Linear relational embeddings are faithful and causal for half of relations

measured in 1 paper

Hernandez et al. approximate a transformer's relation-decoding function by a first-order Taylor expansion LRE(s)=beta*W_r*s+b_r, with W_r the mean Jacobian estimated from 5-8 examples [hernandez-etal-2023-lre] It is validated by faithfulness (decoded top token matches the model's own) and causality (low-rank pseudoinverse inversion redirects the real output) [hernandez-etal-2023-lre] Across 47 relations on GPT-J, GPT-2-XL, and LLaMA-13B, faithfulness exceeds 60% for nearly half the relations, with strong faithfulness-causality correlation (R=0.84 on GPT-J) [hernandez-etal-2023-lre] Relations like "company CEO" (0.06/0.31) fail almost completely despite correct model behavior, so linear relation decoding is real but heterogeneous across relation types [hernandez-etal-2023-lre]

Structure

Linear Direction

Context

first-order Taylor/Jacobian approximation of a relation-decoding function, faithfulness (predictive match) vs. causality (inversion-edit success) as dual validation, heterogeneous linearity across relation types (near-perfect for some, near-zero for others despite correct model behavior), low-rank pseudoinverse needed to invert an ill-conditioned Jacobian

Confirmed in models

GPT-J-6B · GPT-J, GPT-2 XL · GPT-2, LLaMA-13B · Llama

Method

Linear Relational Embedding (LRE)

Papers

Linearity of Relation Decoding in Transformer Language Models — Hernandez, Evan, Sharma, Arnab Sen, Haklay, Tal, Meng, Kevin, Wattenberg, Martin, Andreas, Jacob, Belinkov, Yonatan, Bau, David2023 · arXiv:2308.09124