arXiv:2607. 27078v1 Announce Type: cross Abstract: In this paper, we formulate three communication tasks for empirical optimal transport: distributed coupling sampling, cost-evaluable coupling output, and scalar value-certified sampling.
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In this paper, we formulate three communication tasks for empirical optimal transport: distributed coupling sampling, cost-evaluable coupling output, and scalar value-certified sampling. Our main result is a field-code compiler: any communicated transport field approximating an optimal empirical Monge map to error $η$ can be completed by sparse target-cell residuals into an exact-marginal value-certified sampler with scalar certificate $W_1(μ,ν)\leq U\leq W_1(μ,ν)+2Δ$, where $Δ$ is the public target-partition diameter.
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