What are the tradeoffs between HNSW and IVF indexes for approximate nearest neighbor search?

HNSW (Hierarchical Navigable Small World) builds a multi-layer graph and traverses greedily from coarse to fine layers. It gives excellent recall/latency and needs no training, but uses more memory (stores graph edges) and is costlier to build; key params are M (edges per node) and efConstruction/efSearch. IVF (Inverted File) clusters vectors with k-means into nprobe-searchable partitions; you search only the closest lists. IVF trains faster to query, uses less memory, and scales to huge datasets, especially combined with product quantization (IVF-PQ) to compress vectors, but recall depends heavily on nlist/nprobe tuning and it requires a training step on representative data. Rule of thumb: HNSW for high recall at moderate scale in RAM; IVF-PQ for billion-scale or memory-constrained deployments where some recall loss is acceptable.