Problems with Cosine as a Measure of Embedding Similarity for High Frequency Words
This addresses a fundamental issue in NLP tasks like QA and IR, where cosine similarity is widely used, but the findings are incremental as they focus on a specific limitation without proposing a new method.
The paper identifies that cosine similarity systematically underestimates the similarity of high-frequency words in BERT embeddings compared to human judgments, attributing this to differences in representational geometry based on training data frequency.
Cosine similarity of contextual embeddings is used in many NLP tasks (e.g., QA, IR, MT) and metrics (e.g., BERTScore). Here, we uncover systematic ways in which word similarities estimated by cosine over BERT embeddings are understated and trace this effect to training data frequency. We find that relative to human judgements, cosine similarity underestimates the similarity of frequent words with other instances of the same word or other words across contexts, even after controlling for polysemy and other factors. We conjecture that this underestimation of similarity for high frequency words is due to differences in the representational geometry of high and low frequency words and provide a formal argument for the two-dimensional case.