Embeddings & Vector Search by Hand: Cosine Similarity, Top-k Retrieval & Recall

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Treat six help-centre articles of Fernwick Outdoor, a fictional outdoor-gear shop, as tiny 5-dimensional embeddings: you measure each vector's length, normalise it to length 1 and compare the L1 norm.
• Score the six help articles against a customer question with the dot product and with cosine similarity, and see why a long article wins on dot product but not on cosine.
• Rank ten help articles by cosine similarity to a customer question, pull out the top 3 scores and titles like a vector database does, and count how many pass a similarity cut-off.
• Measure the straight-line distance between each article and the query, rank by it, and see why a short FAQ that points exactly the right way is cosine's #1 but only Euclidean's #3, until you normalise.
• Split Fernwick Outdoor's help centre into overlapping chunks: tokens per article, chunks per article with ROUNDUP, the tokens you actually send to the embedding model and the one-off cost.
• Compare an approximate nearest-neighbour (ANN) index with exact search for six test queries, compute recall@5 per query and on average, then pick the fastest index setting that reaches a 95% recall target.
• Combine a keyword score and a vector score for eight articles: min-max normalise the keyword score, blend both with a weight α, rank the results and return the winner.
• Evaluate the retriever of a help-centre assistant on 12 test questions with a known gold chunk: reciprocal ranks, MRR and hit rate at k = 1, 3, 5 and 10 for vector-only vs hybrid retrieval, then chart the hit-rate curves.