Calibrated, Certified Pruning for Partitioned Vector Search

Accurate, well-routed nearest-neighbour search is vital for sharded vector systems. Progressive per-point lower bounds prune a scan exactly, conformal methods attach a miss guarantee to an approximate search, and per-point routing sends a query to the shards holding its neighbours; no structure combines them, and none certifies a result across shards. This paper presents a calibrated, certified pruning method for partitioned vector search that routes, bounds and certifies from one 0.86 KB sketch per point, independent of the dimension: an 8-bit PCA head, two floats per level and a link list in a graph over the heads, which routes a query to cells or shards. The same bytes give a lower bound equal to Panorama’s level bound plus the quantisation error, so it stays exact over the sketch and a scan that bounds every point certifies its top-k. A per-level relaxation of the bound, chosen by split-conformal calibration on the pruning decision itself, gives a stated per-neighbour miss probability δ, and a second round opens only the shards whose minimum bound is below the first round’s k-th distance. We evaluate at library level on text embeddings and GIST up to 1M points. The realised miss is 0.1–0.4 % against a stated 3.15 %; the router opens within 0–5 shards of an oracle where centroid routing opens 1.6–6× more; the calibrated second round opens 5–7× fewer extra shards than the exact one while ending at 100 % recall; and the method is 3.4× faster than FAISS HNSW and 2.0× faster than Panorama’s graph at 99 % recall on GIST1M. These results demonstrate the feasibility of one sketch as router, exact bound and calibrated certificate. However, on 1M transformer embeddings a single global graph is faster single-threaded, and exact certification costs more than a dense scan; we report where and why.