Neural Entropic Optimal Transport and Gromov-Wasserstein Alignment

Understand

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.

• Entropic regularization has emerged as a promising solution, allowing parametric convergence rates via the plug-in estimator, which can be computed using the Sinkhorn algorithm (or its iterations in the GW case).
• However, Sinkhorn's $O(n^2)$ time complexity for an $n$-sized dataset becomes prohibitive for modern, massive datasets.
• In this work, we propose a new computational framework for the entropic OT and GW problems that replaces the Sinkhorn step with a neural network trained via backpropagation on mini-batches.