Beyond Action Entropy: Quotient-Space Exploration for Genome-Scale Metabolic Model Repair

Repairing scientific models from functional observations differs fundamentally from supervised prediction: feedback may certify a solution without revealing which structural correction is responsible. We study this setting for genome-scale metabolic model (GEM) repair, where multiple reaction edits can explain the same phenotypes and many apparently distinct edits correspond to the same biological mechanism. This many-to-one structure creates a hidden failure mode for conventional exploration: diversity in the output space need not translate into diversity of scientific hypotheses. We introduce QuotientPO, which collapses equivalent repairs into canonical mechanisms and optimizes exploration directly over the resulting quotient space. To make quotient exploration informative under finite rollouts, we derive a kernelized R'enyi estimator that resolves graded crowding among distinct repair cores beyond coarse exact-match counts. On 2,212 held-out GEMs, QuotientPO improves Success@32 from 17.93% to 20.10% (+12.1% relative) while consistently increasing distinct successful-core discovery under the same sampling budget. These results establish quotient-space exploration as a principled approach to mechanism-level discovery under verifier-induced equivalence.