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

Yu Sun, Mengyin Lu, Cong Feng, Guangming Lu, Huimin Han

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 subspace does not and in some cases degrades performance. This mismatch is regime-dependent: it is absent in single-sentence sentiment classification (SST-5), and a matched-cardinality control rules out attribute cardinality as a confound. The gap does not systematically increase across dialogue turns, and the task-aligned subspace remains stable over time. However, two of three models violate a pre-registered within-subspace separability invariance criterion (|Delta AUC| <= 0.03), and one model violates a pre-registered turn-invariance criterion (|Delta L| <= 0.05). These results show that cosine…