6 papers
Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobians
Rui Wu, Hong Xie
Continuous causal discovery typically couples representation learning with structural optimization via non-convex acyclicity penalties, which subjects solvers to local optima and r…
The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions
Rui Wu, Hong Xie, Yongjun Li
Judea Pearl's do-calculus provides a foundation for causal inference, but its translation to continuous generative models remains fraught with geometric challenges. We establish th…
Cohomological Obstructions to Global Counterfactuals: A Sheaf-Theoretic Foundation for Generative Causal Models
Rui Wu, Hong Xie, Yongjun Li
Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfa…
Causal Schrödinger Bridges: Constrained Optimal Transport on Structural Manifolds
Rui Wu, Li YongJun
Generative modeling typically seeks the path of least action via deterministic flows (ODE). While effective for in-distribution tasks, we argue that these deterministic paths becom…
Smooth, Sparse, and Stable: Finite-Time Exact Skeleton Recovery via Smoothed Proximal Gradients
Rui Wu, Yongjun Li
Continuous optimization has significantly advanced causal discovery, yet existing methods (e.g., NOTEARS) generally guarantee only asymptotic convergence to a stationary point. Thi…
The Causal Round Trip: Generating Authentic Counterfactuals by Eliminating Information Loss
Rui Wu, Lizheng Wang, Yongjun Li
Judea Pearl's vision of Structural Causal Models (SCMs) as engines for counterfactual reasoning hinges on faithful abduction: the precise inference of latent exogenous noise. For d…