2 layer neural networks as Wasserstein gradient flows
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The Monge Problem [1] is a problem in Optimal Transport concerning the best way to rearrange mass. It was the earliest formulation of a problem in Optimal Transport and was later generalized to the Kantorovich Problem. Unlike the Kantorovich Problem, which allows the splitting of mass, the Monge Problem asks for the most efficient allocation map that doesn't assign any mass from any source to more than one location.
Motivation
Shallow Neural Networks
Continuous Formulation
Minimization Problem
Wasserstein Gradient Flow
Main Results
References
- ↑ [https://people.math.ethz.ch/~afigalli/lecture-notes-pdf/The-continuous-formulation-of-shallow-neural-networks-as-wasserstein-type-gradient-flows.pdf XAVIER FERNANDEZ-REAL AND ALESSIO FIGALLI, THE CONTINUOUS FORMULATION OF SHALLOW NEURAL NETWORKS AS WASSERSTEIN-TYPE GRADIENT FLOWS]