# Adaptive Temperature Scaling for Robust Calibration of Deep Neural Networks

arXiv: https://arxiv.org/abs/2208.00461 · HTML: https://mlsanity.com/paper/2208.00461/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 31 Jul 2022.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Evaluating model calibration in classification](https://mlsanity.com/paper/1902.06977/) (2019)
- [Local Temperature Scaling for Probability Calibration](https://mlsanity.com/paper/2008.05105/) (2020)
- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Non-Parametric Calibration for Classification](https://mlsanity.com/paper/1906.04933/) (2019)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [Meta-Calibration: Learning of Model Calibration Using Differentiable Expected Calibration Error](https://mlsanity.com/paper/2106.09613/) (2021)
- [Bin-wise Temperature Scaling (BTS): Improvement in Confidence Calibration Performance through Simple Scaling Techniques](https://mlsanity.com/paper/1908.11528/) (2019)
- [On-manifold Adversarial Data Augmentation Improves Uncertainty Calibration](https://mlsanity.com/paper/1912.07458/) (2019)
- [Calibration of Deep Probabilistic Models with Decoupled Bayesian Neural Networks](https://mlsanity.com/paper/1908.08972/) (2019)
- [VoteNet+ : An Improved Deep Learning Label Fusion Method for Multi-atlas Segmentation](https://mlsanity.com/paper/1911.00582/) (2019)
- [Empirical Bayes approach to Truth Discovery problems](https://mlsanity.com/paper/2206.04816/) (2022)

## Built on by (most cited first, 24 of 24)

- [Towards Reliable Misinformation Mitigation: Generalization, Uncertainty, and GPT-4](https://mlsanity.com/paper/2305.14928/) (2023)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [Adaptive Preference Scaling for Reinforcement Learning with Human Feedback](https://mlsanity.com/paper/2406.02764/) (2024)
- [How to Fix a Broken Confidence Estimator: Evaluating Post-hoc Methods for Selective Classification with Deep Neural Networks](https://mlsanity.com/paper/2305.15508/) (2023)
- [To Cool or not to Cool? Temperature Network Meets Large Foundation Models via DRO](https://mlsanity.com/paper/2404.04575/) (2024)
- [Optimizing Calibration by Gaining Aware of Prediction Correctness](https://mlsanity.com/paper/2404.13016/) (2024)
- [Hallucination Detection and Mitigation in Large Language Models](https://mlsanity.com/paper/2601.09929/) (2026)
- [Accuracy-Preserving Calibration via Statistical Modeling on Probability Simplex](https://mlsanity.com/paper/2402.13765/) (2024)
- [Multi-Layer Confidence Scoring for Detection of Out-of-Distribution Samples, Adversarial Attacks, and In-Distribution Misclassifications](https://mlsanity.com/paper/2512.19472/) (2025)
- [Adaptive Cumulative Mass Calibration with Conformal Prediction](https://mlsanity.com/paper/2505.15437/) (2025)
- [Evaluating Temperature Scaling Calibration Effectiveness for CNNs under Varying Noise Levels in Brain Tumour Detection](https://mlsanity.com/paper/2509.24951/) (2025)
- [Probability calibration for precipitation nowcasting](https://mlsanity.com/paper/2510.00594/) (2025)
- [Towards Reliable Test-Time Adaptation: Style Invariance as a Correctness Likelihood](https://mlsanity.com/paper/2512.07390/) (2025)
- [Analytical Softmax Temperature Setting from Feature Dimensions for Model- and Domain-Robust Classification](https://mlsanity.com/paper/2504.15594/) (2025)
- [Aerial Image Classification in Scarce and Unconstrained Environments via Conformal Prediction](https://mlsanity.com/paper/2504.17655/) (2025)
- [Domain Adaptation via Feature Refinement](https://mlsanity.com/paper/2508.16124/) (2025)
- [Calibrated Uncertainty Sampling for Active Learning](https://mlsanity.com/paper/2510.03162/) (2025)
- [Using deep learning for predicting cleansing quality of colon capsule endoscopy images](https://mlsanity.com/paper/2601.13412/) (2026)
- [Enhancing the Reliability of Medical AI through Expert-guided Uncertainty Modeling](https://mlsanity.com/paper/2604.01898/) (2026)
- [Don't Collapse Your Features: Why CenterLoss Hurts OOD Detection and Multi-Scale Mahalanobis Wins](https://mlsanity.com/paper/2605.21493/) (2026)
- [Mitigating Measurement-Induced Training Instability in Hybrid Quantum Neural Networks for Protein Classification](https://mlsanity.com/paper/2606.22551/) (2026)
- [ADS-C: Antidistillation Sampling for Classification](https://mlsanity.com/paper/2607.15467/) (2026)
- [CARD: Calibration via Agreement in Reverse Diffusion for Out-of-Domain MRI Segmentation](https://mlsanity.com/paper/2608.28681/) (2026)
- [HoTS: Homophily-Aware Temperature Scaling for Graph Neural Network Calibration](https://mlsanity.com/paper/2609.32426/) (2026)

## Abstract (arXiv)

In this paper, we study the post-hoc calibration of modern neural networks, a problem that has drawn a lot of attention in recent years. Many calibration methods of varying complexity have been proposed for the task, but there is no consensus about how expressive these should be. We focus on the task of confidence scaling, specifically on post-hoc methods that generalize Temperature Scaling, we call these the Adaptive Temperature Scaling family. We analyse expressive functions that improve calibration and propose interpretable methods. We show that when there is plenty of data complex models like neural networks yield better performance, but are prone to fail when the amount of data is limited, a common situation in certain post-hoc calibration applications like medical diagnosis. We study the functions that expressive methods learn under ideal conditions and design simpler methods but with a strong inductive bias towards these well-performing functions. Concretely, we propose Entropy-based Temperature Scaling, a simple method that scales the confidence of a prediction according to its entropy. Results show that our method obtains state-of-the-art performance when compared to others and, unlike complex models, it is robust against data scarcity. Moreover, our proposed model enables a deeper interpretation of the calibration process.