Abstract Multimarginal Optimal Transport (MOT) has attracted significant interest due to applications in machine learning, statistics, and the sciences. However, most applications, success of MOT is severely limited by a lack efficient algorithms. Indeed, general requires exponential time number marginals k their support sizes n . This paper develops theory about what “structure” makes solvable...

In addition to being extremely non-linear, modern problems require millions if not billions of parameters solve or at least get a good approximation the solution, and neural networks are known assimilate that complexity by deepening widening their topology in order increase level non-linearity needed for better approximation. However, compact topologies always preferred deeper ones as they offe...