# Instance-Wise Monotonic Calibration by Constrained Transformation

arXiv: https://arxiv.org/abs/2507.06516 · HTML: https://mlsanity.com/paper/2507.06516/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 40 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 26 of 26)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [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)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (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)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Calibration of Neural Networks using Splines](https://mlsanity.com/paper/2006.12800/) (2020)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [Paths-over-Graph: Knowledge Graph Empowered Large Language Model Reasoning](https://mlsanity.com/paper/2410.14211/) (2024)
- [Dual Focal Loss for Calibration](https://mlsanity.com/paper/2305.13665/) (2023)
- [Cooperative Starting Movement Detection of Cyclists Using Convolutional Neural Networks and a Boosted Stacking Ensemble](https://mlsanity.com/paper/1803.03487/) (2018)
- [How Flawed Is ECE? An Analysis via Logit Smoothing](https://mlsanity.com/paper/2402.10046/) (2024)
- [Post-hoc Calibration of Neural Networks by g-Layers](https://mlsanity.com/paper/2006.12807/) (2020)
- [Revisit Time Series Classification Benchmark: The Impact of Temporal Information for Classification](https://mlsanity.com/paper/2503.20264/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Well-Tempered Classifier: Some Elementary Properties of Temperature Scaling](https://mlsanity.com/paper/2602.14862/) (2026)

## Abstract (arXiv)

Deep neural networks often produce miscalibrated probability estimates, leading to overconfident predictions. A common approach for calibration is fitting a post-hoc calibration map on unseen validation data that transforms predicted probabilities. A key desirable property of the calibration map is instance-wise monotonicity (i.e., preserving the ranking of probability outputs). However, most existing post-hoc calibration methods do not guarantee monotonicity. Previous monotonic approaches either use an under-parameterized calibration map with limited expressive ability or rely on black-box neural networks, which lack interpretability and robustness. In this paper, we propose a family of novel monotonic post-hoc calibration methods, which employs a constrained calibration map parameterized linearly with respect to the number of classes. Our proposed approach ensures expressiveness, robustness, and interpretability while preserving the relative ordering of the probability output by formulating the proposed calibration map as a constrained optimization problem. Our proposed methods achieve state-of-the-art performance across datasets with different deep neural network models, outperforming existing calibration methods while being data and computation-efficient. Our code is available at https://github.com/YunruiZhang/Calibration-by-Constrained-Transformation