发表机构
SLAC National Accelerator Laboratory, Stanford University; University of California, Davis; National Taiwan University; University of Utah（斯坦福大学SLAC国家加速器实验室; 加州大学戴维斯分校; 国立台湾大学; 犹他大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
CyclOT提出双向神经网络框架，通过同步前向-后向插值学习二次最优传输映射，无需配对样本或凸势参数化，并证明恢复定理与循环损失上界，实验验证了其有效性。
AI 中文摘要
我们研究在高维空间中从非配对样本恢复前向和反向二次最优传输映射的问题。我们引入了一个双向神经框架，其中学习到的映射诱导前向和后向位移插值，而训练目标结合了双向二次作用、判别器限制的Jensen-Shannon端点目标以及两侧循环一致性。该构造既不需要预先计算的样本配对，也不需要显式的凸势参数化。对于支撑在紧凸集上的绝对连续概率测度，在所述的生成器逼近、判别器丰富性和极小值可达性条件下，我们证明了一个总体恢复定理：对于每个给定的精度，只要判别器水平足够大且退火作用权重变得足够小，任何全局极小化器与前向和反向二次Brenier映射之间的相应\\(L^2\\)误差之和低于该精度。此外，循环损失以\\(\lambda W_2^2(\mu_0,\mu_1)\\)为上界。补充结果量化了近似可逆性，并表明精确的端点Jensen-Shannon散度和循环一致性分别控制缺失目标质量和多对一映射坍缩。在Swiss roll、MNIST、CelebA、单细胞扰动数据和胸部X射线图像上的实验评估了端点保真度、传输成本、逆一致性以及所诱导插值的几何形状。
英文摘要
We study the recovery of forward and reverse quadratic optimal-transport maps from unpaired samples in high dimensions. We introduce a bidirectional neural framework in which the learned maps induce forward and backward displacement interpolants, while the training objective combines bidirectional quadratic action, discriminator-restricted Jensen-Shannon endpoint objectives, and two-sided cycle consistency. The construction requires neither precomputed sample pairings nor an explicit convex-potential parameterization. For absolutely continuous probability measures supported on a compact convex set, and under the stated generator-approximation, discriminator-richness, and minimizer-attainment conditions, we prove a population recovery theorem: for every prescribed accuracy, the sum of the corresponding \(L^2\) errors between any global minimizer and the forward and reverse quadratic Brenier maps is below that accuracy, provided the discriminator level is sufficiently large and the annealing action weight becomes sufficiently small. Moreover, the cycle loss is bounded above by \(λW_2^2(μ_0,μ_1)\). Complementary results quantify approximate invertibility and show that exact endpoint Jensen-Shannon divergence and cycle consistency control missing target mass and many-to-one map collapse, respectively. Experiments on Swiss roll, MNIST, CelebA, single-cell perturbation data, and chest X-ray images evaluate endpoint fidelity, transport cost, inverse consistency, and the geometry of the induced interpolations.
Comments55 pages, 13 figures
