Glossary

Negative examples that are challenging because they look similar to the positive but are actually irrelevant. A passage that shares many keywords with a query but doesn't answer it is a hard negative. Training with hard negatives forces the model to learn deeper semantic distinctions rather than relying on surface-level word overlap.

A mathematical space with many dimensions — often hundreds or thousands. Humans can visualize two or three dimensions; embedding models work in spaces with far more. Many geometric intuitions break down in high-dimensional spaces, but the core idea holds: points that are close together are similar, points that are far apart are different.

A mathematical object represented as an ordered list of many numerical values (called components or coordinates) — ranging from dozens to millions — that represents a specific point within a high-dimensional space. The two are inseparable: the vector is the concrete "resident," while the space is the abstract "container" that defines the rules for distances, angles, and relationships. A vector with 1,000 components lives in a 1,000-dimensional space, with each combination of values mapping to a unique point. In machine learning, high-dimensional vectors encode complex objects such as words or images, with relationships between objects reflected in geometric relationships between their vectors.

One of the most popular algorithms for approximate nearest neighbor search. HNSW builds a multi-layered graph where each layer connects vectors to their neighbors, enabling fast navigation to the nearest vectors from any starting point. It offers a strong balance of speed and accuracy.

A search approach that combines semantic search (using embeddings) with lexical search (using keyword matching, typically BM25). By blending both signals, hybrid search captures the strengths of each: the meaning-awareness of embeddings and the precision of keyword matching.