Provides a sheaf-theoretic proof that local causal consistency in generative models does not guarantee global counterfactual coherence.
March 19, 2026
Original Paper
Cohomological Obstructions to Global Counterfactuals: A Sheaf-Theoretic Foundation for Generative Causal Models
arXiv · 2603.17384
The Takeaway
Establishes the fundamental topological limits of counterfactual interventions in continuous models (like Diffusion). It introduces 'Manifold Tearing' as a formal failure mode, forcing researchers to rethink how we model causality in high-dimensional spaces.
From the abstract
Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails fundamentally when the causal graph exhibits non-trivial homology (e.g., structural conflicts or hidden confounders). We formalize structural causal models as cellular sheaves over Wasserstein spaces, providing a strict algebraic topological definition of cohom