Cosine Similarity

Imagine a map where words with similar meanings sit close together. 'King' and 'queen' are near neighbors, while 'bread' sits in a different part of the map. Each word's spot on that map is called its embedding: a list of numbers that stands in for its meaning. Cosine similarity is a score for how close two spots are. But instead of measuring straight-line distance, it compares the angle between them, seen from the map's center. The score always lands between -1 and 1. A score of 1.00 means the two point in the exact same direction, so they are very similar. A score of 0.00 means they are unrelated. A negative score means they point in close to opposite directions.

1. 1Take the dot product of the two vectors. Multiply the matching positions together, then add up the results.
2. 2Compute each vector's magnitude, or length. Square every number in it, add the squares together, then take the square root.
3. 3Divide the dot product by the product of the two magnitudes. The result is always between -1 and 1. A bigger number means the two are more similar.

Use this when comparing embeddings, which are number representations of meaning. It helps you find similar words, similar documents, or which stored chunk of text best matches a search query.

• ⚠Don't compare raw dot products without dividing by the magnitudes. That unfairly favors longer vectors over vectors that are genuinely more similar.
• ⚠Don't compare vectors with different lengths, or dimensions. They must come from the same embedding space, or the comparison means nothing.