Causality--Δ: Jacobian-Based Dependency Analysis in Flow Matching Models

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.

ClaudesLens: Uncertainty Quantification in Computer Vision Models

In a world where more decisions are made using artificial intelligence, it is of utmost importance to ensure these decisions are well-grounded. Neural networks are the modern building blocks for artificial intelligence. Modern neural network-based computer vision models are often used for object classification tasks. Correctly classifying objects with \textit{certainty} has become of great importance in recent times. However, quantifying the inherent \textit{uncertainty} of the output from neural networks is a challenging task. Here we show a possible method to quantify and evaluate the uncertainty of the output of different computer vision models based on Shannon entropy. By adding perturbation of different levels, on different parts, ranging from the input to the parameters of the network, one introduces entropy to the system. By quantifying and evaluating the perturbed models on the proposed PI and PSI metrics, we can conclude that our theoretical framework can grant insight into the uncertainty of predictions of computer vision models. We believe that this theoretical framework can be applied to different applications for neural networks. We believe that Shannon entropy may eventually have a bigger role in the SOTA (State-of-the-art) methods to quantify uncertainty in artificial intelligence. One day we might be able to apply Shannon entropy to our neural systems.