Similarity

📘What it really is

• To compare two embeddings, measure how close the vectors are. The most common measure is cosine similarity: how closely two vectors point in the same direction.
• near 1: very similar meaning;
• near 0: unrelated;

• (negative values are possible but less common with text embeddings).

• In TypeScript:

function cosineSimilarity(a: number[], b: number[]): number {
  let dot = 0, normA = 0, normB = 0;
  for (let i = 0; i < a.length; i++) {
    dot += a[i] * b[i];
    normA += a[i] * a[i];
    normB += b[i] * b[i];
  }
  return dot / (Math.sqrt(normA) * Math.sqrt(normB));
}

• Many embedding models return normalised vectors (length 1), in which case cosine similarity equals the simple dot product, which is faster.

• Similarity isn't truth: close vectors mean "about the same topic", not "answers the question correctly". A passage saying "returns are not accepted on tailored items" is close to a question about returning tailored items, which is good (it's relevant), but the model must read it carefully.

• Scores depend on the model; there's no universal "good" threshold. Find a sensible cut-off by testing (Lesson 5).