Shared neural map aligns multiple sources to one target distribution
Simultaneous Neural Optimal Transport
Machine LearningArtificial Intelligence
Summary
Sometimes, machines need to change different types of data so they all look like one perfect example — but it’s tricky when the data comes mixed without labels. The authors study how to find one single way to fix or transform all these different data types so each matches the perfect example well, not just overall but individually. They built a neural network method to learn this shared fix so it works well for all sources together. They tested their idea on cleaning up images with many different kinds of problems, showing one model can handle all types using this shared mapping idea.
What this means in practice
- •For image processing engineers: Create one model that restores images with various unknown degradations by aligning them to clean images.
- •For signal processing developers: Develop systems that map multiple corrupted signal sources simultaneously to a single clean signal format for noise reduction.
Authors
Milena Gazdieva, Kirill Sokolov, Jiawei Chen, Evgeny Burnaev, Alexander Korotin
Abstract
Optimal Transport (OT) provides a principled framework for learning transformations between probability distributions from unpaired samples. In many applications, however, a single transformation must map several source distributions to a common target distribution. For example, image restoration might require handling different types of degradation without knowing the degradation of each input at inference time. Simple approaches of pooling the source distributions only encourage alignment with the target at the aggregate level and may leave individual sources misaligned. In our paper, we consider the simultaneous OT problem which formalizes the task of learning a shared transport map that minimizes the average transport cost while aligning each source distribution with a prescribed target. We propose a neural method for solving the simultaneous OT problem by learning a shared transport map that minimizes the average transport cost while aligning each source distribution with a prescribed target. We derive a max-min formulation for learning this map. We illustrate its application to image restoration, where a single model handles multiple degradation types using a common collection of clean target images.