What is the role of cosine similarity in embeddings?

Cosine similarity is a measure used to determine how similar two vectors are, based on the angle between them in a high-dimensional space. In the context of embeddings—which are numerical representations of data like text, images, or user preferences—cosine similarity helps quantify semantic or contextual similarity. For example, in natural language processing (NLP), word embeddings like Word2Vec or BERT convert words into vectors, and cosine similarity can show that “dog” and “puppy” have a high similarity score, while “dog” and “car” score lower. The key idea is that vectors pointing in roughly the same direction (small angle) are considered similar, regardless of their magnitudes. This makes it useful for comparing embeddings where the overall direction, not the length of the vector, captures meaningful relationships.

Developers often prefer cosine similarity over other metrics like Euclidean distance because it’s invariant to the scale of the vectors. This is especially important when working with embeddings, which are often normalized (scaled to unit length) during preprocessing. For example, in recommendation systems, user and item embeddings might be normalized to focus on preferences rather than interaction frequency. Cosine similarity simplifies comparisons by ignoring magnitude differences—like whether one user rated more movies than another—and focuses on the alignment of preferences. It’s computationally efficient too, as it can be calculated using a dot product followed by division by the product of vector magnitudes, which is straightforward to implement in libraries like NumPy or PyTorch.

A practical example is semantic search, where documents or sentences are encoded into embeddings, and cosine similarity retrieves the most contextually relevant results. Suppose you’re building a search engine: a query embedding is compared against document embeddings, and the top matches are those with the highest cosine scores. Similarly, in clustering tasks like grouping news articles by topic, cosine similarity helps identify articles with related content. One caveat is that cosine similarity works best when embeddings are preprocessed to ensure meaningful directional relationships. For instance, embeddings trained with contrastive loss (used in models like SBERT) explicitly optimize for this property. By focusing on angle-based similarity, developers can efficiently compare high-dimensional data in a way that aligns with how embeddings encode semantic information.