SGBNet: Scalar-Geometric Bidirectional Network for Edge-Efficient Interatomic Potentials

Machine learning interatomic potentials often suffer from restricted geometric-to-scalar information flow and edge-dominated computation. We propose SGBNet, an equivariant architecture that improves the accuracy-efficiency trade-off through scalar-geometric bidirectional (SGB) interactions and edge-efficient convolution. SGB interactions improve geometric-to-scalar information flow by introducing explicit pathways from higher-order geometric features to invariant scalar features. In the SO(2) branch, conjugate multiplication cancels shared rotation-induced phases to construct scalar features. Edge-efficient SGB convolution leverages the structure of scalar features to move channel mixing from edges to nodes, reducing edge-domain computation. Experiments demonstrate clear accuracy-efficiency gains on molecular benchmarks, slightly improved performance on materials benchmarks, and scalability to large-scale systems. On SPICE-MACE-OFF, all SGBNet variants lie on the accuracy-efficiency Pareto frontier. The compact SGBNet-N maintains comparable MLIPAudit performance to eSEN-3.2M while reducing runtime and memory consumption by 47% and 60%, respectively. Moreover, SGBNet-N is both faster and substantially more accurate than the Euclidean-based ViSNet, narrowing the divide between efficient Euclidean models and more expressive higher-order equivariant architectures.