This is the official implementation of the paper: On the Bottleneck of Graph Neural Networks and its Practical Implications (ICLR'2021), which introduces the over-squashing problem of GNNs.

By Uri Alon and Eran Yahav. See also the [video], [poster] and [slides].

this repository is divided into three sub-projects:

1. The subdirectory tf-gnn-samples is a clone of https://github.com/microsoft/tf-gnn-samples by Brockschmidt (ICML'2020). This project can be used to reproduce the QM9 and VarMisuse experiments of Section 4.2 and 4.2 in the paper. This sub-project depends on TensorFlow 1.13. The instructions for our clone are the same as their original code, except that reproducing our experiments (the QM9 dataset and VarMisuse) can be done by running the script tf-gnn-samples/run_qm9_benchs_fa.py or tf-gnn-samples/run_varmisuse_benchs_fa.py instead of their original scripts. For additional dependencies and instructions, see their original README: https://github.com/microsoft/tf-gnn-samples/blob/master/README.md. The main modification that we performed is using a Fully-Adjacent layer as the last GNN layer and we describe in our paper.
2. The subdirectory gnn-comparison is a clone of https://github.com/diningphil/gnn-comparison by Errica et al. (ICLR'2020). This project can be used to reproduce the biological experiments (Section 4.3, the ENZYMES and NCI1 datasets). This sub-project depends on PyTorch 1.4 and Pytorch-Geometric. For additional dependencies and instructions, see their original README: https://github.com/diningphil/gnn-comparison/blob/master/README.md. The instructions for our clone are the same, except that we added an additional flag to every config_*.yml file, called last_layer_fa, which is set to True by default, and reproduces our experiments. The main modification that we performed is using a Fully-Adjacent layer as the last GNN layer.
3. The main directory (in which this file resides) can be used to reproduce the experiments of Section 4.1 in the paper, for the "Tree-NeighborsMatch" problem. The rest of this README file includes the instructions for this main directory. This repository can be used to reproduce the experiments of

This project was designed to be useful in experimenting with new GNN architectures and new solutions for the over-squashing problem.

Feel free to open an issue with any questions.

This project is based on PyTorch 1.4.0 and the PyTorch Geometric library.

• First, install PyTorch from the official website: https://pytorch.org/.
• Then install PyTorch Geometric: https://pytorch-geometric.readthedocs.io/en/latest/notes/installation.html
• Eventually, run the following to verify that all dependencies are satisfied:

pip install -r requirements.txt

The requirements.txt file lists the additional requirements. However, PyTorch Geometric might requires manual installation, and we thus recommend to use the requirements.txt file only afterward.

Verify that importing the dependencies goes without errors:

python -c 'import torch; import torch_geometric'

Training on large trees (depth=8) might require ~60GB of RAM and about 10GB of GPU memory. GPU memory can be compromised by using a smaller batch size and using the --accum_grad flag.

For example, instead of running:

python main.py --batch_size 1024 --type GGNN

The following uses gradient accumulation, and takes less GPU memory:

python main.py --batch_size 512 --accum_grad 2 --type GGNN

To run a single experiment from the paper, run:

python main.py --help

And see the available flags. For example, to train a GGNN with depth=4, run:

python main.py --task DICTIONARY --eval_every 1000 --depth 4 --num_layers 5 --batch_size 1024 --type GGNN

To train a GNN across all depths, run one of the following:

python run-gcn-2-8.py
python run-gat-2-8.py
python run-ggnn-2-8.py
python run-gin-2-8.py

The results of running the above scripts are (Section 4.1 in the paper):

To experiment with other GNN types:

• Add the new GNN type to the GNN_TYPE enum here, for example: MY_NEW_TYPE = auto()
• Add another elif self is GNN_TYPE.MY_NEW_TYPE: to instantiate the new GNN type object here
• Use the new type as a flag for the main.py file:

python main.py --type MY_NEW_TYPE ...

If you want to cite this work, please use this bibtex entry:

@inproceedings{
    alon2021on,
    title={On the Bottleneck of Graph Neural Networks and its Practical Implications},
    author={Uri Alon and Eran Yahav},
    booktitle={International Conference on Learning Representations},
    year={2021},
    url={https://openreview.net/forum?id=i80OPhOCVH2}
}