# Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networks

arXiv: https://arxiv.org/abs/2610.13693 · HTML: https://mlsanity.com/paper/2610.13693/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 69 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 30 of 44)

- [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)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [A Fully First-Order Method for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2301.10945/) (2023)
- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [RotoGrad: Gradient Homogenization in Multitask Learning](https://mlsanity.com/paper/2103.02631/) (2021)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [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)
- [Amazing Things Come From Having Many Good Models](https://mlsanity.com/paper/2407.04846/) (2024)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [Deep Bilevel Learning](https://mlsanity.com/paper/1809.01465/) (2018)
- [A Consistent and Differentiable Lp Canonical Calibration Error Estimator](https://mlsanity.com/paper/2210.07810/) (2022)
- [Generalized Entropy Regularization or: There's Nothing Special about Label Smoothing](https://mlsanity.com/paper/2005.00820/) (2020)
- [An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learning](https://mlsanity.com/paper/2308.00788/) (2023)

## Abstract (arXiv)

Neural networks (NNs), while highly flexible and versatile, are often poorly calibrated. Post-hoc calibration methods adjust the outputs of an already trained model using a separate calibration dataset and additional calibration parameters. This process adds overhead that requires separate optimization of the calibrator and subsequent model selection. In this paper, we show that standard (post-hoc) calibrators can be trained end-to-end with the backbone via a bilevel Stackelberg formulation. This formulation eliminates the need for a separate calibration set or a dedicated calibration loss by jointly optimizing accuracy and calibration using cross-entropy, introducing only one additional hyperparameter: the calibrator learning rate. Although our framework supports calibrators ranging from temperature and matrix scaling to NN layers, our results show that using the final classification layer itself as the calibrator yields accurate, well-calibrated models with no additional parameters. Our approach outperforms SOTA calibrators with minimal added complexity, while also avoiding the multiplicative overhead of separate calibration components in settings such as multi-task learning.