Part I — Foundations of similarity search

Part I builds the shared foundation for the rest of the site: why brute-force neighbor search fails at scale, how distance and similarity are defined, and why high-dimensional geometry reshapes the problem HNSW solves.
Created: Updated: 2 min read

These are the topics in this section, each on its own page with a stable path you can bookmark or share.

What topics are covered in this section?

Part I builds the shared foundation for everything else on this site: why brute-force neighbor search fails at scale, how distance and similarity are defined, why high-dimensional geometry breaks classical trees, and which algorithms and systems ideas every HNSW stack assumes.

What will you understand when Part I is done?

You will be able to explain the cost model of comparing a query to every vector, choose and critique distance measures, recognize curse-of-dimensionality symptoms, and name the algorithmic primitives – heaps, graphs, approximation – that later Parts assemble into HNSW. Without this base, parameter talk in Part VI and proof talk in Part III float free of meaning.

The four chapters are meant to be read in order, but each stands alone if you arrive from search.

How do the chapters connect?

The opening chapter motivates approximation. The distance chapter fixes how “near” is scored. The geometry chapter explains why space-partition indexes struggle on embeddings. The prerequisites chapter inventories concepts the rest of the curriculum relies on. Glossary hubs on vectors, geometry, and ANN fundamentals deepen any term that feels thin.

Weaviate examples later in the site assume you share this vocabulary.

What should you do next?

Start with “Why can’t nearest-neighbor search just compare a query against every vector?”, then proceed through distance, geometry, and prerequisites. Keep the vector-and-distance-math glossary open in another tab while you read.

Part I is the on-ramp to hierarchical navigable small worlds. Next, open the first chapter above, then continue to Part II when you are ready for proximity graphs and the jump to hierarchy.