# Revisiting Reweighted Risk for Calibration: AURC, Focal, and Inverse Focal Loss

arXiv: https://arxiv.org/abs/2505.23463 · HTML: https://mlsanity.com/paper/2505.23463/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 49 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (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)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [Improving model calibration with accuracy versus uncertainty optimization](https://mlsanity.com/paper/2012.07923/) (2020)
- [Bias-Reduced Uncertainty Estimation for Deep Neural Classifiers](https://mlsanity.com/paper/1805.08206/) (2018)
- [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)
- [Better Uncertainty Calibration via Proper Scores for Classification and Beyond](https://mlsanity.com/paper/2203.07835/) (2022)
- [Non-Parametric Calibration for Classification](https://mlsanity.com/paper/1906.04933/) (2019)
- [A Consistent and Differentiable Lp Canonical Calibration Error Estimator](https://mlsanity.com/paper/2210.07810/) (2022)
- [Top-label calibration and multiclass-to-binary reductions](https://mlsanity.com/paper/2107.08353/) (2021)
- [What Can We Learn From The Selective Prediction And Uncertainty Estimation Performance Of 523 Imagenet Classifiers](https://mlsanity.com/paper/2302.11874/) (2023)
- [Meta-Cal: Well-controlled Post-hoc Calibration by Ranking](https://mlsanity.com/paper/2105.04290/) (2021)
- [Dual Focal Loss for Calibration](https://mlsanity.com/paper/2305.13665/) (2023)
- [AdaFocal: Calibration-aware Adaptive Focal Loss](https://mlsanity.com/paper/2211.11838/) (2022)
- [Meta-Calibration: Learning of Model Calibration Using Differentiable Expected Calibration Error](https://mlsanity.com/paper/2106.09613/) (2021)
- [On Focal Loss for Class-Posterior Probability Estimation: A Theoretical Perspective](https://mlsanity.com/paper/2011.09172/) (2020)
- [A Novel Characterization of the Population Area Under the Risk Coverage Curve (AURC) and Rates of Finite Sample Estimators](https://mlsanity.com/paper/2410.15361/) (2024)
- [What classifiers know what they don't?](https://mlsanity.com/paper/2107.06217/) (2021)

## Abstract (arXiv)

Several variants of reweighted risk functionals, such as focal loss, inverse focal loss, and the Area Under the Risk Coverage Curve (AURC), have been proposed for improving model calibration; yet their theoretical connections to calibration errors remain under-explored. In this paper, we revisit a broad class of weighted risk functions and find a principled connection between calibration error and selective classification. We show that minimizing calibration error is closely linked to the selective classification paradigm and demonstrate that optimizing selective risk in low confidence regions naturally improves calibration. Our proposed loss shares a similar reweighting strategy with dual focal loss but offers greater flexibility through the choice of confidence score functions (CSFs). Furthermore, our approach utilizes a bin-based cumulative distribution function (CDF) approximation, enabling efficient gradient-based optimization with O(nM) complexity for n samples and M bins. Empirical evaluations demonstrate that our method achieves competitive calibration performance across a range of datasets and model architectures.