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

• URL: http://arxiv.org/abs/2603.17385v1
• Date: Wed, 18 Mar 2026 06:07:35 GMT
• Title: The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions
• Abstract summary: Judea Pearl's do-calculus provides a foundation for causal inference, but its translation to continuous generative models remains fraught with geometric challenges.<n>We define the Counterfactual Event Horizon and prove the Manifold Tearing Theorem.<n>We introduce Geometry-Aware Causal Flow (GACF), a scalable algorithm that utilizes a topological radar to bypass manifold tearing.
• Score: 7.073238726507493
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• The Geometric Price of Discrete Logic: Context-driven Manifold Dynamics of Number Representations [6.414826816896125]
  Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries.<n>We argue that task context operates as a non-isometric dynamical operator that enforces a necessary "topological distortion"<n>We validate this geometric evolution across a gradient of tasks, from simple mapping to complex primality testing.
  arXiv  Detail & Related papers  (2026-03-24T13:41:57Z)
• Cohomological Obstructions to Global Counterfactuals: A Sheaf-Theoretic Foundation for Generative Causal Models [7.073238726507493]
  We formalize structural causal models as cellular sheaves over Wasserstein spaces.<n>To ensure tractability, we introduce entropic regularization and derive the Entropic Wasserstein Causal Sheaf Laplacian.<n>Our framework successfully leverages thermodynamic noise to navigate topological barriers in high-dimensional scRNA-seq counterfactuals.
  arXiv  Detail & Related papers  (2026-03-18T06:07:07Z)
• Robust Sequential Tracking via Bounded Information Geometry and Non-Parametric Field Actions [0.0]
  Empirical benchmarks across three domains--LiDAR maneuvering target tracking, high-frequency cryptocurrency order flow, and quantum state tomography--demonstrate that this information geometry analytically truncates outliers.
  arXiv  Detail & Related papers  (2026-03-13T21:40:44Z)
• On Multi-Step Theorem Prediction via Non-Parametric Structural Priors [50.16583672681106]
  In this work, we explore training-free theorem prediction through the lens of in-context learning (ICL)<n>We propose Theorem Precedence Graphs, which encode temporal dependencies from historical solution traces as directed graphs, and impose explicit topological constraints that effectively prune the search space during inference.<n>Experiments on the FormalGeo7k benchmark show that our method achieves 89.29% accuracy, substantially outperforming ICL baselines and matching state-of-the-art supervised models.
  arXiv  Detail & Related papers  (2026-03-05T06:08:50Z)
• Riemannian Flow Matching for Disentangled Graph Domain Adaptation [51.98961391065951]
  Graph Domain Adaptation (GDA) typically uses adversarial learning to align graph embeddings in Euclidean space.<n>DisRFM is a geometry-aware GDA framework that unifies embedding and flow-based transport.
  arXiv  Detail & Related papers  (2026-01-31T11:05:35Z)
• Operational Derivation of Born's Rule from Causal Consistency in Generalized Probabilistic Theories [0.0]
  We show that any admissible state-to-probability map must be affine under mixing.<n>We identify Born's rule as a causal fixed point among admissible probabilistic laws.
  arXiv  Detail & Related papers  (2025-12-14T10:50:42Z)
• Obtaining continuum physics from dynamical simulations of Hamiltonian lattice gauge theories [0.0]
  We introduce a new framework for rigorously controlling the impact of approximate time evolution on the continuum limit.<n>We show that, using the SBTE protocol, which prescribes driving the approximate time evolution error below the working statistical uncertainty, leads to a simplified renormalization procedure.
  arXiv  Detail & Related papers  (2025-06-19T19:28:21Z)
• Bridging General Relativity and Quantum Dynamics Through Finite-Resource Logical Models [0.0]
  A theoretical framework bridging General Relativity (GR) and Quantum Dynamics (QD) is introduced through the application of Kripke semantics and linear logic.<n>Our framework, termed Energy Constrained Linear Causality (ECLC), models quantum transitions and spacetime evolution as logically constrained processes.<n>ECLC provides a unified, resource-aware logic for describing causality, computation and emergence within a finite physical universe.
  arXiv  Detail & Related papers  (2025-03-29T16:05:50Z)
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking [79.16635054977068]
  We consider a chain of parametrically-driven quantum resonators coupled only via weak nearest-neighbour cross-Kerr interaction.<n>Topology is dictated by the structure of the Kerr nonlinearity, yielding a non-trivial bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2025-03-15T00:20:45Z)
• Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computation [52.73824786627612]
  This paper establishes new convergence results for textitgeodesic strongly monotone games.<n>Our key result shows that RGD attains last-iterate linear convergence in a textitgeometry-agnostic fashion.<n>Overall, this paper presents the first geometry-agnostic last-iterate convergence analysis for games beyond the Euclidean settings.
  arXiv  Detail & Related papers  (2023-06-29T01:20:44Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Causal Expectation-Maximisation [70.45873402967297]
  We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs. We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
  arXiv  Detail & Related papers  (2020-11-04T10:25:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.