In a notebook, implement embedding retrieval with cosine similarity. How does cosine relate to the dot product, and when would you choose each?

import numpy as np

def top_k_cosine(q, docs, k=5, eps=1e-12):
    n = np.linalg.norm(docs, axis=1, keepdims=True)
    d = docs / np.maximum(n, eps)
    qn = q / max(np.linalg.norm(q), eps)
    scores = d @ qn
    idx = np.argsort(-scores)[:k]
    return idx, scores[idx]

Cosine is the dot product of unit-length vectors, so normalise once at indexing and any dot-product index ranks by cosine. Raw dot product also rewards vector length. Follow how the embedding model was trained: cosine for most sentence-embedding models, dot product when the model puts meaningful signal, such as popularity, in the norm. Guard against zero vectors.