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Meta Optimal Transport
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We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems. Otherwise, standard methods ignore the knowledge of the past solutions and suboptimally re-solve each problem from scratch. We instantiate Meta OT models in discrete and continuous settings between grayscale images, spherical data, classification labels, and color palettes and use them to improve the computational time of standard OT solvers. Our source code is available at http://github.com/facebookresearch/meta-ot
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Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs
ULOT amortizes fused unbalanced Gromov-Wasserstein optimization: a cross-attention graph network trained to minimize FUGW loss predicts near-optimal transport plans for new graph pairs at quadratic inference cost.
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