An embedding is a numeric vector that represents the meaning or features of an item. Texts with similar meanings tend to receive nearby vectors, even when they use different words.

For search, the system embeds documents once and stores their vectors. It embeds each query with the same model, compares the query vector with stored vectors, and returns the nearest results. This supports matches such as “close my account” with “cancel a subscription.”

Embeddings are useful for semantic search, recommendations, clustering, and retrieval for language models. They are not perfect relevance labels. Quality also depends on chunking, metadata, index settings, and evaluation on real queries.

Semantic search compares learned vector representations, so it can match related meanings across different wording. BM25 (Best Matching 25) uses exact terms, term frequency, document length, and word rarity to rank documents.

Embedding search is strong for natural-language questions, synonyms, and paraphrases. BM25 is strong for names, codes, error strings, numbers, and rare terms. Dense search may return a conceptually related but wrong item, while keyword search may miss a good paraphrase.

Many production systems use both. They retrieve candidates from each method, combine the rankings, and optionally rerank them with a stronger model. Evaluate all variants carefully on the same relevance dataset.

Cosine similarity compares vector direction and ignores length. Dot product rewards both alignment and magnitude. Euclidean distance measures straight-line distance between points, with smaller values indicating a closer match.

When every vector has unit length, cosine similarity equals dot product. Euclidean distance is then a monotonic transformation of the same value, so all three produce the same ranking. Without normalization, their rankings can differ.

Choose the metric used during model training or recommended by its documentation. Normalize consistently at ingestion and query time when required. Test the full retrieval system because changing a database metric without rechecking model assumptions can quietly lower recall.

A vector database stores vectors and searches for nearby items efficiently. It also manages metadata filters, updates, deletion, replication, and approximate nearest neighbor indexes.

A relational database can store vectors, and extensions such as pgvector add strong similarity search. Plain SQL without a vector index usually compares every row, which becomes slow at large scale. The issue is specialized indexing, not that relational databases are unable to hold arrays.

Use a relational database with vector support when data, transactions, and operational simplicity fit one system. Use a dedicated vector engine when scale, latency, filtering, distributed indexing, or vector-specific operations exceed what the existing database handles well.

Dimensionality is the number of numeric values in an embedding vector. A 768-dimensional embedding contains 768 values. The dimensions are learned features, not usually human-readable categories.

More dimensions can represent finer distinctions, but they increase storage, memory bandwidth, network transfer, and distance-computation cost. Higher dimension does not automatically mean better retrieval because model training quality matters more.

Some models support shortened vectors trained to retain useful information. Compare available dimensions on your relevance set. Estimate index and replica memory before choosing. Use the smallest dimension that meets quality goals, and never compare vectors created with different dimensions or incompatible models.

k-nearest-neighbor search returns the k stored vectors closest to a query under a chosen distance metric. Exact search compares the query with every eligible vector and guarantees the true nearest results.

Approximate nearest neighbor (ANN) search uses an index to examine only promising parts of the collection. It can be much faster and use less computation, but may miss some true neighbors.

Use exact search for small datasets, offline evaluation, or filtered sets that are already tiny. Use ANN for large, interactive systems. Tune it by measuring recall against exact results together with latency and memory. The best k for retrieval is separate from the number of index candidates examined.

Cosine similarity measures the angle between two vectors. It divides their dot product by the product of their lengths, producing a high score when the vectors point in similar directions.

It is common because direction often captures semantic information while vector magnitude may be unrelated to relevance. If all vectors are normalized to length one, cosine similarity and dot product produce the same ranking and can be computed efficiently.

Use the metric recommended for the embedding model. Some models are trained for dot product or Euclidean distance, and changing the metric can hurt quality. A high cosine score is not a universal proof of relevance, so select thresholds with labeled data.