Instability and Local Minima in GAN Training with Kernel Discriminators
Instability and Local Minima in GAN Training with Kernel Discriminators
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DOI：
10.48550/arxiv.2208.09938
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发表时间：
2022-08
期刊：
影响因子：
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通讯作者：
Evan Becker;Parthe Pandit;S. Rangan;A. Fletcher
中科院分区：
文献类型：
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作者：
Evan Becker;Parthe Pandit;S. Rangan;A. Fletcher
Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the min-max optimization of the generator and discriminator. This paper analyzes these joint dynamics when the true samples, as well as the generated samples, are discrete, finite sets, and the discriminator is kernel-based. A simple yet expressive framework for analyzing training called the $\textit{Isolated Points Model}$ is introduced. In the proposed model, the distance between true samples greatly exceeds the kernel width, so each generated point is influenced by at most one true point. Our model enables precise characterization of the conditions for convergence, both to good and bad minima. In particular, the analysis explains two common failure modes: (i) an approximate mode collapse and (ii) divergence. Numerical simulations are provided that predictably replicate these behaviors.
