Learning disconnected manifolds: a no GANs land

Typical architectures of Generative AdversarialNetworks make use of a unimodal latent distribution transformed by a continuous generator. Consequently, the modeled distribution always has connected support which is cumbersome when learning a disconnected set of manifolds.We formalize this problem by establishing a no free lunch theorem for the disconnected manifold learning stating an upper bound on the precision of the targeted distribution. This is done by building on the necessary existence of a low-quality region where the generator continuously samples data between two disconnected modes. Finally, we derive a rejection sampling method based on the norm of generators Jacobian and show its efficiency on several generators including BigGAN.

学习断开的歧管：没有GAN土地

生成对抗网络的典型体系结构利用由连续生成器转换的单峰潜在分布。因此，建模的分布始终具有连接的支持，这在学习一组断开的歧管时非常麻烦。.. 我们通过为不连续的流形学习建立无免费午餐定理来对这个问题进行形式化，该定理指出了目标分布的精度上限。这是通过建立必要的低质量区域来实现的，在该区域中，生成器会在两个断开的模式之间连续采样数据。最后，我们基于发电机雅可比定律导出了一种拒绝采样方法，并在包括BigGAN在内的多个发电机上展示了其效率。 （阅读更多）