Crabhaus

What it is

An embedding is a vector, a list of numbers, that a model assigns to text or an image so that items with similar meaning sit close together in a high-dimensional space. Vector similarity measures that closeness, usually with cosine similarity, which compares the angle between two vectors rather than their length.

How it works

A trained encoder turns each input into a fixed-length vector. Training pushes related inputs together and unrelated ones apart, so direction encodes meaning. To compare two items you take their dot product and divide by their magnitudes, giving a score from -1 to 1. Search systems precompute vectors, store them in an index, embed the query, and return the nearest ones.

A concrete example

Ask 'how do I cancel my plan?' and a retrieval app can surface a doc titled 'ending your subscription', because the phrases land near each other in embedding space even though they share no keywords. A plain keyword search would miss it.

Why it matters

Embeddings are the retrieval layer under RAG, semantic search, clustering, recommendation, and agent memory. The embedding model and metric often move answer quality more than the generation model does. Nvidia's Nemotron 3 Embed topping the RTEB benchmark shows embedding quality is now its own race.