A principled minimax training procedure over input convex neural networks learns the optimal quadratic-cost transport map as the gradient of a convex potential.
Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models
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abstract
We propose a potential flow generator with $L_2$ optimal transport regularity, which can be easily integrated into a wide range of generative models including different versions of GANs and flow-based models. We show the correctness and robustness of the potential flow generator in several 2D problems, and illustrate the concept of "proximity" due to the $L_2$ optimal transport regularity. Subsequently, we demonstrate the effectiveness of the potential flow generator in image translation tasks with unpaired training data from the MNIST dataset and the CelebA dataset.
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cs.LG 1years
2019 1verdicts
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Optimal transport mapping via input convex neural networks
A principled minimax training procedure over input convex neural networks learns the optimal quadratic-cost transport map as the gradient of a convex potential.