Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials

arXiv:2609.00528v1 Announce Type: new Abstract: We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that L layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full L-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.

MMGNN: Multi-level, multi-color graph neural networks for molecular property prediction
A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation
Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks
Universality and Approximation Rates of Graph Neural Networks with Random Features

Source: arXiv cs.LG | 2026-09-02

Related