Field Matching: an Electrostatic Paradigm to Generate and Transfer Data
This addresses distribution transfer and generative modeling tasks for machine learning applications, presenting a novel paradigm.
The paper tackles the problem of generative modeling and distribution transfer by proposing Electrostatic Field Matching (EFM), a method inspired by electrical capacitors that maps samples along learned electrostatic field lines, and demonstrates its performance in toy and image data experiments with theoretical justification.
We propose Electrostatic Field Matching (EFM), a novel method that is suitable for both generative modeling and distribution transfer tasks. Our approach is inspired by the physics of an electrical capacitor. We place source and target distributions on the capacitor plates and assign them positive and negative charges, respectively. Then we learn the electrostatic field of the capacitor using a neural network approximator. To map the distributions to each other, we start at one plate of the capacitor and move the samples along the learned electrostatic field lines until they reach the other plate. We theoretically justify that this approach provably yields the distribution transfer. In practice, we demonstrate the performance of our EFM in toy and image data experiments. Our code is available at https://github.com/justkolesov/FieldMatching