What are the performance implications of increasing the number of centroids (clusters) in an IVF index on search speed and recall?

Increasing the number of centroids (clusters) in an Inverted File (IVF) index directly impacts search speed and recall, but the trade-offs depend on how the index is configured and the data distribution. With more centroids, the dataset is partitioned into smaller, more granular clusters. This reduces the number of vectors scanned per query if the search is limited to a fixed number of nearby clusters (controlled by the nprobe parameter). However, smaller clusters also increase the risk of missing relevant vectors if the query’s true nearest neighbors are split across clusters not examined during the search. Balancing speed and recall requires careful tuning of both the number of centroids and nprobe.

Search Speed Implications More centroids generally allow faster searches if the nprobe value remains fixed. For example, an IVF index with 10,000 centroids and nprobe=10 might search 10 clusters containing 0.1% of the dataset each, scanning 1% of total vectors. In contrast, an index with 1,000 centroids and the same nprobe=10 would search 10 clusters covering 1% of the data each, scanning 10% of vectors—slower by an order of magnitude. However, increasing centroids also increases the time spent during the coarse quantization step (comparing the query to all centroids). This overhead is minor for small centroid counts but becomes significant at scale (e.g., 1M centroids), especially on CPUs without SIMD optimizations.

Recall Trade-offs Higher centroid counts can hurt recall if nprobe isn’t adjusted. For instance, if a query’s true nearest neighbors are spread across 15 clusters but the index uses nprobe=10, increasing centroids from 1,000 to 10,000 makes it more likely those neighbors are split into distinct clusters, reducing the chance they’re all included in the 10 probed. To maintain recall, you may need to raise nprobe, which negates the speed gains from smaller clusters. For example, doubling nprobe when doubling centroids keeps the total vectors scanned roughly constant but adds overhead from probing more clusters. Optimal tuning often involves testing: a 10,000-centroid index with nprobe=20 might achieve better recall than a 1,000-centroid index with nprobe=10 at similar speed, but this depends on data clustering behavior.

In practice, the choice depends on the dataset’s inherent structure and latency/recall requirements. Sparse or high-dimensional data may require more centroids to avoid large, poorly separated clusters, while smaller datasets might perform better with fewer centroids and higher nprobe. Tools like FAISS or Milvus allow benchmarking these parameters to find the right balance.