Solving Cosine Similarity Underestimation between High Frequency Words
  by L2 Norm Discounting
Saeth Wannasuphoprasit Yi Zhou Danushka Bollegala
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 (Zhou et al.,
2022). This similarity underestimation problem is particularly severe for
highly frequent words. Although this problem has been noted in prior work, no
solution has been proposed thus far. We observe that the L2 norm of
contextualised embeddings of a word correlates with its log-frequency in the
pretraining corpus. Consequently, the larger L2 norms associated with the
highly frequent words reduce the cosine similarity values measured between
them, thus underestimating the similarity scores. To solve this issue, we
propose a method to discount the L2 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 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.