BCE vs. CE in Deep Feature Learning

Qiufu Li, Huibin Xiao, Linlin Shen
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:36400-36434, 2025.

Abstract

When training classification models, it expects that the learned features are compact within classes, and can well separate different classes. As the dominant loss function for training classification models, minimizing cross-entropy (CE) loss maximizes the compactness and distinctiveness, i.e., reaching neural collapse (NC). The recent works show that binary CE (BCE) performs also well in multi-class tasks. In this paper, we compare BCE and CE in deep feature learning. For the first time, we prove that BCE can also maximize the intra-class compactness and inter-class distinctiveness when reaching its minimum, i.e., leading to NC. We point out that CE measures the relative values of decision scores in the model training, implicitly enhancing the feature properties by classifying samples one-by-one. In contrast, BCE measures the absolute values of decision scores and adjust the positive/negative decision scores across all samples to uniformly high/low levels. Meanwhile, the classifier biases in BCE present a substantial constraint on the decision scores to explicitly enhance the feature properties in the training. The experimental results are aligned with above analysis, and show that BCE could improve the classification and leads to better compactness and distinctiveness among sample features. The codes have be released.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-li25db, title = {{BCE} vs. {CE} in Deep Feature Learning}, author = {Li, Qiufu and Xiao, Huibin and Shen, Linlin}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {36400--36434}, 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/li25db/li25db.pdf}, url = {https://proceedings.mlr.press/v267/li25db.html}, abstract = {When training classification models, it expects that the learned features are compact within classes, and can well separate different classes. As the dominant loss function for training classification models, minimizing cross-entropy (CE) loss maximizes the compactness and distinctiveness, i.e., reaching neural collapse (NC). The recent works show that binary CE (BCE) performs also well in multi-class tasks. In this paper, we compare BCE and CE in deep feature learning. For the first time, we prove that BCE can also maximize the intra-class compactness and inter-class distinctiveness when reaching its minimum, i.e., leading to NC. We point out that CE measures the relative values of decision scores in the model training, implicitly enhancing the feature properties by classifying samples one-by-one. In contrast, BCE measures the absolute values of decision scores and adjust the positive/negative decision scores across all samples to uniformly high/low levels. Meanwhile, the classifier biases in BCE present a substantial constraint on the decision scores to explicitly enhance the feature properties in the training. The experimental results are aligned with above analysis, and show that BCE could improve the classification and leads to better compactness and distinctiveness among sample features. The codes have be released.} }
Endnote
%0 Conference Paper %T BCE vs. CE in Deep Feature Learning %A Qiufu Li %A Huibin Xiao %A Linlin Shen %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-li25db %I PMLR %P 36400--36434 %U https://proceedings.mlr.press/v267/li25db.html %V 267 %X When training classification models, it expects that the learned features are compact within classes, and can well separate different classes. As the dominant loss function for training classification models, minimizing cross-entropy (CE) loss maximizes the compactness and distinctiveness, i.e., reaching neural collapse (NC). The recent works show that binary CE (BCE) performs also well in multi-class tasks. In this paper, we compare BCE and CE in deep feature learning. For the first time, we prove that BCE can also maximize the intra-class compactness and inter-class distinctiveness when reaching its minimum, i.e., leading to NC. We point out that CE measures the relative values of decision scores in the model training, implicitly enhancing the feature properties by classifying samples one-by-one. In contrast, BCE measures the absolute values of decision scores and adjust the positive/negative decision scores across all samples to uniformly high/low levels. Meanwhile, the classifier biases in BCE present a substantial constraint on the decision scores to explicitly enhance the feature properties in the training. The experimental results are aligned with above analysis, and show that BCE could improve the classification and leads to better compactness and distinctiveness among sample features. The codes have be released.
APA
Li, Q., Xiao, H. & Shen, L.. (2025). BCE vs. CE in Deep Feature Learning. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:36400-36434 Available from https://proceedings.mlr.press/v267/li25db.html.

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