Vector Similarity Search: Metrics & Approximate Methods › Vector Similarity Search with ANN and FAISS

In the previous chapter, we explored how embedding models transform text into dense vectors that capture semantic meaning. In the chapter on dense retrieval, we saw how these embeddings power modern search by finding documents whose vectors are "close" to a query vector. However, we need to define what "close" means and how to find the closest vectors efficiently in large collections.

This is the problem of vector similarity search. At small scales, it is trivially solved: compare the query to every vector in your collection and return the best matches. For large-scale RAG systems, this brute-force approach is often too slow. A collection of 10 million documents with 768-dimensional embeddings requires roughly 7.7 billion floating-point operations per query, just for a single distance metric. Handling thousands of concurrent users requires a more efficient approach.

This chapter lays the groundwork for efficient vector search. We start by examining the distance metrics that define what similarity means in vector space, going deep into the geometry and practical implications of each. Then we contrast exact search (which guarantees finding the true nearest neighbors) with approximate search (which trades a small amount of accuracy for dramatic speed improvements). We survey the families of algorithms that make approximate search possible and walk through practical code for each. Finally, we examine the libraries that implement these ideas and the practical limitations you will encounter in production systems. The specific index structures that make approximate search possible, including HNSW and IVF, receive dedicated chapters that follow.