APO: Unsupervised Atomic Policy Optimization for 3D Structure Prediction of Atomic Systems

APO, or Atomic Policy Optimization, replaces FlowDPO’s dependence on ground-truth 3D coordinates with fully unsupervised alignment for crystal and antibody structure prediction. It adapts Group Relative Policy Optimization, a strategy used in DeepSeekMath, to flow-matching models by sampling candidate structures in groups and updating the policy from relative rewards. Its dual reward combines a Spectral Consistency Score, computed through eigen-decomposition of candidate-embedding similarities to identify dominant structural modes, with a Crystal Entropy Proxy that penalizes disordered packing, atomic clashes, and thermodynamically implausible geometries. Across Perov-5, MP-20, MPTS-52, and SAbDab, APO improves both structural fidelity and match rates without labels during alignment. On MP-20 with an OT plus VE path, APO reaches a 63.05% Match Rate versus 62.47% for supervised FlowDPO; on the harder MPTS-52 benchmark, it achieves 21.14% versus 20.27%. For antibody CDR-H3 prediction using an OT path, APO lowers Cα RMSD to 3.21 Å from FlowDPO’s 3.32 Å. An ablation shows that removing spectral consistency reduces Match Rate by 2.23%, while removing entropy worsens geometric accuracy, supporting the complementary roles of global manifold consensus and local physical regularity. The authors also report that APO straightens flow trajectories, particularly for Optimal Transport paths, potentially reducing inference difficulty, although its group-based sampling increases training cost and its entropy proxy does not model detailed electronic interactions.