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Neural Collapse Is Forbidden: Information Floors in Language Models

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Computer Science > Machine Learning

arXiv:2607.09487 (cs)
[Submitted on 10 Jul 2026]

Title:Neural Collapse Is Forbidden: Information Floors in Language Models

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Abstract:Within-class variance in language-model representations is commonly read as incomplete neural collapse. We argue it is allocated information storage, and that the allocation obeys a law. A one-line centering identity voids a family of simplex equiangular-tight-frame claims, including our own earlier ones; in dimensionless variance shares across 14 models, macro-category structure carries only 4-12% of representational variance and within-token context carries 79-91%, stable across a 100x parameter range. On the theory side, token-level weight decay penalizes a category in proportion to its type count, not its occurrence mass, reducing next-token prediction to an imbalanced K-class problem whose optimum orders category norms by type count. A converse floor, proved for binary categories, forces within-category dispersion to be at least proportional to the conditional mutual information I(token; context | category). The law holds: identity dispersion, not total variance, tracks this information across every tested model and partition, under a model-free estimate and even across models, where one model's information predicts another's dispersion; and over pretraining the category share overshoots, decays, and partially recovers, because the information it must carry never left.
Subjects: Machine Learning (cs.LG); Computation and Language (cs.CL); Machine Learning (stat.ML)
Cite as: arXiv:2607.09487 [cs.LG]
  (or arXiv:2607.09487v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2607.09487
arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Bruno Abrahao [view email]
[v1] Fri, 10 Jul 2026 15:04:02 UTC (420 KB)
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