# Improving Multi-Class Calibration through Normalization-Aware Isotonic Techniques

arXiv: https://arxiv.org/abs/2512.09054 · HTML: https://mlsanity.com/paper/2512.09054/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 20 of 20)

- [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)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [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)
- [A Survey on Text Classification: From Shallow to Deep Learning](https://mlsanity.com/paper/2008.00364/) (2020)
- [Calibration tests in multi-class classification: A unifying framework](https://mlsanity.com/paper/1910.11385/) (2019)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Top-label calibration and multiclass-to-binary reductions](https://mlsanity.com/paper/2107.08353/) (2021)
- [Multi-Class Uncertainty Calibration via Mutual Information Maximization-based Binning](https://mlsanity.com/paper/2006.13092/) (2020)
- [Bin-wise Temperature Scaling (BTS): Improvement in Confidence Calibration Performance through Simple Scaling Techniques](https://mlsanity.com/paper/1908.11528/) (2019)
- [Attended Temperature Scaling: A Practical Approach for Calibrating Deep Neural Networks](https://mlsanity.com/paper/1810.11586/) (2018)
- [Calibration by Distribution Matching: Trainable Kernel Calibration Metrics](https://mlsanity.com/paper/2310.20211/) (2023)
- [The PAV algorithm optimizes binary proper scoring rules](https://mlsanity.com/paper/1304.2331/) (2013)

## Built on by (most cited first, 3 of 3)

- [CalArena: A Large-Scale Post-Hoc Calibration Benchmark](https://mlsanity.com/paper/2605.30188/) (2026)
- [Brenier Isotonic Regression](https://mlsanity.com/paper/2603.10452/) (2026)
- [U-SEG: Uncertainty in SEGmentation -- A systematic multi-variable exploration](https://mlsanity.com/paper/2605.15421/) (2026)

## Abstract (arXiv)

Accurate and reliable probability predictions are essential for multi-class supervised learning tasks, where well-calibrated models enable rational decision-making. While isotonic regression has proven effective for binary calibration, its extension to multi-class problems via one-vs-rest calibration produced suboptimal results when compared to parametric methods, limiting its practical adoption. In this work, we propose novel isotonic normalization-aware techniques for multiclass calibration, grounded in natural and intuitive assumptions expected by practitioners. Unlike prior approaches, our methods inherently account for probability normalization by either incorporating normalization directly into the optimization process (NA-FIR) or modeling the problem as a cumulative bivariate isotonic regression (SCIR). Empirical evaluation on a variety of text and image classification datasets across different model architectures reveals that our approach consistently improves negative log-likelihood (NLL) and expected calibration error (ECE) metrics.