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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.00528

Authors: Ming, Pingbing, Wang, Han

Institution: Institute of Applied Physics and Computational Mathematics

Topic: Machine Learning in Materials Science

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Chinese Academy of Sciences

Awards: G2082367026, G4487706731, G5656051064

OpenAlex ID: W7206158269

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