May 2026· arXiv.org· Vol abs/2606.07559· 0 citations· 40 references
Computer SciencePhysics
TL;DR
This work builds an order parameter combining the predicted distribution with embedding overlap, as a density matrix, and shows sharp jumps resembling phase transitions, which characterize this near-synonym mechanism and need recalibration before extrapolation.
Abstract
Language models fine-tuned where the correct completion must outrank a near-synonym competitor often fail silently. The cross-entropy loss falls monotonically while the correct token never overtakes the competitor in the model's ranking. We study this across five transformer architectures from two families spanning a sixfold parameter range, on ten contexts whose correct and competing completions share substantial embedding overlap. We build an order parameter combining the predicted distribution with embedding overlap, as a density matrix because that distribution lives over a non-orthogonal basis. It decomposes additively into a signal term tracking commitment to the correct token and a drag term set by how the embedding bulk leaks probability into the score. This isolates two failure modes. In kinematic failure the signal stays too small and the model never commits. In structural failure the drag worsens during fine-tuning, so the model degrades geometrically as its loss falls. The order parameter also shows sharp jumps resembling phase transitions. We test the spontaneous-symmetry-breaking reading by tracking it after every gradient step, and rule it out. The jumps persist under LoRA even though the token embedding matrix never changes. No geometric phase transition is possible when that geometry cannot move, so the discontinuity lies entirely in the softmax readout. A few dimensionless quantities organize the trajectory across architectures. One is consistent across all five models under full fine-tuning. A second sorts architectures into two classes by their bulk embedding distribution and predicts whether LoRA alone can make a sentence commit. As a blind test, the framework predicts a held-out architecture's critical learning rate to within 2.1% of a later sweep. These results characterize this near-synonym mechanism and need recalibration before extrapolation.
We present \LegoLM{}, a structured weight-sharing compression framework for large language models grounded in a systematic study of why global weight sharing fails and how to fix it. We identify two distinct failure modes. Distributional mismatch: for vector blocks of dimension d<= 2, transformer layers with heterogeneous weight scales impose a scale-mismatch penalty that grows linearly with d and cannot be resolved by increasing K, producing perplexity in the millions.Outlier dominance: for scalar blocks, a fraction ~1/K of weights lies beyond the outermost Lloyd-Max decision threshold and cannot be represented by any centroid; their misrepresentation accumulates across layers, causing catastrophic quality loss. \LegoLM{} resolves both failure modes via three data-free adaptations: 1 scalar-block encoding to eliminate the $d$-linear mismatch component, 2 percentile-selective replacement that identifies and preserves outlier weights verbatim, and 3 boundary-layer protection for the first and last transformer blocks. Across GPT-2 small (124M) and Mistral-7B, \LegoLM{} achieves +0.03% PPL degradation at 4.41X compression on Mistral-7B - outperforming PTQ-8bit in both quality and compression ratio - and -0.02% at 2.67X. Downstream evaluation on LAMBADA and HellaSwag confirms that \LegoLM{} at K=64, p=99% preserves accuracy within noise at 5.12 X compression, exceeding PTQ-8bit's compression ratio while matching its accuracy. We further discover that outlier dominance grows with model scale: full replacement at K=128 degrades GPT-2 small by only +23% but catastrophically degrades Mistral-7B by +1,134,279%, while selective replacement at p=99% rescues both models to under +15%. A controlled ablation confirms that selective replacement is the dominant mechanism: adding it to per-layer K-means also yields near-lossless quality, matching \LegoLM{} within 0.02%.
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.
What a language model internalizes from fine-tuning is usually diagnosed after the fact. We make it an experimental variable. OraclePhys is a systematic fine-tuning framework with three components: OraclePhys-Bench, an exactly-graded structural-mechanics benchmark whose finite-element oracle scores every answer and counterfactual edit -- no human labels, no LLM judging; OraclePhys-30K, a supervision dataset of seven answer forms over byte-identical structure descriptions; and a controlled training study across the seven forms and three verifier roles. The study yields two findings. First, the label's answer form -- not its bit count -- causally determines what fine-tuning teaches: a ranking objective installs an out-of-distribution forward model where the untrained base sits at the guessing prior, a scalar objective at best a partial one, a boolean nothing detectable; the vector-scalar gulf survives a second physics domain, a second model family, and a paraphrased evaluation surface. Second, written or score-filtered answers install this capability, while advantage-weighted scores (GRPO) raise reward yet leave the model statistically equivalent to its start on held-out physics -- within the recipes and budgets tested -- sufficing only for routing. The trained 8B -- the first LLM on spatial structural response -- reaches the task's data-precision frontier: above a frontier LLM at zero- and 32-shot, at a specialist's level. What the label spells out about the target computation is what fine-tuning teaches; what you train on is what you route.
Mingyu Li, Guorui Song, Jing Lin et al.· 0 citations
Post-training can substantially alter language-model behavior, yet aggregate behavior rates do not reveal whether training removes an existing mechanism, creates a new one, or changes how an inherited mechanism is used. We study this question through two mechanistically distinct failures, repetition as a decoding-attractor pathology and sycophancy as a preference-related alignment failure. We introduce behavioral manifold analysis, which isolates behavior-specific geometry by selecting sparse behavior-associated coordinates and lifting them into low-dimensional local charts. We construct these charts in two complementary spaces. ACT captures runtime activation states, while NOC quantifies how strongly the model routes functional information flow through the shared behavior-associated subspace. Across multiple model families, the resulting charts are highly compressed and partially alignable across architectures. Contribution-space charts expose a more architecture-robust shared core, whereas activation-space charts retain stronger family-specific structure. Tracking these charts through controlled post-training reveals a consistent asymmetry. Supervised fine-tuning substantially alters the inherited behavioral geometry, whereas reward optimization changes behavior while largely preserving the underlying chart. This geometric perspective provides a unified framework for understanding the mechanistic distinction between the two objectives. SFT tends to rewrite behavioral geometry, whereas reward optimization primarily reweights it. Code is available at https://github.com/ronglingze/Manifold-Analysis
Juntong Wang, Shengkun Yang, Xiyuan Wang et al.· 0 citations
Vision-Language Models (VLMs) are costly at inference time because they must process long sequences of visual tokens. Existing token pruning methods often degrade under high compression by blindly discarding information, breaking spatial structure or collapsing diversity. We propose SpecFlow, a training-free framework that shifts the paradigm from destructive pruning to conservative condensation, strictly enforcing spatial coverage and statistical conservation to ensure stability. Treating visual tokens as nodes in a $k$NN graph, SpecFlow (i) computes a stable importance field via spectral heat flow to preserve structural coherence, (ii) allocates budgets via adaptive spatial partitioning to guarantee coverage, and (iii) aggregates discarded information into coreset sinks to maintain statistical conservation. The method is plug-and-play, requires no fine-tuning, and is compatible with FlashAttention. Experiments confirm that our SpecFlow outperforms SOTA methods across tasks, VLM architectures, and pruning ratios. Notably, LLaVA-1.5 with SpecFlow retains 95.6% of original performance despite pruning 88.9% of visual tokens, offering an exceptional efficiency-accuracy balance. Code is available at https://github.com/Lzy-dot/SpecFlow
Zhaoyang Li, Yanjun Li, Wangkai Li et al.· 0 citations
Removing the left context from a causal language model reveals a useful kind of boundary: an edge where the model processes the same right-hand tokens with little change. We turn this observation into prefix-removal probing and introduce Right Reset (RR), which measures preservation of the right-hand hidden-state trajectory. A dynamic program converts RR edge scores into variable-length chunks. On flattened text formed by concatenating topically similar records after deleting their separators and layout, RR recovers 47.7% of the original records as clean units, versus 25.9% for a BGE embedding boundary, the strongest tested conventional baseline without task-specific model training. The gain persists after rendering and OCR. Passive scores from the same Qwen3-4B layer and direct prompting of a same-scale instruction model perform substantially worse on flattened records. Across six language models, RR-selected cuts also undergo consistently less local output disruption than unselected candidate edges. An observed-token likelihood-ratio readout is competitive in some architectures, indicating that the central contribution is the intervention: context dependence itself can provide a boundary signal when surface structure is weak.
Known for his clear and elegant writing style, Bertsekas shaped fields from control and optimization to large-scale computation and artificial intelligence.
