Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networks
Abstract
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.
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BibTeX
@misc{kalampalikis2026calibration,
title = {{Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networks}},
author = {Nektarios Kalampalikis and Pablo M. Olmos and Isabel Valera},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13693},
eprint = {2610.13693},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13693},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networks
AU - Nektarios Kalampalikis
AU - Pablo M. Olmos
AU - Isabel Valera
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13693
UR - https://arxiv.org/abs/2610.13693
AB - 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.
ER -