Neural Optimal Transport
This work addresses the computational challenge of optimal transport for researchers and practitioners in machine learning, offering a novel method that is incremental in applying neural networks to an existing problem.
The authors tackled the problem of computing optimal transport maps and plans for strong and weak transport costs by developing a neural-network-based algorithm, proving that neural networks can universally approximate transport plans and demonstrating its performance on toy examples and unpaired image-to-image translation tasks.
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.