Categorical Perception in Large Language Model Hidden States: Structural Warping at Digit-Count Boundaries

TL;DR

This study reveals that large language models exhibit geometric warping in their hidden states at digit-count boundaries, akin to perceptual categorical perception, driven by structural input discontinuities.

Contribution

It demonstrates that structural input-format discontinuities alone can induce categorical perception geometry in LLMs, independent of semantic category knowledge.

Findings

Representational geometry fits a CP-additive model better than a continuous model.

The effect is specific to digit-count boundaries and absent at control positions.

Different models show either explicit categorization or mere geometric warping at boundaries.

Abstract

Categorical perception (CP) -- enhanced discriminability at category boundaries -- is among the most studied phenomena in perceptual psychology. This paper reports that analogous geometric warping occurs in the hidden-state representations of large language models (LLMs) processing Arabic numerals. Using representational similarity analysis across six models from five architecture families, the study finds that a CP-additive model (log-distance plus a boundary boost) fits the representational geometry better than a purely continuous model at 100% of primary layers in every model tested. The effect is specific to structurally defined boundaries (digit-count transitions at 10 and 100), absent at non-boundary control positions, and absent in the temperature domain where linguistic categories (hot/cold) lack a tokenisation discontinuity. Two qualitatively distinct signatures emerge: "classic CP" (Gemma, Qwen), where models both categorise explicitly and show geometric warping, and "structural CP" (Llama, Mistral, Phi), where geometry warps at the boundary but models cannot report the category distinction. This dissociation is stable across boundaries and is a property of the architecture, not the stimulus. Structural input-format discontinuities are sufficient to produce categorical perception geometry in LLMs, independently of explicit semantic category knowledge.