Permutation Group Based Graph Neural Networks (PG-GNN)

The official implementation of Going Deeper into Permutation-Sensitive Graph Neural Networks (ICML 2022).

1  Installation

Follow the steps below to prepare the virtual environment.

Create and activate the environment:

conda create -n pggnn python=3.6
conda activate pggnn

Install dependencies:

pip install -r requirements.txt

2  Experiments

2.1  Synthetic Datasets

Reproduce the results reported in Table 2. The results with different seeds and their corresponding epochs are summarized after each command.

Erdős–Rényi Random Graphs

python main_synthetic.py --dataset ER --task triangle --batch_size 16 --hidden_dim 64 --num_layers 5 --final_dropout 0.0 --lr_patience 20 --seed <seed>

where <seed> takes in {0, 2, 4, 6, 8}.

	seed 0	seed 2	seed 4	seed 6	seed 8
Result	0.020	0.017	0.021	0.022	0.016
Epoch	506	369	506	380	537

python main_synthetic.py --dataset ER --task clique --batch_size 16 --hidden_dim 64 --num_layers 5 --final_dropout 0.0 --lr_patience 25 --seed <seed>

where <seed> takes in {0, 2, 4, 6, 8}.

	seed 0	seed 2	seed 4	seed 6	seed 8
Result	0.025	0.028	0.029	0.032	0.031
Epoch	420	360	283	313	494

Random Regular Graphs

python main_synthetic.py --dataset regular --task triangle --batch_size 16 --hidden_dim 64 --num_layers 5 --final_dropout 0.0 --lr_patience 20 --seed <seed>

where <seed> takes in {0, 2, 4, 6, 8}.

	seed 0	seed 2	seed 4	seed 6	seed 8
Result	0.025	0.026	0.029	0.028	0.027
Epoch	477	514	415	409	371

python main_synthetic.py --dataset regular --task clique --batch_size 16 --hidden_dim 64 --num_layers 5 --final_dropout 0.0 --lr_patience 20 --seed <seed>

where <seed> takes in {0, 2, 4, 6, 8}.

	seed 0	seed 2	seed 4	seed 6	seed 8
Result	0.023	0.023	0.024	0.021	0.022
Epoch	340	283	324	475	336

2.2  TUDataset

Reproduce the results reported in Table 3. The results with different seeds and their corresponding epochs are summarized after each command.

PROTEINS

python main_tu.py --dataset PROTEINS --batch_size 16 --hidden_dim 8 --num_layers 5 --final_dropout 0.5 --graph_pooling_type sum --fold_idx <fold>

where <fold> takes from 0 to 9.

	seed 2	seed 7	seed 10
Result	76.3 ± 2.7	76.8 ± 3.8	76.6 ± 4.6
Epoch	135	168	261

NCI1

python main_tu.py --dataset NCI1 --batch_size 32 --hidden_dim 32 --num_layers 5 --final_dropout 0.0 --graph_pooling_type sum --fold_idx <fold>

where <fold> takes from 0 to 9.

	seed 2	seed 7	seed 10
Result	82.5 ± 1.4	82.8 ± 1.3	83.4 ± 1.8
Epoch	319	332	367

IMDB-BINARY

python main_tu.py --dataset IMDBBINARY --batch_size 16 --hidden_dim 16 --num_layers 5 --final_dropout 0.0 --graph_pooling_type sum --degree_as_tag --fold_idx <fold>

where <fold> takes from 0 to 9. This command is used for the default seed 7. For seeds 2 and 10, please change --graph_pooling_type sum to --graph_pooling_type average.

	seed 2	seed 7	seed 10
Result	77.1 ± 2.4	76.8 ± 2.6	76.8 ± 2.9
Epoch	111	202	201

IMDB-MULTI

python main_tu.py --dataset IMDBMULTI --batch_size 32 --hidden_dim 16 --num_layers 5 --final_dropout 0.5 --graph_pooling_type sum --degree_as_tag --fold_idx <fold>

where <fold> takes from 0 to 9.

	seed 2	seed 7	seed 10
Result	53.4 ± 4.0	53.2 ± 3.6	52.5 ± 3.5
Epoch	114	251	203

COLLAB

python main_tu.py --dataset COLLAB --batch_size 32 --hidden_dim 64 --num_layers 3 --final_dropout 0.5 --graph_pooling_type sum --degree_as_tag --fold_idx <fold>

where <fold> takes from 0 to 9. This command is used for the default seed 7. For seeds 2 and 10, please change --graph_pooling_type sum to --graph_pooling_type average.

	seed 2	seed 7	seed 10
Result	80.3 ± 1.9	80.9 ± 0.8	81.0 ± 1.7
Epoch	105	363	133

2.3  Benchmark Datasets

Download the datasets and reproduce the results reported in Table 4.

Download Datasets

Follow the instructions below to download Benchmark datasets. You can also follow the instructions provided on the official website of Benchmark datasets.

cd data/ 
bash script_download_superpixels.sh

The script script_download_superpixels.sh is located here. If downloaded correctly, the file for MNIST can be found at data/superpixels/MNIST.pkl.

cd data/ 
bash script_download_molecules.sh

The script script_download_molecules.sh is located here. If downloaded correctly, the file for ZINC can be found at data/molecules/ZINC.pkl.

MNIST

python main_benchmark.py --dataset MNIST --batch_size 64 --hidden_dim 128 --num_layers 5 --final_dropout 0.0 --lr_patience 20 --graph_pooling_type average --seed <seed>

where <seed> takes in {0, 3, 6, 9}.

	seed 0	seed 3	seed 6	seed 9
Result	97.39	97.52	97.54	97.56
Epoch	266	268	251	198

ZINC

python main_benchmark.py --dataset ZINC --batch_size 64 --hidden_dim 128 --num_layers 5 --final_dropout 0.0 --lr_patience 25 --graph_pooling_type sum --seed <seed>

where <seed> takes in {0, 3, 6, 9}.

	seed 0	seed 3	seed 6	seed 9
Result	0.298	0.286	0.277	0.269
Epoch	422	424	391	443

2.4  Numerical Simulation

We provide the IPython Notebook file simulation.ipynb to reproduce the results of numerical experiments reported in Figure 9 (Appendix K.2).

3  Cite

If you find this code or our PG-GNN paper helpful for your research, please cite our paper:

@inproceedings{huang2022going,
  title     = {Going Deeper into Permutation-Sensitive Graph Neural Networks},
  author    = {Huang, Zhongyu and Wang, Yingheng and Li, Chaozhuo and He, Huiguang},
  booktitle = {Proceedings of the 39th International Conference on Machine Learning},
  pages     = {9377--9409},
  year      = {2022},
  editor    = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
  volume    = {162},
  series    = {Proceedings of Machine Learning Research},
  month     = {17--23 Jul},
  publisher = {PMLR}
}