Reproduce “Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Jaemoo Choi, Jaewoong Choi, Dohyun Kwon
A new Optimal Transport Plan (OTP) model, developed by researchers including those at Georgia Tech, addresses the "spurious solution problem" in Semi-dual Neural Optimal Transport by introducing a smoothing approach that ensures convergence to the true optimal transport plan, even for stochastic mappings. This method improves accuracy on synthetic benchmarks and achieves competitive performance in unpaired image-to-image translation tasks, such as reducing the FID score from 62.4 to 3.18 on a colorization task.
Key insights
- SNOT frameworks correctly learn the true OT map only when the source distribution `μ` does not place positive mass on measurable sets with a Hausdorff dimension of `d-1` or less.
- SNOT failure cases extend beyond scenarios with non-unique deterministic maps, also occurring when a unique deterministic map exists or when only a stochastic OT plan is possible.
- The proposed OTP model is theoretically guaranteed to converge weakly to the true optimal transport plan `π*` between the original source and target distributions as the smoothing noise level `ϵ` approaches zero.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.