Structural Causal Models

Also known as SCM

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8 papers in the last four weeks, up 60% on the four weeks before. 0.1% of all new papers.

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Latest papers 97

May 25, 2026cs.AI

CausaLab: A Scalable Environment for Interactive Causal Discovery Toward AI Scientists

We introduce CausaLab, a scalable environment for evaluating interactive causal discovery by LLM agents. Unlike prior evaluations, CausaLab evaluates both whether an agent can solve a problem using causal evidence and whether its answer is grounded in a faithful recovered causal mechanism. Each episode places an agent in a synthetic laboratory: it receives prior measurement records, intervenes on a manipulator crystal, and predicts the resonance frequency of a held-out reactor crystal governed by the same mechanism. The hidden data-generating process is a randomly sampled structural causal model (SCM), so success requires recovering both a causal graph and structural equations rather than recalling prior knowledge. Experiments show a persistent gap between prediction and mechanism recovery: in the purely observational 6-node setting, GPT-5.2-high reaches 92% task accuracy but only 0.471 all-edge

F_1

. Mixed observation-intervention strategies improve structural fidelity, while pure intervention remains difficult even for strong agents. We identify premature stopping as a major weakness and show that consistency verification mitigates it. CausaLab therefore separates predictive success from causal understanding and exposes current LLM agents' limits as experimental causal reasoners.

Junlin Yang, Dylan Zhang, Xiangchen Song +7

Tsinghua University · University of Illinois Urbana-Champaign · Carnegie Mellon University +2

Structural Causal Models LLM Agent Evaluation Causal Discovery AI Agent Benchmarks Causal Reasoning in Language Models

May 24, 2026cs.LG

Evolving Causal Regulatory Networks (ECR-Net)

Modern machine learning models excel at pattern recognition but remain brittle, often failing to generalize out of distribution (OOD) because they capture spurious correlations rather than the underlying causal data-generating process. Current causal discovery methods, while powerful, typically assume a static graph structure, rendering them unable to model systems that adapt or undergo structural changes across different environments. We introduce ECR-Net, Evolving Causal Regulatory Networks, a novel, bio-inspired framework for adaptive causal mechanism discovery. Our approach models the data-generating process not as a static graph, but as a dynamic system analogous to a Gene Regulatory Network (GRN), composed of localized, recursive functions where variables can activate and inhibit one another. To discover the latent structure of this network, we employ an evolutionary search algorithm that evolves a population of candidate regulatory graphs, optimizing for a fitness function that measures how well the simulated system dynamics reconstruct the observed data. The key innovation of ECR-Net is its ability to model structural adaptation, it explicitly ingests shifts in the data's statistical properties as signals of an environmental shock. In response, the evolutionary search identifies parsimonious modifications to the causal graph topology, such as link inhibitions or activations that explain the new data regime. We posit that ECR-Net represents a new class of adaptive Structural Causal Models capable of discovering how and why a system's fundamental rules change, offering a path toward robust generalization in complex, non-stationary systems.

Govind Vallabhasseri Binish, Abdhul Ahadh, Rano Roy Kavanal +1

Structural Causal Models Causal Discovery Causal Structure Learning Dynamic Graph Learning

May 19, 2026cs.LG

Score-Based Causal Discovery of Latent Variable Causal Models

Identifying latent variables and the causal structure involving them is essential across various scientific fields. While many existing works fall under the category of constraint-based methods (with e.g. conditional independence or rank deficiency tests), they may face empirical challenges such as testing-order dependency, error propagation, and choosing an appropriate significance level. These issues can potentially be mitigated by properly designed score-based methods, such as Greedy Equivalence Search (GES) (Chickering, 2002) in the specific setting without latent variables. Yet, formulating score-based methods with latent variables is highly challenging. In this work, we develop score-based methods that are capable of identifying causal structures containing causally-related latent variables with identifiability guarantees. Specifically, we show that a properly formulated scoring function can achieve score equivalence and consistency for structure learning of latent variable causal models. We further provide a characterization of the degrees of freedom for the marginal over the observed variables under multiple structural assumptions considered in the literature, and accordingly develop both exact and continuous score-based methods. This offers a unified view of several existing constraint-based methods with different structural assumptions. Experimental results validate the effectiveness of the proposed methods.

Ignavier Ng, Xinshuai Dong, Haoyue Dai +3

Carnegie Mellon University · University of California, San Diego · Mohamed bin Zayed University of Artificial Intelligence

Latent Variable Models Structural Causal Models Causal Discovery Causal Structure Learning Causal Identifiability Causal Discovery with Latent Confounding

May 19, 2026cs.LG

Exploiting Non-Negativity in DAG Structure Learning

This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference, but it remains challenging because acyclicity is a global combinatorial property. Continuous acyclicity constraints have led to important algorithmic advances by replacing the discrete DAG constraint with smooth equality constraints. However, existing formulations still involve difficult non-convex optimization landscapes and may suffer from degenerate first-order optimality conditions. Here, we restrict attention to DAGs with non-negative edge weights and exploit this additional structure to obtain a simpler characterization of acyclicity. Building on this characterization, we formulate a regularized non-negative DAG learning problem and develop an algorithm based on the method of multipliers. We further analyze the benign optimization landscape induced by non-negativity. In the population regime, we show that the true DAG is the unique global minimizer of the proposed augmented-Lagrangian formulation; moreover, the landscape contains no spurious interior stationary points, and the true DAG is the only acyclic KKT point. Numerical experiments on synthetic and real-world data show that the proposed method improves over state-of-the-art continuous DAG-learning alternatives.

Samuel Rey, Madeline navarro, Gonzalo Mateos

Dept. of Signal Theory and Communications, Universidad Rey Juan Carlos, Madrid, Spain · Dept. of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA · Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA

Graph Structure Learning Structural Causal Models Causal Structure Learning Nonconvex Optimization Augmented Lagrangian Method Constrained Optimization

May 19, 2026stat.ML

A Unified Framework for Structure-Aware Clustering and Heterogeneous Causal Graph Learning

In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs (

\text{DAGs}

). However, dependency structures can vary across subjects, and ignoring this structural heterogeneity introduces bias and obscures subpopulation-specific dependencies. To address this, we propose Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM), a unified framework built upon Structural Equation Modeling (SEM) that jointly learns cluster assignments and cluster-specific dependency structures. We encode acyclicity via a smooth constraint and integrate a groupwise truncated Lasso fusion penalty (gTLP) to cluster subjects based on their structural similarity. This yields a nonconvex optimization problem that incorporates sparsity, acyclicity, and structural consensus constraints. We address the nonconvexity by using the augmented Lagrangian method and solve it with an adapted version of the Alternating Direction Method of Multipliers (ADMM) for difference-of-convex programs. For certain graph structures, such as upper triangular adjacency matrices, our algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. Experiments demonstrate that our method recovers cluster-specific causal dependency structures with a high true positive rate and a low false discovery rate. This capability enables the robust discovery of heterogeneous dependencies across subjects where the subpopulation label is unknown.

Honglin Du, Muxuan Liang, Xiang Zhong

Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA · Department of Biostatistics, MD Anderson Cancer Center, Houston, TX 77030, USA

Structural Causal Models Clustering Causal Discovery Causal Structure Learning Alternating Direction Method of Multipliers

May 17, 2026cs.LG

CasualSynth: Generating Structurally Sound Synthetic Data

Large Language Models (LLMs) generate realistic synthetic data but offer no guarantee that their outputs respect the causal mechanisms governing the target domain. We introduce CausalSynth, a framework that decouples causal structure generation from semantic realization, yielding synthetic data that is both causally valid and linguistically rich. The framework operates in three phases. First, a Structural Causal Model (SCM) - a tuple of structural equations defined over a directed acyclic graph (DAG) generates causal skeletons, i.e., variable assignments that satisfy the Global Markov Property of the governing DAG, via ancestral sampling. Second, an LLM acts as a constrained \emph{realizer}, a conditional translator that maps each skeleton to a high-dimensional observation such as a clinical note or a transaction log. Third, an Iterative Consistency Verification module detects structural violations through deterministic extraction and feeds targeted corrections back to the LLM, forming a closed-loop refinement process. We identify the Semantic Backdoor problem the systematic tendency of LLMs to override imposed causal facts with pre-training priors -- and prove that our iterative mechanism reduces the resulting selection bias relative to standard rejection sampling. On three causal benchmarks (ASIA, ALARM, and MIMIC-Struct), CausalSynth preserved conditional independencies with false-positive rates near the nominal

α=0.05

level and achieved realizability rates above 96% with 70B-parameter LLM backbones. The framework additionally supports principled interventional and counterfactual generation through noise retention and graph mutilation.

Zehua Cheng, Wei Dai, Jiahao Sun +1

Department of Computer Science, University of Oxford · FLock.io United Kingdom · Institute of Logic and Computation, TU Wien

Structural Causal Models Synthetic Data Generation Causal Reasoning in Language Models Causal Inference Synthetic Data Evaluation

May 17, 2026cs.LG

TriOpt: A Scalable Algorithm for Linear Causal Discovery

Learning causal relations from observational data is challenging because the graph search space grows super-exponentially with the number of variables. Ordering-based methods reduce this space by first identifying the topological ordering, whereas continuous optimization methods explore most likely regions of the space by casting DAG learning as a differentiable objective with an acyclicity constraint. Despite their conceptual appeal, both paradigms face significant scalability limitations in high-dimensional settings, restricting their practical applicability. In this work, we introduce a new formulation for linear causal discovery that tightly integrates these two paradigms to achieve substantial gains in scalability without sacrificing accuracy. Our approach, TriOpt, decomposes the problem into two efficient stages. First, it recovers the topological ordering by exploiting the Sherman-Morrison rank-1 downdate together with the additive structure of linear kernels, enabling fast and scalable ordering estimation. Second, given this ordering, we reformulate structure learning as a convex continuous optimization problem that entirely avoids the need for enforcing costly acyclicity constraints. We theoretically show that, under the true ordering, TriOpt exactly recovers the underlying linear DAG. Empirically, across synthetic, semi-synthetic, and real-world datasets, TriOpt achieves orders-of-magnitude speedups over state-of-the-art linear causal discovery methods in high-dimensional regimes, while maintaining comparable or superior accuracy.

Rafat Ashraf Joy, Elena Zheleva

University of Illinois Chicago

Structural Causal Models Causal Discovery Causal Structure Learning

May 16, 2026stat.ML

Prediction-Intervention Games and Invariant Sets

We consider the following two-player game: using observational data, the leader chooses a prediction function for a response variable

Y

from given covariates. The follower then reacts with an intervention on some covariates in the underlying structural causal model to maximize their own objective. The leader knows the intervention targets, but may have limited knowledge of the follower's objective. We call this setup a prediction-intervention game, a special case of a Stackelberg game. Finding an optimal strategy for the leader is generally difficult. To avoid severe performance loss, the leader may base their prediction on the causal parents of

Y

, or more generally on an invariant subset of covariates. We prove, for two common classes of follower objectives, that predictors based on the stable blanket, a specific invariant subset, are always better or as good as those based on the causal parents. We further upper bound the leader's post-intervention risk by a worst-case risk over allowed interventions and strengthen existing distribution generalization results to analyze this bound: we give sufficient conditions under which stable-blanket predictors are worst-case optimal, and show by examples that these conditions cannot in general be dropped. Finally, we discuss practical strategies for settings with known and unknown graph, and test them on simulated and real-world data.

Linus Kühne, Felix Schur, Jonas Peters

Seminar for Statistics and ETH AI Center · ETH Zurich · Zurich, Switzerland +1

Structural Causal Models Game Theory Causal Inference Causal Intervention

May 13, 2026stat.ML

Causal Learning with the Invariance Principle

Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple environments (e.g., the way minimum wage affects employment rate is stable across different geographical regions), \textit{only} two auxiliary environments are sufficient to infer the causal graph for arbitrary nonlinear mechanisms. Moreover, we demonstrate that this implies identifiability of the SCM functional mechanisms: as a corollary, we show that \textit{two} auxiliary environments are sufficient to guarantee correct counterfactual inference. We empirically support our theoretical results on synthetic data.

Francesco Montagna, Francesco Locatello

Institute of Science and Technology Austria

Structural Causal Models Causal Discovery Causal Identifiability Causal Inference

May 11, 2026stat.ML

Coarsening Linear Non-Gaussian Causal Models with Cycles

Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for learning such summaries from data assume that both the high- and low-dimensional structures are acyclic, which is helpful for causal effect identification and reasoning but excludes many high-dimensional models and thus limits applicability. We show that in the linear non-Gaussian (LiNG) setting, the high-dimensional acyclicity assumption can be relaxed while still allowing recovery of a low-dimensional causal directed acyclic graph (DAG). We further connect identifiability of this low-dimensional DAG to existing results: LiNG models with cycles are observationally identifiable only up to an equivalence class whose members differ by reversals of directed cycles; our low-dimensional DAG, which is invariant across all members of a given equivalence class, thus forms a natural representative of the class. While existing approaches for learning this observational equivalence class over high-dimensional variables have exponential time complexity, our low-dimensional summary is learned in worst-case cubic time and comes with explicit bounds on the sample complexity. We provide open source code and experiments on synthetic data to corroborate our theoretical results.

Francisco Madaleno, Francisco C Pereira, Alex Markham

Department of Technology, Management and Economics, Technical University of Denmark · Department of Mathematical Sciences,11 University of Copenhagen

Structural Causal Models Causal Discovery Causal Structure Learning Causal Abstraction Causal Identifiability

May 9, 2026cs.AI

CIVeX: Causal Intervention Verification for Language Agents

A valid tool call is not necessarily a valid intervention. Tool-using language agents are guarded by schema validators, policy filters, provenance checks, state predictors, and self-verification, yet such safeguards do not certify that a state-changing action has an identifiable causal effect. In confounded workflows, the action that looks optimal in observational logs can reduce utility when executed. We introduce CIVeX, a causal intervention verifier that maps proposed actions to structural causal queries over a committed action-state graph, checks identifiability, and returns one of four auditable verdicts: EXECUTE, REJECT, EXPERIMENT, or ABSTAIN. Execution requires an assumption-scoped causal certificate carrying graph commitments, an identification argument, a one-sided lower confidence bound (LCB), provenance, and risk limits. On Causal-ToolBench (1,890 instances, 7 seeds), CIVeX yields zero observed false executions across moderate and adversarial confounding. Under adversarial confounding it reaches 84.9% accuracy and 81.1% of oracle utility (+2.23 vs +2.76) and is the only non-oracle method whose constrained utility under a zero-false-execution constraint exceeds the AlwaysAbstain floor. On IHDP and ZOZO Open Bandit (real production logs with uniform-random ground truth), CIVeX matches Oracle correct-execution within 0.1pp and cuts per-execute false-execution by >=50x over naive baselines. A chain-of-thought LLM verifier (Claude Opus, Sonnet) cuts false-execution by an order of magnitude over a terse baseline, yet under adversarial confounding Opus's utility falls to 74% of CIVeX's. Intervention identifiability, not action validity, is the missing primitive for reliable tool use.

Fabio Rovai

The Tesseract Academy

Structural Causal Models Tool-Using Agents Causal Identifiability LLM Agent Reliability

May 9, 2026cs.AI

CauSim: Scaling Causal Reasoning with Increasingly Complex Causal Simulators

Despite surpassing human performance across mathematics, coding, and other knowledge-intensive tasks, large language models (LLMs) continue to struggle with causal reasoning. A core obstacle is the target data itself: causal systems are complex and often expressed in non-executable forms, while ground-truth answers to causal queries are inherently scarce. We introduce CauSim, a framework that turns causal reasoning from a scarce-label problem into a scalable supervised one. CauSim constructs increasingly complex causal simulators: executable structural causal models (SCMs), incrementally built by LLMs, that scale to globally complex systems while maintaining verifiable answers to causal queries. CauSim operates across representations by formalizing non-executable causal knowledge into code, enabling data augmentation, and translating executable SCMs into natural language, enabling supervision in previously difficult-to-supervise representations. We structure our research into two parts: (1) how to construct increasingly complex causal simulators, and (2) a systematic study of what CauSim enables, demonstrating generalization across representations, consistent gains from curriculum scaling and data volume, LLM self-improvement through self-generated simulators, and data augmentation via formalization of existing domain knowledge.

Nicolás Astorga, Anita Kriz, Mihaela van der Schaar

DAMTP, University of Cambridge, Cambridge, UK

Structural Causal Models Knowledge Augmentation for Language Models Synthetic Data Generation Causal Reasoning in Language Models Causal Reasoning Synthetic Data Generation for Language Models

May 8, 2026cs.LG

PerCaM-Health: Personalized Dynamic Causal Graphs for Healthcare Reasoning

Personalized healthcare decisions require reasoning about how physiological and behavioral variables influence an individual patient over time. Existing temporal causal discovery methods are poorly matched to this setting: cohort-level models provide stable but non-personalized structures, while per-patient discovery is unreliable because individual trajectories are short, noisy, irregular, and non-stationary. This creates a fundamental gap between population-level causal modeling and the patient-specific, time-varying mechanisms needed for intervention reasoning. We introduce PerCaM-Health, a framework for learning personalized dynamic causal graphs from longitudinal health data. The framework learns a knowledge-guided population temporal graph, then conservatively adapts and evolves it using patient-specific temporal evidence and rolling-window updates, producing interpretable and auditable graph sequences. By coupling these graphs with temporal structural equations, the framework enables patient-level counterfactual queries, such as estimating short-horizon outcome changes under hypothetical behavioral interventions. Experiments on a semi-synthetic dynamic health benchmark show that PerCaM-Health improves graph recovery, dynamic edge tracking, and intervention direction accuracy compared to cohort-level, per-patient, and non-personalized temporal baselines. These results demonstrate that jointly modeling personalization and temporal evolution yields more reliable causal structure and intervention reasoning.

Elahe Khatibi, Ziyu Wang, Saba A. Farahani +4

University of California, Irvine · Washington University in St. Louis

Structural Causal Models Healthcare Time-Series Causal Discovery Causal Discovery Causal Structure Learning Clinical Reasoning+1

May 7, 2026cs.LG

Data-Driven Covariate Selection for Nonparametric and Cycle-Agnostic Causal Effect Estimation

Estimating causal effects from observational data requires identifying valid adjustment sets. This task is especially challenging in realistic settings where latent confounding and feedback loops are present. Existing approaches typically assume acyclicity or rely on global causal structure learning, limiting applicability and computational efficiency. In this work, we study a local, data-driven method for covariate selection based on conditional independence information. While this method is known to be sound and complete in acyclic causal models, its validity in the presence of cycles has remained unclear. Our main contribution is to show that these guarantees extend to cyclic causal models. In particular, our result relies on the invariance of conditional independence assertions under

σ

-acyclification. These findings establish a unified, cycle-agnostic perspective on covariate selection and causal effect estimation, showing that the method applies across cyclic and acyclic settings without modification. Empirically, we validate this on extensive synthetic data, showing reliable performance in cyclic causal models.

Ana Leticia Garcez Vicente, Gijs van Seeventer, Saber Salehkaleybar

Leiden University Netherlands

Causal Effect Estimation Structural Causal Models Causal Inference

May 7, 2026cs.LG

Causal Reinforcement Learning for Complex Card Games: A Magic The Gathering Benchmark

Causal reinforcement learning (RL) lacks benchmarks for complex systems that combine sequential decision making, hidden information, large masked action spaces, and explicit causal structure. We introduce MTG-Causal-RL, a Gymnasium benchmark built on Magic: The Gathering with a 3,077-dimensional partial observation, a 478-action masked discrete action space, five competitive Standard archetypes, three reward schemes, and a hand-specified Structural Causal Model (SCM) over strategic variables. Every episode exposes causal variables, SCM-predicted intervention effects, and per-factor credit traces, making causal credit assignment, leave-one-out cross-archetype transfer, and policy auditability first-class metrics. We adapt a panel of reference baselines: random, heuristic, masked PPO, a causal-world-model PPO variant, and an architecture-matched scalar control. We propose Causal Graph-Factored Advantage PPO (CGFA-PPO) as a reference causal agent that uses SCM parents of win probability as factor-aligned critic targets with an intervention-calibration loss. All comparisons use paired seeds, paired-bootstrap confidence intervals, and Holm-Bonferroni correction within pre-registered families. Masked PPO and CGFA-PPO reach competitive in-distribution win rates and exceed the random baseline; per-factor calibration trajectories and leave-one-out transfer gaps expose diagnostic structure that scalar win rate alone cannot. We release the benchmark, reference-baseline results, and full evaluation protocol openly. By coupling a strategically rich, partially observed domain with an explicit causal interface and statistical protocol, MTG-Causal-RL gives causal-RL, world-model, and LLM-agent research a shared testbed for questions current benchmarks cannot pose together: causal credit assignment under masked action spaces, structural transfer across archetypes, and SCM-grounded policy auditability.

Cristiano da Costa Cunha, Ajmal Mian, Tim French +1

Department of Computer Science and Software Engineering, University of Western Australia, 6009 WA Australia

RL Benchmarks Structural Causal Models Reinforcement Learning Game-Playing Agents Partially Observable RL Causal RL

May 7, 2026stat.ML

Tuning Derivatives for Causal Fairness in Machine Learning

Artificial-intelligence systems are becoming ubiquitous in society, yet their predictions typically inherit biases with respect to protected attributes such as race, gender, or age. Classical fairness notions, most notably Statistical Parity (SP), demand that predictions be independent of the protected attributes, but are overly restrictive when these attributes influence mediating variables that are considered business necessities. Recent causal formulations relax SP by distinguishing allowed from not-allowed causal paths and by complementing SP with Predictive Parity (PP), requiring the predictor to replicate the legitimate influence of business-necessities. Existing path-based definitions are mainly practical when applied to categorical attributes. This paper introduces a new framework for fairness in structural causal models that is tailored to continuous protected attributes. We formalize SP and PP through path-specific partial derivatives, establish conditions under which these criteria coincide with prior causal definitions, and characterize when a fair predictor, one that satisfies SP along not-allowed paths while achieving PP along allowed paths, exists. Building on this theory, we propose a fair tuning algorithm that either constructs such a predictor or, when not possible, allows for a trade-off between SP and PP. We present experiments on simulated and real data to evaluate our proposal, compare it with previously proposed methods, and show that it performs better when PP is considered.

Filip Edström, Guilherme W. F. Barros, Tetiana Gorbach +1

Department of Statistics, Umeå School of Business, Economics and Statistics, Umeå University, Umeå, 901 87, Sweden. · Integrated Science Lab, Department of Physics, Ume˚a University, Ume˚a, 901 87, Sweden. · Department of Statistics, Ume˚a School of Business, Economics and Statistics, Ume˚a University, Ume˚a, 901 87, Sweden.

Structural Causal Models Algorithmic Fairness

May 7, 2026stat.ML

Relaxed Sparsest-Permutation Formulation for Causal Discovery at Scale

Despite the growing availability of large datasets, causal structure learning remains computationally prohibitive at scale. We revisit sparsest-permutation learning for linear structural equation models and show that exact Cholesky factorization is unnecessary for structure recovery. This observation motivates a support-level relaxation that searches for sparse triangular factors over a precision-support screening graph. The relaxed formulation can be efficiently evaluated via masked zero-fill incomplete Cholesky factorization, enabling scalable comparison of candidate orderings. At the population level, we establish soundness for Markov equivalence class (MEC) recovery under no-cancellation and sparsest Markov representation assumptions, as well as robustness to ordering misspecification. Motivated by these guarantees, we introduce SCOPE, a sparse-Cholesky pipeline that provides a scalable implementation of the relaxed formulation. Experiments on synthetic and real datasets demonstrate that SCOPE matches the MEC recovery accuracy of substantially slower baselines, while achieving significantly reduced runtime and scaling to 10k variables.

Sunmin Oh, Sang-Yun Oh, Gunwoong Park

Department of Statistics, Seoul National University, South Korea · Department of Statistics and Applied Probability, University of California Santa Barbara, CA, USA · Scientific Data Division, Lawrence Berkeley National Laboratory, CA, USA +2

Structural Causal Models Causal Discovery Causal Structure Learning

May 6, 2026cs.LG

Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal models

Structural causal models provide a unified semantics for interventions and counterfactuals, but most identifiability results rely on restrictive assumptions like global monotonicity, which are often violated in embodied interaction, where the same exogenous perturbation can induce opposite responses under different contact contexts. We ask what structure still suffices once global monotonicity is dropped. We introduce non-monotone triangular structural causal models (NM-TM-SCM), which retain triangular recursion but replace global monotonicity with mechanism-wise invertibility and context-independent inverse transport. We prove that these conditions are equivalent to exogenous isomorphism and imply complete counterfactual identifiability, and we give a counterexample showing that local invertibility alone is insufficient. We instantiate the theory in CausalInverter, with triangular invertible layers, orientation gates, and transport-stability regularization. On synthetic non-monotonic mechanisms, the structural bias yields systematic counterfactual gains as non-monotonicity increases. On MuJoCo Door, our model achieves perfect event-level counterfactual recovery, lowers continuous angle error relative to a Transformer baseline, and delivers substantially more stable recovery than Transformer and conditional-flow predictors. On MuJoCo Push, where non-monotonicity is weaker, the same low-data predictors remain competitive or better, consistent with a bias-variance boundary. These results identify a broader identifiable regime between globally monotone triangular models and unconstrained black-box world models.

Pengcheng Tan, Jiang Chen, Dehui Du

Shanghai Key Laboratory of Trustworthy Computing, East China Normal University

Structural Causal Models Causal Counterfactual Generation Counterfactual Prediction Counterfactual Learning Embodied World Models

May 6, 2026stat.ME

Causal discovery under mean independence and linearity

Causal discovery methods such as LiNGAM identify causal structure from observational data by assuming mutually independent disturbances. This assumption is fragile: shared volatility, common scale effects, or other forms of dependence can cause the methods to recover the wrong causal order, even with infinite data. We introduce the Linear Mean-Independent Acyclic Model (LiMIAM), which replaces full independence with weaker one-sided mean-independence restrictions on the disturbances. Under finite-order consequences of these restrictions, source nodes are generically identifiable, and hence a compatible causal order can be recovered recursively. Our proof is constructive and leads to DirectLiMIAM, a sequential residual-based algorithm for causal discovery under dependent noise. In simulations with mean-independent but dependent disturbances, DirectLiMIAM outperforms LiNGAM methods. A large-scale empirical application to the oil market highlights the implausibility of the independence assumption and the ability of DirectLiMIAM to recover a realistic causal ordering, from policy to production and from prices to inflation.

Geert Mesters, Alvaro Ribot, Anna Seigal +1

Structural Causal Models Causal Discovery Causal Identifiability

May 5, 2026cs.CL

NoisyCausal: A Benchmark for Evaluating Causal Reasoning Under Structured Noise

Causal reasoning in natural language requires identifying relevant variables, understanding their interactions, and reasoning about effects and interventions, often under noisy or ambiguous conditions. While large language models (LLMs) exhibit strong general reasoning abilities, they struggle to disentangle correlation from causation, particularly when observations are partially incorrect or irrelevant information is present. In this work, we introduce NoisyCausal, a new benchmark designed to evaluate causal reasoning under structured noise. Each instance is generated from a ground-truth causal graph and contextualized with a natural language scenario by injecting controllable forms of noise, such as irrelevant distractors, value perturbations, confounding, and partial observability. Moreover, we propose a modular reasoning framework that combines LLMs with explicit causal structure to address these challenges. Our method prompts the LLM to extract variables, construct a causal graph from context, and then reformulates the reasoning task as a structured prompt grounded in this graph. Rather than relying on statistical patterns alone, the LLM is guided by symbolic structure, enabling more interpretable and robust inference. Experimental results show that our method significantly outperforms standard prompting and reasoning baselines on NoisyCausal. Furthermore, it generalizes well to external benchmarks such as Cladder without task-specific tuning. Our findings highlight the importance of combining causal abstractions with language-driven reasoning to achieve faithful and robust causal understanding in LLMs.

Zhi Xu, Yun Fu

Northeastern University

Structural Causal Models Causal Reasoning in Language Models Causal Reasoning Language Model Robustness LLM Reasoning

May 5, 2026cs.LG

ReplaySCM: A Benchmark for Executable Causal Mechanism Induction from Interventions

Most causal benchmarks for language models score local answers or graph structure. We introduce ReplaySCM, a 1,300 item benchmark for executable causal mechanism induction from finite interventional evidence. Each item contains binary worlds generated by a latent fully observed acyclic Boolean structural causal model (SCM). A system must output a mechanism map in a restricted Boolean DSL; the submission is parsed, checked for legality and acyclicity, and replayed on training and held-out intervention worlds. Scoring uses replay behavior rather than formula strings, so syntactically different mechanisms receive credit when they behave correctly. ReplaySCM varies the structural information disclosed to the model through Ordered, Block-order, Hidden-order, and Hidden-roots settings, and includes Alternative-SCM tasks that supply a valid reference SCM and ask for a semantically distinct alternative that fits the training worlds, together with a separating intervention and witness. Frontier LLMs infer parts of the functional-parent structure, but held-out replay drops sharply when order or root structure is hidden. We also evaluate a matched support-audit ladder: Original, Extra Worlds, and Counterexample Audit (CEx), that raises mean local predecessor-pattern coverage from 0.8949 to 0.9815 to 1.0; under the audited searches, no discovered semantic alternative remains consistent with the training worlds. The Ordered/Hidden-order gap persists under this stronger evidence. ReplaySCM complements answer-level causal reasoning and graph-discovery benchmarks by evaluating executable replay generalization from finite interventional evidence, without claiming unique identification of the latent SCM.

Serafim Batzoglou

LLM Evaluation Structural Causal Models Causal Interventions in Language Models

May 5, 2026cs.LG

Partially Observed Structural Causal Models

Here we introduce Partially Observed Structural Causal Models (POSCMs) as an extension of structural causal models (SCMs) to settings where upstream contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs thus provide a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level contexts and endogenous variable interventions. To define edge interventions, we separate node mechanisms into edge-local transmission channels that can be modified without changing the source node or the rest of the target mechanism. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We then empirically validate these theoretical results in two external simulators: a biophysically detailed virtual human retina and a gene-regulatory analogue. The experiments reproduce non-identifiability under latent context, expose structure-mechanism confounding under latent edges, and recover pathway-level input-output relationships under targeted interventions, consistent with our positive Markov kernel identifiability results. Together, POSCMs provide an intervention-oriented framework for causal systems in which contexts, graph structure, mechanisms, and measurements are jointly generated and only partially observed.

Turan Orujlu, Jordan Matelsky, Martin V. Butz +2

University of Tübingen · MPI for Biological Cybernetics · University of Pennsylvania +1

Structural Causal Models Causal Identifiability Causal Intervention

May 4, 2026cs.CE

The Design and Composition of Structural Causal Decision Processes

We present two new classes of causal models of decision-making agents. Our approach is motivated by the needs of modeling the economics of computing systems. These systems are composed of subsystems and can exhibit endogenous limits on cognitive resources and value discounting. Structural Causal Decision Models (SCDMs) expand on Structural Causal Influence Models. Like SCIMs, they explicitly represent the causal relationships between model variables and the payoffs of agent decisions. Additionally, agent decisions can be constrained by their causal antecedents, and SCDMs can have open root variables for which no probability distribution or structural equation is given. We show that SCDMs have a well-defined and computationally useful property of composability. Building on SCDMs, we then define a Structural Causal Decision Process (SCDP) as a recurring SCDM with a discount variable. SCDPs benefit from the useful composition properties of SCDMs. Moreover, SCDPs are strictly more expressive than POMDPs because they do not assume rational belief formation. Indeed, an SCDP can endogenously model the memory-formation process, and is thus useful for modeling resource rational agents in dynamic settings. SCDPs are also capable of modeling variable discounting, a tool used widely in social scientific modeling. We pose that SCDPs are a useful framework for policy simulation for the digital economy, mechanism design for information systems, and digital twin modeling of cyberinfrastructure.

Sebastian Benthall, Alan Lujan

International Computer Science Institute, USA · New York University, USA · Johns Hopkins University, Krieger School of Arts and Sciences, USA

Computational Cognitive Modeling Structural Causal Models Sequential Decision Making

May 4, 2026stat.ML

The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy

Pearl's causal hierarchy shows that observational, interventional, and counterfactual queries are qualitatively distinct. We ask a quantitative version of this question: how many additional bits are needed to specify higher-rung causal answers once lower-rung answers are known? We formalize this via query-class description length, the Kolmogorov complexity of the answer oracle induced by an SCM for a class of queries. Our main construction gives binary acyclic SCMs whose observational distribution has constant description length, while the single-variable interventional answer oracle has description length

Θ(n^2)

. A degree-sensitive upper bound shows that finite-gate-schema SCMs of indegree

d

have observational-interventional gap at most

O(nd \log(en/d) + n \log n)

, making the quadratic construction order-optimal in the dense regime and a rooted-tree construction order-optimal for bounded indegree. The quadratic separation persists under

\varepsilon

-accurate total-variation descriptions for every fixed

\varepsilon < 1/4

. At the next rung, the full hard-do interventional oracle can still leave a

Θ(n)

counterfactual description gap. A general ambiguity-to-bits theorem and Shannon analogue show that these gaps equal the logarithm of residual higher-rung ambiguity up to lower-order terms.

Seyed Morteza Emadi

Kenan-Flagler Business School · University of North Carolina at Chapel Hill

Structural Causal Models Causal Inference Counterfactual Reasoning Information-Theoretic Lower Bounds

May 3, 2026stat.ML

Stable Blanket with Hidden Variables and Cycles

Stabilized regression aims to identify a set of predictors whose conditional relationship with a response variable remains invariant across different environments. Existing graphical characterizations of the stable blanket are mainly developed for structural causal models (SCMs) without hidden variables or causal cycles. However, latent variables and feedback relationships naturally arise in many applications, and they can change both the Markov blanket and the set of predictors that remain stable under interventions. This paper studies stable blankets in graphical causal models with hidden variables, causal cycles, and both features simultaneously. For models with hidden variables, we use acyclic directed mixed graphs (ADMGs) and

m

-separation to characterize the Markov blanket and to construct intervention-stable predictor sets. We introduce the notion of an intervened sub-district and use it to describe how interventions may affect districts connected to the response. For models with cycles, we work with directed graphs (DGs) and directed mixed graphs (DMGs) together with

σ

-separation, treating strongly connected components (SCCs) as the basic graphical units. We then combine these ideas to analyze models with both hidden variables and cycles. The main results give graphical characterizations of Markov blankets, stable frontiers, and stable blankets in these generalized settings. In particular, we identify conditions under which the response is conditionally independent of intervention variables given a suitable predictor set, and we describe when such sets are minimal or unique. These results extend the graphical interpretation of stabilized regression beyond acyclic fully observed models.

Hanqing Xiang

Department of Mathematics, KTH Royal Institute of Technology, Sweden · University of Copenhagen

Structural Causal Models Causal Intervention

May 2, 2026cs.AI

Grounding Multi-Hop Reasoning in Structural Causal Models via Group Relative Policy Optimization

Multi-Hop Fact Verification requires complex reasoning across disparate evidence, posing significant challenges for Large Language Models , which may suffer from hallucinations and fractured logical chains. Existing methods, while improving transparency via Chain-of-Thought , often lack explicit modeling of the structural dependencies between evidence and claims. In this work, we introduce an SCM-inspired framework that grounds reasoning in explicit directed dependency graphs, treating verification as a constructive structural reasoning process rather than full causal inference with interventions or counterfactual semantics. We empirically identify an "inverted U-shaped" correlation between reasoning-chain length and accuracy, revealing that excessive structural complexity can degrade performance. To address this, we propose a rule-based reinforcement learning strategy using Group Relative Policy Optimization. This approach dynamically optimizes the trade-off between structural depth and conciseness. Extensive experiments on HoVer and EX-FEVER demonstrate that our SCM-GRPO framework outperforms strong baselines while producing more traceable reasoning structures for complex fact verification.

Yunhan Bu, Quan Zhang, Huaping Zhang +9

Beijing Institute of Technology, Beijing, China · School of Computer Science and Technology, Xinjiang University, Urumqi, China · Military Science Information Research Center, Academy of Military Science, Beijing, China

Structural Causal Models RL for Language Model Reasoning Automated Fact-Checking Multi-Hop Reasoning Reasoning Verification

Apr 29, 2026cs.AI

Binary Spiking Neural Networks as Causal Models

We provide a causal analysis of Binary Spiking Neural Networks (BSNNs) to explain their behavior. We formally define a BSNN and represent its spiking activity as a binary causal model. Thanks to this causal representation, we are able to explain the output of the network by leveraging logic-based methods. In particular, we show that we can successfully use a SAT as well as a SMT solver to compute abductive explanations from this binary causal model. To illustrate our approach, we trained the BSNN on the standard MNIST dataset and applied our SAT-based and SMT-based methods to finding abductive explanations of the network's classifications based on pixel-level features. We also compared the found explanations against SHAP, a popular method used in the area of explainable AI. We show that, unlike SHAP, our approach guarantees that a found explanation does not contain completely irrelevant features.

Aditya Kar, Emiliano Lorini, Timothée Masquelier

CNRS, IRIT · Institut de Recherche en Informatique de Toulouse (IRIT), Centre de Recherche Cerveau et Cognition (CerCo), CNRS, France · Institut de Recherche en Informatique de Toulouse (IRIT), CNRS, France +2

Structural Causal Models Binary Neural Networks Spiking Neural Networks Causal Interpretability

Apr 24, 2026cs.LG

TabSCM: A practical Framework for Generating Realistic Tabular Data

Most tabular-data generators match marginal statistics yet ignore causal structure, leading downstream models to learn spurious or unfair patterns. We present TabSCM, a mixed-type generator that preserves those causal dependencies. Starting from a Completed Partially Directed Acyclic Graph (CPDAG) found by any causal structure discovery algorithm, TabSCM (i) orients edges to a DAG, (ii) fits root-node marginals with KDE or categorical frequencies, and (iii) learns topologically ordered structural assignments. Such assignments are achieved using conditional diffusion models for continuous variables as child nodes and gradient-boosted trees for categorical ones. Ancestral sampling yields semantically valid records and enables exact counterfactual queries. On seven public datasets, encompassing healthcare, finance, housing, environment, TabSCM matches or surpasses state-of-the-art GAN, diffusion, and LLM baselines in statistical fidelity, downstream utility, and privacy risk, while also cutting rule-violation rates and providing causally meaningful and robust conditional interventions. Because generation is decomposed into explicit equations, it runs up to 583

\times

faster than diffusion-only models and exposes interpretable knobs for fairness auditing and policy simulation, making TabSCM a practical choice for realism, explainability, and causal soundness.

Sven Jacob, Bardh Prenkaj, Weijia Shao +1

Federal Institute for Occupational Safety and Health (BAuA), Dresden, Germany · School of Computation, Information and Technology, Technical University of Munich, Munich, Germany · Munich Center for Machine Learning (MCML)

Structural Causal Models Causal Counterfactual Generation Synthetic Tabular Data Generation

Apr 22, 2026stat.ML

Efficient Symbolic Computations for Identifying Causal Effects

Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic computation. However, standard approaches based on Gröbner bases become computationally infeasible beyond small settings due to their doubly exponential complexity. In this work, we study how to practically use symbolic computation for deciding rational identifiability. In particular, we present an efficient algorithm that provably finds the lowest degree identifying formulas. For a causal effect of interest, if there exists an identification formula of a prespecified maximal degree, our algorithm returns such a formula in quasi-polynomial time.

Benjamin Hollering, Pratik Misra, Nils Sturma

Max Planck Institute for Mathematics in the Sciences, Germany · Binghamton University, USA · École Polytechnique Fédérale de Lausanne, Switzerland

Structural Causal Models Symbolic Reasoning Causal Identifiability

Mar 12, 2026cs.LG

Multi-Task Anti-Causal Learning for Reconstructing Urban Events from Residents' Reports

Many real-world machine learning tasks are anti-causal: they require inferring latent causes from observed effects. In practice, we often face multiple related tasks where the structural dependencies are a hybrid of task-invariant and task-specific mechanisms. We propose Multi-Task Anti-Causal learning (MTAC), a framework for estimating causes from outcomes and confounders by explicitly exploiting such cross-task invariances. MTAC learns a structural equation model (SEM) that factorizes the outcome-generation process into (i) a task-invariant mechanism and (ii) task-specific mechanisms via a shared backbone with task-specific deviations. Building on the learned forward model, MTAC performs maximum A posteriori (MAP) based inference to reconstruct causes by jointly optimizing latent mechanism variables and cause magnitudes under the learned structural model. We evaluate MTAC on the application of urban event reconstruction from resident reports, spanning three tasks: parking violations, abandoned properties, and unsanitary conditions. On real-world data collected from Manhattan and Newark, MTAC consistently improves reconstruction accuracy over strong baselines, achieving up to 33.04% MAE reduction and demonstrating the benefits of learning transferable mechanisms across tasks.

Liangkai Zhou, Susu Xu, Shuqi Zhong +1

Stony Brook University Stony Brook, New York, United States · Johns Hopkins University Baltimore, Maryland, United States

Structural Causal Models Multi-Task Learning Causal Inference