Neural Collapse Is Forbidden: Information Floors in Language Models
2026-07-10 • Machine Learning
Machine LearningComputation and Language
AI summaryⓘ
The authors studied how language models organize information in their internal representations. They argue that the variation seen within categories isn’t a flaw but intentional storage of contextual information, following a consistent pattern they call a law. Their analysis shows that most variation is due to context, not category type, and this pattern holds across many models of different sizes. They also provide theoretical support explaining how category frequency influences representation norms and show a mathematical lower limit on variation within categories based on information theory. Overall, their findings reveal that information distribution inside language models is systematic and predictable.
language modelsneural collapserepresentation variancecontextual informationequiangular tight frameweight decaymutual informationcategory normstoken embeddingsnext-token prediction
Authors
Bruno Abrahao
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.