Limitless Stability for Graph Convolutional Networks
Authors: Christian Koke
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | These new theoretical results are supported by corresponding numerical investigations. We focus on investigating structural perturbations, as corresponding results are most involved and novel: We first consider a graph on 5 nodes with an adjacency matrix A with Op1q-entries (c.f. 30 in Appendix N). We then scale A by 1{δa and 1{δb (with 1 δa 1 δb 1) respectively and consider the norm-difference between associated Laplacians and resolvents. Fig. 6 (a) then illustrate the theoretical result (c.f. Section 5) that resolventinstead of Laplacian-differences capture the convergence behaviour. |
| Researcher Affiliation | Academia | Anonymous authors Paper under double-blind review |
| Pseudocode | No | No pseudocode or algorithm block is explicitly labeled or provided in the paper. Figure 2 shows an "Update Rule for a GCN" as a diagram, not pseudocode. |
| Open Source Code | No | No statement regarding open-source code availability for the methodology described, nor links to repositories, are provided in the paper. |
| Open Datasets | Yes | Feature vectors are generated on the QM7 dataset. The dataset we consider is the QM7 dataset, introduced in Blum & Reymond (2009); Rupp et al. (2012). |
| Dataset Splits | No | No explicit information about training, validation, or test dataset splits (e.g., percentages, sample counts, or citations to predefined splits) is provided in the paper. The paper mentions evaluating on the QM7 dataset and averaging over "100 random unit-norm choices of f" for a specific experiment, but this is not a general dataset split. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory amounts, or cloud resources) used for running experiments are provided in the paper. |
| Software Dependencies | No | No specific software dependencies with version numbers (e.g., Python, PyTorch, TensorFlow, or other libraries) are mentioned in the paper. |
| Experiment Setup | Yes | Finally, we investigate the transferability of a two-layer GCN with 16 nodes per hidden Layer combined with the aggregation method of Section 6 into a graph-level map Ψp 2. Filters are of the form (2) up to order k 11. Coefficients tbg ku are sampled uniformly from r 100, 100s. |