Radial Kernel Attention for Global Feature Exchange in Polymer Machine Learning Force Fields

Abstract

We introduce Radial Kernel Attention (RKA) for long-range modeling in polymer machine learning force fields. Existing approaches often rely on local neighbor graphs, which limit communication across polymer chains and their surrounding environments, whereas explicit all-pair attention incurs quadratic computational cost. RKA maps interatomic distances from the cluster centroid to learned radial features and combines their kernelized overlap with content-dependent queries and keys. Factorized aggregation and readout enable global feature exchange at linear complexity in the number of atoms for fixed feature dimensions. To ensure physically consistent predictions, we insert the invariant scalar update between EquiformerV3 local blocks and obtain conservative forces by differentiating the total energy, including its dependence on radial coordinate . Our models are trained on official OPoly26 training set for 12 epochs and evaluated directly after training on the complete official validation set. A matched 5M comparison shows that RKA reduces per-atom energy and force MAEs by 67.4% and 36.3%, respectively. The 20M RKA model attains a total-energy MAE of 15.81 meV (per-atom MAE of 0.1182 meV/atom) and a force MAE of 2.619 meV/Angstrom,improving all three metrics over UMA-S-1.2 and UMA-S-1.2.1 on the same validation structures. RKA provides a compact pathway for information exchange beyond local graph connectivity in polymer machine learning force fields.