用Transformer学习分布嵌入，快速生成新分布间的最优传输映射
Embedding Empirical Distributions for Computing Optimal Transport Maps
- 用Transformer提取不同长度分布数据的嵌入表示
- 通过超网络将嵌入转化为神经网络最优传输映射
- 适用于多分布间快速匹配，适合信号处理与生成建模场景
分布数据在现代信号处理中日益重要，亟需在多个概率分布间计算最优传输（OT）映射。然而，现有神经网络OT方法主要集中于高效计算两分布间的单一映射。为此，我们提出一种新方法，用于学习新经验分布的传输映射。具体地，采用Transformer架构从长度各异的分布数据中生成嵌入；这些嵌入随后输入超网络，生成神经网络形式的最优传输映射。通过多项数值实验验证了嵌入质量与生成映射的有效性。模型实现与代码已公开于 https://github.com/jiangmingchen/HOTET。
原文摘要 · Abstract (English)
Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT methods predominantly focused on the efficient computation of a single map between two distributions. To address this challenge, we introduce a novel approach to learning transport maps for new empirical distributions. Specifically, we employ the transformer architecture to produce embeddings from distributional data of varying length; these embeddings are then fed into a hypernetwork to generate neural OT maps. Various numerical experiments were conducted to validate the embeddings and the generated OT maps. The model implementation and the code are provided on https://github.com/jiangmingchen/HOTET.
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