Position: Spectral GNNs Rely Less on Graph Fourier Basis than Conceived
Authors: Yuhe Guo, Huayi Tang, Jiahong Ma, Hongteng Xu, Zhewei Wei
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | For issue 1, we trace how the mathematical analogies were established, review concerns raised in previous literature, present experimental findings that question this analogy, and specifically, reflect on how this questionable belief has persisted. |
| Researcher Affiliation | Academia | 1Gaoling School of Artificial Intelligence, Renmin University of China. Correspondence to: Zhewei Wei <EMAIL>. |
| Pseudocode | No | The paper describes methods and theoretical analyses but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to any code repositories. |
| Open Datasets | Yes | Measurement of localization on empirical graphs. We follow Mc Graw & Menzinger (2008) to evaluate the localization of normalized and unnormalized eigenvectors on Cora dataset (Yang et al., 2016; Sen et al., 2008) by loc(ui) = P j [1,n] u4 i,j . As shown in Figure 3, experiments on Cora dataset exhibit significant localization phenomenon on high-frequency eigenvectors |
| Dataset Splits | No | In Appendix C, we introduce the inductive and transductive learning settings in graph learning, using graph classification and node classification tasks, respectively. Spectral filtering layers are integrated into the models. We will analyze how a complex spectral polynomial filter can affect the stability and generalization of GNNs under inductive and transductive settings. |
| Hardware Specification | No | The paper discusses experimental findings and methods but does not provide specific details about the hardware used to run the experiments, such as GPU or CPU models. |
| Software Dependencies | No | The paper describes theoretical concepts and methods but does not provide specific details about software dependencies or their version numbers, such as programming languages or libraries used for implementation. |
| Experiment Setup | No | The paper discusses theoretical models, stability analysis, and generalization bounds. While it refers to "experiments" in Section 3.3, it does not provide concrete experimental setup details such as hyperparameter values (learning rates, batch sizes, epochs), optimizer settings, or other specific training configurations. |