Withdrawn Paper Argues Cosine Similarity Validity Depends on Embedding Normalization
A machine learning paper argues that cosine similarity is geometrically valid when embeddings are constrained to the unit sphere, contrary to recent warnings against its use. The paper responds to prior work showing that cosine similarity can be made arbitrary through diagonal matrix transformations in unnormalized embeddings. The paper has since been withdrawn by its author and was noted as an incomplete blog post draft.
Bouhsine's paper, now withdrawn, challenged conclusions from Steck, Ekanadham, and Kallus that cautioned against using cosine similarity on learned embeddings from matrix factorization models. The prior work demonstrated that cosine similarity could be rendered arbitrary through a diagonal gauge matrix transformation. Bouhsine argued this critique conflates a problem with incompatible training objectives rather than cosine similarity itself. The paper proved that when embeddings are constrained to the unit sphere during or after training, the gauge matrix ambiguity disappears and cosine distance becomes equivalent to half the squared Euclidean distance, ensuring identical neighbor rankings. The author noted in comments that the paper was a blog post companion draft requiring updates before proper preprint submission, and subsequently withdrew it.
What's missing
The paper does not discuss practical implications for existing deployed systems using unnormalized embeddings, nor does it address computational costs of enforcing unit sphere constraints during training.
What different sources said
- arXiv cs.LGCenter
In Defense of Cosine Similarity: Normalization Eliminates the Gauge Freedom
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