Problems with Cosine as a Measure of Embedding Similarity for High Frequency Words
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.032 | 0.188 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.005 | 0.011 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.006 | 0.010 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".