用雅可比向量积分析生成模型中特征依赖关系，揭示局部线性结构。
Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models
- 通过雅可比向量积研究隐变量扰动在流模型中的传播机制。
- 在合成数据和图像上验证了雅可比估计与实际相关性的匹配度。
- 适用于需要理解生成特征依赖结构的研究者，如可解释性与因果推断。
流匹配通过学习速度场将基础分布转换为数据分布。本文研究小的隐变量扰动在这些流中的传播方式，发现雅可比-向量积（JVP）为生成特征的依赖结构提供了实用视角。我们推导了高斯及高斯混合设置下最优漂移及其雅可比的闭式表达，揭示即使全局非线性的流也具有局部仿射结构。在低维合成基准上，数值计算的JVP能准确恢复解析雅可比；在图像领域，将流与属性分类器组合，得到属性级JVP估计器，在MNIST和CelebA上成功恢复了经验相关性。对小分类器-雅可比范数进行条件化可降低相关性，结果符合共同原因结构假设，但该条件化并非正式的do干预。
原文摘要 · Abstract (English)
Flow matching learns a velocity field that transports a base distribution to data. We study how small latent perturbations propagate through these flows and show that Jacobian-vector products (JVPs) provide a practical lens on dependency structure in the generated features. We derive closed-form expressions for the optimal drift and its Jacobian in Gaussian and mixture-of-Gaussian settings, revealing that even globally nonlinear flows admit local affine structure. In low-dimensional synthetic benchmarks, numerical JVPs recover the analytical Jacobians. In image domains, composing the flow with an attribute classifier yields an attribute-level JVP estimator that recovers empirical correlations on MNIST and CelebA. Conditioning on small classifier-Jacobian norms reduces correlations in a way consistent with a hypothesized common-cause structure, while we emphasize that this conditioning is not a formal do intervention.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。