Field Codes for Distributed Coupling Samplers and Certified Empirical Transport
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. The certificate accuracy is controlled by $Δ$ alone. The field error $η$ controls residual communication under a cell-margin condition; without a margin, $η$ alone does not...
| Authors | Hung Mai, Hai Nguyen, Luong Doan et al. |
|---|---|
| Primary category | cs.CC |
| Published | 29 July 2026 |
| Last updated at source | 30 July 2026 |
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