The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions

TL;DR

This paper explores the geometric and topological limitations of causal interventions in continuous models, introducing theorems and an algorithm to address manifold tearing in high-dimensional data.

Contribution

It establishes fundamental limits of interventions, introduces the Causal Uncertainty Principle, and proposes GACF to mitigate manifold tearing in causal inference.

Findings

Deterministic flows develop finite-time singularities under extreme interventions.

The Causal Uncertainty Principle quantifies the trade-off between intervention extremity and identity preservation.

GACF effectively bypasses manifold tearing in high-dimensional biological data.

Abstract

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.