Neural Collapse Is Forbidden: Information Floors in Language Models

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.

BootOOD: Self-Supervised Out-of-Distribution Detection via Synthetic Sample Exposure under Neural Collapse

Out-of-distribution (OOD) detection is critical for deploying image classifiers in safety-sensitive environments, yet existing detectors often struggle when OOD samples are semantically similar to the in-distribution (ID) classes. We present BootOOD, a fully self-supervised OOD detection framework that bootstraps exclusively from ID data and is explicitly designed to handle semantically challenging OOD samples. BootOOD synthesizes pseudo-OOD features through simple transformations of ID representations and leverages Neural Collapse (NC), where ID features cluster tightly around class means with consistent feature norms. Unlike prior approaches that aim to constrain OOD features into subspaces orthogonal to the collapsed ID means, BootOOD introduces a lightweight auxiliary head that performs radius-based classification on feature norms. This design decouples OOD detection from the primary classifier and imposes a relaxed requirement: OOD samples are learned to have smaller feature norms than ID features, which is easier to satisfy when ID and OOD are semantically close. Experiments on CIFAR-10, CIFAR-100, and ImageNet-200 show that BootOOD outperforms prior post-hoc methods, surpasses training-based methods without outlier exposure, and is competitive with state-of-the-art outlier-exposure approaches while maintaining or improving ID accuracy.

Model Rectification via Unknown Unknowns Extraction from Deployment Samples

Model deficiency that results from incomplete training data is a form of structural blindness that leads to costly errors, oftentimes with high confidence. During the training of classification tasks, underrepresented class-conditional distributions that a given hypothesis space can recognize results in a mismatch between the model and the target space. To mitigate the consequences of this discrepancy, we propose Random Test Sampling and Cross-Validation (RTSCV) as a general algorithmic framework that aims to perform a post-training model rectification at deployment time in a supervised way. RTSCV extracts unknown unknowns (u.u.s), i.e., examples from the class-conditional distributions that a classifier is oblivious to, and works in combination with a diverse family of modern prediction models. RTSCV augments the training set with a sample of the test set (or deployment data) and uses this redefined class layout to discover u.u.s via cross-validation, without relying on active learning or budgeted queries to an oracle. We contribute a theoretical analysis that establishes performance guarantees based on the design bases of modern classifiers. Our experimental evaluation demonstrates RTSCV's effectiveness, using 7 benchmark tabular and computer vision datasets, by reducing a performance gap as large as 41% from the respective pre-rectification models. Last we show that RTSCV consistently outperforms state-of-the-art approaches.