It is argued that within-class variance in language-model representations is allocated information storage, and that the allocation obeys a law, and that the allocation obeys a law.
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.
It is proposed that a model's uncertainty about a token is reflected not only in the breadth of its output distribution but also in whether a confident prediction is \emph{fragile} under perturbation of its attention pathways, a training-free estimator that masks attention heads and measures the BALD mutual information among the resulting subnetworks.
Minsoo Kim, Sungyoung Ji, Kisung Moon et al.· 0 citations
Attention collapse in autoregressive language models -- manifested as repetitive token loops where the model becomes trapped in self-reinforcing attractors -- is a persistent pathology that existing decoding-time heuristics fail to address at its root cause. We present a principled framework that penalises or compensates anomalous confidence arising from collapsed generation patterns, by comparing a token's observed frequency against its corpus prior through an adjacent-conditional probability construction. The resulting self-normalising penalty ratio $R=f(m,n,p)/f(np,n,p)$ requires no ad hoc standardisation and admits a closed-form logit offset with zero approximation error. The correction is isolated from the loss gradient and accumulated into a frozen output-layer bias via exponential moving average, enabling deployment as a repair mechanism for models that have already collapsed without requiring intrusive modifications to standard training pipelines. Experimental validation on a 1.5B-parameter model demonstrates that the frozen-bias mechanism can rescue a model already trapped in a collapsed attractor, reducing 2-gram repetition from 0.073 to near 0 while preserving generation quality.
Joint-Embedding Predictive Architectures (JEPAs) are effective for images, video, and audio, yet deterministic JEPA-style latent prediction has not become a standard objective for text encoders. We argue that this gap reflects a mismatch between squared-error latent prediction and the conditional structure of language. The key requirement is conditional concentration: given a context and target location, the target representation should lie near a single meaningful point. Local image prediction often satisfies this through spatial continuity, whereas masked text can admit multiple valid token or span completions whose representations need not share a coherent center. We formalize this mismatch through three conditions---predictability, non-collapse, and low conditional variance---and show how their failure creates centroid degeneracy and collapse pressure in text. Matched I-JEPA and T-JEPA experiments reveal the predicted sequence: mutual-information saturation and elevated target variance precede train--validation instability, effective-rank degeneration, cosine collapse, and poor downstream transfer. The same pattern appears across five independent data seeds, indicating that it is not a sampling artifact. These results do not rule out predictive learning for language; they show that text-compatible JEPA objectives must preserve multiple plausible completions rather than compress them into a single latent point.
Do large language models contain domain-specific parametric shells: concentrated, causally necessary neuron populations whose removal selectively degrades a target domain while sparing others? We apply a uniform causal methodology across two domain granularities, three model families (1.5B to 7B parameters), and eight domains. At the academic subject level, zero neurons exceed 60\% domain selectivity across 939,008 combined FFN neurons and causal damage matrices are flat, despite domain identity being linearly decodable above 85\% accuracy. At the language and modality level, 0.65--1.14\% of neurons exceed 60\% selectivity, damage matrices are near-perfectly diagonal (ratios up to 595:1), and shell neuron sets are essentially disjoint (IoU $<0.003$). Masking code-selective neurons reduces mathematical reasoning accuracy by 16--24 percentage points across all models; masking Spanish or Chinese neurons leaves it at or below random. Shell strength increases monotonically with scale and shells are spatially interleaved in a pattern that precludes group-level selective quantization. Parametric shells form where and only where training data was modular at the token level.
M. Armstrong, Navid Ayoobi, Arjun Mukherjee· 0 citations
An architecture-agnostic sufficient condition is established linking behavioral similarity to inference-prompt coverage, small excess population log-loss, and similar effective target distributions---a possible training-side account rather than an empirical explanation of the observed trends.
Behavior manifold analysis is introduced, which isolates behavior-specific geometry by selecting sparse behavior-associated coordinates and lifting them into low-dimensional local charts, and provides a unified framework for understanding the mechanistic distinction between the two objectives.
Juntong Wang, Shengkun Yang, Xiyuan Wang et al.· 0 citations