AI Architecture Algorithms Embeddings Machine Learning RAG Retrieval-Augmented Generation

HNSW Vector Search Explained: The Shortcut Graph Behind Fast Retrieval

HNSW vector search is one of the quiet constraints behind a useful RAG system. A support assistant with a few hundred document chunks can compare a question with every chunk. At millions of vectors, that simple approach turns every question into a large numerical scan. Hierarchical Navigable Small World graphs, usually shortened to HNSW, offer […]

Algorithms Collatz Conjecture Dynamical Systems Mathematical Proof Mathematics Number Theory

The Collatz Conjecture: The Simple Rule No One Can Prove

Quick summary The rule: Divide even positive integers by two; multiply odd ones by three and add one. The conjecture: Repeating the rule is proposed to reach one for every positive integer. Unexpected paths: A sequence can climb sharply before falling, as the article’s example starting at 27 illustrates. Evidence is not proof: Testing many […]

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