The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911525107662848 |
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| author | Wu, Rui Xie, Hong Li, Yongjun |
| author_facet | Wu, Rui Xie, Hong Li, Yongjun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17385 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions Wu, Rui Xie, Hong Li, Yongjun Machine Learning 62A01, 49Q22, 60H10 I.2.0; G.3 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. |
| title | The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions |
| topic | Machine Learning 62A01, 49Q22, 60H10 I.2.0; G.3 |
| url | https://arxiv.org/abs/2603.17385 |