On Temperature Scaling and Conformal Prediction of Deep Classifiers

Lahav Dabah, Tom Tirer
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:11813-11845, 2025.

Abstract

In many classification applications, the prediction of a deep neural network (DNN) based classifier needs to be accompanied by some confidence indication. Two popular approaches for that aim are: 1) Calibration: modifies the classifier’s softmax values such that the maximal value better estimates the correctness probability; and 2) Conformal Prediction (CP): produces a prediction set of candidate labels that contains the true label with a user-specified probability, guaranteeing marginal coverage but not, e.g., per class coverage. In practice, both types of indications are desirable, yet, so far the interplay between them has not been investigated. Focusing on the ubiquitous Temperature Scaling (TS) calibration, we start this paper with an extensive empirical study of its effect on prominent CP methods. We show that while TS calibration improves the class-conditional coverage of adaptive CP methods, surprisingly, it negatively affects their prediction set sizes. Motivated by this behavior, we explore the effect of TS on CP beyond its calibration application and reveal an intriguing trend under which it allows to trade prediction set size and conditional coverage of adaptive CP methods. Then, we establish a mathematical theory that explains the entire non-monotonic trend. Finally, based on our experiments and theory, we offer guidelines for practitioners to effectively combine adaptive CP with calibration, aligned with user-defined goals.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-dabah25a, title = {On Temperature Scaling and Conformal Prediction of Deep Classifiers}, author = {Dabah, Lahav and Tirer, Tom}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {11813--11845}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/dabah25a/dabah25a.pdf}, url = {https://proceedings.mlr.press/v267/dabah25a.html}, abstract = {In many classification applications, the prediction of a deep neural network (DNN) based classifier needs to be accompanied by some confidence indication. Two popular approaches for that aim are: 1) Calibration: modifies the classifier’s softmax values such that the maximal value better estimates the correctness probability; and 2) Conformal Prediction (CP): produces a prediction set of candidate labels that contains the true label with a user-specified probability, guaranteeing marginal coverage but not, e.g., per class coverage. In practice, both types of indications are desirable, yet, so far the interplay between them has not been investigated. Focusing on the ubiquitous Temperature Scaling (TS) calibration, we start this paper with an extensive empirical study of its effect on prominent CP methods. We show that while TS calibration improves the class-conditional coverage of adaptive CP methods, surprisingly, it negatively affects their prediction set sizes. Motivated by this behavior, we explore the effect of TS on CP beyond its calibration application and reveal an intriguing trend under which it allows to trade prediction set size and conditional coverage of adaptive CP methods. Then, we establish a mathematical theory that explains the entire non-monotonic trend. Finally, based on our experiments and theory, we offer guidelines for practitioners to effectively combine adaptive CP with calibration, aligned with user-defined goals.} }
Endnote
%0 Conference Paper %T On Temperature Scaling and Conformal Prediction of Deep Classifiers %A Lahav Dabah %A Tom Tirer %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-dabah25a %I PMLR %P 11813--11845 %U https://proceedings.mlr.press/v267/dabah25a.html %V 267 %X In many classification applications, the prediction of a deep neural network (DNN) based classifier needs to be accompanied by some confidence indication. Two popular approaches for that aim are: 1) Calibration: modifies the classifier’s softmax values such that the maximal value better estimates the correctness probability; and 2) Conformal Prediction (CP): produces a prediction set of candidate labels that contains the true label with a user-specified probability, guaranteeing marginal coverage but not, e.g., per class coverage. In practice, both types of indications are desirable, yet, so far the interplay between them has not been investigated. Focusing on the ubiquitous Temperature Scaling (TS) calibration, we start this paper with an extensive empirical study of its effect on prominent CP methods. We show that while TS calibration improves the class-conditional coverage of adaptive CP methods, surprisingly, it negatively affects their prediction set sizes. Motivated by this behavior, we explore the effect of TS on CP beyond its calibration application and reveal an intriguing trend under which it allows to trade prediction set size and conditional coverage of adaptive CP methods. Then, we establish a mathematical theory that explains the entire non-monotonic trend. Finally, based on our experiments and theory, we offer guidelines for practitioners to effectively combine adaptive CP with calibration, aligned with user-defined goals.
APA
Dabah, L. & Tirer, T.. (2025). On Temperature Scaling and Conformal Prediction of Deep Classifiers. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:11813-11845 Available from https://proceedings.mlr.press/v267/dabah25a.html.

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