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

arXiv: https://arxiv.org/abs/2605.22746 · HTML: https://mlsanity.com/paper/2605.22746/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 19 of 19)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [NeMo: a toolkit for building AI applications using Neural Modules](https://mlsanity.com/paper/1909.09577/) (2019)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [MatchboxNet: 1D Time-Channel Separable Convolutional Neural Network Architecture for Speech Commands Recognition](https://mlsanity.com/paper/2004.08531/) (2020)
- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [Regression Prior Networks](https://mlsanity.com/paper/2006.11590/) (2020)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage?](https://mlsanity.com/paper/2402.06160/) (2024)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Revisiting Softmax for Uncertainty Approximation in Text Classification](https://mlsanity.com/paper/2210.14037/) (2022)

## Abstract (arXiv)

Real-world sensor-based learning systems require uncertainty estimation that is both reliable and computationally efficient. Evidential Deep Learning (EDL) provides single-pass uncertainty estimation by modeling the class probabilities via Dirichlet distributions, where the Dirichlet parameters are predicted by a learned neural network mapping. However, this approach can lead to computational challenges, as Dirichlet expected objectives are more complex than standard supervised learning losses, complicating their analysis and implementation. We address this issue by approximating the objective of the first-order empirical risk minimization problem induced by EDL with a plug-in loss evaluated at the Dirichlet mean and show that, under mild assumptions, the approximation error decays with growing evidence for a broad class of loss functions, including mean-squared error and cross-entropy loss. As a special case, our analysis provides justification for the use of softmax in the context of uncertainty estimation, since under a particular evidence-to-Dirichlet mapping, our framework includes the standard softmax classifier. We validate the proposed simplified objectives on the Google Speech Commands dataset and show that they achieve predictive accuracy and selective prediction performance comparable to classical EDL, while being simpler to implement using standard deep learning losses and training pipelines. To the best of our knowledge, this empirical analysis is the first to obtain coverage-accuracy trade-offs for speech recognition tasks through EDL.