@inproceedings{wannasuphoprasit-etal-2023-solving,
    title = "Solving Cosine Similarity Underestimation between High Frequency Words by $\ell_2$ Norm Discounting",
    author = "Wannasuphoprasit, Saeth  and
      Zhou, Yi  and
      Bollegala, Danushka",
    editor = "Rogers, Anna  and
      Boyd-Graber, Jordan  and
      Okazaki, Naoaki",
    booktitle = "Findings of the Association for Computational Linguistics: ACL 2023",
    month = jul,
    year = "2023",
    address = "Toronto, Canada",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2023.findings-acl.550",
    doi = "10.18653/v1/2023.findings-acl.550",
    pages = "8644--8652",
    abstract = "Cosine similarity between two words, computed using their contextualised token embeddings obtained from masked language models (MLMs) such as BERT has shown to underestimate the actual similarity between those words CITATION.This similarity underestimation problem is particularly severe for high frequent words. Although this problem has been noted in prior work, no solution has been proposed thus far. We observe that the $\ell_2$ norm of contextualised embeddings of a word correlates with its log-frequency in the pretraining corpus.Consequently, the larger $\ell_2$ norms associated with the high frequent words reduce the cosine similarity values measured between them, thus underestimating the similarity scores.To solve this issue, we propose a method to \textit{discount} the $\ell_2$ norm of a contextualised word embedding by the frequency of that word in a corpus when measuring the cosine similarities between words.We show that the so called \textit{stop} words behave differently from the rest of the words, which require special consideration during their discounting process.Experimental results on a contextualised word similarity dataset show that our proposed discounting method accurately solves the similarity underestimation problem.An anonymized version of the source code of our proposed method is submitted to the reviewing system.",
}

Cosine similarity between two words, computed using their contextualised token embeddings obtained from masked language models (MLMs) such as BERT has shown to underestimate the actual similarity between those words CITATION.This similarity underestimation problem is particularly severe for high frequent words. Although this problem has been noted in prior work, no solution has been proposed thus far. We observe that the $\ell_2$ norm of contextualised embeddings of a word correlates with its log-frequency in the pretraining corpus.Consequently, the larger $\ell_2$ norms associated with the high frequent words reduce the cosine similarity values measured between them, thus underestimating the similarity scores.To solve this issue, we propose a method to \textit{discount} the $\ell_2$ norm of a contextualised word embedding by the frequency of that word in a corpus when measuring the cosine similarities between words.We show that the so called \textit{stop} words behave differently from the rest of the words, which require special consideration during their discounting process.Experimental results on a contextualised word similarity dataset show that our proposed discounting method accurately solves the similarity underestimation problem.An anonymized version of the source code of our proposed method is submitted to the reviewing system.
Wannasuphoprasit, Saeth Zhou, Yi Bollegala, Danushka
Solving Cosine Similarity Underestimation between High Frequency Words by ℓ_2 Norm Discounting