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

TL;DR

This work investigates how the intrinsic dimension ($ID$) of LLM activations tracks linguistic complexity, contrasting formal and functional dimensions across multiple models and layers. It combines $ID$ profiling with Information Imbalance ($\Delta$) analyses and targeted ablations to locate a generic-ID peak that marks a deep linguistic processing phase, while also capturing more nuanced signals for center-embedding vs. right-branching and RC attachment. Across six LLMs, formal complexity consistently elevates $ID$ around the peak, whereas functional contrasts show distinct, often earlier or later signatures, with ablations confirming a causal role for layers near the peak. The findings suggest that $ID$-based probes reveal universal processing stages in LLMs and offer a principled tool for comparing linguistic processing across architectures and languages, with implications for cognitive-linguistic theory and model interpretability.

Abstract

We explore the intrinsic dimension (ID) of LLM representations as a marker of linguistic complexity, asking if different ID profiles across LLM layers differentially characterize formal and functional complexity. We find the formal contrast between sentences with multiple coordinated or subordinated clauses to be reflected in ID differences whose onset aligns with a phase of more abstract linguistic processing independently identified in earlier work. The functional contrasts between sentences characterized by right branching vs. center embedding or unambiguous vs. ambiguous relative clause attachment are also picked up by ID, but in a less marked way, and they do not correlate with the same processing phase. Further experiments using representational similarity and layer ablation confirm the same trends. We conclude that ID is a useful marker of linguistic complexity in LLMs, that it allows to differentiate between different types of complexity, and that it points to similar stages of linguistic processing across disparate LLMs.

Figures (12)

• Figure 1: ID profiles through LLM layers (means and error bars across 5 partitions). Vertical dashed line marks maximum ID on generic sequences, and shaded area the corresponding span, estimated as explained in App. \ref{['app:id_peak']}.
• Figure 2: Information Imbalance $\Delta$ between coordinated/subordinated sentences (top) and right-branching/center-embedding sentences (bottom): means across 5 partitions with error bars (often invisible). Shaded area marks generic ID-peak span, with a vertical dashed line at the generic-ID maximum. Higher $\Delta$ means lower similarity.
• Figure 3: Ablation accuracy (proportion of cases in which ablating a layer did not change next-token prediction) of coordinated/subordinated sentences. Means and (invisible) standard error bars over 5 partitions.
• Figure 4: ID values across layers and estimated peak spans for all LLMs given an input of naturalistic corpus sequences. Mean values with (invisible) error bars.
• Figure 5: Accuracies in three probing tasks (bigram shift, coordination inversion and odd man out) across layers, for all models. Means and standard errors across five seeds.