Token-embedding orientation is shared within families but drops across them

measured in 1 paper

Lee et al. measure token-embedding geometry across the GPT-2, Llama-3, and Gemma-2 model families [lee-etal-2025-shared-global-and-local-geometry-of-language-model-embeddings] Relative orientation/cosine structure is near-identical within a model family but drops sharply across families trained on different data [lee-etal-2025-shared-global-and-local-geometry-of-language-model-embeddings] A k-NN-neighborhood PCA intrinsic-dimension estimator finds low-ID tokens form semantically coherent clusters while high-ID tokens do not [lee-etal-2025-shared-global-and-local-geometry-of-language-model-embeddings] EMB2EMB, a linear least-squares (OLS) map fit over 100k shared tokens, transfers CAA-style steering vectors (refusal, sycophancy, corrigibility) between differently-sized models [lee-etal-2025-shared-global-and-local-geometry-of-language-model-embeddings]

Structure

Intrinsic-dimension profile across depth, Linear Direction

Context

within-family vs. cross-family dissociation in token-embedding orientation similarity, sharpening the platonic-representation convergence claim with a negative cross-family control, local intrinsic dimension of individual tokens predicting semantic cluster coherence, a fitted linear map transferring extracted steering directions between differently-sized/architected models

Confirmed in models

GPT-2-Medium · GPT, Llama-3.1-8B-Instruct · Llama, Gemma-2-9B-it · Gemma

Method

PCA, Intrinsic dimension estimation (TwoNN), Cross-model direction transfer via ridge regression

Papers

Shared Global and Local Geometry of Language Model Embeddings — Lee, Andrew, Weber, Melanie, Viégas, Fernanda, Wattenberg, Martin2025 · arXiv:2503.21073