# Structured Matrix Scaling for Multi-Class Calibration

arXiv: https://arxiv.org/abs/2511.03685 · HTML: https://mlsanity.com/paper/2511.03685/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Builds on (most cited first, 11 of 11)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [AutoGluon-Tabular: Robust and Accurate AutoML for Structured Data](https://mlsanity.com/paper/2003.06505/) (2020)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [fastai: A Layered API for Deep Learning](https://mlsanity.com/paper/2002.04688/) (2020)
- [TabRepo: A Large Scale Repository of Tabular Model Evaluations and its AutoML Applications](https://mlsanity.com/paper/2311.02971/) (2023)
- [Rethinking Early Stopping: Refine, Then Calibrate](https://mlsanity.com/paper/2501.19195/) (2025)

## Built on by (most cited first, 9 of 9)

- [Beyond IID: How General Are Tabular Foundation Models, Really?](https://mlsanity.com/paper/2606.30410/) (2026)
- [Conditional Coverage Diagnostics for Conformal Prediction](https://mlsanity.com/paper/2512.11779/) (2025)
- [CalArena: A Large-Scale Post-Hoc Calibration Benchmark](https://mlsanity.com/paper/2605.30188/) (2026)
- [The Well-Tempered Classifier: Some Elementary Properties of Temperature Scaling](https://mlsanity.com/paper/2602.14862/) (2026)
- [Divide et Calibra: Multiclass Local Calibration via Vector Quantization](https://mlsanity.com/paper/2605.21060/) (2026)
- [V-ECE: Estimating General Expected Calibration Errors](https://mlsanity.com/paper/2602.24230/) (2026)
- [Let Confidence Change, Not the Prediction: Prediction-Preserving Repair for Post-hoc Calibration](https://mlsanity.com/paper/2609.01072/) (2026)
- [Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networks](https://mlsanity.com/paper/2610.13693/) (2026)
- [A CaLLM Judge is a Better Judge: Mitigating Bias in LLM-as-a-judge](https://mlsanity.com/paper/2610.18108/) (2026)

## Abstract (arXiv)

Post-hoc recalibration methods are widely used to ensure that classifiers provide faithful probability estimates. We argue that parametric recalibration functions based on logistic regression can be motivated from a simple theoretical setting for both binary and multiclass classification. This insight motivates the use of more expressive calibration methods beyond standard temperature scaling. For multi-class calibration however, a key challenge lies in the increasing number of parameters introduced by more complex models, often coupled with limited calibration data, which can lead to overfitting. Through extensive experiments, we demonstrate that the resulting bias-variance tradeoff can be effectively managed by structured regularization, robust preprocessing and efficient optimization. The resulting methods lead to substantial gains over existing logistic-based calibration techniques. We provide efficient and easy-to-use open-source implementations of our methods, making them an attractive alternative to common temperature, vector, and matrix scaling implementations.