A scale-dependent transition between two ID regimes is found: at low lexical diversity, conditions with fewer unique final words produce higher ID, while at high lexical diversity, this ordering reverses, and conditions with more unique words produce higher ID.
Abstract
Intrinsic dimensionality (ID) is widely used to probe the representational complexity of language models, but it remains unclear whether ID differences reflect properties of language itself or artefacts of how the underlying dataset was constructed. In this paper, we focus specifically on how lexical diversity, the number of unique last-token items present in a dataset, affects ID estimates of that dataset. We find a scale-dependent transition between two regimes: at low lexical diversity, conditions with fewer unique final words produce higher ID, while at high lexical diversity, this ordering reverses, and conditions with more unique words produce higher ID. We derive an exact, parameter-free formula for the point at which this reversal occurs, which matches the observed transition point at every scale tested. On the one hand, our results highlight how care must be taken when interpreting the intrinsic dimensionality of a set of representations as a straightforward cue of their complexity. On the other hand, our discovery of the two ID regimes reveals a general principle of organisation of linguistic data in LLMs that sheds new light on their inner manifold structures.
As Large Language Models (LLMs) grow more capable across diverse tasks, their (in)ability to generalize remains difficult to quantify and poorly understood beyond limited domains. In particular, LLMs are known to struggle generalizing multilingually, to languages outside of English, and that are poorly attested in their training data. To understand why this may be, and what enables some models to perform better than others, we turn to a long history of work across the cognitive sciences, arguing that successful generalization derives from appropriate representations in similarity space. We look at how well LLMs'representations capture the hierarchical similarity structure between distinct languages. Strikingly, we show LLMs'latent representations largely recover the hierarchical structure of the Indo-European language family tree -- grouping languages that are members of the same subfamily closely together in representation space. Furthermore, we show that the degree to which models reflect the similarity structure of languages correlates with their performance on XNLI, a multilingual natural language inference benchmark. This extends classic work on similarity-driven generalization at scale, showing how models that represent similar languages similarly generalize better from one language to another.
Supantho Rakshit, Adele E. Goldberg, Henry Conklin· 0 citations
Human language exhibits lawful structure at the level of words (frequency, vocabulary growth) and word pairs (co-occurrence across distance). Here we show that the arrangement of words in sequence -- a central determinant of meaning -- obeys a comparable law. Using large language models as probabilistic probes, we measured the reduction in target perplexity conferred by prior context at distance d beyond that of the same words scrambled; this difference, the contextual persistence function P(d), isolates the influence of arrangement. Across ten corpora spanning six language families and written and spoken modalities, P(d) decayed approximately as 1/d ($P(d) \propto d^{-\alpha}$, mean $\alpha = 1.04$; median $r^2 = 0.96$). The effect vanished in scrambled and synthetic controls, replicated across independent probes, and did not appear in genomic or protein sequences under domain-native models. An exponent near 1 distributes contextual influence approximately uniformly across logarithmic timescales. The results establish a scaling law of contextual persistence in human language.
Recent work showed that language models represent character counts on curved 1D manifolds, with attention heads performing geometric transformations to enable computation. We test whether this generalizes across four ordinal tasks (bracket depth, indentation, table position, numeric magnitude) in Gemma-2-2B, Gemma-2-9B, and Qwen3-4B. We find that 1D manifolds with place-cell feature tiling emerge for tasks where the ordinal variable is locally computable from token identity, while tasks requiring cross-position integration or semantic extraction produce higher-dimensional or incoherent representations. Geometric computation is architecture-dependent: Qwen3-4B shows substantially stronger twisting than Gemma models for indentation, and its twisters preserve ordinal order, unlike its numeric twisters. Activation patching confirms that the identified manifold subspaces concentrate task-relevant information, with manifold-direction ablation causing dramatically larger probe accuracy drops than random-direction controls.
This work investigates how decoder-only transformers resolve lexical ambiguity through layer-by-layer analysis of three models spanning three parameter sizes, finding that representations become maximally distinct in middle layers, then partially reconverge in late layers, while the KL divergence between their next-token predictions reaches its maximum in the final layers.
K. Scott, Narun Pat, Veronica Liesaputra· 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
This work identifies a curse of ambiguity: in large language models, and more broadly in all neural networks that produce discrete probability distributions, the more ambiguous a next-token distribution is, the harder it is to learn accurately.
Nicolas Zucchet, Hyun Dong Lee, Scott W. Linderman· 0 citations