揭示因果干预的拓扑极限，提出可规避奇异性的高效算法
The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions
- 用拓扑雷达识别数据流形撕裂点，实现安全因果干预
- 证明极端干预必然导致确定性流形在有限时间产生奇点
- 适用于单细胞测序等高维数据的因果推断，适合机器学习与生物医学研究者
Judea Pearl 的 do-演算为因果推断提供了基础，但其向连续生成模型的迁移面临几何挑战。本文确立了此类干预的根本限制：定义反事实事件视界，并证明流形撕裂定理——确定性流在极端干预下必在有限时间内产生奇点。提出因果不确定性原理，揭示干预强度与身份保留之间的权衡关系。最后引入几何感知因果流（GACF）算法，利用拓扑雷达规避流形撕裂，在高维 scRNA-seq 数据上验证有效。
原文摘要 · Abstract (English)
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.
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