vibed/edu/.nbd/tickets/d9f850.md

+++ title = "§4 What Is a Vector Database?" priority = 5 status = "done" ticket_type = "task" dependencies = [] +++

§4 What Is a Vector Database? — Stub to fill

File: edu/src/vector-db.md, section ### 4. What Is a Vector Database?

Replace this stub line with full content:

A vector database is a data store built around one core operation [...] 🚧 Full content tracked in [nbd:d9f850].

This is a reading lesson — no Rust code. Target 500–700 words. Bold lead phrases.

Learning objectives

• Understand the core operation: approximate nearest-neighbour (ANN) search
• Know the primary use cases that motivate vector databases
• Understand how vector databases differ from relational DBs and full-text search
• Know the key performance metrics: recall@k, QPS, index build time, memory

Content to write

The core operation. Given a query vector q and n stored vectors, find the k vectors most similar to q. Exact KNN is O(n·d) per query — at n=1M and d=768 this means 768M operations per query, too slow for interactive use. Vector databases use ANN algorithms (see §5) that trade a small accuracy loss for orders-of-magnitude speed gains.

Use cases. Each described in one concrete sentence:

• Semantic search: find documents matching the meaning of a query, not just the words
• Recommendation: given an item, return the k most similar items (§11) or surface content preferred by similar users
• Retrieval-Augmented Generation (RAG): retrieve relevant passages before prompting an LLM, so the answer is grounded in facts (§12)
• Duplicate/near-duplicate detection: find items semantically identical or very close to a given item
• Anomaly detection: items far from all stored vectors are likely anomalous
• Multi-modal search: find images matching a text description, using CLIP-style joint embeddings

vs. relational databases. SQL WHERE clauses do exact matches and range queries on scalar values. There is no built-in notion of "nearest" for float arrays. Extensions like pgvector (PostgreSQL) and sqlite-vec (SQLite / Turso) add vector search to existing databases — this course uses sqlite-vec via the libsql crate.

vs. full-text search (BM25/TF-IDF). Keyword search cannot handle synonymy (car ≠ automobile without explicit expansion) or concept-level similarity. Vector search captures both. Hybrid search — combining BM25 and ANN scores — is a common production pattern that outperforms either alone.

Key metrics.

• Recall@k: fraction of the true k nearest neighbours that the ANN algorithm returns. A recall@10 of 0.95 means 95% of correct results are found.
• QPS: queries per second the index can serve at a given recall target.
• Index build time: one-time cost paid before serving queries.
• Memory footprint: HNSW stores graph edges in RAM; this limits how large the index can grow on a single machine.

Where sqlite-vec / Turso fits. sqlite-vec is appropriate for embedded applications, local development, and small-to-medium corpora (up to a few million vectors). Dedicated cloud vector databases (Pinecone, Qdrant, Weaviate) handle larger scale and add features like multi-tenancy, filtering, and distributed search.