Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914303475449856 |
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| author | Rezvan, Reza Gille, Gustav Schauer, Moritz Torkar, Richard |
| author_facet | Rezvan, Reza Gille, Gustav Schauer, Moritz Torkar, Richard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02793 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models Rezvan, Reza Gille, Gustav Schauer, Moritz Torkar, Richard Machine Learning Artificial Intelligence 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. |
| title | Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.02793 |