Comparing Classification and Feature Learning by Analyzing Their Loss Functions in Normalized Spaces with Different Scale Factors

Qiufu Li, Huibin Xiao, Linlin Shen, Weijia Fan, Xi Jia +1

Classification and feature learning are two closely interrelated fundamental tasks. Feature learning in supervised settings is typically achieved by training classification models, under the common assumption that higher classification accuracy implies better feature quality. In this paper, we first point out that classification accuracy reflects the sample-wise local properties of a model on a dataset, whereas feature learning aims to learn features with good dataset-level global properties, such as intra-class compactness and inter-class separability. From the first principle of feature learning, we redesign the binary cross-entropy (BCE) loss, a counterpart of the cross-entropy (CE) loss used in classification. Then, in normalized feature space, we analyze the minima of the BCE and CE losses and show that both can lead to neural collapse, where sample features from different classes become maximally compact and maximally separated. More importantly, by investigating the convergence behaviors of the two losses as the scale factor $γ$ varies in the normalized space, we reveal how classification accuracy and feature quality change differently across spaces of different sizes.…