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

AI summary

Overview

Research area: Natural Language Processing / LLM interpretability and psycholinguistics — using intrinsic dimension (ID) of LLM hidden representations as a measure of linguistic complexity.

Technical level: Intermediate. Readers need some familiarity with LLM internals (residual stream, layers, attention/MLP blocks), dimensionality-reduction concepts, and basic psycholinguistic constructs (embedding, relative-clause attachment, agreement).

One-sentence scope: Across six LLMs (7B–14B parameters), the authors test whether the intrinsic dimension of layer-wise representations tracks three classic linguistic complexity contrasts — coordination vs. subordination, right-branching vs. center-embedding, and unambiguous vs. ambiguous relative-clause attachment — and find that it does, but with a distinct layer-wise signature for each contrast.

What This Paper Is About

LLMs have strong linguistic abilities, but how linguistic structure is processed inside their layers is still poorly understood. Prior work showed that LLMs have a consistent per-layer intrinsic-dimension profile, with a peak in intermediate layers that seems to mark a phase of deep linguistic processing — but that work looked only at generic corpus data or coarse data-type distinctions. This paper asks a finer-grained question: does ID respond to specific, well-controlled complexity contrasts that psycholinguists have studied for decades, and if so, do different kinds of complexity produce different ID profiles?

Key Contributions

1. A granular use of ID as a complexity probe. The authors move beyond generic corpus text and coarse data-type splits to three minimal-pair manipulations — coordination vs. subordination, right-branching vs. center-embedding, and unambiguous vs. ambiguous relative-clause attachment — each instantiated in a purpose-built dataset.

2. A cross-model replication across six LLMs. ID profiles are tested on Gemma-2-9b, Llama-3-8B, OLMo-2-13B, Mistral-7B-v0.1, Pythia-12B, and Qwen-2.5-14B, showing that the complexity signatures are consistent across architectures.

3. Two converging lines of evidence beyond ID. Representational similarity (Information Imbalance, Δ) and layer-pruning interventions are used to corroborate the ID findings, with pruning providing a proof of concept for a causal link between an ID peak on a layer and its impact on model behavior.

4. A proposed link between complexity type and ID signature. The paper argues that the formal complexity contrast (nesting via subordination) is tied to the generic-ID-peak phase, while the two more functional contrasts (long-distance agreement, attachment ambiguity) manifest differently — a distinction the authors flag as a hypothesis for future case studies rather than a settled result.

Main Findings

• Higher complexity yields higher ID, consistently across six LLMs. For each of the three contrasts, the more complex condition produced higher ID profiles, matching predictions from the (psycho)linguistic literature. As a preliminary check, all datasets and all LLMs showed higher per-token surprisal for the more complex condition (one-sided t-test, α = 0.05).

• The timing of the ID divergence differs by contrast. Coordination vs. subordination curves first overlap and then diverge, typically under or just before the generic-ID peak (considerably earlier for Qwen only), with subordination higher from that point onward. Right-branching vs. center-embedding diverges earlier, with center-embedding higher only until the generic-ID peak (a bit later for Pythia).

• A post-peak reversal for center-embedding vs. right-branching. After the generic-ID peak, the two curves merge or, for 4/6 models, reverse so that right-branching ID is higher. The authors relate this to right-branching sentences ending in a nested clause ("The politicians advised the potters [that were waiting]"), since ID is measured on the last token.

• Ambiguity produces a different, weaker pattern. Ambiguous vs. unambiguous attachment shows a general downward ID trend, clearer after the generic-ID peak, with ambiguous consistently higher but the difference tending to be small. The generic-ID peak does not act as a clear delimiter here, and the authors caution that final-token variation across pairs (nouns, adverbs, adjectives) may shape the overall trajectory independently of the contrast.

• Absolute ID scales with input length. Maximum ID is orders of magnitude below the ambient dimension and largely correlates with input length: highest for the 100-word generic sequences, next for the 18-word 4-clause coordinated/subordinated sentences, then lower and comparable for the 8-word right-branching/center-embedding inputs and the 13-word-on-average unambiguous/ambiguous inputs.

• Asymmetric representational divergence for coordination/subordination. Δ is generally extremely low in both directions; by the theoretical simulations of Acevedo et al. (2026), Δ = 0.1 (the largest value on the paper's y axes) corresponds to 90% of shared features. For 5/6 models, Δ(coord → subord) becomes progressively larger than Δ(subord → coord) just under the generic-ID peak, except for Qwen, where the peak marks divergence but no asymmetry.

• No asymmetry for center-embedding vs. right-branching. Both directions stay very close, decreasing only slightly across layers, which the authors read as the LLMs capturing that the pairs carry the same denotational meaning. In both experiments, Δ sometimes spikes on the very last layers.

• Pruning implicates the generic-ID-peak layers for nesting. Pruning had a stronger effect on subordinated than coordinated sentences for all models (typically clearer in earlier layers), and for 4/6 LLMs there was a clear accuracy dip when pruning layers in the generic-ID-peak phase. The two outliers: Qwen shows a subordination-specific dip just after the peak, and Gemma a late-peak dip that is actually stronger for coordination.

• No differential pruning effect for the other two contrasts. Right-branching vs. center-embedding and unambiguous vs. ambiguous showed no condition-specific pruning differences and no layer-specific dips, except strong initial- and final-layer effects.

Methodology in Plain English

The central idea is that complex data are harder for a representation system to encode, so they occupy more effective dimensions. When sentences are embedded into an LLM layer, they lie near a low-dimensional manifold; the intrinsic dimension is the number of degrees of freedom needed to describe that manifold under minimal information loss, and it is far smaller than the full hidden-space dimensionality.

The authors extract the last-token representation from the residual stream at every layer (the last token is the only one that attends to the whole sequence and the one used to predict the next token), giving a set of N representations in ℝ^(N×D) per dataset-model-layer combination. They then estimate ID with the TwoNN estimator, chosen for its minimal assumptions (local data uniformity up to the second nearest neighbor) and its high correlation with other estimators.

For similarity, they use Information Imbalance (Δ), a directional measure of neighborhood divergence between representation spaces, where Δ(A → B) ≠ Δ(B → A). For pruning, they remove layer l's attention + MLP contribution so that residual stream representations from layer l−1 feed directly into layer l+1, then compute a pruning accuracy score: the proportion of inputs for which the pruned model predicts the same next token as the intact network. A continuous version using KL divergence is reported in the appendix.

Datasets were built with GPT-4 / ChatGPT 4 generation followed by manual editing. Coordination/subordination used 50k 4-clause sentence pairs from 17 propositional verbs, 65 pure intransitive verbs, and 74 nouns (30 proper nouns and 44 profession names), split into partitions of 10k sentences with all experiments repeated 5 times. Right-branching/center-embedding used 50K matched sentence pairs plus 100 transitive verbs, also partitioned into 10k-sentence chunks with 5 repetitions. The attachment dataset contains 10,880 triplets (32,640 sentences), split into 5 equal partitions of 2176 items each, with experiments also repeated 5 times. The paper reports means and standard errors across partitions.

Why This Matters

Impact on research. The paper turns ID into a usable instrument for asking linguistic questions, rather than only describing generic layer-wise model dynamics. It also contributes to debates about the "universality" of LLM representations, suggesting that the conjectured universality is at least partly due to similarities in how LLMs organize linguistic processing. For linguistics, ID estimation is offered as a new tool for tracking degrees of linguistic complexity, which the authors note remains an open problem in the field.

Real-world applications (the paper does not test these directly; they follow from its methods):

• Model compression and layer pruning: knowing which layers carry nested-structure processing is directly relevant to deciding which layers can be safely removed.
• Structured evaluation of LLM linguistic competence: minimal-pair complexity contrasts with ID readouts offer a way to test whether a model actually handles hierarchical structure rather than surface cues.
• Ambiguity-aware and safety-relevant deployment: the finding that ambiguous inputs produce elevated ID indicates a measurable internal signature of unresolved interpretations, useful for detecting inputs where a model's reading is unstable.
• In silico cognitive modeling: as computational models of language processing, LLMs can be probed with the same contrasts used in human experiments, complementing human sentence-processing research.

Industry relevance. The results bear on batching and compute-allocation decisions (deeper processing phases are localized in specific layer ranges), on interpretability tooling for diagnosing why a model fails on nested structures, and on the broader argument that better understanding of inner workings leads to more efficient and controllable models.

Future Directions

1. Scale and training dynamics. Due to compute restrictions the authors could not extend to larger models; they call for studying how the observed patterns depend on model size within families of related LLMs, and tracking their emergence during training using models that release intermediate checkpoints.

2. Languages and naturalistic data. The results should be reproduced in languages other than English and with more naturalistic data than the controlled minimal pairs used here.

3. More linguistic phenomena. The authors state they have only started scraping the surface of possible phenomena and want an expanded list of case studies to test whether the relation between ID increases and linguistic complexity is truly general.

4. Formal vs. functional complexity. The paper notes that subordination is a formal complexity contrast while the other two are more functional, and proposes further case studies along this divide to establish whether the differing ID signatures are a general property of formal vs. functional complexity.

5. Mechanistic explanation. Establishing a clear mechanistic account of the relation between the intrinsic dimension of representations and linguistic complexity is described as the most important aim of future work.

Target Audience

Researchers in LLM interpretability and representation analysis; computational and psycholinguists working on syntactic complexity, embedding, agreement, and relative-clause attachment; cognitive scientists evaluating LLMs as in silico models of language processing; and engineers working on model compression, layer pruning, or structured evaluation of language models who want a layer-resolved, causally probed view of where linguistic structure is handled. Readers without background in either representational geometry or psycholinguistic complexity contrasts will need to consult the paper's appendices and cited related work.

Authors’ 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.