Mixture Density Generative Adversarial Networks
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Generative Adversarial Networks have surprising ability for generating sharp and realistic images, though they are known to suffer from the so-called mode collapse problem. In this paper, we propose a new GAN variant called Mixture Density GAN that while being capable of generating high-quality images, overcomes this problem by encouraging the Discriminator to form clusters in its embedding space, which in turn leads the Generator to exploit these and discover different modes in the data. This is achieved by positioning Gaussian density functions in the corners of a simplex, using the resulting Gaussian mixture as a likelihood function over discriminator embeddings, and formulating an objective function for GAN training that is based on these likelihoods. We show that the optimum of our training objective is attained if and only if the generated and the real distribution match exactly. We further support our theoretical results with empirical evaluations on one synthetic and several real image datasets (CIFAR-10, CelebA, MNIST, and FashionMNIST). We demonstrate empirically (1) the quality of the generated images in Mixture Density GAN and their strong similarity to real images, as measured by the Fréchet Inception Distance (FID), which compares very favourably with state-of-the-art methods, and (2) the ability to avoid mode collapse and discover all data modes.
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