Structure Before Collapse: Transient semantic geometry in next-token prediction

The JEPA Paradox in Language: The Geometry of Linguistic Alternatives

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.

Neural Collapse Is Forbidden: Information Floors in Language Models

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.

Attention-Path Fragility as an Uncertainty Signal in Large Language Models

We propose 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. We instantiate this as ASMI (Attention-Subnetwork Mutual Information), a training-free estimator that masks attention heads and measures the BALD mutual information among the resulting subnetworks, with a semantic-agreement kernel to discount surface-form disagreement. The signal is not a restatement of output confidence: on grounded QA an out-of-fold test shows it adds error-predictive information beyond single-pass confidence and entropy, concentrated in \emph{confident-but-fragile} predictions, where acting on it roughly halves the retained error of a confidence filter. The distinctness is regime-graded, so ASMI predicts its own domain of applicability, strong where answers are routed through provided context and bounded by design where they are recalled from parametric knowledge. Sem-ASMI reads the signal from a single greedy response, without the stochastic generations the strongest baselines require, and ties or beats Semantic Entropy on ten of the twelve grounded benchmark-backbone settings. Across the same twelve settings, the best ASMI variant, typically the adaptive one reusing the ten samples already drawn for the baselines, ties or leads the strongest baseline in eight, significantly in three under a paired test. On parametric QA all variants revert to or below the zero-cost MSP baseline, exactly as predicted, and the estimates are near-deterministic across reruns. A head-level analysis shows that what tracks this boundary is not the presence of head-level fragility but whether that fragility couples to errors.

From Patterns to Semantic Anchoring

The Changing Geometry of Grammar: Dimensionality and Neighborhood Reorganization across Transformer Layers

Transformer representations describe trajectories through high-dimensional vector spaces, which are shaped dynamically as tokens incorporate relational context across layers. Such data tend to concentrate on lower-dimensional sub-manifolds, a form of compression quantified by the Intrinsic Dimensionality (ID), the minimum number of independent variables needed to represent them without significant information loss. In this work, we ask whether the grammatical role of tokens, as marked by their part-of-speech (PoS) tag, shapes the local geometry of this manifold. To this end: (1) We investigate the layer-wise evolution of ID, finding that closed-class items expand earlier and collapse sooner than open-class ones; (2) We show its expansion and contraction to be explained by changes in the neighborhood structure, and hence in the relations between words within a sentence; (3) We compare encoders (ModernBERT, bigbird-roberta-large) and decoders (gemma-2-2B, Llama-3.2-3B), finding that the two families evolve differently across layers, consistently with how each integrates context;(4) We show that geometric features alone recover a token's grammatical role, and use them to interpret how the semantic content of each PoS evolves across layers in a downstream classification task.

AdaMTP: An Adaptive Training Paradigm for Multi-Token Prediction

Multi-Token Prediction (MTP) has emerged as an effective paradigm that augments a shared Large Language Model backbone with auxiliary heads, training the model to predict several future tokens in parallel to enrich its supervision signal and accelerate inference. However, existing training frameworks adopt a rigid, fixed-length prediction horizon, disregarding the highly non-uniform information density of natural language and code. Forcing the auxiliary heads to predict across high-entropy semantic boundaries injects noisy, conflicting training signals; because these heads share the backbone's latent representations, the resulting gradients backpropagate and interfere with the model's core capabilities. We propose AdaMTP, an adaptive training paradigm that dynamically aligns the prediction horizon with the intrinsic predictability of the sequence. At its core, an entropy-based segmentation algorithm leverages the base model to detect sudden surges in uncertainty as semantic boundaries, partitioning sequences into variable-length groups. Each token is assigned an adaptive prediction depth, and a dynamically masked MTP objective suppresses the loss for predictions that cross these boundaries, attenuating the noisy gradients that degrade the backbone. Across mathematical reasoning, code generation, and general benchmarks on three backbones (Llama-3.1-8B, Qwen-2.5-7B, Gemma-3-12B), AdaMTP consistently outperforms standard MTP in both task performance and inference speedup.