarantee of setting Dirichlet parameter $α=e+1$. In this paper, we propose a mathematically principled framework, Variational Inference Evidential Deep Learning (VI-EDL). By reformulating evidential learning through the lens of variational inference, we derive an Evidence Lower Bound (ELBO), which prevents the evidence from growing excessively. Theoretically, we rigorously establish a generalization bound and reveal how the predicted uncertainty, feature and network complexity affect this bound, and why setting $\boldsymbolα = \mathbf{e} + \mathbf{1}$ can minimize it. Extensive experiments on standard visual and medical datasets demonstrate that VI-EDL achieves state-of-the-art performance, showing excellent performance in out-of-distribution detection, noise detection and autonomous driving scenario. The code is available in https://github.com/seutjw/VI-EDL.