How Powerful are Spectral Graph Neural Networks
Authors: Xiyuan Wang, Muhan Zhang
ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In numerical experiments, we first test the expressive power of Jacobi Conv to approximate filter functions on synthetic datasets. Jacobi Conv achieves the lowest loss on learning the filter functions compared to state-of-the-art spectral GNNs. We also show that Jacobi Conv outperforms all baselines on ten real-world datasets by up to 12%. |
| Researcher Affiliation | Academia | 1Institute for Artificial Intelligence, Peking University 2Beijing Institute for General Artificial Intelligence. Correspondence to: Muhan Zhang <muhan@pku.edu.cn>. |
| Pseudocode | No | No pseudocode or algorithm blocks are explicitly labeled or presented in a structured format. |
| Open Source Code | Yes | Our code is available at https://github. com/Graph PKU/Jacobi Conv. |
| Open Datasets | Yes | For homogeneous graphs, we include three citation graph datasets, Cora, Cite Seer and Pub Med (Yang et al., 2016), and two Amazon co-purchase graphs, Computers and Photo (Shchur et al., 2018). We also use heterogeneous graphs, including Wikipedia graphs Chameleon and Squirrel (Rozemberczki et al., 2021), the Actor co-occurrence graph, and the webpage graph Texas and Cornell from Web KB3 (Pei et al., 2020). |
| Dataset Splits | Yes | We perform the node classification task, where we randomly split the node set into train/validation/test sets with a ratio of 60%/20%/20%. |
| Hardware Specification | No | All experiments are conducted on an Nvidia A40 GPU on a Linux server. |
| Software Dependencies | No | We leverage Pytorch Geometric and Pytorch for model development. (No specific version numbers are provided.) |
| Experiment Setup | Yes | Model hyperparameter for Synthetic Datasets. We use optuna to perform random searches. Hyperparameters were selected to minimize average loss on the fifty images. The best hyperparameters selected for each model can be found in our code. For linear GNNs, we use different learning rate and weight decay for the linear layer W, parameters of PCD θ, and the linear combination parameters α. We select learning rate from {0.0005, 0.001, 0.005, 0.01, 0.05}, weight decay from {0.0, 5e 5, 1e 4, 5e 4, 1e 3}. We select PCD s γ from {0.5, 1.0, 1.5, 2.0}. Jacobi Basis a and b are selected from [ 1.0, 2.0]. Model hyperparameter for real-world datasets. Hyperparameters were selected to optimize accuracy scores on the validation sets. We use different dropout for X and XW. Both dropout probabilities are selected from [0.0, 0.9]. |