Hierarchical SPANN — routing at the depth of a 100B tree

FIG. 08 // HSPANN.ROUTING_STANDIN 70M FINEWEB VECTORS AS LEAF CENTERS · FAN-OUT 63

Routing accuracy on a tree shaped like a 100B index

A shallow tree still needs a wider beam at larger scales: the same beam keeps fewer of the nearest centers as the tree deepens, while a query touches a smaller share of the machines.

Routing only: real vectors stand in for leaf centers at the depth and level widths of each index size. The measure is the fraction of the query’s 10 nearest centers retained, not end-to-end vector recall. 512 lists searched per query · beam = internal nodes retained per level · 1,000 queries (300 at 10B, 200 at 100B).