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Neural Optimal Transport
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Neural Optimal Transport
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We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans between probability distributions. We evaluate the performance of our optimal transport algorithm on toy examples and on the unpaired image-to-image translation.
Forward citations
Cited by 10 Pith papers
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Stability of the Monge Map in Semi-Dual Optimal Transport
Semi-dual optimal transport has a degenerate saddle-point structure equivalent to constrained optimization, with necessary and sufficient conditions derived for Monge map convergence independent of dual potential optimality.
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Convex relaxation approaches for high-dimensional optimal transport
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Stability of the Monge Map in Semi-Dual Optimal Transport
Semi-dual OT formulation has degenerate saddle-point structure; necessary and sufficient conditions for Monge map convergence are derived without requiring dual potential optimality.
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Stability of the Monge Map in Semi-Dual Optimal Transport
Semi-dual optimal transport has a degenerate saddle-point structure whose solution is a constrained optimization problem, giving necessary and sufficient conditions for Monge map convergence independent of dual optimality.
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