Vector Search easy
Your embedding model outputs unnormalized vectors whose magnitudes vary widely. A teammate wants to switch the index from cosine similarity to dot product because it is cheaper to compute. What is the consequence?
- A No change in ranking, since cosine similarity and dot product always produce identical orderings.
- B Ranking improves automatically, since dot product ignores vector magnitude entirely in scoring.
- C Queries fail at runtime, since vector indexes reject dot product on vectors that are unnormalized.
- D Ranking changes, since dot product favors large-magnitude vectors that cosine normalizes away.
Answer: D. Ranking changes, since dot product favors large-magnitude vectors that cosine normalizes away.
Cosine and dot product give the same ranking **only for normalized vectors**. Without normalization, dot product boosts high-magnitude vectors regardless of direction. The safe way to get the speed of dot product is to normalize vectors at ingest and at query time, and then the two metrics are equivalent.
One system design question a day, with spaced repetition so the ones you miss come back.
Get the appRelated questions
- You are building an IVF index on 20 million vectors. A teammate asks why the build needs a 'training' step before any vectors can be added. What is the reason?
- An HNSW index serves a marketplace where about 30% of listings are updated or removed each week. Each update is applied as a delete plus an insert, and deletes mark tombstones. Over a month, recall@10 drifts from 97% to 89% and p99 latency rises at the same ef_search. What is happening, and what should you do?
- Users delete documents in your primary database, but the deleted documents keep appearing in vector search results for hours. The vector index is rebuilt nightly. What is the best fix?
- You are setting an SLO for a new ANN-backed recommendation search over 50 million vectors. A product manager asks for 100% recall@10 with single-digit millisecond latency. What is a realistic response?
- A B2B SaaS app serves 500 customers, and every query searches only one customer's documents. One large customer runs heavy batch queries that slow down search for everyone. Which sharding approach fits best?
- Your HNSW index (M=16) reaches recall@10 of 91% at ef_search=64 with a p99 of 6 ms. The target is 97% recall within a 15 ms p99. A full rebuild takes 14 hours. What is the right tuning order?