How are embeddings indexed for efficient retrieval?

Embeddings are indexed for efficient retrieval using specialized data structures and algorithms designed to handle high-dimensional vector similarity searches. The core challenge is quickly finding the closest vectors (nearest neighbors) in a space with hundreds or thousands of dimensions, where traditional indexing methods like B-trees become impractical. To address this, approximate nearest neighbor (ANN) algorithms are used, which prioritize speed over perfect accuracy. Common approaches include tree-based methods (e.g., Annoy), graph-based techniques (e.g., HNSW), and quantization-based methods (e.g., FAISS). These systems preprocess embeddings into optimized structures that allow rapid similarity comparisons during queries.

One widely used technique is vector quantization, which reduces storage and search complexity by grouping similar vectors into clusters. For example, FAISS employs product quantization to split high-dimensional vectors into smaller subvectors, each assigned to a centroid in a codebook. During a search, distances are computed using precomputed lookup tables, drastically speeding up comparisons. Another approach is hierarchical navigable small world (HNSW) graphs, which organize vectors into layers of interconnected nodes. Queries traverse the graph from coarse to fine layers, efficiently narrowing down candidates. Tree-based methods like Annoy partition the space recursively using random projections, creating binary trees that allow fast traversal by eliminating large portions of the dataset early in the search.

Developers implementing these systems must balance trade-offs between speed, accuracy, and memory usage. For example, FAISS offers GPU acceleration for large-scale datasets but requires careful tuning of parameters like the number of clusters. Annoy is lightweight and easy to deploy but may require building multiple trees for higher accuracy. Practical considerations include choosing an indexing method that aligns with dataset size (e.g., HNSW for billion-scale datasets) and supporting real-time updates (e.g., using incremental indexing strategies). Tools like Milvus or Elasticsearch’s dense vector indexing integrate these algorithms, providing abstractions for developers while allowing customization for specific latency or recall requirements.