A Convergence Analysis of Gradient Descent on Graph Neural Networks
Authors: Pranjal Awasthi, Abhimanyu Das, Sreenivas Gollapudi
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section we verify our theoretical results via simulations. |
| Researcher Affiliation | Industry | Pranjal Awasthi Google Research pranjalawasthi@google.com Abhimanyu Das Google Research abhidas@google.com Sreenivas Gollapudi Google Research sgollapu@google.com |
| Pseudocode | No | Explanation: The paper does not contain any sections or figures explicitly labeled as "Pseudocode" or "Algorithm" presenting structured steps. |
| Open Source Code | Yes | Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] See supplementary material. |
| Open Datasets | No | We generate an unknown ground truth network in the case of Re LU GNNs by choosing each column of W to be a random unit length vector. For the case of linear networks we generate positive deļ¬nite matrices W 1 , W 2 by picking random Gaussian entries, and then adding a small multiplicative factor of 0.001 times the identity matrix. |
| Dataset Splits | No | Explanation: The paper does not specify traditional dataset splits (e.g., training, validation, testing percentages or counts) as it operates in a 'realizable setting' with data generated from an unknown GNN. |
| Hardware Specification | No | Our experiments are run using one GPU. |
| Software Dependencies | No | We simulate population gradient descent and implement our networks using the JAX programming language [Bradbury et al., 2018]. |
| Experiment Setup | Yes | For the case of one round GNNs with Re LU activations we set the embedding size r = 10, and h = 10 (number of hidden units in the Re LU GNN). We use the same value of r for the case of deep linear GNNs, where r equals the input dimensionality and also the dimensionality of the matrices W 1 , and W 2 . |