A Fast Proximal Point Method for Wasserstein Distance

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Graph Optimal Transport for Cross-Domain Alignment (2020, background): “( iii ) Efﬁciency : compared with conventional linear programming solvers, our solution can be readily obtained using iterative procedures that only require matrix-vector products (Xie et al., 2018), hence readily applicable to large deep neural networks.”
UNITER: UNiversal Image-TExt Representation Learning (2019, background): “Unfortunately, the exact minimization over T is computational intractable, and we consider the IPOT algorithm [53] to approximate”
Gromov-Wasserstein Learning for Graph Matching and Node Embedding (2019, methodology): “Additionally, we can apply the inexact proximal point method (Xie et al., 2018; Chen et al., 2018a), running one-step Sinkhorn-Knopp projection in each inner iteration.”
Towards Faithful Neural Table-to-Text Generation with Content-Matching Constraints (2020, methodology): “The details of the IPOT algorithm are shown in Appendix C. Constrained Content Matching via OT To apply the OT distance to our setting, we need to first specify the atoms in the discrete distributions.”