Bridging Topological Over-Squashing and Physical Long-Range Interactions in ML Interatomic Potentials

Despite the success of Geometric Graph Neural Networks (GGNNs), their reliance on local message passing inherently limits the receptive field, leading to the over-squashing of distant information. Current solutions—ranging from graph rewiring to global attention—address this as a purely topological bottleneck, often neglecting the explicit electronic degrees of freedom (e.g., charge transfer and electrostatics) that physically govern long-range couplings. To resolve this disconnect, we propose HMP-Net, a framework that integrates over-squashing remedies with chemically meaningful interaction channels. Our approach introduces a differentiable hierarchy that routes information through learned “master nodes”, enabling direct global reasoning while preserving local chemical fidelity. Crucially, we clarify the theoretical ambiguity between topological and physical long-range interactions, establishing practical boundaries for when explicit physical modeling suffices and when architectural interventions are strictly necessary to capture global electronic states.