Continuous Diffusion Graph Neural Network

Introduction

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and topology correspond to the discretisation choices of temporal and spatial operators. Our approach allows a principled development of a broad new class of GNNs that are able to address the common plights of graph learning models such as depth, oversmoothing, and bottlenecks. Key to the success of our models are stability with respect to perturbations in the data and this is addressed for both implicit and explicit discretisation schemes. We develop linear and nonlinear versions of GRAND, which achieve competitive results on many standard graph benchmarks.

Running the experiments

Requirements

Dependencies (with python >= 3.7): Main dependencies are torch==1.8.1 torch-cluster==1.5.9 torch-geometric==1.7.0 torch-scatter==2.0.6 torch-sparse==0.6.9 torch-spline-conv==1.2.1 torchdiffeq==0.2.1 To create the required environment run

python3 -m venv env
source env/bin/activate
pip install -r requirements.txt

Dataset and Preprocessing

create a root level ./data folder. This will be automatically populated the first time each experiment is run. For example to run for Cora:

cd src
python run_GNN.py --dataset Cora 

Troubleshooting

Most problems installing the dependencies are caused by Cuda version mismatches with pytorch geometric. We recommend checking your cuda and pytorch versions

nvcc --version
python -c "import torch; print(torch.__version__)"

and then following instructions here to install pytorch geometric https://pytorch-geometric.readthedocs.io/en/latest/notes/installation.html

Cite us

If you found this work useful, please consider citing

@article
{chamberlain2021grand,
  title={GRAND: Graph Neural Diffusion},
  author={Chamberlain, Benjamin Paul and Rowbottom, James and Goronova, Maria and Webb, Stefan and Rossi, 
  Emanuele and Bronstein, Michael M},
  journal={Proceedings of the 38th International Conference on Machine Learning,
               {ICML} 2021, 18-24 July 2021, Virtual Event},
  year={2021}
}

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