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On the Ability of Graph Neural Networks to Model Interactions Between Vertices (NeurIPS 2023)

Code implementation for the experiments in On the Ability of Graph Neural Networks to Model Interactions Between Vertices (NeurIPS 2023), based on the PyTorch and PyTorch Geometric frameworks.

Walk Index Sparsification (WIS)

Implementations for the (L - 1)-WIS edge sparsification algorithm and its efficient 1-WIS variant, described by Algorithms 1 and 2 in the paper, can be found at edges_removal/walk_index_sparsification.py.

:ledger: A quickstart Jupyter Notebook for using 1-WIS can be found at wis_quickstart_example.ipynb.

Installing Requirements

Tested with python 3.8.

• Install PyTorch from the official website (tested with version 1.11.0), including torchvision.
• Install PyTorch Geometric from the official website (tested with version 2.0.4), including torch-sparse and torch-scatter.
• The requirements.txt file includes additional requirements, which can be installed via:

pip install -r requirements.txt

For experiments with the OGBN-ArXiv dataset:

• Install the OGB library from the official website.
• Install Julia for running the spectral sparsification algorithm from Spielman & Srivastava 2011 (tested with version 1.8.3).

1. Empirical Demonstration of Theoretical Analysis

1.1 Generating Data

python is_same_class_dataset_generator.py

• By default, the generated dataset will be placed at "data/gisc".
• Use the -h flag for information on the customizable run arguments.

1.2 Running Experiments

The following command reproduces the experiments reported in Table 1 of the paper. Before running, make sure that the dataset_path field in the configuration file points to the dataset generated in the previous step.

python is_same_class_experiments_plan_runner.py --plan_config_path is_same_class/experiments_plans/is_same_class_experiments_plan.json

• A folder with log files and results of the experiments will be automatically created under the directory specified by outputs_dir in the configuration file.
• It is recommended to use a GPU by adding an available gpu id to the gpu_ids_pool field in the configuration file.
• See is_same_class/experiments_plans/is_same_class_experiments_plan.json for further configuration options, which are documented in common/experiment/fit_experiment_base.py and is_same_class/experiments/is_same_class_experiment.py.

1.3 Printing Results

The following command prints the mean and standard deviation of accuracies for experiments ran in the previous step, per model, dataset, and learning rate.

python is_same_class_accuracy_printer.py --experiments_dir outputs/gisc

• The experiments_dir parameter specifies the directory in which the experiment results are located, determined by outputs_dir in the previous step (default folder is outputs/gisc).

2. Edge Sparsification

2.1. Computing Edge Removal Order

Random, Spectral, and Walk Index Sparsification

The following commands produce files with edge removal orders for the specified algorithms, per dataset.

python ./edges_removal/call_removal_scripts.py --dataset cora --output_folder ./outputs/edges_removal/ --gpu_id 0 random spectral wis one_wis
python ./edges_removal/call_removal_scripts.py --dataset dblp --output_folder ./outputs/edges_removal/ random spectral one_wis 
python ./edges_removal/call_removal_scripts.py --dataset ogbn-arxiv --output_folder ./outputs/edges_removal/ random spectral one_wis --julia_spectral

• Supported algorithms are random pruning ("random"), the spectral sparsification algorithm from Spielman & Srivastava 2011 ("spectral"), (L - 1)-WIS ("wis") and 1-WIS ("one_wis"). The L used for (L - 1)-WIS is determined by the gnn_depth argument (default is 3).
• The gpu_id parameter specifies an available GPU to use for speeding up (L - 1)-WIS, otherwise CPU is used.
• If the julia_spectral flag is used, the spectral sparsification algorithm will be run using the Julia implementation from Laplacians.jl (as opposed to a Python one). This is necessary only for the larger scale OGBN-ArXiv dataset.
• For randomized algorithms (random and spectral sparsification), ten removal orders are computed for each dataset.
• Use the -h flag for information on more customizable run arguments.

Adaptation of UGS (Chen et al. 2021)

The following commands create the edge removal orders using GCN, per dataset, for a variant of the UGS algorithm from Chen et al. 2021 — see the paper for more details.

python edge_removal_plan_runner.py --plan_config_path edges_removal/experiments_plans/cora_gcn_ugs_mask_generation_config.json
python edge_removal_plan_runner.py --plan_config_path edges_removal/experiments_plans/dblp_gcn_ugs_mask_generation_config.json
python edge_removal_plan_runner.py --plan_config_path edges_removal/experiments_plans/arxiv_gcn_ugs_mask_generation_config.json

• The plan_config_path argument points to a configuration file with relevant hyperparameters, which are documented in common/experiment/fit_experiment_base.py and edges_removal/edges_removal_experiment.py.
• To create the UGS edge removal orders for other datasets and models, use the appropriate configuration files in edges_removal/experiments_plans named <dataset>_<model>_ugs_mask_generation_config.json.
• Creates ten removal orders for each dataset.
• It is recommended to use a GPU by adding an available gpu id to the gpu_ids_pool field in the configuration files.

2.2. Running Experiments

The following commands train and evaluate GCN over the Cora, DBLP, and OGBN-ArXiv datasets across edge sparsity levels, with edges removed for each algorithm according to the order computed in previous step.

python edge_removal_plan_runner.py --plan_config_path edges_removal/experiments_plans/cora_gcn_removal_experiments_config.json
python edge_removal_plan_runner.py --plan_config_path edges_removal/experiments_plans/dblp_gcn_removal_experiments_config.json
python edge_removal_plan_runner.py --plan_config_path edges_removal/experiments_plans/arxiv_gcn_removal_experiments_config.json

• The plan_config_path argument points to a configuration file with relevant hyperparameters, which are documented in common/experiment/fit_experiment_base.py and edges_removal/edges_removal_experiment.py.
• To run experiments for other datasets and models, use the appropriate configuration files in edges_removal/experiments_plans named <dataset>_<model>_removal_experiments_config.json.
• It is recommended to use GPUs by adding gpu ids to gpu_ids_pool and setting num_parallel to more than one in the configuration files.

2.3. Plotting Results

The following commands produce plots of the mean test accuracy across different runs for each edge sparsity level and algorithm.

python ./edges_removal/analyze_experiments_summary.py ./outputs/cora_gcn/ ./outputs/plots/
python ./edges_removal/analyze_experiments_summary.py ./outputs/dblp_gcn/ ./outputs/plots/
python ./edges_removal/analyze_experiments_summary.py ./outputs/ogbn-arxiv_gcn/ ./outputs/plots/

The first argument specifies the directory from which to read the results from, and the second specifies the output folder for the plots.

Example plots:

Citation

For citing the paper you can use:

@inproceedings{razin2023ability,
  title={On the Ability of Graph Neural Networks to Model Interactions Between Vertices},
  author={Razin, Noam and Verbin, Tom and Cohen, Nadav},
  booktitle={Advances in Neural Information Processing Systems},
  year={2023}
}