<ul><li>The paper discusses the problem of approximating an n-dimensional probability measure with an m-dimensional measure.</li><li>The approach involves the use of Monge-Kantorovich (Wasserstein) p-cost to quantify the performance of the approximation.</li><li>The complexity is constrained by bounding the Sobolev norm of the coverable support by an 'f' function.</li><li>The study also presents a gradient analysis of the functional and proposes interpretations for regularization in improvement of training.</li></ul>

Monge-Kantorovich Fitting With Sobolev Budgets

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