用电场模型生成与迁移数据，物理原理清晰且可证明有效
Field Matching: an Electrostatic Paradigm to Generate and Transfer Data
- 用神经网络学习电容两极间的静电场线
- 沿场线移动样本实现分布间精确转换，理论可证有效
- 适合生成与迁移任务，代码开源便于复现
我们提出电场匹配（Electrostatic Field Matching, EFM），一种适用于生成建模与分布迁移的新型方法。该方法受电容器物理原理启发：将源分布与目标分布分别置于电容两极，并赋予正负电荷。通过神经网络逼近电容的静电场，再沿学习到的电场线从一极移动样本至另一极，实现分布映射。理论上，该方法可保证分布转移的正确性。在合成数据与图像数据实验中，我们验证了EFM的有效性。代码已公开于https://github.com/justkolesov/FieldMatching。
原文摘要 · Abstract (English)
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
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