8 papers · 1 filter
Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates
Rui Wu, Zongyuan Chen, Hong Xie +2
Smooth acyclicity constraints answer whether a weighted support is a DAG, whereas structure learning asks which support change should be made. Existing analyses establish degenerac…
Learning Generated Controls under Fractured Geometry: Projective Residualization and Variation-Allocation Frontiers
Rui Wu, Zongyuan Chen, Hong Xie +2
Many two-stage estimators assess the first-stage learner by prediction error, even when the next stage uses its residual. In control-function instrumental variables, that residual…
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…