Answering complex queries on knowledge graphs is important but particularly challenging
because of the data incompleteness. Query embedding methods address this issue by …

Sinkhorn algorithm has been used pervasively to approximate the solution to optimal
transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical …

As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown
the potential for matching problems of structured data like point clouds and graphs …

Softassign is a pivotal method in graph matching and other learning tasks. Many softassign-
based algorithms exhibit performance sensitivity to a parameter in the softassign. However …

Capacity constrained optimal transport is a variant of optimal transport, which adds extra
constraints on the set of feasible couplings in the original optimal transport problem to limit …

Optimal transport (OT) studies the most economical transformation of one probability
measure into another, attracting attention across diverse fields and inspiring various OT …

By further exploring and deeply analyzing the concrete algebraic structures and essential
computational properties about the Wasserstein-1 metric matrices of one-and two …

The multimarginal optimal transport problem with Coulomb cost arises in quantum physics
and is vital in understanding strongly correlated quantum systems. Its intrinsic curse of …

Numerically solving multi-marginal optimal transport (MMOT) problems is computationally
prohibitive, even for moderate-scale instances involving $ l\ge4 $ marginals with support …

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to
the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes …