Mean-field theory of graph neural networks in graph partitioning
This provides theoretical insights into GNN performance for graph partitioning, which is incremental as it builds on existing methods.
The paper tackled the problem of theoretically analyzing the performance of graph neural networks (GNNs) in graph partitioning, developing a mean-field theory for a minimal GNN architecture that demonstrated good agreement with numerical experiments.
A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas Bayesian inference requires the assumption of a specific model. A fundamental question is then whether GNN has a high accuracy in addition to this flexibility. Moreover, whether the achieved performance is predominately a result of the backpropagation or the architecture itself is a matter of considerable interest. To gain a better insight into these questions, a mean-field theory of a minimal GNN architecture is developed for the graph partitioning problem. This demonstrates a good agreement with numerical experiments.