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- ColBERTKeep one vector per token, not one per document, and score by late interaction: each query token takes its best match anywhere in the document (MaxSim), summed. It recovers the term-level precision single-vector retrieval blurs away, at index-friendly speed. The math, the case where it clearly wins, and how it sits between dense and cross-encoder retrieval — with runnable code.Read →
- Sentence-BERTThe model that turned BERT into fast, comparable sentence embeddings — the ancestor of every embedding model behind vector search and RAG. Why plain BERT can’t be compared without a pass per pair, the siamese fix with mean pooling, and the O(n²)→O(n) arithmetic that took a task from 65 hours to 5 seconds. Worked math plus runnable code.Read →
- Product QuantizationThe compression that makes billion-scale vector search fit in memory. Split a vector into subvectors, quantize each with a 256-entry codebook, and store a 512-byte vector in 8 — while m small codebooks span k^m codes. The compression math, asymmetric distance lookups, and IVFPQ — worked math plus runnable code.Read →
- GraphRAGRAG for the global questions vector retrieval can't answer. GraphRAG builds a knowledge graph from the corpus, detects communities of related entities, summarizes each, and map-reduces those summaries — so "what are the main themes across everything?" gets a comprehensive answer. Why top-k retrieval under-covers global queries, and the graph pipeline — worked math plus runnable code.Read →
- Dense Passage RetrievalThe dual-encoder method that made dense retrieval beat BM25 for open-domain QA. DPR encodes questions and passages into a shared vector space and matches by dot product; its efficiency trick is in-batch negatives — a batch of B pairs yields a B×B similarity matrix whose diagonal is the positive and whose off-diagonal gives B×(B−1) negatives for free. Why matching on meaning beats keywords, and how the free-negatives trick trains it — worked math plus runnable code.Read →
- HNSWThe graph index behind fast approximate nearest-neighbor search — the default in nearly every vector database. HNSW wires points into a navigable small-world graph and searches it greedily (hop to the neighbor closest to the query), organized into a skip-list-style hierarchy of layers whose height grows like ln(N) — so search is O(log N) instead of O(N). Greedy navigation, the exponential level assignment, and why squaring the dataset only doubles the layers — worked math plus runnable code.Read →