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The Monge Gap: A Regularizer to Learn All Transport Maps



Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another.
Recent works have drawn inspiration from Brenier’s theorem, which states that when the ground cost is the squared-Euclidean distance, the “best” map to morph a continuous measure in into another must be the gradient of a convex function.
To exploit that result, , Makkuva et al. (2020); Korotin et al. (2020) consider maps , where is an input convex neural network (ICNN), as defined by Amos et al. 2017, and fit with SGD using…



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Improved Modelling of Federated Datasets using Mixtures-of-Dirichlet-Multinomials

In practice, training using federated learning can be orders of magnitude slower than standard centralized training. This severely limits the amount of experimentation and tuning that can be done, making it challenging to obtain good performance on a...

IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 2024

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Introducing Apple’s On-Device and Server Foundation Models

Introducing Apple’s On-Device and Server Foundation Models Article Source link and Credit