Approximate nearest neighbor (ANN) methods like Faiss with HNSW or IVF indices accelerate similarity searches by reducing the number of comparisons needed to find matches, while maintaining acceptable accuracy. These methods avoid exhaustively comparing a query embedding against every item in the dataset, which is computationally expensive for large datasets. Instead, they use precomputed structures to narrow the search space. For example, HNSW builds a hierarchical graph where nodes represent embeddings, and searches traverse this graph in a way that prioritizes promising regions. IVF divides the dataset into clusters (e.g., using k-means) and limits searches to the most relevant clusters for a query. By focusing on subsets of data rather than the entire dataset, these methods drastically reduce computation time while still identifying neighbors that are "close enough" for practical use.
The trade-off between speed and accuracy is managed through tunable parameters. For HNSW, parameters like the number of connections per node or the search depth control how thoroughly the graph is explored. In IVF, the number of clusters and the number of clusters probed per query (e.g., probing 10 out of 100 clusters) determine the balance. These parameters allow developers to prioritize speed or precision based on their needs. Since Sentence Transformer embeddings often encode semantic relationships in a dense vector space, the underlying structure tends to be smooth, meaning nearby points in the embedding space are semantically similar. This allows ANN methods to approximate exact results effectively—even with aggressive parameter settings, the most relevant neighbors often remain in the reduced search space.
For example, in a dataset of 1 million embeddings, a brute-force search would require 1 million comparisons. With IVF-100 (100 clusters), probing the 5 nearest clusters might reduce comparisons to 5,000–10,000 (0.5–1% of the original workload) while retaining 95%+ accuracy. HNSW’s layered graph traversal can achieve sublinear search times, scaling logarithmically with dataset size. Faiss further optimizes performance using SIMD instructions or GPU acceleration. In practice, applications like recommendation systems or semantic search tolerate minor accuracy losses (e.g., missing the 5th-nearest neighbor) if results are returned in milliseconds instead of seconds. Proper tuning, combined with the inherent structure of Sentence Transformer embeddings, ensures ANN methods deliver usable results without significant quality degradation.