Parameterized Hypercomplex Graph Neural Networks (PHC-GNNs)

PHC-GNNs (Le et al., 2021): https://arxiv.org/abs/2103.16584

PHM Linear Layer Illustration	PHC-GNN Layer Computation Diagram

Overview

Here we provide the implementation of Parameterized Hypercomplex Graph Neural Networks (PHC-GNNs) in PyTorch Geometric, along with 6 minimal execution examples in the benchmarks/ directory.

This repository is organised as follows:

• phc/hypercomplex/ contains the implementation of the PHC-GNN with all its submodules. This directory resembles the quaternion/ in most cases, with the user-defined phm-dimension n. For more details, check the subdirectory README.md
• phc/quaternion/ contains the implementation for quaternion GNN with all its submodules. For more details, check the subdirectory README.md
• benchmarks/ contains the python training-scripts for 3 datasets from Open Graph Benchmark (OGB) and 3 datasets from Benchmarking-GNNs. Additionally, we provide 6 bash-scripts with default arguments to run our models.

Generally speaking, the phc/hypercomplex/ subdirectory also includes the quaternion-valued GNN, with the modification to only work on torch.Tensor objects. The phc/quaternion/ subdirectory was first implemented with the fixed rules of the quaternion-algebra, such as how to perform addition, and multiplication which can be summarized in the quaternion-valued affine transformation. The phc/hypercomplex/ directory generalizes such operations to work directly on torch.Tensor objects, making it applicable to many already existing projects.
For completeness and to share our initial motivation of this project, we also provide the implementations from the phc/quaternion/ subdirectory.

Installation

Requirements

To run our examples, the main requirements are listed in the environment_gpu.yml file. The main requirements used are the following:

python=3.8.5
pytest=6.2.1
cudatoolkit=10.1
cudnn=7.6.5
numpy=1.19.2
scipy=1.5.2
pytorch=1.7.1
torch-geometric=1.6.1
ogb=1.2.4

Conda

Create a new environment:

git clone https://github.com/bayer-science-for-a-better-life/phc-gnn.git
cd phc-gnn
conda env create -f environment_gpu.yml
conda activate phc-gnn

Install Pytorch Geometric and this module with pip by executing the bash-script install_pyg.sh

chmod +x install_pyg.sh
bash install_pyg.sh

#install this library
pip install -e .

Run the implemented pytests in the subdirectories, by executing:

pytest .

Getting started

Run our example scripts in the benchmarks/ directory. Make sure to have the phc-gnn environment activated. For more details, please have a look at benchmarks/README.md.

Reference

If you make use of the implementations of quaternion or parameterized hypercomplex GNN in your research, please cite our manuscript:

@misc{le2021parameterized,
      title={Parameterized Hypercomplex Graph Neural Networks for Graph Classification}, 
      author={Tuan Le and Marco Bertolini and Frank Noé and Djork-Arné Clevert},
      year={2021},
      eprint={2103.16584},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2103.16584}
}

License

GPL-3