Predict the shape of recall and latency on an IVF index of 10M vectors as nprobe sweeps from 1 to 50.

**IVF** (Inverted File) is a vector index that partitions the corpus into nlist clusters using k-means. At query time, the query is compared to each cluster's centroid, and only the nprobe closest clusters are scanned exhaustively. The rest are skipped. When you sweep nprobe from 1 to 50 on a 10M-vector index with nlist = 4096, two things happen: **Recall@10** starts low because at nprobe=1 you only scan one partition (~2500 vectors of the 10M), and the true neighbors may live in adjacent partitions you skipped. Recall climbs fast through nprobe=4 to nprobe=16 as you sweep up the rest of the neighborhood. By nprobe=32 it has plateaued around 0.92 to 0.97, and nprobe=50 adds almost nothing. **Latency** rises approximately linearly. Each extra partition adds about 10e6 / 4096 ~ 2440 additional distance comparisons. nprobe=50 is roughly 12.5x the work of nprobe=4. The production tuning rule: pick the smallest nprobe that hits your recall SLO. For a recall target of 0.92, that is usually nprobe = 8 to 16 on a corpus like this.

**Recall is concave, latency is linear. Tune to the elbow.** IVF search has a clean parametric structure. For a corpus of N vectors split into nlist partitions, each probed partition scans about N / nlist vectors. With N = 10e6 and nlist = 4096, that is ~2440 distance computations per partition. Total work per query is therefore approximately nprobe times the per-partition scan, plus the upfront centroid scan (4096 distances), which dominates only at very small nprobe. **Recall@10 curve.** At nprobe=1 you scan one partition and recall sits around 0.50 to 0.65; many true neighbors are stranded in the next few closest partitions. By nprobe=4 recall jumps to ~0.80; by nprobe=16 it is in the 0.90s; by nprobe=32 it is plateaued at ~0.95. The shape is concave: the first few partitions capture most of the true neighbors because Voronoi cells near the query contain most of them. **Latency curve.** Approximately linear in nprobe once the centroid scan cost is absorbed. nprobe=50 is ~50x the per-partition work of nprobe=1; nprobe=50 versus nprobe=4 is ~12.5x the marginal scan cost. **Production rule.** Pick the smallest nprobe that hits the recall SLO. If product needs recall >= 0.92, you would typically land at nprobe = 8 or 16. Anything past that pays linear latency for sub-percent recall gains. The same logic applies in faiss, Milvus, and Qdrant's IVF backends.