Field Matching: an Electrostatic Paradigm to Generate and Transfer Data

Alexander Kolesov, S. I. Manukhov, Vladimir Vladimirovich Palyulin, Alexander Korotin
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:31202-31222, 2025.

Abstract

We propose Electrostatic Field Matching (EFM), a novel method that is suitable for both generative modelling 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. We then learn the capacitor’s electrostatic field 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-kolesov25a, title = {Field Matching: an Electrostatic Paradigm to Generate and Transfer Data}, author = {Kolesov, Alexander and Manukhov, S. I. and Palyulin, Vladimir Vladimirovich and Korotin, Alexander}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {31202--31222}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/kolesov25a/kolesov25a.pdf}, url = {https://proceedings.mlr.press/v267/kolesov25a.html}, abstract = {We propose Electrostatic Field Matching (EFM), a novel method that is suitable for both generative modelling 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. We then learn the capacitor’s electrostatic field 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.} }
Endnote
%0 Conference Paper %T Field Matching: an Electrostatic Paradigm to Generate and Transfer Data %A Alexander Kolesov %A S. I. Manukhov %A Vladimir Vladimirovich Palyulin %A Alexander Korotin %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-kolesov25a %I PMLR %P 31202--31222 %U https://proceedings.mlr.press/v267/kolesov25a.html %V 267 %X We propose Electrostatic Field Matching (EFM), a novel method that is suitable for both generative modelling 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. We then learn the capacitor’s electrostatic field 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.
APA
Kolesov, A., Manukhov, S.I., Palyulin, V.V. & Korotin, A.. (2025). Field Matching: an Electrostatic Paradigm to Generate and Transfer Data. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:31202-31222 Available from https://proceedings.mlr.press/v267/kolesov25a.html.

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