The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions
This addresses foundational issues in causal inference for continuous settings, with potential applications in fields like genomics, though it appears incremental in extending existing causal frameworks.
The paper tackles the geometric challenges of applying causal inference to continuous generative models by proving fundamental limits, including the Manifold Tearing Theorem and a Causal Uncertainty Principle, and introduces a scalable algorithm validated on high-dimensional data.
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 the fundamental limits of such interventions. We define the Counterfactual Event Horizon and prove the Manifold Tearing Theorem: deterministic flows inevitably develop finite-time singularities under extreme interventions. We establish the Causal Uncertainty Principle for the trade-off between intervention extremity and identity preservation. Finally, we introduce Geometry-Aware Causal Flow (GACF), a scalable algorithm that utilizes a topological radar to bypass manifold tearing, validated on high-dimensional scRNA-seq data.