用配对最优传输训练全条件流模型，解决连续条件下的稀疏数据问题。
Pairwise Optimal Transports for Training All-to-All Flow-Based Condition Transfer Model
- 设计新损失函数，同时学习所有条件对间的最优传输路径。
- 理论证明在极限下收敛到无限多条件对的最优传输结果。
- 适用于化学性质等连续条件场景，代码已开源。
本文提出一种基于流的框架，用于学习条件分布间的全对全转移映射，近似配对最优传输。针对连续条件常伴随大量条件且每类观测稀疏的问题，提出新型损失函数，实现所有条件对间最优传输的联合学习。该方法在理论上保证：当样本无限时，可收敛至所有条件对间的最优传输解。学习得到的传输映射被用于条件流匹配中的数据点耦合。在合成数据、基准数据集及以连续物理性质为条件的化学数据集上均验证了有效性。项目代码见 https://github.com/kotatumri-room/A2A-FM。
原文摘要 · Abstract (English)
In this paper, we propose a flow-based method for learning all-to-all transfer maps among conditional distributions that approximates pairwise optimal transport. The proposed method addresses the challenge of handling the case of continuous conditions, which often involve a large set of conditions with sparse empirical observations per condition. We introduce a novel cost function that enables simultaneous learning of optimal transports for all pairs of conditional distributions. Our method is supported by a theoretical guarantee that, in the limit, it converges to the pairwise optimal transports among infinite pairs of conditional distributions. The learned transport maps are subsequently used to couple data points in conditional flow matching. We demonstrate the effectiveness of this method on synthetic and benchmark datasets, as well as on chemical datasets in which continuous physical properties are defined as conditions. The code for this project can be found at https://github.com/kotatumuri-room/A2A-FM
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