Neural Collapse in Multi-label Learning with Pick-all-label Loss
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929391492136960 |
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| author | Li, Pengyu Li, Xiao Wang, Yutong Qu, Qing |
| author_facet | Li, Pengyu Li, Xiao Wang, Yutong Qu, Qing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15903 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Neural Collapse in Multi-label Learning with Pick-all-label Loss Li, Pengyu Li, Xiao Wang, Yutong Qu, Qing Machine Learning 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. |
| title | Neural Collapse in Multi-label Learning with Pick-all-label Loss |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2310.15903 |