Spectrally Decomposed Equivariant Graph Neural Networks for Interatomic Potentials

Machine Learning Interatomic Potentials (MLIPs) based on Equivariant Graph Neural Networks (EGNNs) have greatly advanced the quantitative simulation of atomic systems. However, accurately resolving fine-grained structural geometry remains a critical challenge. In this work, we demonstrate through spectral analysis that the reliance of modern EGNNs on a single macroscopic cutoff radius inherently acts as a spatial low-pass filter. This structural bottleneck induces radial spectral confusion, suppressing the network's capability for fine-grained geometric modeling. To overcome this limitation, we propose the Multi-Cutoff Spectral Decomposition (MCSD) mechanism. As a universal, plug-and-play module, MCSD explicitly decomposes atomic interactions across multiple spatial scales. By leveraging envelope associativity to unify the neighborhood graph, this method decouples scale parameters from tensor product complexity, enabling multi-resolution representations with minimal overhead. Extensive evaluations across representative EGNN backbones demonstrate that MCSD not only consistently reduces prediction errors for energy, forces, and macroscopic stress tensors, but also significantly enhances the prediction fidelity of higher-order properties (such as lattice thermal conductivity), all while maintaining the smoothness of the potential energy surface and the energy conservation of long-term molecular dynamics simulations. The code is available at the anonymous repository: https://anonymous.4open.science/r/MCSD-C854.