LLM hidden states warp categorically at digit-count boundaries
measured in 1 paper- In six LLMs, hidden-state distances warp categorically at digit-count boundaries (9->10, 99->100) versus matched non-boundary controls (15, 150); an RSA "CP-Additive" model (log-distance plus a boundary boost) beats a continuous model at 100% of primary layers. [cacioli-2026-categorical-perception-digit-boundaries] - Boundary crossing explains 5-27% of representational-distance variance beyond magnitude; the decade-100 effect is 3.9-12.7x the decade-10 effect, with a manifold rotation of 81.6-89.6 degrees at the boundary. [cacioli-2026-categorical-perception-digit-boundaries] - Patching along a ridge-regression "category direction" shifts discrimination confidence 70.1x more than random directions (Layer 5), dose-dependent and specific. [cacioli-2026-categorical-perception-digit-boundaries] - Five instruct models (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Gemma-2-9B-IT, Qwen2.5-7B-Instruct, Phi-3.5-mini-instruct) plus a Llama-3-8B base control; causal patching run on Llama-3-8B-Instruct only. [cacioli-2026-categorical-perception-digit-boundaries]