Bachelor's Thesis

Welcome to the GitHub repository for my bachelor thesis titled A Theoretical and Empirical Investigation into the Equivalence of Graph Neural Networks and the Weisfeiler-Leman Algorithm.

Here, you will find all the code used to conduct experiments, as well as the LaTeX code for creating the written version of the thesis. Please note that we employed Weights&Biases to record our experimental results. To access these results, kindly refer to wandb.ai/eric-bill/BachelorThesisExperiments.

Experimental Code

All the code used for the experiments can be found in the Code folder. Firstly, we will list the requirements needed to execute the datasets, and then we will discuss how to test the classification and regression datasets separately.

Requirements

• Python 3.10
• numpy
• pandas
• scipy
• sklearn
• torch 1.13.x
• torch-geometric 2.3.x
• wandb

Classification Datasets

If you want to try out a 1-WL+NN or GNN setup with any classification dataset from the TUDataset library, simplye/main.pyand provide the following arguments: runpython Code/main.py` and provide the following arguments:

• --dataset Name of the dataset to be tested
• --max_epochs Maximum number of epochs a model should be trained for
• --batch_size Number of samples per batch
• --lr Initial learning rate
• --k_fold Number of folds for k-fold cross-validation
• --seed Random seed for initializing all random samplers used
• --k_wl Number of Weisfeiler-Lehman iterations, or if -1 it runs until convergences
• --model Model to use. Options are "1WL+NN:Embedding-{Sum,Max,Mean}", "1WL+NN:{Sum,Max,Mean}", "1WL+NN:{GAT,GCN,GIN}:{Sum,Max,Mean}" or "{GAT,GCN,GIN}:{Sum,Max,Mean}"
• --wl_convergence {True,False} Whether to use the convergence criterion for the Weisfeiler-Lehman algorithm
• --tags Tags that are to be added to the recording of the run on wandb.ai
• --num_repition Number of repitions
• --transformer_kwargs Arguments for the transformer. For example, for the OneHotDegree transformer, the argument is the maximum degree.
• --encoding_kwargs Arguments for the encoding function. For example, for Embedding, the argument is the embedding dimension with the key "embedding_dim"
• --mlp_kwargs Arguments for the MLP. For example, for the MLP, the argument is the number of hidden layers with the key "num_layers"
• --gnn_kwargs Arguments for the GNN. For example, for GIN, the argument is the number of MLP layers with the key "num_layers"
• --use_one_hot {True,False} Whether to use one-hot encoding for the node features. Only for 1-WL+NN:GNN models.

Regression Datasets

To ensure consistency in the regression datasets, we created separate Python scripts for each fixed split. To test any of these datasets, follow these steps.

1. cd Code/
2. python filename where filename is substituted by the following:

• gnn_alchemy_{10K, full} To test GNN configurations on ALCHEMY
• gnn_zinc_{10K, full} To test GNN configurations on ZINC
• main_alchemy_{10K, full} To test 1-WL+NN configurations on ALCHEMY
• main_zinc_{10K, full} To test 1-WL+NN configurations on ZINC

LaTeX code

You can locate all of our LaTeX code in the LaTeX folder. To make it easier to write the thesis, we have separated subparts of it into individual .tex files. The file that brings all of these together is called main.tex. To compile the thesis, you only need to compile this file.