# Improving Calibration by Relating Focal Loss, Temperature Scaling, and Properness

arXiv: https://arxiv.org/abs/2408.11598 · HTML: https://mlsanity.com/paper/2408.11598/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)
- [Calibration in Deep Learning: A Survey of the State-of-the-Art](https://mlsanity.com/paper/2308.01222/) (2023)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [Robust Bi-Tempered Logistic Loss Based on Bregman Divergences](https://mlsanity.com/paper/1906.03361/) (2019)
- [AdaFocal: Calibration-aware Adaptive Focal Loss](https://mlsanity.com/paper/2211.11838/) (2022)
- [On Focal Loss for Class-Posterior Probability Estimation: A Theoretical Perspective](https://mlsanity.com/paper/2011.09172/) (2020)

## Built on by (most cited first, 4 of 4)

- [Toward Calibrated Mixture-of-Experts Under Distribution Shift](https://mlsanity.com/paper/2606.20544/) (2026)
- [Revisiting Reweighted Risk for Calibration: AURC, Focal, and Inverse Focal Loss](https://mlsanity.com/paper/2505.23463/) (2025)
- [Beyond Caption-Based Queries for Video Moment Retrieval](https://mlsanity.com/paper/2603.02363/) (2026)
- [Structured Proper Loss Geometries for Multiclass Classification: Theory and Controlled Empirical Evaluation](https://mlsanity.com/paper/2606.29471/) (2026)

## Abstract (arXiv)

Proper losses such as cross-entropy incentivize classifiers to produce class probabilities that are well-calibrated on the training data. Due to the generalization gap, these classifiers tend to become overconfident on the test data, mandating calibration methods such as temperature scaling. The focal loss is not proper, but training with it has been shown to often result in classifiers that are better calibrated on test data. Our first contribution is a simple explanation about why focal loss training often leads to better calibration than cross-entropy training. For this, we prove that focal loss can be decomposed into a confidence-raising transformation and a proper loss. This is why focal loss pushes the model to provide under-confident predictions on the training data, resulting in being better calibrated on the test data, due to the generalization gap. Secondly, we reveal a strong connection between temperature scaling and focal loss through its confidence-raising transformation, which we refer to as the focal calibration map. Thirdly, we propose focal temperature scaling - a new post-hoc calibration method combining focal calibration and temperature scaling. Our experiments on three image classification datasets demonstrate that focal temperature scaling outperforms standard temperature scaling.