Cut your Losses with Squentropy

Like Hui, Mikhail Belkin, Stephen Wright
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:14114-14131, 2023.

Abstract

Nearly all practical neural models for classification are trained using the cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiment on multi-class classification problems showing that the squentropy loss outperforms both the pure cross-entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can frequently be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true ”plug-and-play” replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-hui23a, title = {Cut your Losses with Squentropy}, author = {Hui, Like and Belkin, Mikhail and Wright, Stephen}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {14114--14131}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/hui23a/hui23a.pdf}, url = {https://proceedings.mlr.press/v202/hui23a.html}, abstract = {Nearly all practical neural models for classification are trained using the cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiment on multi-class classification problems showing that the squentropy loss outperforms both the pure cross-entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can frequently be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true ”plug-and-play” replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.} }
Endnote
%0 Conference Paper %T Cut your Losses with Squentropy %A Like Hui %A Mikhail Belkin %A Stephen Wright %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-hui23a %I PMLR %P 14114--14131 %U https://proceedings.mlr.press/v202/hui23a.html %V 202 %X Nearly all practical neural models for classification are trained using the cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiment on multi-class classification problems showing that the squentropy loss outperforms both the pure cross-entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can frequently be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true ”plug-and-play” replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.
APA
Hui, L., Belkin, M. & Wright, S.. (2023). Cut your Losses with Squentropy. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:14114-14131 Available from https://proceedings.mlr.press/v202/hui23a.html.

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