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[CS.AI] Radial Kernel Attention for Long-Range Modeling in Polymer Machine Learning Force Fields

Published at: 2026-11-04 22:00 Last updated: 2026-11-05 00:45
#Machine Learning #optimization #Graph

We introduce Radial Kernel Attention (RKA) for long‑range interaction modeling in polymer machine‑learning force fields. Conventional local neighbor graphs restrict communication to intra‑chain and nearby environments, while full all‑pair attention incurs a quadratic cost $O(N^2)$ that quickly becomes prohibitive. RKA maps atomic distances to the cluster centroid into learnable radial features and combines their overlap with content‑dependent queries and keys, enabling global information exchange.\n\nImplementation-wise, RKA uses factorized aggregation and readout, so that with fixed feature dimensions the overall computational complexity remains linear $O(N)$ in the number of atoms. We insert an invariant scalar‑update layer between EquiformerV3 local blocks and obtain conservative forces by differentiating the total energy, which includes radial‑coordinate dependence.\n\nThe models are evaluated on polymer‑derived clusters from the OPoly26 dataset. Training follows the official split for 12 epochs, after which we directly evaluate on the full official validation split. Compared with a matched 5M baseline, RKA reduces per‑atom energy MAE by 67.4% and force MAE by 36.3%. The 20M‑parameter RKA model achieves a total‑energy MAE of 15.81 meV and a force MAE of 2.619 meV/Å, with a per‑atom energy MAE of 0.1182 meV/atom, outperforming the UMA‑S‑1.2 series.\n\nThese results demonstrate that RKA provides a compact global communication pathway that markedly improves energy and force predictions on the tested polymer clusters.\n\nReview: By leveraging radial feature mapping and linear‑complexity global aggregation, RKA overcomes the computational bottleneck of long‑range interactions, offering an efficient and scalable solution for large‑scale polymer force‑field modeling.

Original Source: https://arxiv.org/abs/2610.41675

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