# Mode Collapse and Regularity of Optimal Transportation Maps

This work builds the connection between the regularity theory of optimal transportation map, Monge-Amp\{e}re equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse. According to the regularity theory of Monge-Amp\{e}re equation, if the support of the target measure is disconnected or just non-convex, the optimal transportation mapping is discontinuous... (read more)

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