Similarity Search: Finding Relevant Documents

Now that you understand embeddings and how vector spaces work, let's learn how to find similar documents efficiently.

This section covers:

1. Distance metrics — Different ways to measure "similarity" between embeddings
2. Exact vs Approximate search — Brute force vs fast algorithms
3. Vector databases — Systems optimized for embedding search
4. Trade-offs — Speed vs recall, storage vs quality

The Core Problem

Given: - A query embedding (from user question) - Millions of document embeddings (in a database)

Find: - The K most similar document embeddings (top-K nearest neighbors)

In real-time (< 100ms ideally).

Topics

• Distance Metrics — Cosine, Euclidean, Dot Product (with full derivations)
• Exact vs Approximate Search — Brute force vs HNSW vs IVF algorithms
• Vector Databases — Chroma, Pinecone, Weaviate, FAISS comparisons

Why This Matters for RAG

• Fast retrieval = responsive user experience
• Better indexing = better recall (fewer relevant docs missed)
• Different metrics = different results (cosine vs Euclidean behave differently in your data)

Key Insight

For most RAG systems, cosine similarity with HNSW indexing is the right choice. It's fast, accurate, and well-understood.

Reading Order

1. Start here (done!)
2. Distance Metrics — Understand the math
3. Exact vs Approximate Search — Learn how to search efficiently
4. Vector Databases — See production systems

Then move to Retrieval Methods to learn about hybrid search.