text: 488,98,1359004813942525953,206818334,Ivan Oseledets,1/n Analyzing GAN convergence is hard. We derived exact rates and oscillations providing complete analysis from Poincare constant and weighted Laplacian. Check our new paper <LINK> w @vforvalya1 and Artem Babenko. This is the first time the convergence is analyzed in the functional space (not for a fixed NN approx). I really enjoyed working on this paper: the concepts match each other very well! Check how it helps to understand data augs for GAN. We link local GAN training convergence to the fundamental properties of the density.,https://arxiv.org/abs/2102.04448,"Recent work demonstrated the benefits of studying continuous-time dynamics governing the GAN training. However, this dynamics is analyzed in the model parameter space, which results in finite-dimensional dynamical systems. We propose a novel perspective where we study the local dynamics of adversarial training in the general functional space and show how it can be represented as a system of partial differential equations. Thus, the convergence properties can be inferred from the eigenvalues of the resulting differential operator. We show that these eigenvalues can be efficiently estimated from the target dataset before training. Our perspective reveals several insights on the practical tricks commonly used to stabilize GANs, such as gradient penalty, data augmentation, and advanced integration schemes. As an immediate practical benefit, we demonstrate how one can a priori select an optimal data augmentation strategy for a particular generation task. ",Functional Space Analysis of Local GAN Convergence,3,"['1/n Analyzing GAN convergence is hard. We derived exact rates and oscillations providing complete analysis from Poincare constant and weighted Laplacian. Check our new paper <LINK> w @vforvalya1 and Artem Babenko.', 'This is the first time the convergence is analyzed in the functional space (not for a fixed NN approx). I really enjoyed working on this paper: the concepts match each other very well! Check how it helps to understand data augs for GAN.', 'We link local GAN training convergence to the fundamental properties of the density.']",21,02,535