A Variational Mean-Field Control Framework for Graph Representation Learning

Area of Science:

• Artificial Intelligence
• Machine Learning
• Graph Representation Learning

Background:

• Current graph neural networks (GNNs) use uniform message-passing, which struggles with graph properties like heterophily.
• This limitation hinders a generalizable understanding and design of graph learning models.

Purpose of the Study:

• To develop a generalizable framework for adaptive GNN design using mean-field control (MFC).
• To create a novel GNN model, Nash-GNN, that adaptively learns representations for diverse graph data.

Main Methods:

• Conceptualized GNN learning via mean-field control, optimizing variational critical points for node representations.
• Developed a mathematical framework using MFC to jointly learn diffusive and reactive mobility patterns.
• Solved the MFC variational problem using Hamiltonian flows and partial differential equations (PDEs) for an end-to-end deep model.

Main Results:

• Nash-GNN achieved state-of-the-art performance on various benchmarks, including heterophilic graphs and human connectomes.
• The MFC framework unified existing PDE-based GNNs as special cases of mean-field games.
• Demonstrated adaptive calibration of node representations based on graph properties.

Conclusions:

• The proposed MFC framework provides a principled approach to adaptive GNN design.
• Nash-GNN offers significant empirical gains and a new perspective on graph representation learning mechanisms.
• This work opens avenues for next-generation GNNs that dynamically adapt to graph structures and properties.