Neural Collapse in Multi-label Learning with Pick-all-label Loss

• URL: http://arxiv.org/abs/2310.15903v4
• Date: Thu, 20 Jun 2024 09:18:01 GMT
• Title: Neural Collapse in Multi-label Learning with Pick-all-label Loss
• Abstract summary: We study deep neural networks for the multi-label classification (MLab) task through the lens of neural collapse (NC) We prove for the first time that a generalized NC phenomenon holds the "pick-all-label" formulation, which we term as MLab.
• Score: 28.46350033490066
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study deep neural networks for the multi-label classification (MLab) task through the lens of neural collapse (NC). Previous works have been restricted to the multi-class classification setting and discovered a prevalent NC phenomenon comprising of the following properties for the last-layer features: (i) the variability of features within every class collapses to zero, (ii) the set of feature means form an equi-angular tight frame (ETF), and (iii) the last layer classifiers collapse to the feature mean upon some scaling. We generalize the study to multi-label learning, and prove for the first time that a generalized NC phenomenon holds with the "pick-all-label" formulation, which we term as MLab NC. While the ETF geometry remains consistent for features with a single label, multi-label scenarios introduce a unique combinatorial aspect we term the "tag-wise average" property, where the means of features with multiple labels are the scaled averages of means for single-label instances. Theoretically, under proper assumptions on the features, we establish that the only global optimizer of the pick-all-label cross-entropy loss satisfy the multi-label NC. In practice, we demonstrate that our findings can lead to better test performance with more efficient training techniques for MLab learning.

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