# CLUE: Neural Networks Calibration via Learning Uncertainty-Error alignment

arXiv: https://arxiv.org/abs/2505.22803 · HTML: https://mlsanity.com/paper/2505.22803/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 69 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 30 of 44)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [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)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Unsupervised Quality Estimation for Neural Machine Translation](https://mlsanity.com/paper/2005.10608/) (2020)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [On Hallucination and Predictive Uncertainty in Conditional Language Generation](https://mlsanity.com/paper/2103.15025/) (2021)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [Analyzing Uncertainty in Neural Machine Translation](https://mlsanity.com/paper/1803.00047/) (2018)
- [Improving model calibration with accuracy versus uncertainty optimization](https://mlsanity.com/paper/2012.07923/) (2020)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Calibration of Neural Networks using Splines](https://mlsanity.com/paper/2006.12800/) (2020)

## Built on by (most cited first, 2 of 2)

- [Uncertainty Estimation by Human Perception versus Neural Models](https://mlsanity.com/paper/2506.15850/) (2025)
- [FALCON-Discover: Discovering Concentrated False-Confidence Regions for Calibration](https://mlsanity.com/paper/2607.18278/) (2026)

## Abstract (arXiv)

Reliable uncertainty estimation is critical for deploying neural networks (NNs) in real-world applications. While existing calibration techniques often rely on post-hoc adjustments or coarse-grained binning methods, they remain limited in scalability, differentiability, and generalization across domains. In this work, we introduce CLUE (Calibration via Learning Uncertainty-Error Alignment), a novel approach that explicitly aligns predicted uncertainty with observed error during training, grounded in the principle that well-calibrated models should produce uncertainty estimates that match their empirical loss. CLUE adopts a novel loss function that jointly optimizes predictive performance and calibration, using summary statistics of uncertainty and loss as proxies. The proposed method is fully differentiable, domain-agnostic, and compatible with standard training pipelines. Through extensive experiments on vision, regression, and language modeling tasks, including out-of-distribution and domain-shift scenarios, we demonstrate that CLUE achieves superior calibration quality and competitive predictive performance with respect to state-of-the-art approaches without imposing significant computational overhead.