Structural Causal Model

We propose Low-Rank Quantile Surfaces (LRQS), a bivariate causal model in which, in the causal direction, an unknown monotone transformation of the conditional quantile surface admits a low-rank functional decomposition. LRQS subsumes location-scale noise models and post-nonlinear heteroscedastic noise models, while allowing multiple quantile bases to represent changes beyond location-scale effects. We prove generic identifiability of LRQS: the transformed quantile surface is low rank in the causal direction, whereas reverse representability under the corresponding constraints occurs only for exceptional, fine-tuned cause marginals. We provide a simple-yet-powerful causal score using a nonparametric fitting procedure that alternates between rank-constrained approximation of discretized quantile surfaces and isotonic estimation of the unknown monotone transformation. Experiments on synthetic mechanisms with higher-rank distributional shape variation and strong nonlinear distortions, together with standard bivariate benchmarks, show that LRQS is especially effective when conditional distributional shape or observation distortion goes beyond existing location-scale assumptions.

Causal discovery aims to uncover causal structures from data and is fundamental to scientific reasoning and intervention-based decision making. Its evaluation relies heavily on structural causal models (SCMs), which specify a causal graph together with the mechanisms that generate data, yet existing studies differ substantially in graph families, mechanisms, and evaluation protocols. The emergence of causal discovery foundation models (CDFMs) further complicates evaluation: performance may reflect not only causal discovery ability, but also overlap between pretraining environments and test SCMs, making results on fixed synthetic benchmarks difficult to interpret. We introduce CausalArena, a unified and evolvable benchmark for causal discovery under a common protocol. Synthetic SCMs supply controlled breadth over structures and mechanisms; semantic operational SCMs provide human-auditable, semantically grounded environments beyond standard synthetic generators; and formula-grounded SCMs test discovery under explicit scientific mechanisms. Public real-world datasets provide an additional external-validity check. Experiments across classical, neural, and pretrained methods reveal substantial ranking shifts across SCM families and protocols, showing that strong performance in one benchmark regime does not reliably transfer to others. These results highlight benchmark diversity and pretraining--evaluation overlap as central challenges for evaluating causal discovery in the foundation model era.

Explaining why a specific outcome occurred, and which inputs deserve the blame or credit, is central to philosophical, scientific, and policy analysis. Existing tools split into two camps. The theory of actual causality (AC) gives principled verdicts, but only for toy-sized models, because computing them requires enumerating counterfactual scenarios. Scalable attribution methods like SHAP (or even causal SHAP) at least partially ignore the causal structure that generated the data, and can give answers that conflict with a careful causal analysis. We close this gap with Probabilistic Causal Impact (PCI). PCI builds on actual causality and on Pearl's notions of probability of necessity and sufficiency, but recasts the question of explainability as an estimation problem on a probabilistic causal model that is easily approximated via Monte Carlo. By specifying a distribution over "candidate explanations," a distribution over counterfactual values, and a scoring function, PCI provides tractable, causally grounded, graded explanations, generalizing AC and Pearl's probability of causation as degenerate cases. We evaluate PCI in synthetic and real-world examples, spanning consistency checks with AC, scaling experiments, complex continuous-valued dynamical systems, and a real-world deployed causal machine learning model trained on millions of datapoints.

Scientific agents must learn not only how to reason, but also what to believe. However, existing LLM agents typically express scientific hypotheses in free-form text, leaving their beliefs implicit and difficult to test or revise. We introduce EvoSCM, which equips scientific agents with explicit structural causal models that evolve as new experimental evidence is collected. EvoSCM maintains a population of competing SCM hypotheses, each encoding a candidate causal explanation of the environment, and evolves them through a closed discovery loop. In each round, the agent abduces latent mechanisms from accumulated evidence, designs discriminative interventions, and commits to falsifiable predictions that it tests through experimentation. Discrepancies between prediction and observation are inductively distilled into correction rules that revise the causal structures and mechanisms of each hypothesis, and the agent then deductively validates the revised population against accumulated evidence and structural consistency to guide the next round. We evaluate EvoSCM on DiscoverPhysics, a benchmark requiring agents to uncover the hidden dynamics of noncanonical physical worlds through experimentation. EvoSCM consistently improves scientific discovery over baselines, yielding more accurate explanations and predictions while making more effective use of experimental interactions.

Probabilities of causation (PoCs) characterize individual causal responses that cannot be directly observed and therefore generally require partial identification. Tian and Pearl first derived theoretically sharp bounds for binary PoCs, including the probability of necessity (PN), the probability of sufficiency (PS), and the probability of necessity and sufficiency (PNS). Mueller et al. subsequently tightened the bounds for binary PNS by incorporating causal information encoded in covariates and mediators. More recently, Li and Pearl, as well as Shu et al., extended PoCs to multivalued settings and derived corresponding theoretical bounds. These developments naturally raise the question of whether additional causal knowledge can further tighten the bounds in multivalued settings. This paper addresses this question by deriving tighter bounds for multivalued PoCs through the incorporation of causal information encoded in covariates and mediators. We illustrate the theoretical results with toy examples, while simulation studies further demonstrate that the proposed bounds are tighter than existing nonbinary bounds.

Hospital quality improvement (QI) programs routinely face multiple candidate interventions to optimize hospital flow, but existing methods struggle to estimate and rank the causal effects of such interventions. This work focuses on one of the most standard hospital metrics, the average length of stay (LOS), and its causal estimand, the average time saved. To characterize this causal effect, qualitative approaches rely on expert judgment to map patient trajectories, making them susceptible to cognitive biases; quantitative approaches rely on data-driven models, which fail when interventions are hypothetical with no historical data or have complex causal mechanisms that require clinical reasoning rather than data alone. We propose expert-guided g-computation, or egg-computation, which combines the complementary strengths of both approaches by connecting the Gantt charts commonly used to map patient trajectories with the causal DAG literature. We introduce a causal model over Gantt charts and establish identification using a variant of g-computation that seeks expert input only for components unidentifiable from data. To make egg-computation practical, we develop an LLM-assisted pipeline that reliably scales up expert reasoning. In simulations, egg-computation outperforms conventional causal inference methods when patients have diverse causal structures and intervention mechanisms. In a study of eleven candidate QI interventions at an urban safety-net hospital, the LLM pipeline generated graphs and time-saving estimates highly concordant with those of human experts. Beyond healthcare, egg-computation is a broadly applicable framework for estimating the average time saved for candidate interventions whose causal mechanisms can be represented using Gantt charts.

Predicting the answer to interventional ``what if'' questions --- the outcome of an action never taken --- requires a \emph{mechanistic}, causal model, not a curve fit; and learning such a model requires \emph{experiments}, because passive data leaves its mechanisms unidentified. Experiments are expensive, so the central problem is \emph{data efficiency}. We present the Model Discovery Agent (MDA), which couples a large language model (LLM), used as a \emph{proposer} of candidate structures, with standard Bayesian machinery --- sequential Monte Carlo (SMC) for parameter and structure posteriors, simulation-based inference (SBI) for intractable likelihoods, and value-of-information (VoI) for experiment design --- to discover latent mechanistic world models from few interventions. MDA operates in the M-open setting: when the truth lies outside the current hypothesis class, a predictive check flags the inadequacy and the proposer expands the hypothesis space with a new model whose parameters are then identified by designed experiments. We show that \emph{discovery and design reinforce}: the design step identifies the mechanism the discovery step proposes, and the identified mechanism improves predictions, enabling further discoveries from the remaining unexplained residuals. On three different benchmarks --- covering physics (\DPbench, \citep{wiemann2026discoverphysics}), chemistry (\CHEMbench, \citep{kabra2026autoscilab}) and biology (\HHbench, a new partially observed single-neuron electrophysiology benchmark we create) --- we show that MDA sets a new SOTA in terms of data-efficient model learning and reliable interventional prediction ability.

In medical applications, raw data is frequently associated with significant privacy concerns, lending particular importance to the encoding of summary statistics from the literature. On the other hand, deep learning has become an invaluable tool for assessing symptoms based on visual or auditory sensor data. DeepProbLog allows for an extensible neuro-symbolic approach that accommodates connectionist components to analyse patient images within a transparent and rigorous probabilistic framework, namely probabilistic logic programming under the distribution semantics. Framed as a case study in stroke detection from multimodal data, this contribution explores the pathway from summary statistics available in the literature to a DeepProbLog-based diagnostic system. It suggests a workflow using established maximum entropy techniques to complete available probabilistic information and the probabilistic logic programming system ProbLog 2 to move from the entropy-maximising causal model to a discriminative neuro-symbolic model expressible within DeepProbLog. The relative performance of models derived from less complete data is analysed alongside the potential of the probabilistic inductive logic programming system ProbFOIL 2 for compressing large discriminative models, and the perspectives and implications of using DeepProbLog for diagnostic reasoning are discussed.

Causal perception occurs when agents with competing Structural Causal Models (SCMs) of the same system infer different probability distributions, including the hypothetical distributions implied by each agent's SCM under the same set of interventions. It shapes how agents reason about the system and how they perceive its fairness. Causal perception is a promising probabilistic framework, but it has remained purely theoretical. This work provides the first implementation of the causal perception framework of Álvarez and Ruggieri (2025). We operationalize structural (agents disagree on the causal graph) and parametrical (agents agree on the causal graph but disagree on its weights) causal perception. We design algorithms for computing interventional and counterfactual distributions and propose suitable distance measures to quantify the disagreement. Using the German Credit dataset, we illustrate how causal perception affects accuracy and fairness in a multi-expert decision setting. We show that the perception verdict is sensitive to the choice of distance metric and threshold. We also show that causal perception changes fairness assessments and threshold-based decisions. Bias proves situated with respect to the agent's SCM, demonstrating that competing worldviews in fairness problems cannot be ignored.

Explaining the predictions of neural networks is a central challenge in trustworthy AI. Existing explanation methods, such as those based on feature attribution or minimal sufficient sets, typically treat input features as independent, which can yield misleading explanations when inputs exhibit structured dependencies. We address this by formalizing explanations as Halpern-Pearl (HP) actual causes, modeling input dependencies using Boolean Structural Causal Models (SCMs). We compute HP causes by applying bound propagation and branch-and-bound techniques, while providing formal guarantees of completeness and minimality. Our experiments show that we substantially outperform brute-force and ILP baselines in scalability, and outperform heuristic search as graph size grows, computing all minimal actual causes on instances with search spaces of up to $2.3\times10^{13}$ candidate (cause, contingency) pairs, on SCMs with up to 28 nodes, within a 180s per-instance budget. In a case study, we further show that ignoring input dependencies inflates the number of reported causes, 14.9% of which are spurious under our SCM.

Counterfactual inference approaches for sequential decision-making typically assume deterministic causal models, where all randomness stems from latent variables. However, Markov Decision Processes (MDPs) are inherently stochastic. We address this by formalising counterfactual policy optimisation under probabilistic nondeterministic causal models, which properly separates latent confounding from irreducible stochasticity, and here propose a first practical optimisation problem for identifying robust counterfactual policies under a sensitivity analysis framework. We validate our approach on a sepsis treatment simulator, where diabetes status acts as a hidden global confounder.

Structural causal models are the standard language for reasoning about interventions and counterfactuals, but they describe static variables, typically measured once, and usually forbid cyclic dependencies. Many systems we care about, such as patients, climates, and economies, instead evolve continuously in time, are observed at irregular time points, and contain feedback loops. We argue that neural operator learning provides a natural foundation for causal reasoning in this setting, and propose Orca, a framework in which each node of the causal graph is a function of time and each mechanism is a learned map between function spaces. We extend existing neural operator architectures to express causal mechanisms: a mechanism computes the function value of a node from its parent nodes by taking several parent functions as input, respects the arrow of time, and treats latent exogenous noise as a function that can be inferred and reused for counterfactuals. We formalize the model class and demonstrate counterfactual reasoning on synthetic continuous-time examples. Code is available at https://github.com/gerritgr/orca

Markov Decision Processes (MDPs) are widely used as decision-making models, commonly specified over factored state spaces through state variables and their valuations. The exponential blowup in the number of states renders many reasoning tasks in MDPs challenging. Abstractions are promising techniques to reduce MDPs and thus mitigate scalability issues. In this work, we introduce a notion of causality on factored MDPs and a novel property-driven causal abstraction technique that retains many characteristics of the original MDP model. For this, we rely on causal relations over state variable predicates and identify those states that share the same reasons for fulfilling or violating a given abstraction property. We theoretically and empirically compare various causal MDP abstractions using different model types such as MDPs, interval MDPs, or stochastic games. Our evaluation demonstrates the potential of our approach: For several standard benchmarks, we obtain small abstractions that allow us to compute near-optimal policies for the original MDP. Furthermore, our causal abstractions often generalize to related large-scale MDP models.

Pearl's structural causal model (SCM) framework, built on directed acyclic graphs (DAGs) and the do-calculus, is the dominant formal language for causal reasoning. Yet it carries two structural restrictions: every relationship must be pre-specified as a directed causal edge, and feedback cycles are forbidden. This paper examines two classes of phenomena that strain these restrictions. First, symmetric physical and economic constraints, the ideal gas law being the canonical case, carry no intrinsic causal direction. Direction emerges only under intervention, and which variable is solved for must be specified as part of the intervention. We formalize such constraints as causal zeros within an Extended Causal Model by adding an activation operator, subject to local solvability and graph-admissibility conditions. Second, for the class of finite-propagation state-space systems considered here, we treat apparent instantaneous cycles as artifacts of suppressed time and ground both causal zeros and feedback in Causal Differential Equations (CDEs). In these, the transient regime is a time-unrolled acyclic causal process, and causal zeros arise as the defining functions of attracting equilibrium manifolds; periodic and chaotic attractors define further regimes of the same dynamics, treated through attractor-relative intervention. We give the extended do-calculus, identifiability conditions, counterfactual semantics, and open problems.

Power grids, markets, and interacting populations, settle into feedback driven equilibria observed through unknown sensors. Our Equilibrium Causal Game (ECG) joins a game to its cyclic causal model, hidden inputs, sensor map, and rules for interventions and equilibrium selection; interventions edit declared objects and recompute equilibrium. Under stated conditions, ECG-separation is sound but incomplete in our examples. Back-door/half-trek routes identify observed queries. Yet for an untouched rotationally symmetric Gaussian block, second moments determine only a source-frame rotation, across which distinct-variable effects generically change. Unknown sensing creates a separate ambiguity. In passive stable linear models without self-effects, unknown wiring and full-rank unknown sensing leave $B$ completely unidentified for $d\ge2$. Under LiNG, non-Gaussianity removes the source rotation; mechanism interventions separate sensing from interactions. With unknown support, invariant sensing, aligned responses, and well-posed single-target interventions identify $(H,B)$ up to declared equivalence. Of $d$ targets, $d-1$ suffice exactly when the sole untargeted node directly parents all others; otherwise $d$ are needed. Acquisition probes are excluded; known wiring gives no universal count. With nonlinear sensing, isotropic Gaussian source blocks admit hidden twists within and across blocks in labelled environments preserving required radial laws. Conversely, under stated positivity, informative one-block changes, rank, and irreducibility conditions, the finest independent source-block representation is identified within the stated alternative class up to block permutation and blockwise coordinate changes, but not downstream mechanisms or the sensor/interaction split. Together, these results show which causal conclusions equilibrium data support and which require targeted experiments.

Topos causal models recast causal inference inside a topos: a causal world is a presheaf, an intervention is a sub-model named by a characteristic map into the subobject classifier $\Om$, and reasoning is Kripke-Joyal forcing in an intuitionistic internal language. We give the first axiom-free machine-checked account of this 1-topos core, in Cubical Agda over a previously verified probability monad and do-calculus; the framework is otherwise developed on paper, with central claims stated rather than proved. Three of our results go beyond faithful transcription. We exhibit a contextuality obstruction the programme does not treat: pairwise-consistent local causal data with no global model, detected by a degree-one holonomy class. We delimit the claim that interventions are modelled by the subobject classifier: an intervention and an observation name the same subobject, so $\Om$ fixes the target of a do-operation but not the operation itself, which is surgery on the kernels --- where, on a confounder, the interventional and observational laws differ. And we settle the modal unit --- inflationarity is derivable from $j\top = \top$ and naturality, not a fourth axiom. We also machine-check the classifier of sieves with its classification theorem, the pullback collating local mechanisms, and the Kripke-Joyal forcing clauses. The development assumes no axioms and typechecks under Agda's \texttt{--safe} flag, with the ordered field discharged at $\mathbb{Q}$; type-level sheafification and a directed do-calculus are future work.

Causal discovery from observational tabular data remains fundamentally challenging, primarily due to the heterogeneity of underlying causal mechanisms and the high-dimensional combinatorial search space of Directed Acyclic Graphs (DAGs). In this paper, we propose \textbf{DAG-FM}, a novel foundation model architecture that amortizes causal discovery. Unlike direct matrix prediction, DAG-FM decomposes the causal discovery process into two auto-regressive stages using two specialized Transformer-based sub-modules: a leaf-node predictor and a parent-node predictor. To effectively model complex row-column interactions, we adopt a robust tabular interaction block to output feature-wise representations. Crucially, to handle diverse and unknown Functional Causal Model (FCM) assumptions in real-world scenarios, we introduce Mixture-of-Leaf-Experts (MoLE), allowing the model to dynamically route and adapt to identifiable mechanism families. Through an iterative inference algorithm, DAG-FM seamlessly extracts causal orderings and constructs valid DAGs. Extensive experiments demonstrate that DAG-FM achieves state-of-the-art performance on both synthetic benchmarks and complex real-world datasets, significantly outperforming traditional classical algorithms and recent foundation models in both accuracy and scalability.

Many real-world processes can be represented as compositions of functions along a directed acyclic graph (DAG). In causal modelling, these correspond to the underlying mechanisms; in engineering, to multiple fidelity levels; and in gene-regulatory networks, to transcription factors. These functions are partially observed across the DAG, with noisy and heterogeneously sampled measurements, posing significant challenges for reconstruction, uncertainty propagation, and inference. To tackle these challenges, we place priors over functions and naturally arrive at Deep Gaussian Processes over DAGs. We theoretically study their prior-collapse behaviour, and the effect of graph topology and intermediate observations on the preservation of information. We obtain almost-sure lower bounds on the asymptotic frequency of depths at which the distinction between inputs is preserved, identify broad kernel classes for which these hold, and prove an observation by \cite{dunlop2018} on the role of input connections. We offer a structured variational approximation that retains graph dependencies, preserves compositional uncertainty, and captures the explaining-away behaviour of colliders. Finally, we empirically validate our theoretical results and our methodology, and model a latent-collider DAG, a protein signalling network, and a multi-fidelity heavy-ion collision emulation task, attaining state-of-the-art performance while recovering low-fidelity contributions and yielding interpretability of the simulator hierarchy.

Large language models (LLMs) increasingly act as integrated data-science agents, combining abstract reasoning with advanced tool use. Yet the relevant benchmark landscape largely divides into symbolic causal reasoning benchmarks without realistic data analysis or data analysis benchmarks without a principled causal data-generating structure. Furthermore, existing causal evaluation datasets are often restricted to curated examples from existing sources, with diversity coming from limited templatized variations rather than from systematic generation of novel synthetic causal structures. We introduce CausalDS, a benchmark for evaluating causal reasoning in agentic data-science workflows. Each benchmark instance is a scene consisting of a sampled structural causal model (SCM) with generated observational data and an accompanying synthetic natural-language story grounded in a realistic domain. We optionally ground the composition of the benchmark components in empirical distributions obtained from real-world datasets, thus retaining empirical structure while reducing the "causal parrot" risk through completely synthetic generation. From each scene, we then derive tasks spanning all three of Pearl's rungs, with typical data-science prediction tasks appearing as Rung 1. Most tasks include a data science coding component, where the model typically needs to use several tools to arrive at the final answer due to the frequent presence of imperfect observations, which are generated by an observation model. Additionally, recognizing when a question admits no warranted answer and abstaining is treated as a first-class scored outcome. The benchmark thus jointly evaluates symbolic causal reasoning, data science, uncertainty quantification, abstention, and tool use/coding.

Scientists often seek to draw causal inferences from structured data that is not independently and identically distributed, such as spatial data, network data, or molecular data. We develop geometric causal models (GCMs), a framework for causal inference from dependent data that exploits underlying symmetries of the data generating process. For example, in spatial data, we consider processes that are symmetric under translations, or in graph data, symmetric under permutations of the nodes. We show how symmetries, formalized with group theory, can enable causal identification and estimation. We deploy ergodic theory for amenable groups to establish identification, and combine geometric deep learning with scalable Bayesian inference for estimation. We recover i.i.d. causal models and do-calculus when the data is a sequence and the symmetry is permutation equivariance, and find novel types of causal models when we use alternate structures and symmetries. As an example, we construct a causal model that satisfies the symmetries of DNA. This GCM enables new estimators for the effects of genetic variation, combining deep functional genomics models to describe outcomes and DNA language models to describe propensities. We illustrate on semisynthetic data.

Causal discovery with nonlinear mechanisms and latent confounders remains challenging. Existing methods often rely on either linear assumptions or causal sufficiency, limiting their applicability. We propose an MDL-based causal discovery framework that explicitly accounts for latent confounders while allowing flexible nonlinear mechanisms by minimizing the luckiness normalized maximum likelihood (LNML) code-length. The causal relationship between each variable pair is determined by selecting the shortest code-length of the causal model, and we introduce the notion of $Δ$-pseudo-collinearity to identify dependencies induced by latent confounders. Based on these ideas, we develop a greedy algorithm, termed Pseudo-Collinearity Guided Causal Discovery (PCG-CD). Experiments on synthetic and real-world datasets demonstrate that the proposed method accurately recovers directed causal relationships and effectively detects latent confounders.

Algorithmic recourse addresses the challenge of providing tailored recommendations to users affected by unfavorable machine learning decisions, in potentially high-stakes scenarios. Traditional approaches to recourse often rely on the closest counterfactual explanations or assume a priori knowledge of a user's causal structure, resulting in interventions that overlook individual contexts and specific feature interactions. To overcome these limitations, we study a human-in-the-loop framework that iteratively approximates the user's structural causal model through interactive queries via Bayesian inference before producing recourse recommendations. This framework exploits humans' feedback to improve the identification of causal effects, allowing personalized recourse that is plausible, cost-effective, and aligned with the actual causal dependencies of each user. As a proof of concept, we evaluate this framework through simulated human responses. Our simulations across linear and non-linear causal models show promising results, though challenges remain in capturing complex, non-linear structures, emphasizing the importance of accurate approximations and robust noise distribution modeling.

Decision theory provides a formal framework for how agents should make choices under uncertainty, drawing on ideas from philosophy, probability, and causality. Despite significant progress, the field still lacks a unified modeling language, and key concepts - such as the distinction between subjective and objective elements, or what it means for a decision theory to perform well - are often left implicit. This can make it difficult to evaluate and compare competing theories, particularly in controversial cases. In this paper, we address these issues by introducing a formal framework for decision theory based on nonparametric structural equation models (NPSEMs), a well-established tool in causal inference. NPSEMs provide a unified foundation for representing agents, counterfactuals, and causal relationships, allowing for unambiguous definitions of EDT and CDT. Building on this foundation, we propose a novel decision theory - personal decision theory - which instructs agents to maximize a subjective model of their own counterfactual utility. We introduce a formal performance metric based on hypothetical interventions that enforce a given decision theory across a population - such as might be achieved through education or policy -- and show that, under certain assumptions, personal decision theory is optimal with respect to this metric. Throughout, we use the smoking lesion problem as a running example and conclude with a formal analysis of Newcomb's problem. Our aim is to provide decision theory with a clearer modeling language and firmer evaluative ground, thereby enabling more rigorous comparisons and facilitating conceptual progress in the field.

Post-hoc explanation methods are routinely used to interpret scientific machine learning models, with the deliverable understood to be insight into the phenomenon the model has been trained on. The transition may be taken to be secured once the model is reliable enough and the explanation faithful enough. We argue it is not. Reliability checks that the model's predictions match the phenomenon's outcomes, and faithfulness checks that the explanation matches the model, but neither checks whether the model works as the phenomenon works, which is what a claim about structure requires. The chain can support candidate hypotheses under external corroboration, but it cannot, on its own, support claims about how the phenomenon is in fact structured.

Learning causal models from fragmented biomedical data is challenging because clinical, molecular, and imaging variables are often incomplete or not jointly observed. We propose RetiSEM, a domain-constrained structural equation modelling (SEM) framework for causal graph recovery and mediation analysis under limited multimodal resources. This proposed work organises variables into biologically informed blocks, applies forbidden-edge constraints, and decomposes pathway-level effects into TE, NDE, and NIE components. We evaluate RetiSEM across ten synthetic benchmark scenarios that vary in dimensionality, nonlinearity, causal depth, and pathway structure, together with a fragmented real-world setting that combines NHANES clinical variables with externally derived retinal representations. This approach achieves lower structural error and higher causal accuracy than unconstrained baselines across the synthetic benchmarks. In the real-data analysis, retinal variables behave mainly as downstream biomarker-like indicators, with smaller but detectable indirect effects. These findings support our strategy as an interpretable framework for testing structured causal hypotheses in limited-resource biomedical AI. The code and resources for this work are publicly available at: https://github.com/Inamullah-Colab/ReitSEM.

Headline accuracies on the Tuebingen cause-effect pairs are routinely compared across papers even though each is measured under its authors' own protocol -- different pair subsets, weightings, model-selection, and decision rates. We argue this is the wrong comparison and run the right one: a same-hands re-evaluation in which every method is run by us on the identical 102 pairs, with one strict rule -- no tuning and a decision forced on every pair. As a clean reference point we introduce a deliberately minimal baseline: sorted-conditional compression, which feeds quantized, sorted, first-differenced data to an off-the-shelf compressor (bz2) and has zero fitted parameters. Under the common ruler the ranking differs sharply from the literature. Our baseline reaches 74.7% weighted accuracy (p = 3.7e-7); on the same 100 pairs that SLOPE is evaluated on it scores 76.0%, a 1.2-point gap below the authors' own forced-decision SLOPE (77.2%) that is well inside noise (McNemar p = 0.39). A faithful re-run of RECI lands at 70.7% -- inside the original authors' reported error bar, not the 77.5% often quoted (which we trace to a mis-copied cell). SLOPE's published 82.4% is a decided-subset figure: scoring the authors' own stored output only on the pairs its significance test chose to answer reproduces 81.7%. Under the common ruler the methods cluster in the low-to-mid 70s and the zero-parameter compressor ties the strongest of them. We document the mechanisms that inflate published figures (test-set model selection, significance-gated abstention) and contribute two further results: compression score magnitude is a model-free confounding flag (p = 2.8e-68), and a pre-registered falsification test fails in an instructive way that bounds the method's theoretical interpretation. Code, pre-registrations, and per-pair outputs are released.

Signed pairwise interaction scores fundamentally conflate uniqueness (U), redundancy (R), and synergy (S). We prove this on a minimal 3-way XOR structural causal model: faithful indices such as Shapley-Taylor return zero per pair, whereas projective indices such as Shapley Interaction spread the third-order effect into pair scalars that conflate the three mechanisms. We introduce Stochastic Hi-Fi, a post-hoc, retraining-free predictability decomposition that estimates per-feature U/R/S profiles by interventional masked inference. The estimator provides exact interventional semantics, finite-sample Monte Carlo bounds, strict variance reduction from coupled diamond sampling, and uniform finite-vocabulary convergence. Across tabular SCMs, Stochastic Hi-Fi recovers structure missed by scalar baselines (up to 411x larger interaction-magnitude recovery ratios). It also separates redundant and synergistic heads in the GPT-2 IOI circuit. On NIH ChestX-ray14, Stochastic Hi-Fi matches GradCAM on Pointing Game and improves substantially on Deletion AUC.

Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in $F_1$, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.

Theory of mind (ToM), the capacity to ascribe mental states to others and use those ascriptions for prediction and inference, is widely assumed to be essential for effective human-machine integration. Existing AI-ToM models address \emph{how} to mentalize, but leave the question of when largely unaddressed. The central question is: under what situational and agent-level conditions is ToM engagement causally warranted in conflict? This paper presents a structural causal model formalized as a directed acyclic graph (DAG), treating ToM as a mechanism activated by situational and agent-level conditions rather than as an always-on capacity. The model specifies four exogenous variables capturing situational and agent-level conditions, five endogenous mediators, and a mechanistic ToM node producing engagement states through three distinct causal pathways: a tractability pathway, a reasoning-depth pathway, and an enabling-cause pathway. The primary outcome is epistemic accuracy, which decouples social reasoning from behavioral policy and generalizes across social phenomena beyond conflict. The framework gives AI systems a principled, resource-rational decision procedure for mentalizing, with implications for efficiency, trust, and the development of robust artificial social intelligence. Simulation validation, empirical human-machine teaming studies, and ethical considerations arising from conflict-optimized mentalizing are discussed.

Causality in robotics aims to produce more interpretable and flexible robot behaviours by enabling robots to predict the consequences of their actions; however, deploying causal models with existing systems (e.g., navigation) operating in real environments remains understudied. This paper addresses the challenging problem of transferring causal models in real-robot experiments for a navigation scenario. We study this problem in two ways: (i) using the causal model as an offline evaluation module that predicts the competence of recorded real-robot navigation trajectories and relates it to quantitative navigation performance, and (ii) using the causal model as an online adaptation module that intervenes when the predicted competence of the default navigation is low. We validate our approach in a physical service robot that patrols around corridors. We show that the predicted competence correlates positively with path efficiency, and negatively with path irregularities (suboptimal behaviour). The model predictions also show strong agreement with human annotations (Cohen's kappa value of 0.88). In online experiments, the proposed method improves navigation performance in complex scenarios such as cornering and obstacle avoidance, yielding higher predicted competence and better navigation metrics than the default navigation baseline. In simpler scenarios, where the baseline already performs near-optimally, the causal adaptation provides limited benefit. These results indicate that causal models are particularly effective in enhancing navigation under increased task complexity. Overall, our results demonstrate that causal models developed for behavioural interpretation can be successfully integrated into real-robot navigation systems.

An artificial intelligence must have a model of its environment that is causal, supporting reasoning about interventions and counterfactuals, and also combinatorial, supporting generalization to unseen combinations of objects. In this work, we formally study when and how such a model can be learned. We develop relational structural causal models, extending structural causal models (Pearl 2009) to settings where objects and their relations vary. First, we show how answers to not only causal but also observational queries about unseen combinations of objects can not be identified without further assumptions. To enable such identification--including in the presence of unobserved confounding--we define relational causal graphs and derive symbolic identification criteria. Finally, we propose relational neural causal models, a provably correct approach that outperforms non-relational baselines on simulated traffic scenes with varying cars, signals, and pedestrians.

We introduce COMET (Causal Object-centric Model for Efficient Tree search), a model-based reinforcement learning algorithm that performs Monte Carlo Tree Search in a slot-structured latent space. COMET pairs a frozen unsupervised object-centric encoder with a transformer-based world model, in which actions are bound to objects through a novel action-slot fusion mechanism that is used in slot transition prediction. Policy and value heads use object-causal attention, modulating token interactions by learned per-slot relevance scores so that decision-making concentrates on task-relevant entities. COMET adds an explicit object-level inductive bias to MuZero-style latent planning. Across eight visually and dynamically diverse tasks from the Object-Centric Visual RL benchmark, ManiSkill, Robosuite, and VizDoom, COMET achieves a higher mean normalized score during the early stages of training compared to object-centric and monolithic baselines.

Latent reasoning models (LRMs) replace explicit chain-of-thought with continuous thoughts. Recent work treats observable latent-state patterns, such as BFS-like frontiers and decodable arithmetic computation, as evidence for internal reasoning mechanisms. Evaluating two LRMs (Coconut and CODI) against controls lacking the proposed recurrence or curriculum, we find these patterns also appear in the controls and do not always causally affect behavior. Causal interventions reveal that latent-thought utilization is not binary but graded, scaling with a thought's causal effect on model behavior. Geometric analyses reveal this effect concentrates in low-rank directions whose step-to-step geometry grows more structured as their behavioral influence increases. Latent thoughts should therefore be treated as hidden computation, not hidden explanation: decodability, attention, or static structure alone cannot establish mechanism. LRM interpretability thus requires matched controls and causal tests.

A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.

When an LLM agent fails -- issues a refund it should not have, calls the wrong tool, leaks data -- existing tooling answers what happened (observability) or whether it passed (evaluation), but not which step caused the failure. The obvious heuristics are wrong: the step that executes the harmful action is usually not the step that decided on it, and LLM-judge attribution is correlational and unreliable (state-of-the-art step-level accuracy on the Who&When benchmark is about 14%). We present Causal Agent Replay (CAR), which answers the question by intervention: it models an agent run as a structural causal model, applies a do-operation to a step, and re-executes the trajectory forward under the same stochastic policy, measuring the shift in the outcome distribution. We define an intervention algebra over agent steps, a single-step contrastive estimator whose point-of-commitment rule resolves a confound specific to stochastic run-forward, and a budget-bounded Monte-Carlo Shapley estimator that splits credit across interacting steps. Every effect is reported with confidence intervals. We validate against synthetic structural causal models with planted ground truth: the contrastive estimator recovers the pivotal step, and Shapley recovers a two-step interaction (0.44, 0.45, ~0; efficiency sum 0.909 versus the analytic 0.91). CAR is open source and runs on hosted or free local models.

Vertical federated learning (VFL) is a distributed learning paradigm that leverages vertically partitioned features across isolated parties without sharing raw samples; however, it remains vulnerable to active sample reconstruction attacks. Existing defenses fail to achieve a satisfactory trade-off between model utility and privacy protection, due to either suppressing task-relevant information alongside privacy-sensitive features or relying on end-to-end supervised training to converge the defense module, which exposes the model to early-epoch vulnerability. To address this challenge, we adopt a structural causal model (SCM) insight and construct CausShield. From a task-learning standpoint, causal features within a raw sample are those that are directly relevant and contributory to the learning objective, whereas non-causal features are task-irrelevant but often encode sample-specific private information, thereby facilitating reconstruction. Importantly, we lay a theoretical foundation to prove this insight. CausShield thus decomposes the shared representations between the client and the coordinating server in VFL into task-relevant and task-irrelevant components to ensure full-cycle privacy protection. Nonetheless, the decomposition is inherently challenging due to the dual objectives of preserving model utility while mitigating privacy leakage. We address this via a carefully formulated optimization problem, which is solved through unsupervised representation learning. We further theoretically prove that CausShield preserves the convergence behavior of standard VFL. Extensive experiments compare CausShield against seven SOTAs, including InvL (USENIX Security'25), and evaluate robustness against advanced reconstruction attacks such as URVFL (NDSS'25). Results demonstrate that CausShield consistently outperforms in privacy protection, model utility, and computational efficiency.

Software-in-the-loop (SIL) simulation is a cornerstone for the validation of modern automotive safety functions. However, many current frameworks utilize ideal sensing, which bypasses the functional insufficiencies of perception algorithms, leading to over-optimistic safety assessments. This paper proposes a perception-informed SIL testing methodology that bridges the gap between ground-truth simulation and real-world perception behavior. We present a framework for incorporating causal probabilistic models into standardized, scenario-based simulation toolchains, applicable to both Advanced Driver Assistance Systems (ADAS) and Autonomous Driving Systems (ADS). Our approach enables the systematic injection of realistic perception errors, such as loss of detection, sizing inaccuracies, and positioning offsets, derived from physical triggering conditions like fog, rain, and object-merging scenarios. By evaluating these ``faults'' within a standardized simulation environment, we demonstrate that perception-informed testing reveals latent operational risks that ideal SIL environments fail to capture, providing a scalable pathway for SOTIF (ISO 21448) validation.

Causal modeling of physical temporal phenomena must handle interventions that act along trajectories, nonstationary induced laws, path-dependent effects, and feedback mediated by dynamics, all challenging in standard causal models. We introduce Hamiltonian Causal Models (HCMs), a trajectory-level framework in which observed variables interact with local environments and interventions act as controls of Hamiltonian mechanisms. HCMs separate immutable equations of motion from intervenable mechanisms and define causal effects as discrepancies between interventional path laws. A key motivation for HCMs is their natural interface with non-equilibrium thermodynamics. Entropy production quantifies the irreversibility of a process and is a central causal observable: it is estimable from data and witnesses causal effects along the system's evolution that are invisible to endpoint and cumulative versions of the standard average treatment effect. As in physics, cause and effect are not primitives of the relation between two random variables but arise from the non-invertibility of the thermodynamic arrow. With this, our paper reconciles the language of statistical causal models and non-stationary thermodynamics, offering new tools to describe causality in a wide range of physical systems.

Many current agentic systems and LLM pipelines correct mistakes by optimizing outcome reward. This addresses only the what of failure: when an outcome diverges from prediction, the why and when of the mismatch are not systematically logged, reviewed, or corrected, so the same error can recur episode after episode. We argue that this is a structural problem, not merely a model-capacity one. We propose long-horizon temporal regret as a first-class objective alongside outcome regret and epistemic regret over the working causal model. Temporal regret captures when failure persists: how long a miscalibrated causal model is tolerated before correction. Epistemic regret captures why failure persists: residual uncertainty or error in the working causal model. Together, the three regrets give a falsifiable account of what, why, and when a long-lived agent can fail. Modeling the agent as a stream of E episodes, we prove three conditional results under explicit causal-probing, persistence, and detectability assumptions. First, under observationally equivalent confounding, outcome-only learning cannot distinguish causal from spurious structure without an intervention channel, so temporal miscalibration can persist linearly even after outcome regret is driven to zero. Second, with a persistent causal log and budgeted probes, total probe complexity is logarithmic in the episode horizon, inducing O(log E) temporal regret. Third, under K detectable change-points, the rate extends to O(K log E). We instantiate Trivium and pre-register five falsifiable predictions. On CausalBench-Seq, Trivium follows the predicted logarithmic envelope while outcome-only baselines grow linearly. A pilot real-LLM stream provides preliminary external-validity evidence across one full E = 500 run and three E = 100 frontier-model pilots. Self-learning here means revising an external causal model, not retraining LLM weights.

Advertising platforms use randomized lift tests to measure incrementality, but privacy-preserving reporting systems degrade the observed signal through match-rate loss, linkability loss, attribution-window loss, aggregation-threshold suppression, randomized reporting noise, and segment-heterogeneous signal loss. This paper formulates privacy-constrained advertising measurement as a robust causal decision problem under the mentioned signal losses. Given a randomized experiment and an ambiguity set for privacy-induced degradation, the framework projects the observation-compatible fiber of clean/unfiltered experimental worlds onto the incrementality functional and returns certified, rejected, and unresolved decisions. The main result gives a sharp decision frontier. Reports outside the frontier support uniformly valid certification or rejection, whereas reports inside it contain too little information for any method to uniformly distinguish above-threshold incrementality from non-incrementality. Supporting results give finite-sample certification, sample-complexity guarantees, a minimax lower bound showing that signal loss reduces effective information, and a reporting-granularity tradeoff. On 2.0M Criteo Uplift rows and the 64K-row Hillstrom email experiment, clean conversion lift is positive in both datasets, with lifts 0.00112 and 0.00495, respectively. Population certification survives mild degradation in Criteo and severe degradation in Hillstrom, while all considered finite-sample stress settings in both datasets remain unresolved after simultaneous uncertainty and reporting noise are included. Overall, the research contributes a decision-theoretic layer for privacy-aware incrementality measurement whose output is the strongest causal-claim justified by degraded ads signals.

Metamodels for discrete-event simulations approximate the behavior of simulation models without running expensive simulations. Prior work introduced modular dynamic Bayesian networks (MDBNs) -- a class of metamodels that can estimate a range of probabilistic and causal queries (PCQs) using a single, trained model -- but the method was limited to Markovian systems. In this paper, we initiate an extension of MDBNs to non-Markovian queues by approximating non-exponential distributions using phase-type distributions. This approach raises novel challenges, including balancing metamodeling accuracy and tractability when choosing the number of phases, efficiently learning metamodel parameters, and choosing the sampling interval that is used to approximate a continuous-time simulation by a discrete-time MDBN. We provide preliminary solutions to these challenges, yielding the first causal metamodeling technique for non-Markovian systems. Experiments on a G/M/1 queue demonstrate that the MDBN can produce accurate answers to PCQs with orders-of-magnitude speedup of inference times relative to direct simulation.

For many real-world systems, causal ground truth is difficult to obtain, making claims about causal effects hard to assess. We develop methods for evaluating collections of $\binom{n}{2}$ bivariate causal statements over a set of $n$ variables. In the setting of acyclic linear statements, any such collection can be extended to a unique multivariate causal model, but we argue that this induced model is implausible if it imposes substantial additional confounding to explain observed correlations. We introduce a compatibility score that quantifies this notion of plausibility, notably without relying on the faithfulness assumption. Additionally, we define an incompatibility score for purely graphical bivariate causal statements, based on global consistency constraints that are derived from acyclicity and faithfulness assumptions. We give theoretical and empirical evidence that both scores can successfully distinguish correct from incorrect causal statements in generic settings. Moreover, we demonstrate the practical applicability of our methods by analyzing causal claims made by large language models. Our work aims to provide a foundation for assessing the reliability of causal information derived from human experts or artificial intelligence in settings where alternative forms of validation are unavailable.

Building on recent formalizations of root cause analysis for rare events (``outliers'') in structural equation models, we propose a formal definition of a causal pathway and discuss its testable implications. We identify conditions under which these implications depend only on a causal abstraction defined by the pathway of rare events, rather than on the full causal graph of the underlying system. Accordingly, we introduce an abstraction of causal structure to pathways of rare events that bridges simple verbal causal explanations and detailed causal modeling.

Under standard graphical assumptions, the Markov boundary of a target variable is the smallest set of features that renders every other feature redundant. Once the boundary is observed, the target is conditionally independent of the rest of the table. This is a tempting object for tabular prediction, since it names exactly the columns a model should need. Yet modern regressors are still trained on the full feature set. We ask whether the Markov boundary is genuinely useful for prediction on SCM3K, a 3,450-task synthetic SCM benchmark with feature counts from 40 to 1000 and six SCM families, evaluated with six regressors. The answer is more nuanced than the theory suggests. Restricting a regressor to the oracle boundary often improves prediction substantially, and the improvement grows as the feature space becomes larger and sparser. But the natural pipeline of recovering the boundary with causal discovery and training on the recovered mask does not deliver. Existing estimators exhaust the compute budget before reaching the regime where the boundary helps most, and even where they run they rarely beat the full feature set. We trace this to three causes. Discovery optimizes structural recovery rather than prediction. False negatives and false positives carry sharply asymmetric predictive cost. The exact boundary is only one of many feature sets that beat all features. We then develop what these facts imply for prediction-aligned feature selection and for tabular models that learn to use causal structure.

Causal analysis is a crucial task in many domains, including manufacturing, social science, and medicine. However, despite recent progress, the conceptual and methodological complexity of causal methods makes them largely inaccessible to domain experts. This gap prevents experts from leveraging these advances and hinders researchers who lack access to real-world data for validation. To bridge this divide, we introduce ORCA, a copilot for end-to-end causal analysis. ORCA orchestrates agents to understand the user's goals and guide them through the most appropriate causal analysis workflow, from fully automatic to highly user-guided execution. It features causal discovery, causal effect estimation, explainability and Root-Cause-Analysis (RCA). ORCA evaluates and compares performance, generates key metrics and diagrams, and generates insights through structured reports. We highlight its effectiveness across several real-world use-cases.

Mechanistic interpretability produces circuit-level causal analyses of neural network behaviour, but discovered circuits often remain isolated experimental artefacts: there is no shared formal representation for what circuits compute, how they relate, or when two findings provide evidence for the same mechanism. This work provides a formal infrastructure for cumulative mechanistic science by treating circuit interpretation as inductive theory construction. Each circuit is characterised at two levels: a Causal Functional Signature (CFS), which grounds component behaviour in causal attribution evidence and token role profiles, and an architectural signature $τ_{\mathrm{arch}}$, learned by inductive logic programming (ILP) from scale-invariant structural predicates. Together, these constitute a formal coherence layer that makes mechanistic claims explicit, comparable via $θ$-subsumption, and portable across model scales. CFS reveals qualitatively distinct computational strategies across task types, including attention-mediated copying versus MLP-mediated binding. ILP signatures achieve substantially better structural separation than graph kernel and feature-vector baselines, and support principled transfer across model scales and architecture families.

Cascade attacks in LLM multi-agent systems (MAS) arise when adversarial influence propagates across agents and leads to escalated system-level failures through complex agent interactions. Detecting such cascades is challenging, as their signals are distributed, tightly coupled across interaction channels, and often appear plausibly benign locally but may unfold quickly either within a single turn or gradually across multiple turns. Existing defenses, being largely local and text-centric, fail to capture such cross-channel, temporally coordinated dynamics of cascade propagation. Therefore, we propose CASPIAN, the first framework that provides a unified, cross-channel causal analysis of cascade behavior in LLM-MAS through online monitoring of dynamic influence propagation across agents. CASPIAN models multi-agent interactions using a unified, dynamic causal influence matrix across channels, estimated efficiently via a late-interaction conditional transfer entropy (LI-CTE) formulation, thereby enabling the detection of cascade onset from emergent system-level structure rather than isolated anomalies. It further performs online causal attribution, identifying the origin, bridge, and amplifier agents driving the cascade and reconstructing its principal propagation pathways, capabilities not supported by existing methods. Across diverse multi-agent frameworks and benchmarks, CASPIAN consistently outperforms semantic guardrails, LLM-based judges, and graph-based anomaly detectors in both detection accuracy and early cascade identification while operating with sub-1% relative overhead latency. These results demonstrate that unified cross-channel causal modeling is essential for reliably detecting and understanding cascade failures in LLM multi-agent systems.

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.

End-to-end autonomous driving, which bypasses traditional modular pipelines by directly predicting future trajectories from sensor inputs, has recently achieved substantial progress. However, existing methods often overlook the causal inter-dependencies in ego-vehicle planning, ignoring the reciprocal relations between the ego vehicle and surrounding agents. This causal oversight leads to inconsistent and unreliable trajectory predictions, especially in interaction-critical scenarios where ego decisions and neighboring agent behaviors must be reasoned about jointly. To address this limitation, we propose CaAD, a Causality-aware end-to-end Autonomous Driving framework that captures these dependencies within a shared latent scene representation. First, we propose an ego-centric joint-causal modeling module that builds on the marginal prediction branch, and learns causal dependencies between the ego vehicle and interaction-relevant agents. Second, we employ a causality-aware policy alignment stage implemented with joint-mode embeddings to align the stochastic ego policy with planning-oriented closed-loop feedback computed from surrounding traffic and map context. On the Bench2Drive and NAVSIM benchmarks, CaAD demonstrates strong closed-loop planning performance, achieving a Driving Score of 87.53 and Success Rate of 71.81 on Bench2Drive, and a PDMS of 91.1 on NAVSIM. The project page is available at https://moonseokha.github.io/CaAD/.

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.

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.

Machine learning classifiers in dynamic environments face concept drift -- changes in the data-generating process that degrade performance. Conventional evaluation via static test sets or noise perturbations fails to preserve causal dependencies in tabular data, often producing causally invalid assessments. Post-hoc tools like SHAP and LIME offer correlational insights that may not reflect the causal mechanisms driving model failure. We propose a framework that complements existing drift detection by leveraging Structural Causal Models as "Digital Twins" of data-generating processes, enabling precise causal interventions while preserving structural dependencies. Our technique, Causal Parametric Drift Simulation, stress-tests classifiers to identify vulnerabilities before deployment. Experiments on the Open Sourcing Mental Illness (OSMH) dataset demonstrate that this approach exposes latent vulnerabilities invisible to standard statistical monitors.

Sparse autoencoders (SAEs) decompose transformer residual streams into interpretable feature dictionaries, yet the relationship between SAE width and causal influence on model output has not been systematically characterised. We introduce causal dimensionality kappa(L, M, T), defined as the effective rank of the expected Jacobian outer product at layer L, and show it can be estimated via the SAE width sweep paired with attribution patching. Across seven SAE widths from 16,384 to 1,048,576 features on Gemma-2-2B layer 12, representational capacity grows 15.6x while causal capacity grows only 4.35x: a robust separation we term the representational-causal wedge. A saturating fit yields kappa-hat approximately 1,990 with kappa-hat / d_model = 0.86 and participation-ratio lower bound kappa_PR approximately 280. Crucially, kappa is invariant to model scaling: Gemma-2-9B and Gemma-2-2B yield identical N_causal = 328 at the same SAE width despite a 3.46x parameter increase (the count is forced to 2% of SAE width by calibration; the substantive empirical claim is shape invariance of the AtP score distribution under matched seq=512 conditions). Across eight network depths kappa is constant while the absolute attribution threshold drops 20x from layer 1 to layer 23. Five controls (architecture invariance, threshold robustness, geometric privilege, synthetic ground-truth recovery, and a four-cell encoder/decoder ablation) pin down what kappa measures and what it does not. Our findings establish kappa as a measurable, model-intrinsic property of transformer layers: sub-linearly recoverable by SAE width, invariant to model scaling, and structured across network depth.

Accurately predicting opponents' behavior from interactions is a fundamental capability for large language model (LLM)-based agents in multi-agent and game-theoretic environments. Existing approaches often entangle opponent modeling with prediction, relying on implicit contextual reasoning and limiting adaptability in dynamic interactions. To this end, we propose Structured Opponent Modeling (SOM), a two-stage opponent modeling framework that distinctly separates opponent model construction and opponent prediction. At the construction stage, SOM employs a Structural Causal Model (SCM), a graph-based formalism for representing dependencies among variables, to capture directed links between opponents' observations and actions, yielding an explicit and structured opponent representation. At the prediction stage, the LLM performs structured reasoning along clear pathways derived from the SCM, improving both prediction accuracy and stability. Extensive experiments on diverse multi-agent benchmarks demonstrate that SOM consistently outperforms state-of-the-art LLM-based reasoning baselines, enabling more accurate and adaptable strategic decision-making in complex and dynamic multi-agent interactions.

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.

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.

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.

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.

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.

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.