LRE affine-map linearity scores correlate with hallucination rate across four real instruction-tuned LLMs

Lu, Liu, Gerstner, Hirlimann, Rohweder & Schütze (2026) fit relation-specific affine maps o = W_r s + b_r via ridge regression (the Linear Relational Embeddings framework) across Gemma-7B-IT, Llama-3.1-8B-Instruct, Mistral-7B-Instruct-v0.3, and Qwen2.5-7B-Instruct [lu-etal-2026-relational-linearity-is-a-predictor-of-hallucinations] The resulting linearity score correlates with hallucination-vs-refusal rate on unknown entities at Pearson r=0.741-0.816 across 15 natural LRE relations, and r=0.573-0.812 on a new SyntHal synthetic-unknown-entity benchmark [lu-etal-2026-relational-linearity-is-a-predictor-of-hallucinations] Purely correlational -- the authors explicitly flag that establishing causality would require representation patching or steering, not yet performed [lu-etal-2026-relational-linearity-is-a-predictor-of-hallucinations]