<p>This study introduces a novel graph neural network architecture for the general problem of attributed graph transformation, where both the input and output are attributed graphs, and the evolution of the output graphs, including the attributes of nodes and edges, is governed by complex interactions that capture the intricate dependencies within the transformation process. Research in this area has been limited due to two key challenges: (1) the complexity of jointly modeling four types of atomic interactions, i.e., node-to-edge, node-to-node, edge-to-node, and edge-to-edge; and (2) the challenge of modeling dependencies between nodes and edges that span distant parts of the graph and develop through multiple iterative steps in the transformation process. To overcome these challenges, we present a scalable equilibrium model, NEC<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10115_2025_2468_Article_IEq1.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$^{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mi>∞</mi> </mmultiscripts> </math></EquationSource> </InlineEquation>, which incorporates both node-to-edge and edge-to-node message passing. Furthermore, we develop an efficient optimization algorithm based on the implicit function theorem [<CitationRef CitationID="CR1">1</CitationRef>] and provide a well-posedness analysis of NEC<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10115_2025_2468_Article_IEq1.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$^{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mi>∞</mi> </mmultiscripts> </math></EquationSource> </InlineEquation>. Experiments were conducted on four synthetic random graph datasets, four real-world datasets, and two synthetic dynamical system datasets, employing multiple evaluation metrics for node and edge prediction. The results show that NEC<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10115_2025_2468_Article_IEq1.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$^{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mi>∞</mi> </mmultiscripts> </math></EquationSource> </InlineEquation> consistently outperforms all baseline models, achieving up to a tenfold decrease in MSE on BA random graphs, edge prediction accuracy ranging from 94% to nearly 100% on synthetic datasets, and exceptional results in tasks involving molecular reactions and high-order brain networks, highlighting its strength in modeling complex graph transformations.</p>

Implicit graph neural network for deep graph transformation

期刊论文
发表日期：

2025年5月26日

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Lei Zhang,
Qisheng Zhang,
Zhiqian Chen,
Yanshen Sun,
Chang-Tien Lu,
Liang Zhao

摘要

This study introduces a novel graph neural network architecture for the general problem of attributed graph transformation, where both the input and output are attributed graphs, and the evolution of the output graphs, including the attributes of nodes and edges, is governed by complex interactions that capture the intricate dependencies within the transformation process. Research in this area has been limited due to two key challenges: (1) the complexity of jointly modeling four types of atomic interactions, i.e., node-to-edge, node-to-node, edge-to-node, and edge-to-edge; and (2) the challenge of modeling dependencies between nodes and edges that span distant parts of the graph and develop through multiple iterative steps in the transformation process. To overcome these challenges, we present a scalable equilibrium model, NEC $^{\infty }$ $^{\infty}$ , which incorporates both node-to-edge and edge-to-node message passing. Furthermore, we develop an efficient optimization algorithm based on the implicit function theorem [1] and provide a well-posedness analysis of NEC $^{\infty }$ $^{\infty}$ . Experiments were conducted on four synthetic random graph datasets, four real-world datasets, and two synthetic dynamical system datasets, employing multiple evaluation metrics for node and edge prediction. The results show that NEC $^{\infty }$ $^{\infty}$ consistently outperforms all baseline models, achieving up to a tenfold decrease in MSE on BA random graphs, edge prediction accuracy ranging from 94% to nearly 100% on synthetic datasets, and exceptional results in tasks involving molecular reactions and high-order brain networks, highlighting its strength in modeling complex graph transformations.