Revisiting Essential and Nonessential Settings of Evidential Deep Learning

TL;DR

This paper identifies nonessential components in Evidential Deep Learning (EDL) and proposes Re-EDL, a streamlined variant that preserves the essential projected probability from subjective logic while relaxing the prior-weight rigidity, variance-minimizing empirical risk, and KL-divergence regularization. By treating the prior weight as a tunable hyperparameter and directly optimizing the Dirichlet expectation via the projected probability, Re-EDL achieves improved uncertainty quantification and outperforms baselines across classical, few-shot, video-modality, and noisy settings. The essential insight is that projected probability, coupled with a gentler evidence activation (softplus) and a magnitude-aware class score parameter, better preserves logit information and mitigates overconfidence without extra regularization burdens. Empirical results, including OOD detection metrics like AUPR, confirm the method’s effectiveness and suggest a new baseline for single-forward-pass uncertainty estimation in diverse domains.

Abstract

Evidential Deep Learning (EDL) is an emerging method for uncertainty estimation that provides reliable predictive uncertainty in a single forward pass, attracting significant attention. Grounded in subjective logic, EDL derives Dirichlet concentration parameters from neural networks to construct a Dirichlet probability density function (PDF), modeling the distribution of class probabilities. Despite its success, EDL incorporates several nonessential settings: In model construction, (1) a commonly ignored prior weight parameter is fixed to the number of classes, while its value actually impacts the balance between the proportion of evidence and its magnitude in deriving predictive scores. In model optimization, (2) the empirical risk features a variance-minimizing optimization term that biases the PDF towards a Dirac delta function, potentially exacerbating overconfidence. (3) Additionally, the structural risk typically includes a KL-divergence-minimizing regularization, whose optimization direction extends beyond the intended purpose and contradicts common sense, diminishing the information carried by the evidence magnitude. Therefore, we propose Re-EDL, a simplified yet more effective variant of EDL, by relaxing the nonessential settings and retaining the essential one, namely, the adoption of projected probability from subjective logic. Specifically, Re-EDL treats the prior weight as an adjustable hyperparameter rather than a fixed scalar, and directly optimizes the expectation of the Dirichlet PDF provided by deprecating both the variance-minimizing optimization term and the divergence regularization term. Extensive experiments and state-of-the-art performance validate the effectiveness of our method. The source code is available at https://github.com/MengyuanChen21/Re-EDL.

Figures (9)

• Figure 1: A conceptual framework diagram illustrating the essential and nonessential settings discussed in Section \ref{['redl']}. By relaxing the nonessential settings while retaining the essential ones, the proposed Re-EDL method achieves more superior uncertainty estimation with reduced complexity.
• Figure 2: Precision-Recall (PR) curves and Receiver Operating Characteristic (ROC) curves of differentiating OOD data (SVHN) from ID data (CIFAR-10) in the classical setting. The adopted uncertainty measure is uncertainty mass (UM).
• Figure 3: Parameter analysis of the hyperparameter $\lambda$, evaluated by averaged AUPR for OOD detection on CIFAR-10.
• Figure 4: Precision-Recall (PR) curves of differentiating OOD data (SVHN) from ID data (CIFAR-10).
• Figure 5: Receiver Operating Characteristic (ROC) curves of differentiating OOD data (SVHN) from ID data (CIFAR-10).