Mean-field theory of graph neural networks in graph partitioning
By Tatsuro Kawamoto, Masashi Tsubaki, Tomoyuki Obuchi. 2018
61 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Statistical and Nonlinear Physics
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Zhiyuan Liu
- Maosong Sun
- Stephan Günnemann
- Aleksandar Bojchevski
- Jie Zhou
- Johannes Klicpera
- Zhengyan Zhang
- Cheng Yang
In Statistical and Nonlinear Physics
- Stephan Günnemann
- Johannes Klicpera
- Aleksandar Bojchevski
- Zhiyuan Liu
- Hoang NT
- Maosong Sun
- Takanori Maehara
- Cheng Yang
Citations in the corpus
- Predict then Propagate: Graph Neural Networks meet Personalized PageRank (2018, background): “Deep GNNs that avoid the oversmoothing issue have been proposed in recent works by combining residual (skip) connections with batch normalization (Kawamoto et al., 2018; Chen et al., 2019).”
- Graph Neural Networks: A Review of Methods and Applications (2018, background): “Recently, it has been proved that an untrained GNN with a simple architecture also perform well [21].”
- Revisiting Graph Neural Networks: All We Have is Low-Pass Filters (2019, methodology): “[13] took the mean-field approach to analyze a simple GCN model to statistical physics.”