这篇论文提出了一种能直接用神经网络做双样本检验的新方法，比传统方法更灵活，效果也很好。
提出一种基于零流准则的统计差异度量ZFD，并设计零流双样本检验ZF2ST。该方法通过分离证据学习与假设评估，允许使用灵活神经网络进行检验。在合成数据和图像数据集上的实验表明，ZF2ST在检测结构化分布变化时具有强检验功效，同时保持校准的I类错误率。
Zero-Flow Two-Sample Tests
We propose a new approach to two-sample testing for deciding whether two sets of samples are drawn from the same distribution. The test is built on a statistical discrepancy based on the zero-flow criterion, termed zero-flow discrepancy (ZFD). We prove the validity of ZFD and propose a practical testing procedure, termed the zero-flow two-sample test (ZF2ST). The key idea is to learn how samples from the two distributions are locally misaligned and use the resulting directional pattern as evidence of distributional difference. By separating witness learning from hypothesis evaluation, ZF2ST can use flexible neural networks while maintaining valid statistical calibration. We develop both regression-based and power-maximized approaches for learning the witness. Experiments on synthetic and image datasets demonstrate that ZF2ST can achieve strong testing power for structured distributional changes while maintaining well-calibrated type-I error.