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When Cosine Similarity Fails to Reflect Linearly Accessible Structure in Dialogue Models

arXiv · AI, language, vision and robotics · article · Sep 18, 2026 · UTC

Cosine similarity is widely used to analyze transformer representations, implicitly assuming that similarity reflects task-relevant structure. We study when this assumption fails in dialogue-conditioned large language models. Across three 7-8B chat-tuned models, ambient cosine similarity substantially underestimates linearly decodable persona structure on the same hidden states; numerically, linear probe AUC is in the 0.73-0.97 range while cosine kNN is in the 0.56-0.77 range on a 30-class task. A low-dimensional supervised subspace recovers much of this gap, whereas a matched-rank PCA subspac

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