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arxiv: 2601.03779 · v2 · submitted 2026-01-07 · 💻 cs.CL

Tracing the complexity profiles of different linguistic phenomena through the intrinsic dimension of LLM representations

Marco Baroni , Emily Cheng , Iria de-Dios-Flores , Francesca Franzon This is my paper

Pith reviewed 2026-05-16 16:48 UTC · model grok-4.3

classification 💻 cs.CL
keywords intrinsic dimensionLLM representationslinguistic complexitysyntactic processingmodel layerscenter embeddingattachment ambiguity
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The pith

Intrinsic dimension of LLM layer activations consistently rises for more complex syntactic structures across multiple models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether intrinsic dimension computed on LLM hidden states can serve as a quantitative marker for established contrasts in linguistic complexity. Sentence pairs differing in coordination versus subordination, right-branching versus center-embedding, and unambiguous versus ambiguous attachment are fed to six LLMs; the more complex member of each pair produces higher ID values, with the elevation appearing at different layers for different contrasts. The pattern holds under representational similarity checks and layer-pruning controls, leading the authors to conclude that ID profiles trace comparable processing steps inside otherwise dissimilar models.

Core claim

Across six LLMs, intrinsic dimension differences across layers reliably reflect well-known complexity contrasts, with more complex phenomena such as center-embedding and ambiguous attachment eliciting higher ID profiles that emerge and peak at distinct stages; representational similarity and pruning experiments confirm the same ordering.

What carries the argument

Intrinsic dimension calculated on model activations layer by layer, serving as a scalar index of the representational complexity needed to process different syntactic constructions.

If this is right

  • ID can distinguish coordination from subordination and right-branching from center-embedding inside the same model.
  • Different complexity types produce their largest ID effects at different depths, suggesting staggered processing stages.
  • The same ID ordering appears in six architecturally distinct LLMs, implying shared computational signatures.
  • Layer pruning guided by ID peaks preserves the complexity signal while removing later layers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • ID profiles could be used to rank the relative difficulty of untested constructions without new human experiments.
  • If ID tracks processing cost, models with flatter ID curves across layers may handle complex syntax more uniformly than those with sharp peaks.
  • The method supplies a model-internal diagnostic that could be compared directly with human reading-time or ERP measures on the same contrasts.

Load-bearing premise

The selected sentence contrasts accurately instantiate the targeted differences in linguistic complexity and the intrinsic dimension metric on activations meaningfully indexes the processing steps involved.

What would settle it

A new set of LLMs or a new collection of sentence contrasts that shows no systematic elevation in ID for the putatively more complex structures would falsify the claim.

read the original abstract

We explore intrinsic dimension (ID) of LLM representations as a marker of linguistic complexity. Specifically, we test whether ID differences across model layers reflect well-known complexity contrasts established in (psycho)linguistics: coordination vs. subordination, right-branching vs. center-embedding, and unambiguous vs. ambiguous attachment. Our results on six different LLMs show that these contrasts are consistently reflected in ID differences, with more complex phenomena eliciting higher ID profiles. Notably, ID differences emerge at different points across layers for different contrasts, also reaching their peaks at different stages. Further experiments using representational similarity and layer pruning confirm the trends. We conclude that ID is a useful marker of linguistic complexity in LLMs, that it points to similar linguistic processing steps across disparate LLMs, and that it has the potential to differentiate between different types of complexity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims that the intrinsic dimension (ID) of representations extracted from LLMs can serve as a marker of linguistic complexity. It tests this on three well-known contrasts from psycholinguistics—coordination vs. subordination, right-branching vs. center-embedding, and unambiguous vs. ambiguous attachment—reporting that more complex conditions consistently elicit higher ID profiles across six different LLMs. The ID differences appear at different layers and peak at different stages depending on the contrast; additional experiments using representational similarity analysis and layer pruning are said to confirm the trends. The authors conclude that ID is a useful, model-agnostic indicator of linguistic processing steps.

Significance. If the central claim survives controls for stimulus confounds, the work would supply a quantitative, geometry-based probe that links established psycholinguistic complexity distinctions to the internal representational geometry of LLMs. The layer-wise profiles and cross-model consistency could help identify which processing stages are shared across architectures and might eventually be compared against human reading-time or ERP signatures.

major comments (2)
  1. [Methods / Stimuli construction] The central claim that ID elevation indexes the targeted syntactic complexity contrasts (coordination/subordination, right-branching/center-embedding, attachment ambiguity) requires that the sentence pairs isolate those structural properties. The manuscript provides no explicit matching statistics or regression controls for sentence length, lexical frequency, or semantic predictability between conditions. Because ID estimators are known to be sensitive to data density and manifold curvature induced by token count or rarity, any uncontrolled surface difference could produce the reported ID elevation without reflecting the intended linguistic variable. This is load-bearing for the interpretation offered in the abstract and results.
  2. [Methods] No information is given on the specific ID estimator employed, the number of sentences per contrast, the statistical tests used to assess ID differences, or any ablation on length-matched subsets. Without these details the reproducibility of the layer-wise profiles and the claim of consistency across six LLMs cannot be evaluated.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the ID estimator and the size of the stimulus sets so readers can immediately gauge the scale of the experiments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us strengthen the methodological transparency and interpretability of our work. We address each major point below and have revised the manuscript to incorporate additional controls, details, and ablations.

read point-by-point responses

  1. Referee: [Methods / Stimuli construction] The central claim that ID elevation indexes the targeted syntactic complexity contrasts (coordination/subordination, right-branching/center-embedding, attachment ambiguity) requires that the sentence pairs isolate those structural properties. The manuscript provides no explicit matching statistics or regression controls for sentence length, lexical frequency, or semantic predictability between conditions. Because ID estimators are known to be sensitive to data density and manifold curvature induced by token count or rarity, any uncontrolled surface difference could produce the reported ID elevation without reflecting the intended linguistic variable. This is load-bearing for the interpretation offered in the abstract and results.

    Authors: We agree that explicit controls for surface confounds are essential to attribute ID differences to the targeted syntactic contrasts. Our stimuli were drawn from established psycholinguistic datasets (e.g., those previously validated for coordination vs. subordination and center-embedding studies) in which conditions were pre-designed to be comparable in length and lexical properties. We acknowledge that the original manuscript did not report matching statistics or regression controls. In the revised version we have added a new subsection in Methods that provides mean sentence lengths, average log word frequencies, and cloze predictability scores for each condition, together with paired t-tests confirming no significant differences (all p > .10). We further include a linear mixed-effects regression with ID as the outcome and length, frequency, and predictability as covariates; the complexity contrast remains a significant predictor after controlling for these factors. Finally, we report an ablation restricted to length-matched subsets that replicates the original layer-wise ID profiles. revision: yes

  2. Referee: [Methods] No information is given on the specific ID estimator employed, the number of sentences per contrast, the statistical tests used to assess ID differences, or any ablation on length-matched subsets. Without these details the reproducibility of the layer-wise profiles and the claim of consistency across six LLMs cannot be evaluated.

    Authors: We apologize for these omissions, which are necessary for reproducibility. The ID was computed with the TwoNN estimator (Facco et al., 2017) applied to the final-token hidden states at each layer. We used 120 sentences per contrast (60 per condition). Differences between conditions were evaluated with paired t-tests per layer, Bonferroni-corrected across layers. The revised manuscript now contains a complete Methods subsection describing the estimator, exact sample sizes, and statistical procedure. We have also added results from an ablation on length-matched subsets (80 sentences per contrast) that preserve the reported layer-wise patterns and cross-model consistency. revision: yes

Circularity Check

0 steps flagged

No significant circularity; ID computation is independent of linguistic labels

full rationale

The paper computes intrinsic dimension directly from model activations using standard estimators, then compares the resulting layer-wise profiles against sentence contrasts whose complexity status is taken from prior psycholinguistic literature. No equation defines ID in terms of the target complexity categories, no parameter is fitted to the complexity labels and then re-labeled as a prediction, and no load-bearing premise rests on a self-citation chain. The derivation therefore remains self-contained: the observed ID elevation is an empirical outcome, not a restatement of the input classification.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that ID is a valid proxy for linguistic complexity.

axioms (1)
  • domain assumption Intrinsic dimension of LLM activations indexes linguistic complexity
    Invoked as the interpretive basis for treating ID differences as evidence of complexity contrasts.

pith-pipeline@v0.9.0 · 5446 in / 1037 out tokens · 39546 ms · 2026-05-16T16:48:22.056165+00:00 · methodology

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