Reducing Mode Collapse With Monge–Kantorovich Optimal Transport for Generative Adversarial Networks
提出Monge GAN，将模式崩溃问题转化为Monge最优传输映射问题，利用Kantorovich公式计算最优传输距离，在图像和数值数据集上验证了减少模式崩溃的效果。
Mode collapse has been a persisting challenge in generative adversarial networks (GANs), and it directly affects the applications of GAN in many domains. Existing works that attempt to solve this problem have some serious limitations: models using optimal transport (OT) strategies (e.g., Wasserstein distance) lead to vanishing or exploding gradients; increasing the number of generators can cause several generators focusing on the same mode; and approaches that modify the loss also do not satisfactorily resolve mode collapse. In this article, we reduce mode collapse by formulating it as a Monge problem of OT map. We show that the Monge problem can be transformed to the distribution transformation problem in GAN, and a rectified affine neural network can be considered as a measurable function. In this way, we propose Monge GAN that uses this measurable function to transform the generated data distribution into the original data distribution. We utilize the Kantorovich formulation to obtain the OT cost, which is regarded as the OT distance between the two distributions. Finally, we conduct extensive experiments on both image and numerical datasets to validate our Monge GAN in reducing model collapse.