CyclOT: Learning Quadratic Optimal Transport Maps via Synchronized Forward-Backward Interpolants

תקציר מקורי באנגליתarXiv:2609.13892v1 Announce Type: cross Abstract: We study the recovery of forward and reverse quadratic optimal-transport maps from unpaired samples in high dimensions. We introduce a bidirectional neural framework in which the learned maps induce forward and backward displacement interpolants, while the training objective combines bidirectional quadratic action, discriminator-restricted Jensen-Shannon endpoint objectives, and two-sided cycle consistency. The construction requires neither precomputed sample pairings nor an explicit convex-potential parameterization. For absolutely continuous probability measures supported on a compact convex set, and under the stated generator-approximation, discriminator-richness, and minimizer-attainment conditions, we prove a population recovery theore