Relaxed Wasserstein with Applications to GANs

If you are figuring what GANs are about, check on these two Highly Technical Reference pages on the subject. In the meantime:

Relaxed Wasserstein with Applications to GANs by Xin Guo, Johnny Hong, Tianyi Lin, Nan Yang

Generative Adversarial Networks (GANs) provide a versatile class of models for generative modeling. To improve the performance of machine learning models, there has recently been interest in designing objective functions based on Wasserstein distance rather than Jensen-Shannon (JS) divergence. In this paper, we propose a novel asymmetric statistical divergence called Relaxed Wasserstein (RW) divergence as a generalization of Wasserstein-L2 distance of order 2. We show that RW is dominated by Total Variation (TV) and Wasserstein-L2 distance, and establish continuity, differentiability, and duality representation of RW divergence. Finally, we provide a nonasymptotic moment estimate and a concentration inequality for RW divergence. Our experiments show that RWGANs with Kullback-Leibler (KL) divergence produce recognizable images with a ReLU Multi-Layer Perceptron (MLP) generator in fewer iterations, compared to Wasserstein-L1 GAN (WGAN).

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