One Global Beam Across Many GPUs: High-Throughput Beam Search at Billion-Record Frontier Scale

Abstract: Beam search repeatedly makes many children, removes duplicates, and keeps the best $B$. We show how many GPUs can perform these steps as one search even when the retained set does not fit on one device. States and candidates stay on the GPUs; the CPU receives only small control and ancestry records. We prove that an abstract distributed pipeline returns the monolithic reduced-key top-$B$ for the same complete candidates, integer scores, Hash128 equivalence, and a fully specified physical-layout tie order, provided that its implementation performs one global reduction per key and race-free routing. A static audit of the historical one-T4 pin leaves cross-buffer uniqueness unresolved and identifies a separate multi-rank scatter risk; neither is a reproduced failure, and other revisions inherit neither defects nor correctness without comparison. On eight H200 GPUs, a Cube4 run completed saturated depth 8 at $B_{\rm eff}=2{,}900{,}361{,}216$ in $931.266$ s: $69{,}608{,}669{,}184$ nominal parent--generator pairs, or a derived $74.746$ million pairs/s. The puzzle remained unsolved and depth 9 was stopped at user request. A separate two-T4 Megaminx run measured $30.274$ million logical children/s at $B_{\rm eff}=82{,}837{,}504$. Those tasks and hardware differ, so they do not establish strong scaling. Separately, on one eight-RTX-3060 host, fixed-count eight-GPU speedup was $7.487$ under a common execution profile and $5.605$ under selected stable profiles; weak actual-work throughput gain was $6.113$ and $7.295$. These profile-sensitive ratios use each series' own one-GPU baseline.