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This paper analyzes the training process of GANs via stochastic differentialequations (SDEs). It first establishes SDE approximations for the training ofGANs under stochastic gradient algorithms, with precise error bound analysis.It then describes the long-run behavior of GANs training via the invariantmeasures of its SDE approximations under proper conditions. This work buildstheoretical foundation for GANs training and provides analytical tools to studyits evolution and stability.

SDE approximations of GANs training and its long-run behavior