# Improving evidential deep learning via multi-task learning

arXiv: https://arxiv.org/abs/2112.09368 · HTML: https://mlsanity.com/paper/2112.09368/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 51 references that are in the map.
- First posted on arXiv 17 Dec 2021.

## Builds on (most cited first, 27 of 27)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [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)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [DeepDTA: Deep Drug-Target Binding Affinity Prediction](https://mlsanity.com/paper/1801.10193/) (2018)
- [Delving into Deep Imbalanced Regression](https://mlsanity.com/paper/2102.09554/) (2021)
- [On Mean Absolute Error for Deep Neural Network Based Vector-to-Vector Regression](https://mlsanity.com/paper/2008.07281/) (2020)
- [Regression Prior Networks](https://mlsanity.com/paper/2006.11590/) (2020)
- [Self-Attention Based Molecule Representation for Predicting Drug-Target Interaction](https://mlsanity.com/paper/1908.06760/) (2019)
- [On the Robustness of Monte Carlo Dropout Trained with Noisy Labels](https://mlsanity.com/paper/2103.12002/) (2021)
- [Gradient conjugate priors and multi-layer neural networks](https://mlsanity.com/paper/1802.02643/) (2018)
- [Multi-View Self-Attention for Interpretable Drug-Target Interaction Prediction](https://mlsanity.com/paper/2005.00397/) (2020)

## Built on by (most cited first, 13 of 13)

- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications](https://mlsanity.com/paper/2309.13207/) (2023)
- [Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression](https://mlsanity.com/paper/2308.09065/) (2023)
- [Deep Evidential Learning for Bayesian Quantile Regression](https://mlsanity.com/paper/2308.10650/) (2023)
- [Outlier-Detection for Reactive Machine Learned Potential Energy Surfaces](https://mlsanity.com/paper/2402.17686/) (2024)
- [Overcoming Non-stationary Dynamics with Evidential Proximal Policy Optimization](https://mlsanity.com/paper/2503.01468/) (2025)
- [Temporal Distribution Shift in Real-World Pharmaceutical Data: Implications for Uncertainty Quantification in QSAR Models](https://mlsanity.com/paper/2502.03982/) (2025)
- [MEDL-U: Uncertainty-aware 3D Automatic Annotation based on Evidential Deep Learning](https://mlsanity.com/paper/2309.09599/) (2023)
- [Taylor-Sensus Network: Embracing Noise to Enlighten Uncertainty for Scientific Data](https://mlsanity.com/paper/2409.07942/) (2024)
- [Ensemble-Based Dirichlet Modeling for Predictive Uncertainty and Selective Classification](https://mlsanity.com/paper/2604.06032/) (2026)

## Abstract (arXiv)

The Evidential regression network (ENet) estimates a continuous target and its predictive uncertainty without costly Bayesian model averaging. However, it is possible that the target is inaccurately predicted due to the gradient shrinkage problem of the original loss function of the ENet, the negative log marginal likelihood (NLL) loss. In this paper, the objective is to improve the prediction accuracy of the ENet while maintaining its efficient uncertainty estimation by resolving the gradient shrinkage problem. A multi-task learning (MTL) framework, referred to as MT-ENet, is proposed to accomplish this aim. In the MTL, we define the Lipschitz modified mean squared error (MSE) loss function as another loss and add it to the existing NLL loss. The Lipschitz modified MSE loss is designed to mitigate the gradient conflict with the NLL loss by dynamically adjusting its Lipschitz constant. By doing so, the Lipschitz MSE loss does not disturb the uncertainty estimation of the NLL loss. The MT-ENet enhances the predictive accuracy of the ENet without losing uncertainty estimation capability on the synthetic dataset and real-world benchmarks, including drug-target affinity (DTA) regression. Furthermore, the MT-ENet shows remarkable calibration and out-of-distribution detection capability on the DTA benchmarks.