Beyond Cosine Similarity
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914306829844480 |
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| author | Ai, Xinbo |
| author_facet | Ai, Xinbo |
| contents | Cosine similarity, the standard metric for measuring semantic similarity in vector spaces, is mathematically grounded in the Cauchy-Schwarz inequality, which inherently limits it to capturing linear relationships--a constraint that fails to model the complex, nonlinear structures of real-world semantic spaces. We advance this theoretical underpinning by deriving a tighter upper bound for the dot product than the classical Cauchy-Schwarz bound. This new bound leads directly to recos, a similarity metric that normalizes the dot product by the sorted vector components. recos relaxes the condition for perfect similarity from strict linear dependence to ordinal concordance, thereby capturing a broader class of relationships. Extensive experiments across 11 embedding models--spanning static, contextualized, and universal types--demonstrate that recos consistently outperforms traditional cosine similarity, achieving higher correlation with human judgments on standard Semantic Textual Similarity (STS) benchmarks. Our work establishes recos as a mathematically principled and empirically superior alternative, offering enhanced accuracy for semantic analysis in complex embedding spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05266 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond Cosine Similarity Ai, Xinbo Artificial Intelligence 68T50 I.2.7 Cosine similarity, the standard metric for measuring semantic similarity in vector spaces, is mathematically grounded in the Cauchy-Schwarz inequality, which inherently limits it to capturing linear relationships--a constraint that fails to model the complex, nonlinear structures of real-world semantic spaces. We advance this theoretical underpinning by deriving a tighter upper bound for the dot product than the classical Cauchy-Schwarz bound. This new bound leads directly to recos, a similarity metric that normalizes the dot product by the sorted vector components. recos relaxes the condition for perfect similarity from strict linear dependence to ordinal concordance, thereby capturing a broader class of relationships. Extensive experiments across 11 embedding models--spanning static, contextualized, and universal types--demonstrate that recos consistently outperforms traditional cosine similarity, achieving higher correlation with human judgments on standard Semantic Textual Similarity (STS) benchmarks. Our work establishes recos as a mathematically principled and empirically superior alternative, offering enhanced accuracy for semantic analysis in complex embedding spaces. |
| title | Beyond Cosine Similarity |
| topic | Artificial Intelligence 68T50 I.2.7 |
| url | https://arxiv.org/abs/2602.05266 |