Distance-Dependent Angular Resolution for Equivariant Interatomic Potentials

Equivariant machine-learned interatomic potentials (MLIPs) typically use the same angular resolution on every edge, regardless of interatomic distance. We introduce radial gates with learnable cutoff radii that adapt angular resolution to interatomic distance within each message-passing block. We further introduce a band mixture-of-experts (Band-MoE) that uses these learned radial cutoffs to route edges deterministically to parameter-sharing experts with different maximum retained degrees. Separately, we also show that a reflection-symmetric simplification of the edge-frame operator can lead to 25.9% parameter reduction. We reach $2.10\times$ batched inference speedup with 50% training memory reduction, while maintaining accuracy close to the noise thresholds for forces and energy at maximum angular degree of 4. We show that at higher angular degree ($L=8$), our method outperforms the baseline model by $27\%$ with an inference speedup of $2.31\times$. We evaluate the method on non-periodic molecules from OMol25 and periodic inorganic crystals from OMat24. The Band-MoE and the learnable radial cutoff methodologies are applicable to other MLIPs.