Searching by meaning: vector databases and retrieval

An accessible university-level course on semantic search. We start from the limit of keyword search, which ignores meaning, and rebuild search by meaning: represent a text as a vector, measure proximity, index millions of vectors without comparing them all, make the index durable, marry it with the lexical world, and finally feed a language model. From the geometry of embeddings to RAG.

1. 00
   Foreword

   Why search by meaning, what this course covers, and how to read it.
   8 min
2. 01
   Embeddings and the geometry of similarity

   Meaning as a position in space, and three ways to measure how close two meanings are.
   26 min
3. 02
   Exact search and the curse of dimensionality

   Comparing every vector gives the perfect answer. Here is its price, and the trap that high dimension sets for our intuition.
   28 min
4. 03
   HNSW: navigating a proximity graph

   What if finding the nearest neighbor became a short stroll of a few hops, instead of a scan across millions of vectors?
   30 min
5. 04
   The landscape of ANN indexes

   Four index families, three riches you can never keep all at once: how to choose between recall, speed and memory?
   28 min
6. 05
   Testing the approximate: the differential oracle

   An index can pass every test, two reviews, and still return bad results. How do you catch an algorithm that lies?
   26 min
7. 06
   Making the index durable

   An index living in RAM vanishes on restart. How do you write it to disk once and for all, without ever corrupting it, even if power cuts out mid-insertion?
   30 min
8. 07
   The lexical side: BM25 and hybrid search

   Semantic search, brilliant on paraphrases, misses an exact invoice number. How do you marry vectors to the world of exact words, without one score scale crushing the other?
   32 min
9. 08
   From retrieval to RAG

   We can retrieve the right passages, by meaning, by the letter, by their fusion. But retrieving is not answering. How do we wire our engine to a language model so it composes a grounded answer, without making things up?
   40 min