Plug-in Losses for Evidential Deep Learning: A Simplified Framework for Uncertainty Estimation that Includes the Softmax Classifier

Problem
This paper addresses the gap in reliable and computationally efficient uncertainty estimation in sensor-based learning systems, specifically within the framework of Evidential Deep Learning (EDL). EDL utilizes Dirichlet distributions to model class probabilities, but the complexity of Dirichlet expected objectives poses significant challenges for implementation and analysis. The authors propose a simplified framework that approximates the EDL objective using plug-in losses, which is particularly relevant for practitioners seeking to integrate uncertainty estimation into their models without incurring high computational costs. This work is presented as a preprint and has not yet undergone peer review.

Method
The core technical contribution is the introduction of a plug-in loss framework that approximates the first-order empirical risk minimization problem associated with EDL. The authors demonstrate that the approximation error diminishes with increasing evidence for a wide range of loss functions, including mean-squared error and cross-entropy. Notably, the framework encompasses the softmax classifier under a specific mapping from evidence to Dirichlet parameters, thereby justifying its use in uncertainty estimation contexts. The authors validate their approach using standard deep learning architectures and training pipelines, which enhances accessibility for practitioners. The training compute details are not explicitly disclosed, but the focus on standard losses suggests a reduction in computational overhead compared to traditional EDL methods.

Results
The proposed plug-in loss framework was evaluated on the Google Speech Commands dataset. The results indicate that the simplified objectives achieve predictive accuracy and selective prediction performance that are comparable to classical EDL methods. Specifically, the authors report that their approach yields effective coverage-accuracy trade-offs, which is a novel contribution in the context of speech recognition tasks. While exact numerical results are not provided in the abstract, the comparative performance against classical EDL suggests a meaningful improvement in implementation efficiency without sacrificing model performance.

Limitations
The authors acknowledge that their framework relies on certain mild assumptions regarding the evidence-to-Dirichlet mapping, which may not hold in all scenarios. Additionally, the empirical validation is limited to the Google Speech Commands dataset, raising questions about the generalizability of the findings to other domains or datasets. The paper does not address potential limitations related to the scalability of the approach in more complex or high-dimensional settings, nor does it explore the implications of using different neural network architectures.

Why it matters
This work has significant implications for the integration of uncertainty estimation in real-world applications, particularly in domains where computational efficiency is critical. By simplifying the implementation of EDL through plug-in losses, the authors provide a pathway for practitioners to adopt uncertainty-aware models without the burden of complex loss functions. This could lead to broader adoption of EDL techniques in various applications, enhancing the reliability of AI systems in uncertain environments. Furthermore, the establishment of coverage-accuracy trade-offs in speech recognition tasks opens avenues for future research in uncertainty quantification across different modalities.

Authors: Berk Hayta, Hannah Laus, Simon Mittermaier, Felix Krahmer
Source: arXiv:2605.22746
URL: https://arxiv.org/abs/2605.22746v1