do-calculus application

This work addresses the lack of a systematic approach to composing and ordering do-calculus rules, which hinders efficient exploration of the space of equivalent interventional queries. The paper introduces, for the first time, a derivation graph structure that formally captures the application and composition logic of do-calculus rules, systematically representing equivalence relations between observational and interventional probabilities under the do-calculus framework. Building upon this representation, the authors devise a streamlined identification procedure requiring at most four simplification steps. This approach not only reveals the intrinsic organizational structure underlying do-calculus reasoning but also enables the generation of multiple equivalent estimands for the same causal quantity, substantially improving estimation efficiency and facilitating practical applications of do-calculus.

Reinforcement learning and causal inference have long remained disconnected, lacking a systematic integration of their shared counterfactual structure, which limits agents’ generalization and reasoning capabilities in complex environments. This work proposes the first unified causal reinforcement learning framework by modeling the environment as a structural causal model, thereby uncovering the implicit causal mechanisms underlying reinforcement learning. The framework seamlessly integrates online learning, off-policy evaluation, and causal calculus. Building on this foundation, it further extends to novel tasks such as intervention selection, imitation learning, and counterfactual policy learning. This study establishes a theoretical basis for merging causality with reinforcement learning, offering a new pathway toward intelligent decision-making that is generalizable, interpretable, and cross-modal.

Causal analysis has long suffered from dual challenges: domain experts struggle with its conceptual and algorithmic complexity, while researchers lack access to realistic scenarios for empirical validation. To address these issues, we propose the first end-to-end, interactive, and methodologically rigorous autonomous causal analysis agent, powered by large language models (LLMs). It fully automates causal discovery, causal inference, algorithm selection, hyperparameter optimization, and natural-language interpretation—supporting both tabular and time-series data. The system integrates over 20 state-of-the-art causal algorithms and incorporates tool calling, multi-step reasoning, and explainability generation. Evaluated across multiple benchmarks, it significantly outperforms existing approaches in accuracy, reliability, and scalability. Crucially, it establishes the first bidirectional feedback loop between causal researchers and domain practitioners, effectively bridging the gap between theoretical advances and real-world deployment.

Real-world causal effects often exhibit context dependence (e.g., age, country, genotype), rendering conventional causal discovery methods inadequate for modeling cross-context heterogeneity. To address this, we propose the first decentralized causal discovery framework grounded in topos theory. Our method formalizes causal statements as locally true propositions, introduces *j*-stability and Lawvere–Tierney modalities to enable constructive, context-invariant reasoning, and defines *j*-do calculus—a novel causal operational semantics unifying intuitionistic logic with Pearl’s *do*-calculus. The framework uniformly integrates score-based, constraint-based, and gradient-based approaches. Evaluated on real-world biological and economic datasets, it significantly outperforms baseline methods in both causal accuracy and computational efficiency.

Learning causal graphs from observational data remains challenging due to the combinatorial constraint of acyclicity. Method: This paper proposes ALIAS, the first end-to-end differentiable framework for directed acyclic graph (DAG) learning without explicit acyclicity constraints. It introduces a novel differentiable parameterization mapping continuous space to the complete DAG space, enabling single-step, fully differentiable DAG generation and reducing computational complexity to O(n²). ALIAS jointly optimizes structure and parameters via policy-gradient-based reinforcement learning guided by standard causal scoring criteria (e.g., BIC). Contribution/Results: Extensive experiments demonstrate that ALIAS significantly outperforms state-of-the-art methods on both synthetic and real-world benchmarks. Notably, it maintains robust and efficient causal discovery performance under challenging conditions—including high dimensionality and strong latent confounding—thereby advancing scalable, differentiable causal structure learning.

Reinforcement learning (RL) struggles to discover and leverage causal relationships, resulting in limited interpretability and suboptimal decision-making efficiency. Method: This paper proposes the first online causal RL framework that tightly couples causal graph modeling, active intervention learning, and policy optimization in a closed loop. Contributions/Results: (1) We introduce the first alternating optimization mechanism for dynamic causal structure learning and policy refinement; (2) we develop the first fault-alert simulation benchmark enabling direct interventions in state space; (3) we provide theoretical guarantees showing that causal guidance induces a positive feedback loop for performance improvement. Experiments demonstrate significant gains over state-of-the-art methods on root-cause localization tasks, with enhanced robustness and interpretability. The code is publicly available.

This work addresses the dual challenges in automated theoretical research—generating novel results and reliably evaluating their validity—particularly the difficulty large language models face in detecting fabricated papers. We propose the first causal inference research framework that integrates machine-verifiable formal methods with a self-improving agent. Built upon the Lean proof assistant and the CausaLean formal library, our approach establishes an end-to-end autonomous pipeline spanning topic selection, conjecture formulation, formalization, and proof generation. A statement auditing mechanism is introduced to ensure semantic consistency between formalized theorems and their intended scientific claims. Experiments yield multiple new causal inference theorems that are both machine-verified and manually validated. All code and execution logs are publicly released.

Traditional cluster-DAGs (C-DAGs) impose partition admissibility—requiring variable clustering to yield an acyclic C-DAG—severely limiting applicability in complex systems. This work breaks that restriction by introducing *cyclic C-DAGs*, which admit arbitrary variable clusterings, including those inducing cycles. To support sound causal reasoning under cyclicity, we reformulate d-separation for clustered variables, extend the do-calculus with cluster-level inference rules, and establish a complete and sound framework for cluster-level causal identification. We prove that the framework correctly identifies all cluster-intervention effects that are causally identifiable from the underlying causal graph. Empirical evaluation demonstrates that cyclic C-DAGs significantly broaden the scope of C-DAGs in macro-scale modeling, modular system analysis, and multi-scale causal inference, thereby providing a rigorous foundation for higher-order causal abstraction.

Large language models face limitations in causal reasoning due to the complexity of causal systems and the scarcity of executable ground-truth data. To address this, this work proposes CauSim, a novel framework that, for the first time, automatically constructs verifiable structural causal model (SCM) simulators from non-executable causal knowledge. The approach reframes causal reasoning as a scalable supervised learning problem by leveraging curriculum-based complexity progression, bidirectional translation between natural language and executable models, and domain-informed data augmentation. These mechanisms enable cross-representational generalization and model self-improvement. Experimental results demonstrate that CauSim substantially enhances performance across diverse causal reasoning tasks, empirically validating a positive relationship among simulator complexity, data scale, and model capability.

This study investigates whether large language model agents genuinely understand causal mechanisms or merely rely on predictive capabilities. To this end, the authors develop a scalable, interactive environment for causal discovery that requires agents to infer structural causal models from both observational and interventional data and generalize to novel scenarios. They propose a novel evaluation framework that decouples predictive accuracy from the ability to recover true causal graphs and introduce a domain-specific language to trace the evolution of agents’ causal hypotheses. Experimental results reveal that even the strongest current models (e.g., GPT-5.2-high) achieve 92% prediction accuracy yet attain only a 0.471 F1 score in causal graph recovery. Combining observational and interventional strategies simultaneously improves both metrics to approximately 80%, and maintaining hypothesis consistency effectively mitigates premature convergence in reasoning.