Convergence dynamics of Generative Adversarial Networks: the dual metric flows
This work provides a theoretical framework for understanding GAN convergence dynamics, which is crucial for researchers and practitioners working on improving GAN stability and mitigating issues like mode collapse.
This paper investigates the convergence dynamics of Generative Adversarial Networks (GANs) in the limit of small learning rates. It shows that GAN learning dynamics tend to a limit dynamics, similar to single network training, and introduces 'dual metric flows' as the appropriate framework for these evolution equations in metric spaces. The theory is applied to specific GAN instances to understand and mitigate mode collapse.
Fitting neural networks often resorts to stochastic (or similar) gradient descent which is a noise-tolerant (and efficient) resolution of a gradient descent dynamics. It outputs a sequence of networks parameters, which sequence evolves during the training steps. The gradient descent is the limit, when the learning rate is small and the batch size is infinite, of this set of increasingly optimal network parameters obtained during training. In this contribution, we investigate instead the convergence in the Generative Adversarial Networks used in machine learning. We study the limit of small learning rate, and show that, similar to single network training, the GAN learning dynamics tend, for vanishing learning rate to some limit dynamics. This leads us to consider evolution equations in metric spaces (which is the natural framework for evolving probability laws) that we call dual flows. We give formal definitions of solutions and prove the convergence. The theory is then applied to specific instances of GANs and we discuss how this insight helps understand and mitigate the mode collapse. Keywords: GAN; metric flow; generative network