Title: Stop Guessing: Choosing the Optimization-Consistent Uncertainty Measurement for Evidential Deep Learning
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: uncertainty estimation;

Abstract: Evidential Deep Learning (EDL) has emerged as a promising framework for uncertainty estimation in classification tasks by modeling predictive uncertainty with a Dirichlet prior. Despite its empirical success, prior work has primarily focused on the probabilistic properties of the Dirichlet distribution, leaving the role of optimization dynamics during training underexplored.  In this paper, we revisit EDL through the lens of optimization and establish a non-trivial connection: minimizing the expected cross-entropy loss over the Dirichlet prior implicitly encourages solutions akin to multi-class Support Vector Machines, maximizing decision margins. Motivated by this observation, we introduce the \emph{optimization-consistency principle}, which deems an uncertainty measure valid if its value decreases as samples approach the global optimum of the training objective. This principle provides a new criterion for evaluating and designing uncertainty measures that are consistent with the optimization dynamics. Building on this foundation, we further propose a novel measure, \emph{Margin-aware Predictive Uncertainty (MPU)}, which directly captures the separation between target and non-target evidence. Extensive experiments on out-of-distribution detection and classification-with-rejection benchmarks demonstrate the effectiveness of our propositions.