Generative Adversarial Networks: Dynamics
Authors: Matias G. Delgadino, Bruno B. Suassuna, Rene Cabrera
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study quantitatively the overparametrization limit of the original Wasserstein-GAN algorithm. Effectively, we show that the algorithm is a stochastic discretization of a system of continuity equations for the parameter distributions of the generator and discriminator. We show that parameter clipping to satisfy the Lipschitz condition in the algorithm induces a discontinuous vector field in the mean field dynamics, which gives rise to blow-up in finite time of the mean field dynamics. We look into a specific toy example that shows that all solutions to the mean field equations converge in the long time limit to time periodic solutions, this helps explain the failure to converge of the algorithm. |
| Researcher Affiliation | Academia | Matias G. Delgadino EMAIL Department of Mathematics University of Texas at Austin Austin, TX 78712, USA; Bruno B. Suassuna EMAIL Departamento de Matematica Pontif ıcia Universidade Cat olica do Rio de Janeiro Rio De Janeiro, RJ 22451-900, Brazil; Rene Cabrera EMAIL Department of Mathematics University of Texas at Austin Austin, TX 78712, USA |
| Pseudocode | No | The paper describes algorithms conceptually and mathematically (e.g., 'We follow a simplified version of parameter training algorithm...'), but does not provide any structured pseudocode or algorithm blocks with numbered steps or code-like formatting. |
| Open Source Code | No | The paper does not contain any statements or links indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | The paper uses theoretical probability measures like 'the standard Gaussian N(0, 1)' and a 'bimodal distribution' in a toy example, but it does not utilize or provide access information for any named, publicly available datasets for empirical validation. |
| Dataset Splits | No | The paper focuses on theoretical analysis and does not conduct experiments on datasets that would require specific training, validation, or test splits. Therefore, no dataset split information is provided. |
| Hardware Specification | No | The paper does not describe any specific hardware (e.g., GPU, CPU models) used for running experiments. Mentions of 'GPU compute time' are in reference to prior work by others, not the authors' own experimental setup. |
| Software Dependencies | No | The paper mentions algorithms like 'SGD', 'RMSProp', and 'Adam', but it does not specify any software libraries or frameworks with version numbers that would be necessary to replicate the work described. |
| Experiment Setup | No | The paper is theoretical and focuses on mathematical dynamics. It does not describe an experimental setup with specific hyperparameters, model initialization, or training schedules. While a 'learning rate h > 0' is mentioned, it is in the context of the theoretical model's parameters rather than an empirical experiment. |