Gamma Mixture Modeling for Cosine Similarity in Small Language Models

Kevin Player

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arXiv · 2510.05309

Gamma Mixture Modeling for Cosine Similarity in Small Language Models

Kevin Player

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Abstract

We study the cosine similarity of sentence transformer embeddings and observe that they are well modeled by gamma mixtures. From a fixed corpus, we measure similarities between all document embeddings and a reference query embedding. Empirically we find that these distributions are often well captured by a gamma distribution shifted and truncated to [-1,1], and in many cases, by a gamma mixture. We propose a heuristic model in which a hierarchical clustering of topics naturally leads to a gamma-mixture structure in the similarity scores. Finally, we outline an expectation-maximization algorithm for fitting shifted gamma mixtures, which provides a practical tool for modeling similarity distributions.

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Kevin Player. 2025-10-06. Gamma Mixture Modeling for Cosine Similarity in Small Language Models. https://arxiv.org/abs/2510.05309

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