What counts as a large cosine similarity?

Machine learning represents words as vectors and measures the similarity of words by the angles between the vectors. For vectors x and y, where θ is the angle between the vectors, and so This is the cosine similarity between the words represented by x and y. Small angles have large cosines, and so words with larger cosine similarities are closer together than words with smaller cosine similarities. The cosine similarity between a word and itself equals 1, and we’d expect unrelated words to have a cosine similarity near 0. You can do a sort of arithmetic with vector embeddings of words. The canonical example is that “king” − “man” + “woman” ≈ “queen” Implicit in this equation is that we’re really adding vector representations of the words. Let a, b, c, and d be the vector embeddings of the words king, man, woman, and queen. What we’re really asserting is that a − b + c ≈ d, except that’s not true! Or at least it’s not true unless you view it in the right context. The angle between a −…