Linear-time Shape Alignment with ROSHAMBO3

Three-dimensional (shape) similarity is a useful primitive for virtual screening and molecular machine learning, but current open implementations are limited in performance by a quadratic inner loop across pairs of query- and database-molecule atoms. ROSHAMBO3 achieves an 80-150x speedup over the previous open SOTA ROSHAMBO2 by combining both query-amortized Gaussian fields that make the inner loop linear and system-scale optimization at the algorithmic, GPU, and host layers, screening up to $53 \times 10^6$ conformer pairs/sec and achieving 50--70% of GPU theoretical peak throughput. We further describe the human expert--AI interaction loop that guided the exploration and implementation of ROSHAMBO3 and discuss implications for the scientific software commons.