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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.","url_abs":"https://arxiv.org/abs/2310.15903v4","url_pdf":"https://arxiv.org/pdf/2310.15903v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"neural-collapse-in-multi-label-learning-with","repo_url":"https://github.com/heimine/nc_mlab","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"all","task_name":"All"},{"task_slug":"multi-label-classification-2","task_name":"MUlTI-LABEL-ClASSIFICATION"},{"task_slug":"multi-label-classification","task_name":"Multi-Label Classification"},{"task_slug":"multi-label-learning","task_name":"Multi-Label Learning"},{"task_slug":"multi-class-classification","task_name":"Multi-class Classification"},{"task_slug":"tag","task_name":"TAG"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2310.15903","atlas_url":"https://app.syntology.ai/?focus=2310.15903","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2310.15903"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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