Causal Graph

Mechanistic interpretability defines features as the fundamental units of a neural network and circuits as the weighted subgraphs that carry out its computation. Because individual neurons are polysemantic, Cross-Layer Transcoders (CLTs) were introduced as a way to approximate a model's circuits by generating an attribution graph. The nodes of that graph, however, are unlabeled features: reading a graph means pruning it and then working out by hand what each surviving node means. To make CLTs easier to use for circuit discovery, we introduce Circuit-Diff, which intervenes on the model itself with a low-rank factual edit and takes the features whose role in the attribution graph changes under that edit as related to the edited knowledge. On the edits we examine, the flagged nodes are not only detectors of the object token: read off the CLT's released feature dashboards, they include features for the history, geography and associations surrounding the old and new objects. We formalize the method, measure how reliable a frozen CLT remains after a factual edit, test the selected nodes causally by patching them on up to 24 CounterFact edits, give a case study, and release an open-source implementation built on the circuit-tracer package, together with two further tools (multi-prompt aggregation and rule-based supernode labeling).

Large language models (LLMs) have been applied to causal discovery, but candidate-graph generation rarely treats premature omission of potentially relevant causal relations as an explicit design objective. We propose MaSCoD, a multi-agent framework that organizes candidate third variables and local structural patterns before direct-edge judgment. We evaluate MaSCoD on Auto-MPG, DWD, and Sachs using GPT-5.4 as the primary backbone and GPT-4o for replication. MaSCoD exhibits a dataset- and backbone-dependent retention-selectivity profile rather than uniform superiority. Across all six dataset-backbone settings, Full, which supplies structural hypotheses before direct-edge judgment, achieved higher mean Recall and F1 than No Phase 1, which instead constructs them within the judgment procedure, while also increasing false-positive rates. Additional reference-edge retention over all evaluated baselines was observed on DWD with GPT-5.4 and on Sachs with GPT-4o, rather than uniformly across settings. Partial ablations showed that supplying both information components did not always outperform supplying only one. For GPT-5.4, stage-wise analysis showed that the Full-No Phase 1 retention gap was already present after direct-edge judgment, while reconciliation introduced additional reference-edge loss for Full on Sachs. These findings support structural pre-organization as an explicit design and evaluation target for omission control and motivate evaluating context construction jointly with its utilization in judgment.

Large language models (LLM) deployed as autonomous pricing agents may sustain supracompetitive prices through tacit coordination. We develop a causal graph divergence framework that separately measures structural faithfulness and intent faithfulness of LLM pricing agents in Bertrand competition. Across nine LLMs under duopoly and triopoly conditions, collusive behavior and chain-of-thought (CoT) faithfulness dissociate along both dimensions: the most collusive model accurately reports cooperative intent yet reasons structurally unfaithfully, while the most structurally faithful model sustains supra-Nash pricing under both market structures. These findings establish that CoT monitoring alone cannot serve as a standalone safeguard against algorithmic collusion.

We present a method for recovering the moral graph of a causal DAG from a probability distribution over discrete variables, using fully connected tensor networks (FCTNs) with nuclear-norm-regularized bond corrections. Each bond matrix is parameterized as a baseline all-ones matrix plus a low-rank correction $C_{ij} = U_{ij}V_{ij}^\top$, and the nuclear norm of the correction implemented via the variational Frobenius norm penalty on the factors drives unnecessary bonds to zero. We prove that under faithfulness, positivity, and a no-implicit-rerouting assumption on the local tensor architecture, \textbf{every} optimal FCTN with zero reconstruction error $\varepsilon = 0$ has effective graph exactly equal to the moral graph. For the approximate regime ($\varepsilon > 0$), we provide explicit recovery bounds using the Fannes-Audenaert continuity of conditional mutual information, and derive a sufficient condition on the regularization parameter $β$. The effective graph is read directly from the optimized bond matrices.

When a statistical agency or regulator releases synthetic data in place of sensitive records, it chooses the generator that produces the table, and can shape that generator so unfair pathways are absent. DECAF made this concrete on one non-private GAN: three fairness definitions become three sets of edge cuts on the generator's causal graph. Whether the mechanism belongs to DECAF, or to causal factorisation itself, was untested. We port all three definitions to nine generators from three unrelated families (marginals-based, GAN, and diffusion, each with differentially private variants), across three levels of formal privacy guarantee, over 2,520 matched-pair runs on Adult and COMPAS datasets. The mechanism transfers everywhere, and our new causal diffusion backbone yields the fairest release of any family we tested, at fidelity close to the marginals tier. Applying the cut barely moves fidelity, only costs a downstream classifier about $0.07$ to $0.15$ AUC on average, and adding privacy guarantees don't make the data less fair.

TRACE (Math & Lienhart, arXiv:2602.01135) reads causal graphs over event types out of a pretrained autoregressive sequence model by thresholding a per-position conditional-mutual-information estimate at a fixed tau. We independently replicate its headline synthetic result: with tau selected on a validation split, mean per-sequence F1 against exact interventional truth reaches 0.90-0.91 at vocabulary size 1000 (paper: 0.91) and 0.86-0.91 from 100 to 2000. First, the optimal threshold is pinned to the truth margin, not to any constant: at every size the errors at tau* straddle the delta = 0.05 margin defining ground truth (missed true edges lie just above it, accepted false ones just below), and the blind optimum lands near delta/2 times the estimator's calibration, confirmed out of sample at 5000. Second, at a single global threshold TRACE mostly recovers a direct, adjacent-influence graph: lag-1 true edges are recalled at 0.97-0.99, while true edges at lag 2 or more read orders of magnitude lower---the reading-scale price of randomizing mediating positions, which an exact test of direct causal effect requires when the truth is unknown. A per-lag threshold family recovers a third to a half of lag-2 truth; on lag-uniform data one validated threshold recalls every lag at 0.40-0.87, 8-26 pp below an atomic-intervention control at lags 3-6. Third, the default lag decay of the paper's synthetic benchmark concentrates about 85% of interventional truth at lag 1 and pushes the rest below the estimator's noise floor, so headline F1 there certifies lag-1 recovery only and conflates the benchmark's skew with the algorithm's own limit; a flatter decay separates the two. Fourth, F1 saturates from N = 2 particles at the selected threshold---a property of the threshold's margin over the noise floor, not of the estimator, which converges as N^(-1/2). We distill five practitioner rules.

Effective humanitarian response depends on the rapid synthesis of heterogeneous, high-volume information sources - a task that routinely exceeds human analytical capacity in the critical early hours of a crisis. We present a pipeline that combines structured disaster records from EM-DAT with unstructured documents from ReliefWeb and the European Media Monitor (EMM) to produce source-grounded disaster storylines and causal knowledge graphs supporting situational awareness for responders and analysts. Using Retrieval-Augmented Generation, the pipeline extracts structured storylines - tabular event profiles covering 17 fields, from severity and key drivers to child-sensitive impact indicators - and constructs causal knowledge graphs where each node and edge is enriched with citation-grounded explanatory narratives, enabling full traceability back to primary sources. We evaluate the system on three diverse crisis use cases through a human evaluation involving 9 domain expert and 9 non-expert evaluators. Results confirm high retrieval precision, strong faithfulness of extracted causal relations, and a clear expert preference for citation-grounded components over ungrounded alternatives. The pipeline is designed to scale to the full EM-DAT catalogue, with the goal of publicly releasing a narrative-enriched version of the database.

Causal discovery aims to uncover the underlying causal relationships given data generated from a system. The goal, however, is not merely to predict causal edges given data, but also to be able to interpret and explain either observed or hypothesized phenomena, such as a particularly large causal effect. We consider this task of conditional causal discovery and cast it as a Bayesian inference problem, in which we target the posterior over causal graphs and parameters conditional on an event such as a causal-effect constraint. Unfortunately, this poses a computational challenge: existing approaches to Bayesian causal discovery struggle when the event has small posterior mass. To address this, we adapt rare-event estimation techniques to perform inference the joint graph-parameter space. Our method gradually drives a particle population toward the constrained region while maintaining samples that approximate the conditional posterior. Empirical evaluation on synthetic graphs validates the accuracy of our approach at small and large scales, and we show in a case study on the Sachs protein dataset how our method can be used to aid scientific exploration by providing pathway-level summaries.

Coupon campaigns seek to lift both conversion and revenue, but gross merchandise value (GMV) follows a deterministic funnel from conversion to conditional order value and is zero-inflated and heavy-tailed. We propose FunnelCausalNet, an uplift estimator coupling a binary conversion head with a nonnegative conditional-value head through $μ_{\mathrm{gmv}}=μ_{\mathrm{conv}}μ_{\mathrm{val}}$. Under explicit RCT, support, rate-gap, and cross-head covariance-control assumptions, an idealized leading-order MSE comparison identifies a regime in which funnel composition can reduce pointwise variance; this is a heuristic, not a guarantee for the shared-representation neural model. The estimator is paired with marginal split-conformal CATE summaries, combined through a Bonferroni union as audit bands, and a Lagrangian budgeted allocator using RCT-anchored estimates for subsidy-aware ROI accounting. On semi-synthetic multi-tier Criteo-MT7, FunnelCausalNet's mean AUUC_GMV is within one seed standard deviation of the leading feature-interaction baseline among eleven baselines, while a controlled ablation reduces GMV effect error versus direct GMV regression by 18--48% across tested zero-inflation regimes. On de-identified industrial Hotel-Coupon RCT logs with about 4.9 million hold-out exposure records per seed, expected-outcome evaluation sweeps full LP frontiers; FunnelCausalNet has the best seed-averaged mean DeltaROI at all seven correlated anchors from 10% to 60%, which we treat as descriptive frontier consistency rather than independent significance. On sparse binary-spend public benchmarks, revenue-focused rankers can dominate uplift-curve proxies, defining an explicit regime boundary.

Virtual cells employ machine learning models to simulate and predict cellular behaviors, serving as a critical computational framework for investigating health and disease. Injecting causal graphs into virtual cells can improve the interpretability, but such graphs are usually not available in real-world applications. Recently, many methods have been proposed to construct causal graphs from data, which group genes based on their similarities to form concepts and extract their causal relationships. However, since this automatic process is unsupervised, the causal graphs usually contain errors. In this paper, we propose a human-guided causal knowledge injection method for virtual cells. We developed a gene-similarity-aware causal graph visualization supported by a hybrid optimization algorithm to help explore both the causal relationships between concepts and the similarities between genes. Based on the exploration, we further developed a counterfactual analysis strategy supported by a counterfactual visualization and a causal path visualization to help validate and refine causal graphs. The effectiveness of our method is demonstrated through two real-world case studies, the extraction of scientifically meaningful causal insights, and positive feedback from domain experts.

Modern telecommunication, cloud, and microservice systems emit correlated alarm cascades when components fail. Root cause analysis (RCA) aims to identify the small set of alarms that initiate each cascade. A common approach learns a causal graph from observational logs and predicts all zero-in-degree alarms in each incident-induced subgraph. However, the learned graph remains fixed and cannot benefit from expert diagnoses of historical incidents. We close this loop with EvoCause. Expert labels constrain which alarms should be source nodes but do not specify the edge edits needed to satisfy those constraints. EvoCause uses a large language model (LLM) to propose semantically plausible graph edits, while deterministic code validates node identities and acyclicity and retains the best graph on a labeled alignment set. At test time, the refined graph alone produces transparent predictions without an LLM call. We also release TeleRCA, an expert-annotated benchmark from a production telecommunication network containing $485{,}681$ alarm events spanning $194$ alarm types over $5{,}621$ resources. On synthetic data, EvoCause initialized with the PC causal discovery algorithm outperforms the unrefined PC baseline, raising Node F1, Case EM, and Graph F1 by $11.59$, $9.40$, and $4.59$ percentage points, respectively, while reducing nSHD by $0.2379$. On TeleRCA, replacing human-readable alarm titles with anonymous identifiers lowers Node F1 and Case EM by $6.12$ and $8.04$ percentage points, respectively, indicating that alarm-name information contributes to graph refinement.

Learning causal graphs from interventional data is a challenging problem with broad applications. In molecular biology, for example, a central goal is to uncover gene regulatory networks from large-scale perturbation data. An ideal algorithm for this task should scale to thousands of nodes, incorporate interventions even when their targets are unknown, quantify uncertainty, and provide identifiability guarantees. However, existing approaches---e.g. approaches using score-based optimization or approximate Bayesian inference---often fail to meet all of these criteria. To address these limitations, we develop Amortized Bayesian Causal Discovery of Extended Factor Graphs (ABCDEFG). Our method guarantees exact acyclicity, scales to graphs with thousands of nodes, and naturally handles interventions even when their targets are unknown. Additionally, ABCDEFG estimates a posterior distribution whose maximum a posteriori estimate provably identifies the true causal graph up to an equivalence class. On simulated datasets, ABCDEFG achieves state-of-the-art accuracy, producing a well-calibrated posterior distribution while outperforming previous score-based and approximate Bayesian methods. Applied to large-scale single-cell perturbation data, ABCDEFG identifies both established and novel gene targets of growth factors.

Causal discovery methods have shown strong performance in temporal systems, but they typically rely on regular and discrete lag structures, limiting their applicability to regularly sampled data. However, many real-world tasks require dealing with irregularly sampled streams of events, such as sensor streams, healthcare data, and financial transactions. In this work, we propose an extension of PCMCI+, a state-of-the-art method for causal discovery on regular multivariate time series, to allow for handling irregular time series. Instead of modelling causal relations through fixed-lag dependencies, our method aggregates causal influence over predefined temporal windows. We evaluate our method on synthetic irregular event streams with known causal structures under different signal-to-noise ratios, showing that it consistently recovers the underlying causal graph and substantially outperforms the standard PCMCI+ on irregularly sampled data.

This paper proposes a causal independence principle for value -- the value Causal Markov Condition (v-CMC) -- and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability-value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define v-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a Bellman-type recursion as a special case of the v-CMC, thereby generalizing standard Bellman recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.

The interconnected nature of global financial systems makes them vulnerable to systemic risks, where the failure of a few institutions can trigger catastrophic cascading defaults. Traditional risk models often fail to capture the complex, non-linear dynamics of these networks. While Graph Neural Networks (GNNs) have shown promise in modeling relational data, they primarily learn correlative patterns and function as black boxes, offering little insight into the causal mechanisms of shock propagation. This limitation is critical for regulators who require explainable models to perform stress tests and devise effective interventions. We introduce CausalGraphX, a novel framework that integrates GNNs with counterfactual reasoning to provide explainable assessments of systemic risk. CausalGraphX employs a Graph Attention mechanism to learn representations of institutional vulnerability and uses an adversarial regularization technique to ensure these representations capture causal drivers rather than spurious correlations. Furthermore, we propose an optimization-based approach to generate counterfactual explanations, answering questions such as, "What minimum capital injection would have prevented Bank A's default under a specific stress scenario?" We validate CausalGraphX on large-scale synthetic financial networks. Our results demonstrate that CausalGraphX significantly outperforms traditional and deep learning baselines in predicting cascading defaults while providing sparse, plausible, and actionable counterfactual explanations.

We formalize verification in causal graphical models: deciding whether a given observational formula identifies a target interventional distribution. This opens a problem complementary to identification, asking not whether any identifying formula exists, but whether the given formula is identifying. We show that even sound and complete solutions to identification do not solve verification. We propose a falsifier as a first practical route forward, prove that it induces an almost-surely correct verifier for regular exponential-family models, and use the resulting verifier to develop the gateway test, which finds all sets admissible for use in a front-door formula.

Quantifying directional influence between node populations is a fundamental problem in graph-based modeling, particularly in spatial biological systems where cell-cell interactions shape functional outcomes. Existing approaches based on attention, attribution, or correlation capture associations but do not provide a principled framework for evaluating directional effects under controlled perturbations. We introduce a framework for structured counterfactual interventions in graph-based models to estimate directional influence between node types. Our approach trains a Neighbor Influence Model (NIM) to predict node states from local neighborhoods and applies constrained interventions that modify neighborhood composition while preserving key spatial and structural properties. We define the Counterfactual Directionality Score (CDS), which measures the change in predicted node state induced by targeted perturbations, and provide a theoretical interpretation of CDS as a finite-difference measure of local intervention sensitivity. To obtain valid uncertainty estimates, we introduce a core-level bootstrap procedure that accounts for dependencies within spatial samples. Experiments on synthetic spatial graphs with known directional structure show that CDS recovers directional influence, remains well calibrated under null conditions, and is robust to confounding signals, while preliminary results on spatial transcriptomics data reveal biologically plausible and consistent interactions across tissue cores.

Music recordings and live streams are often affected by noise, reverberation, spectral imbalances, or artifacts that degrade listening quality. While speech enhancement has matured into a well-defined research area, music enhancement is less established because musical signals combine overlapping sources, wide bandwidths, strong dynamics, and intentional production effects. We study real-time music enhancement under strict causal and low-latency constraints. We formulate the task around recovery of the intended produced mix from acoustic and production-oriented degradations, adapt compact causal networks to music, and compare speech-derived real-time baselines, an external music-denoising model, an offline restoration reference, and a music-specific MusicFilterNet-MS variant. On the tested hardware, all causal models run faster than real time, but improvements depend strongly on the dataset, degradation type, and metric family; under several objective criteria, indiscriminate enhancement can worsen the degraded input. The main contribution is therefore a benchmark and an analysis rather than a universal best model: real-time music enhancement is feasible, but robust improvement requires degradation-aware modeling, stereo-aware processing, identity-preserving correction, and evaluation beyond a single objective score.

How can an agent build a structured map of its world from nothing but an ongoing sequence of raw sensory input and its own movements, especially when natural variation means exact sensory patterns rarely repeat? The Clone-Structured Causal Graph algorithm (CSCG), a normative hippocampus model, shows how an interpretable map can be learned from aliased observations. However, CSCG requires a predefined discrete alphabet, and its expectation-maximization formulation is not easily combined with existing neural network modules, preventing the end-to-end processing of raw image sequences. We remove this barrier by reformulating CSCG as a single, fully differentiable module, gradCSCG, and coupling it to a learned vector-quantized variational autoencoder (VQ-VAE) perceptual front-end. A soft emission forward pass allows the map-learning objective to flow back into perception, while a set of loss-balancing mechanisms mitigates module collapse during joint training. We demonstrate, first, that gradient training reproduces CSCG's results on original symbolic grid worlds by recovering room topology from heavily aliased observations. Second, we show that map recovery remains robust on MNIST image sequences, where each visit to a location yields a newly sampled image of its assigned digit. Across four heavily aliased environments, the end-to-end pipeline successfully uncovers the underlying adjacency graph with high edge precision and recall, directly from visual input. This work provides a proof of principle that CSCG can serve as a composable building block in a deep learning architecture.

True causal relationships are rarely known, and inferring causal graphs from data is hard. A fundamental challenge is how to assess whether a given causal graph is good in the absence of a ground truth. We propose falsifying candidate causal graphs based on whether they can explain the propagation of an outlier event. Our approach leverages a key principle: weak outliers rarely cause strong ones. While this principle has previously been used in root cause analysis to identify root causes without prior knowledge of the graph, we turn it on its head and use it to falsify candidate causal graphs whose implied outlier propagation is inconsistent with the data. To this end, we present the first statistical tests for the hypothesis that a candidate graph is the true causal graph, and show they have false positive control, power guarantees against incorrect causal graphs, and can operate with a single outlier sample.

Expert background knowledge is often available in practical applications of causal discovery. Such constraints on the true causal graph can help causal discovery in terms of identifiability of causal effects and accuracy of the learned structure, but also in reducing the space of candidate causal graphs. As causal discovery can become computationally expensive for large number of variables, it is crucial to utilize background knowledge effectively during the causal discovery process. However, most current methods only use background knowledge in a postprocessing step after causal discovery to refine the learned graph. In this work, we develop a framework for utilizing background knowledge during the causal discovery process, focusing especially on scalable causal discovery methods that recover only a subset of the whole graph. We implement our framework for multiple algorithms and empirically show that utilizing background knowledge can both reduce computational requirements and increase the quality of the learned structures.

Causal discovery from unstructured data is a challenging yet underexplored task in high-expertise domains such as healthcare, finance, and education. Existing methods typically leverage the general knowledge of large language models (LLMs) to identify causal factors from unstructured data and annotate them into structured data for causal graph construction. However, they remain limited by two key challenges (CHs): (CH1) insufficient identification of latent factors, which are implicit in the data yet essential for causal discovery, due to the lack of domain-specific knowledge; and (CH2) unreliable factor annotation, caused by the lack of domain-grounded reasoning, which propagates errors to the resulting causal graphs. To address these challenges, we introduce a novel Domain Knowledge-enhanced Causal Discovery framework (DKCD) for causal discovery from unstructured data in high-expertise domains with three interconnected components: (1) Knowledge Mining: It retrieves relevant domain knowledge based on observable factors to support subsequent causal reasoning. (2) Knowledge-guided Causal Reasoning: Reasoning with relevant knowledge, it discovers latent causal factors to address CH1 and generates key causal clues for more accurate data annotation to address CH2. (3) Causal Structure Discovery: It constructs the final causal graphs based on a more complete factor set and accurate annotations. Experiments on two domain-specific datasets show that DKCD significantly improves both causal factor identification and causal graph construction.

Causality has become an increasingly important tool for gaining a deeper understanding of complex systems. Among various causal analysis methods, causal discovery, which identifies causal relationships among variables from data, has been widely used to uncover underlying causality in diverse processes. However, while multistage processes are prevalent in many fields, existing causal discovery methods may produce counterintuitive results, given the known process knowledge, and may not be computationally efficient for handling large datasets typical of multistage processes. To address this gap, we propose a novel causal discovery method called Order-based Causal Discovery for Multistage Processes (OCDM). OCDM is designed to infer the causal structure of multistage data while preserving their inherent hierarchical and sequential structure by explicitly incorporating process knowledge into the causal discovery process. Specifically, we propose a structural knowledge-informed order-inferring algorithm that infers the causal order of variables by incorporating information about the stage from which each variable originates, based on an order-based causal discovery framework naturally suited for inherently ordered multistage data. Furthermore, to eliminate spurious edges from the initial causal graph generated based on the inferred causal order, we introduce a novel pruning technique using stochastic gated neural networks, which offers greater computational efficiency compared to existing methods. Through experiments on various datasets, we demonstrate that OCDM effectively infers the causal structure of multistage processes, outperforming existing methods.

Long-horizon language agents increasingly maintain executable world models in the form of planning graphs, where tool calls, validators, memory updates, recovery branches, and final answers are connected by typed dependencies. When a rollout fails, repairing the most visible error can leave the underlying error-amplification path intact, while replaying the full graph is expensive and difficult for long-context models to use reliably. We study world-model correction: selecting a compact subgraph of a failed planning graph whose repair stabilizes subsequent rollouts. We first instantiate a strong family of engineering correctors, including pointwise error scans, TopK and window selection, local graph expansion, cascade repair, and full-context LLM repair. We then propose WM-SAR, a spectral subgraph repair method that estimates node-edge amplification, greedily grows a connected repair region by marginal residual-spectral relief, and sends only this region to an LLM for root-cause repair. Theoretically, we connect residual spectral radius to rollout error and planning regret, motivating repair as stabilization rather than attribution alone. Across synthetic calling-tree graphs, benchmark-inspired agent topologies, and cross-model LLM repair experiments, WM-SAR achieves stronger long-horizon stabilization and root-cause recovery under compact token budgets, matching much larger repair contexts while exposing the LLM to a cleaner causal subgraph.

We consider sparse multivariate stochastic systems that evolve in continuous time according to a causal mechanism and present methodology to recover the system's time-infinitesimal transition mechanism from mere cross-sectional data. This observational paradigm is motivated by applications such as gene expression analysis, where destructive experimental techniques may only allow recording data once over a cell's lifetime. Precisely, we assume the system follows a time-homogeneous diffusion process that has reached an equilibrium distribution at observation time. Further, we assume the causal mechanism is fully described by the diffusion drift, is acyclic, and its causal structure graph is known. In this setting, we prove that the full causal mechanism, i.e., the drift function, can be non-parametrically identified under a weak non-explosion criterion. We derive a non-parametric kernel estimator for this challenging inverse problem and prove its consistency. Moreover, we propose a cross-validation scheme for hyperparameter tuning, illustrate the behavior of our estimator in simulations, and we discuss connections with irreversible generative diffusion models and low-frequency sampled data.

Venture capital (VC) investment decisions face distinct challenges, such as multi-source heterogeneous data, non-stationary time series, and the demand for explainable predictions in high-stakes, low-data settings. To overcome these issues, we introduce \textbf{FinInvest-GTCN}, a Graph-Temporal-Causal Network that redefines the task from content recommendation to quantitative risk-return assessment. This architecture combines a relational graph encoder to capture the investment ecosystem's topology, a multi-scale temporal fusion module to handle long-term dependencies and non-stationarity, and a causal decision head that generates risk-adjusted predictions with interpretable causal attributions. A core innovation is the Meta-Causal Adaptation (MCA) strategy, which facilitates robust fine-tuning for new, data-scarce sectors by aligning updates with causally-plausible structures derived from meta-pretraining. Comprehensive experiments on proprietary VC datasets show that FinInvest-GTCN delivers state-of-the-art results, markedly lowering the primary Risk-Adjusted Mean Squared Error (RA-MSE) to 2.51 from a baseline of 3.05 and boosting the cumulative return of a simulated portfolio by 18.7%. Ablation studies underscore the essential role of each component, while additional analyses confirm the model's stability, interpretability, and enhanced adaptability. This work pioneers a data-driven, explainable framework for investment decision support.

Lifted inference exploits indistinguishabilities in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. In this article, we show how lifting can be applied to efficiently compute causal effects in relational domains. More specifically, we introduce parametric causal factor graphs (PCFGs) to incorporate causal knowledge in lifted models and give a formal semantics of interventions therein. We further present the Lifted Causal Inference (LCI) algorithm to compute causal effects on a lifted level, thereby drastically speeding up causal inference compared to propositional inference, e.g., in causal Bayesian networks. In addition, we present partially directed parametric causal factor graphs (PD-PCFGs) as a generalisation of PCFGs to handle partial causal knowledge and extend LCI to perform lifted causal inference in a PD-PCFG, thereby extending the applicability of lifted causal inference to a broader range of models requiring less prior knowledge about causal relationships.

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.

Verification of multi-agent systems requires the ability to check meticulous topological properties when it comes to agents that can move through space in continuous time. This demands a logic with sufficient expressiveness to capture these dynamics. MuTGL logic has interesting properties for expressing entangled space-time properties. However, this logic lacks the expressivity needed to analyse reachability within specific distance bounds, or to track the length or the cost of communication chains: these are fundamental for decentralized monitoring, or graph-theoretic analysis of distributed protocols, where algorithmic complexities often relates with the system's communication graph diameter. We then introduce an extension of muTGL, including a new operator called the space horizon. This addition allows us to bound the distance of communication chains, hence enhancing the logic's expressiveness. We show that this operator allows to encode modalities from other logics, such as reachability or escaping which were not available in vanilla muTGL, while allowing a deeper entanglement of spatial and temporal properties. We provide a centralized offline monitoring algorithm for this logic and illustrate it on several examples on simulations of Consensus-Based Bundle Algorithms, distributed protocols for task allocation.

Causal discovery is critical for understanding complex data-generating mechanisms, yet traditional algorithms often struggle with highly non-linear and noisy systems, or suffer from severe computational bottlenecks. Recent tabular foundation models based on Prior-Data Fitted Networks (PFNs) have demonstrated remarkable zero-shot inference capabilities, but their potential for explicit structural causal discovery remains underexplored. To bridge this gap, we propose DCD-PFN, a decoupling-aware foundation model for causal discovery. Instead of directly amortizing global graph reconstruction, DCD-PFN focuses on local causal discovery through a decoupling-based paradigm. Through pre-training on diverse synthetic Structural Causal Models (SCMs), the model learns sample-wise decoupling weights that enable Markov boundary (MB) identification. Furthermore, by leveraging parallelized local discovery, DCD-PFN efficiently reconstructs global causal graphs while remaining grounded in the theoretical foundations of decoupling-based causal discovery. Experiments demonstrate that our foundation model achieves robust zero-shot generalization.

Explainable Artificial Intelligence aims to make black-box models more trustworthy by presenting, in a human-understandable manner, the elements that lead to the model's output. This involves both (i) identifying components and connections with genuine causal influence on outputs and (ii) translating such structures into an interpretable representation. For the former, we introduce CIExplainer, a novel perturbation-based method grounded in causal inference for explaining Graph Neural Networks (GNNs). CIExplainer identifies the subgraph with the highest causal effects on GNN predictions using the Potential Outcome Framework. We evaluate and compare CIExplainer on various GNN architectures (GCN, GraphSAGE, GAT, GIN) and datasets. To bridge subgraph explanations with human interpretability, we further propose G2TeXplainer, a method that transforms causal subgraphs into natural language explanations that capture both feature-level and relational information.

Geographic tipping points in ecosystems, climate subsystems, or ice sheets pose severe challenges for localized early warning. Classical spatial indicators such as Moran's I summarize global spatial structure, but they struggle with three issues: spatial dilution, Euclidean assumptions, and correlated noise. This paper introduces SpatioTemporal Causal Network Diagnostics (ST-CND), a framework that addresses these three issues by representing the geographic field as a time-evolving directed causal network. The core workflow is as follows: (1) infer which spatial nodes help predict other nodes via transfer entropy, replacing fixed Euclidean neighborhoods with data-driven information-flow topology; (2) estimate local recovery rates within each candidate subnetwork via dynamic mode decomposition; and (3) identify the most vulnerable subnetwork by combining three signals, namely high internal fluctuation, high internal synchronization, and low external coupling, thereby suppressing false alarms from spatially correlated noise. Validated on synthetic bifurcations and two observational sea-surface temperature benchmarks, namely Indo-Pacific SST and North Atlantic AMOC, ST-CND delivers localized and interpretable warnings. On the AMOC task, it achieves an AUROC of 0.783 and a critical-subnetwork IoU of 0.378, outperforming recurrence-network and lambda-AR1 baselines. The framework provides an interpretable and scalable pipeline for spatial early warning in Earth system science.

Multimodal models can name the action units (AUs) behind a facial emotion, but their AU->emotion rationales are typically plausible rather than faithful: nothing forces the AUs a model invokes to be the AUs that actually drive its prediction. We cast AU->emotion reasoning as a counterfactual-consistency problem between the rationale, the label, and a structural AU->emotion causal graph G, and propose FACR, which grounds the reasoner in an independently induced, polarity-aware G and trains a counterfactual-faithfulness objective: a do-intervention on an AU that G marks causal for a class must move the prediction, while one it marks irrelevant must leave it unchanged. Faithfulness is thereby both trainable and measurable through a matching interventional metric, which we evaluate against a known causal structure, the PSPI pain-AU composition, as no existing affective-reasoning benchmark allows. We are explicit that this metric tests fidelity to the supplied structure rather than its rediscovery: it asks whether the trained reasoner invokes the AUs the structure marks causal, on held-out subjects and a second dataset. Under subject-independent evaluation on UNBC-PAIN, the objective raises the agreement between the invoked AUs and the PSPI composition from a no-objective baseline of 0.08 to 0.57, at a small detection cost; an unfaithfulness control attributes the gain to the objective. On a cross-dataset emotion transfer, the objective likewise raises fidelity to G on a seven-class task (0.50 to 0.84). Finally, we attach a language verbalizer and extend the audit to the generated text: biasing each action unit's emission by its latent activation makes the rationale faithful by construction, so that ablating an AU removes it from the explanation, a property that transfers to a second language-model backbone, whereas a freely generated rationale is unfaithful.

Shapley value-based feature attribution methods face challenges in scenarios involving complex feature interactions and causal relationships, even when a causal structure is provided. Existing methods typically adopt a node-centric view, attributing importance solely to individual features. Consequently, they often fail to simultaneously capture the externality and exogenous influence of features, leading to unreasonable interpretations. To overcome these limitations, we propose a novel feature attribution method called DAG-SHAP, which is based on edge intervention. DAG-SHAP treats each feature edge as an individual attribution object, ensuring that both externality and exogenous contributions of features are appropriately captured. Additionally, we introduce an approximation method for efficiently computing DAG-SHAP. Extensive experiments on both real and synthetic datasets validate the effectiveness of DAG-SHAP. Our code is available at https://github.com/ZJU-DIVER/DAG-SHAP.

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.

Can a learned model capture how faults propagate through a large-scale network and use this knowledge to causally attribute customer impact to its underlying root cause? Existing root cause analysis techniques often rely on static rules, correlation heuristics, or topology-local reasoning, which struggle to generalize in dynamic environments where faults propagate across complex physical and logical dependencies. We present NetCause, a self-supervised learning-based framework that models network incidents as graph-temporal processes and uses counterfactual simulation to rank candidate root causes. This approach produces an interpretable ranking of root cause hypotheses and integrates naturally with operator-defined mitigation and remediation actions. We train the model on over 1,500 incidents collected over six months from a leading cloud provider's production network and evaluate it on 31 expert-labeled incidents. NetCause consistently improves root cause ranking quality in the regime most relevant to operational decision-making, achieving a 16.1% accuracy improvement over a rule-based heuristic baseline. While training is computationally intensive, inference is lightweight, requiring only seconds of GPU runtime per incident (well below typical telemetry collection latencies).

Cloud-computing relies on large-scale networks which are inherently complex systems. In this paper, we present a novel approach to root cause analysis (RCA) of cloud network incidents, leveraging graph-based causal discovery techniques. Our method addresses the limitations of rule-based automation by introducing a spatiotemporal grouping strategy and an automation ontology to reduce the dimensionality of the problem. We construct a causal graph from binary time series data using bivariate Granger causality and conditional independence tests. For inference, we introduce a probabilistic method that assigns edge-specific conditional probabilities as a function of time lag, allowing for interpretable, time-aware root cause scoring via causal graph traversal. We evaluated the system using a labeled dataset of 35 production incidents from a major cloud provider. The model successfully recalled the correct root cause in 85.7% of incidents and produced an exact match in 74.3%. In production, the deployed system has been used in over 800 real-world incidents, with positive qualitative feedback from network engineers. These results highlight the practicality of a data-driven, causal approach to RCA in dynamic and large-scale operational environments.

Granger Causal Discovery (GCD) is fundamental for analyzing temporal dependencies in complex systems. However, existing neural GCD methods predominantly rely on a "one-size-fits-all" paradigm, struggling to capture distribution shifts and dynamic regime changes inherent in real-world time series. This often leads to entangled representations and spurious causal graphs. In this paper, we propose CausalMoE, a billion-scale multimodal Granger causal foundation model that explicitly models patch-level heterogeneity. CausalMoE introduces a Pattern-Routed Mixture of Heterogeneous Experts, which dynamically identifies latent temporal patterns and routes patches to specialized domain experts, effectively decoupling regime-specific mechanisms from shared dynamics. To ensure interpretable graph recovery, we design a Causality-Aware Self-Attention mechanism operating across variables, yielding sparse Granger causal graphs via proximal optimization. Furthermore, CausalMoE is the first to integrate LLMs and VLMs to align numerical signals with textual and visual priors, regularizing causal estimation in complex scenarios. Extensive experiments demonstrate that CausalMoE establishes a new state-of-the-art on fully supervised benchmarks, while effectively generalizing to few-shot settings where traditional methods fail.

Advanced AI systems have extensive knowledge of their environments; in fact, their knowledge may (far) exceed that of their developers or users. Consequently, a desirable property for an AI system is that it is honest -- that it accurately reports its beliefs about the world. Designing an AI system to be honest may be difficult, especially if we want to ask it questions about latent variables in the environment -- variables which are hidden from the human interacting with it. This gives rise to the problem of eliciting latent knowledge (ELK): the problem of training an AI agent to honestly report its beliefs. In this paper, we make ELK formally precise using Causal Influence Diagrams (CIDs). CIDs can be used to describe the relationship between an agent's training environment and its subjective representation of the world. We use CIDs to formalise the distinction between observable and latent variables, to specify what exactly it means for an agent to be honest, and to formally define goal misgeneralisation. We show that, under certain circumstances, developers can incentivise an agent to honestly answer questions by providing correct feedback during training. However, a natural, but undesirable, way for an agent to generalise is to provide answers which humans would evaluate as true, rather than honest answers. We prove an impossibility theorem stating: There is no feedback-based training strategy that depends only on agent behaviour and with certainty produces an honest agent, even if feedback is perfect during training.

Causal discovery aims to uncover causal structures from observational data, which is crucial for real-world decision-making. However, different causal discovery algorithms can produce divergent results that conflict with each other, complicating the identification of accurate causal graphs. Traditional approaches rely on numerical values and statistical assumptions, often ignoring rich domain-specific information, such as feature descriptions, which could also help structure learning. While recent works explore using Large Language Models (LLMs) to infer causal relations via direct queries, such methods can be unreliable due to a lack of alignment with the actual data. To address these limitations, we propose Causal Ensemble Agent (CEA), a novel framework that aggregates structural insights from statistical discovery experts across different graph levels via linear opinion pooling, and uses an LLM as a meta-referee to dynamically reweight experts when the aggregated confidence is close to the decision boundary, thereby composing an improved and more complete causal graph. Extensive experiments on both synthetic and real-world datasets demonstrate that CEA achieves the strongest overall performance across a wide range of causal discovery methods, highlighting the effectiveness of using LLMs for meta-analysis in causal discovery.

Language models, as multi-task learners, acquire a wide range of abilities during training. A fundamental question is how much task-specific data is needed to learn a given task. Answering this for natural language is difficult: tasks are hard to delineate and can confound one another. To rigorously investigate the relationship between data frequency and learnability, we turn to a controlled setting using formal languages induced from probabilistic finite automata. These serve as a methodological testbed to demonstrate that standard correlational evaluation practices are inherently flawed. To enable causal analysis, we introduce the binning semiring, an algebraic object that lets us control how often a targeted property occurs in a sampled corpus. We formulate the experimental pipeline as a causal graphical model and derive decomposed Kullback-Leibler divergence metrics to measure the learnability of specific sub-tasks. Our experiments show that evaluating learnability without causal intervention leads to incorrect conclusions due to confounders in correlational analysis, and serve as a warning about correlational pitfalls in natural-language settings.

Ask a pretrained biomedical language model whether "cortisol 28 ug/dL" and "stock-market volatility" are related, and it returns a cosine similarity of 0.83 on a scale where 1.0 means identical. The two share no mechanism. This is not a corner case: every off-the-shelf biomedical encoder we tested (BioBERT, PubMedBERT, BioM-ELECTRA) scores unrelated cross-domain pairs between 0.76 and 0.92 when the answer should be near zero. Accuracy on cross-domain discrimination is 0%. Retrieval systems survive this, because a language model downstream filters the noise. A Large Behavioural Model (LBM), a foundation model whose subject is a person rather than a sentence, does not: it reasons over a graph of a user's life and treats embedding proximity as evidence that two events are causally linked. False proximity writes a false causal edge, and everything downstream inherits the error. Here, embedding geometry is not a tuning knob; it is correctness. We report the fix. A contrastive pass over 72,034 pairs raises PubMedBERT BIOSSES correlation from 0.633 to 0.828 and within-vs-across-domain separation from 1.05x to 1.63x. A second pass, BODHI, mines hard negatives from edges absent in a biomedical knowledge graph and lifts separation to 2.30x and the discrimination gap to +0.392, at a 4.5% BIOSSES cost. On an Intel Xeon 6737P with AMX, OpenVINO cuts single-query latency from 1367 ms to 10 ms (133x) and reaches 555 sentences/sec. One finding contradicts standard advice: FP16 beats INT8 on this silicon at every serving batch size, and we explain why. The same model on a no-AMX Ice Lake instance runs 13-27x slower. We release the benchmark suite, training corpora, the BODHI generator, and the OpenVINO scripts.

Causal graphs provide a high-level language for making mechanisms transparent. Recent work uses Large Language Models (LLMs) to recover causal graphs of external-world processes. Instead, in this paper, we use causal graphs to model LLM inference itself, providing stakeholders with a transparent view of how the model perceives and organizes high-level concepts to produce a prediction. We propose a four-phase method for constructing such graphs. Given a target LLM and a set of textual examples, our method discovers class-discriminative, human-interpretable concepts and maps each input to LLM-perceived concept states. We then introduce an MCMC-inspired counterfactual augmentation procedure that expands the sparse observational data through chains of counterfactuals. This enables stable causal discovery with $σ$-CG, yielding informative, interpretable graphs. We apply our method to three LLMs across disease diagnosis, sentiment analysis, and LLM-as-a-judge classification tasks. We evaluate the learned graphs for predictive fidelity and structural stability, and the MCMC-inspired augmentation for convergence and downstream utility. Our results show that the discovered causal graphs capture meaningful dependencies consistent with LLMs' reasoning. Together, this paper provides a foundation for concept-level explainability of LLMs.

Understanding and reasoning about the physical world is the foundation of intelligent behavior, yet state-of-the-art vision-language models (VLMs) still fail at causal physical reasoning, often producing plausible but incorrect answers. To address this gap, we introduce CausalPhys, a benchmark of over 3,000 carefully curated video- and image-based questions spanning four domains: Perception, Anticipation, Intervention, and Goal Orientation. Each question is paired with an expert-annotated causal graph capturing object-attribute-event dependencies, enabling interpretable and fine-grained evaluation of causal understanding. Building on this, we formulate a causal-graph-grounded metric that quantitatively measures how well a model's chain-of-thought reasoning aligns with the correct causal relations, moving beyond answer-only accuracy and enabling systematic diagnosis of VLMs' causal reasoning failures. Using this metric, we conduct a comprehensive analysis of leading VLMs, revealing systematic gaps in capturing causal dependencies and underscoring the need for causality-aware learning. To address these limitations, we further propose Causal Rationale-informed Fine-Tuning (CRFT), which explicitly aligns VLM reasoning with causal structures. Extensive experiments demonstrate that CRFT substantially enhances both reasoning accuracy and interpretability across multiple model backbones. By unifying dataset curation, causal evaluation, and causality-informed learning, CausalPhys establishes a strong foundation for advancing modern VLMs toward causally grounded physical reasoning.

Root-Cause Analysis (RCA) seeks to identify the variables responsible for abnormal system behavior in complex domains such as manufacturing, cloud computing, and healthcare. Existing approaches face a critical bottleneck: graph-based causal methods can identify intervention targets but typically require a known or accurately estimated causal graph, while graph-free statistical methods either localize marginal anomalies rather than structural causes, or rely on restrictive assumptions about graph structure or functional form. We propose StableRCA, a local mechanism-level RCA framework that avoids global graph discovery by estimating local Markov boundaries and detecting conditional distribution shifts within them. Leveraging the Independent Causal Mechanism principle, we show that intervention targets can be identified with probability converging exponentially in sample size under faithful Markov boundary recovery and non-degenerate mechanism shifts. Experiments on synthetic benchmarks and five real-world datasets demonstrate that StableRCA is robust to graph misspecification, effective under multiple intervention targets, scalable to large systems, and reliable across diverse application domains. Code is available at: https://anonymous.4open.science/r/StableRCA-E362

As urban environments continue to evolve rapidly, accurately modeling the dynamic behaviour of Points of Interest is essential for supporting data-driven urban planning and commercial decision-making. While recent advancements in spatio-temporal graph learning have improved POI forecasting, most methods rely on proximity-based graphs and correlation-driven modeling, which overlook the functional dependencies between POIs and fail to capture the causal effects of urban interventions. In this paper, we introduce a novel research problem -- cold-start POI check-in forecasting, which aims to predict the future check-in pattern of a newly introduced POI, by modeling its temporal evolution and functional interactions with nearby POIs in a structured urban spatial context. To address these challenges, we propose CausalPOI, a spatio-temporal graph-based causal representation learning framework. CausalPOI leverages Spatio-Temporal Functional Interaction Graph to model semantic and spatial relationships between POIs, and constructs structurally aligned treatment and control graphs to simulate factual and counterfactual scenarios. Extensive experiments on real-world SafeGraph datasets demonstrate that CausalPOI significantly outperforms state-of-the-art baselines across the board, validating its effectiveness in spatio-temporal forecasting, semantic interaction modeling, and causal effect estimation, providing a more interpretable and actionable foundation for urban intervention analysis. Source code is available at Github.

The do-calculus defines a general system of inference for interventional queries, allowing causal quantities to be transformed through successive applications of its rules. This process induces a rich space of equivalent interventional expressions, but combining and ordering these rules remains challenging. In this work, we introduce derivation graphs, which represent how do-calculus rules are applied and combined, and characterize the full space of observational and interventional probabilities which are equivalent under the do-calculus. The structure of these graphs yields a simple procedure that uses at most four applications of do-calculus rules. Finally, we show how applying identification algorithms to equivalent causal queries produces multiple valid estimands for the same causal quantity, eventually yielding more efficient estimators.

In nature, events that affect some individuals or groups but not others constitute an implicit intervention and are known as natural experiments. For example, the COVID-19 pandemic was an intervention by the coronavirus on the sub-population infected with COVID. We ask, do natural experiments occur in existing real-world datasets? If yes, how should we treat them? To detect natural experiments in data, we use causal discovery to recover the underlying causal graph and perform feature selection based on causal links. If downstream performance improves by treating the data as interventional rather than observational, we argue that this suggests the dataset contains natural experiments. We first validate this hypothesis by simulating datasets with and without natural experiments using synthetic graphs. We then perform a systematic empirical evaluation on a large suite of real-world datasets. Our results indicate that real-world datasets do contain natural experiments and we can take advantage of those natural experiments to improve model performance using causal inference. Our work represents the initial foray into this area, offering a preliminary exploration within a limited scope.

In graphical causal model, causal discovery aims to construct a causal graph based on numerical data and domain knowledge in plain text. However, the evaluation of causal discovery methods remains a challenge in the area as the progress of domain researches often makes benchmark causal graphs contain mis-aligned knowledge. This problem especially affects the evaluation of large language model (LLM) based causal discovery methods as they are sensitive to the new discoveries in the literature. This work is the first to systematically study the quality of benchmark causal graphs. Specifically, we design a pipeline that automatically retrieves relevant research papers from scientific databases, and prompts LLMs to check the consistency between the benchmark causal graphs and domain research papers. We evaluate 11 popular real-world benchmarks, for which our pipeline in total proceeds 38,081 domain papers. Our results show that popular benchmarks vary significantly in their consistency with domain research, with clear implications for causal discovery research.

Latent reasoning enables Large Language Models (LLMs) to perform multi-step inference within continuous hidden states, offering efficiency gains over explicit Chain-of-Thought (CoT). However, the opacity of these continuous thought vectors hinders their reliability and controllability. This paper bridges the gap between mechanistic interpretability and actionable control. We first present a systematic analysis using structural, causal, and geometric probes, revealing that latent vectors encode compressed, faithful representations of reasoning steps, with early vectors acting as critical causal hubs. Building on this, we operationalize these interpretability insights into a suite of training-free, decode-time interventions that refine the latent reasoning process by imposing the identified geometric and semantic priors. Extensive experiments across multiple model scales and diverse task domains demonstrate that our approaches consistently improve reasoning accuracy. Our interpretability-guided interventions consistently unlock latent capabilities and improve reasoning accuracy without any parameter updates.

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.

Learning causal relationships between variables from data is a fundamental research area with many applications across disciplines. Most existing causal discovery algorithms rely on the assumptions that (i) the underlying system is acyclic, (ii) the exogenous noise variables are Gaussian, and (iii) the intervention targets for the data-generating experiments are known. While these assumptions simplify the analysis, they are violated in real-life systems. Most existing methods that address these issues either assume the underlying model is linear or are constrained to operate in limited interventional settings. To that end, we propose SCOUT, a novel causal discovery framework for learning nonlinear cyclic causal relationships from soft interventional data with unknown targets. Our approach maximizes the data log-likelihood to recover the graph structure, using two normalizing-flow architectures: contractive residual flows and neural spline flows. Through experiments on synthetic and real-world data, we show that SCOUT outperforms state-of-the-art methods in both causal graph recovery and unknown target recovery across various interventional and noise settings.

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.

Random delays weaken the temporal correspondence between actions and subsequent state feedback, making it difficult for agents to identify the true propagation process of action effects. In cross-task scenarios, changes in task objectives and reward formulations further reduce the reusability of previously acquired task knowledge. To address this problem, this paper proposes a transferable delay-aware reinforcement learning method based on implicit causal graph modeling. The proposed method uses a field-node encoder to represent high-dimensional observations as latent states with node-level semantics, and employs a message-passing mechanism to characterize dynamic causal dependencies among nodes, thereby learning transferable structured representations and environment dynamics knowledge. On this basis, imagination-driven behavior learning and planning are incorporated to optimize policies in the latent space, enabling cross-task knowledge transfer and rapid adaptation. Experimental results show that the proposed method outperforms baseline methods on DMC continuous control tasks with random delays. Cross-task transfer experiments further demonstrate that the learned structured representations and dynamics knowledge can be effectively transferred to new tasks and significantly accelerate policy adaptation.

Causal queries are often only partially identifiable from observational data, and experiments that could tighten the resulting bounds are typically costly. We study the problem of selecting, prior to observing experimental outcomes, a cost-constrained subset of experiments that maximally tightens bounds on a target query. We formalize this as the max-potency problem, where epistemic potency measures the worst-case reduction in bound width guaranteed by an experiment, and show that this problem is NP-hard via a reduction from 0-1 knapsack. Building on the polynomial-programming framework of Duarte et al. (2023), we give a general procedure for evaluating epistemic potency in discrete settings. To control the super-exponential search space, we introduce two graphical pruning criteria that depend only on the causal graph and the query: a novel path-interception rule that exploits district structure to certify zero potency in linear time, and an identifiability check based on the ID algorithm. On Erdos-Renyi random graphs and 11 bnlearn benchmark networks, the two criteria together prune 50-88% of candidate experiments on average without solving a single polynomial program. For the general subset search, we show that ID-pruned experiments are combinatorially inert, yielding a super-exponential reduction in the number of subsets evaluated. We close with an end-to-end demonstration on observational NHANES data, selecting optimal experiments for estimating the effect of physical activity on diabetes.

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.

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.

Heterophily is a prevalent property of real-world graphs and is well known to impair the performance of homophilic Graph Neural Networks (GNNs). Prior work has attempted to adapt GNNs to heterophilic graphs through non-local neighbor extension or architecture refinement. However, the fundamental reasons behind misclassifications remain poorly understood. In this work, we take a novel perspective by examining recurring inductive subgraphs, empirically and theoretically showing that they act as spurious shortcuts that mislead GNNs and reinforce non-causal correlations in heterophilic graphs. To address this, we adopt a causal inference perspective to analyze and correct the biased learning behavior induced by shortcut inductive subgraphs. We propose a debiased causal graph that explicitly blocks confounding and spillover paths responsible for these shortcuts. Guided by this causal graph, we introduce Causal Disentangled GNN (CD-GNN), a principled framework that disentangles spurious inductive subgraphs from true causal subgraphs by explicitly blocking non-causal paths. By focusing on genuine causal signals, CD-GNN substantially improves the robustness and accuracy of node classification in heterophilic graphs. Extensive experiments on real-world datasets not only validate our theoretical findings but also demonstrate that our proposed CD-GNN outperforms state-of-the-art heterophily-aware baselines.

We present a systematic evaluation of large language model families -- spanning both proprietary cloud APIs and locally-hosted open-source models -- on two purpose-built benchmarks for System Dynamics AI assistance: the \textbf{CLD Leaderboard} (53 tests, structured causal loop diagram extraction) and the \textbf{Discussion Leaderboard} (interactive model discussion, feedback explanation, and model building coaching). On CLD extraction, cloud models achieve 77--89% overall pass rates; the best local model reaches 77% (KimiK2.5GGUFQ3, zero-shot engine), matching mid-tier cloud performance. On Discussion, the best local models achieve 50--100% on model building steps and 47--75% on feedback explanation, but only 0--50% on error fixing -- a category dominated by long-context prompts that expose memory limits in local deployments. A central contribution of this paper is a systematic analysis of \textit{model type effects} on performance: we compare reasoning vs.\ instruction-tuned architectures, GGUF (llama.cpp) vs.\ MLX (mlx_lm) backends, and quantization levels (Q3 / Q4_K_M / MLX-3bit / MLX-4bit / MLX-6bit) across the same underlying model families. We find that backend choice has larger practical impact than quantization level: mlx_lm does not enforce JSON schema constraints, requiring explicit prompt-level JSON instructions, while llama.cpp grammar-constrained sampling handles JSON reliably but causes indefinite generation on long-context prompts for dense models. We document the full parameter sweep ($t$, $p$, $k$) for all local models, cleaned timing data (stuck requests excluded), and a practitioner guide for running 671B--123B parameter models on AppleSilicon.

Anomaly detection in multivariate time series is a central challenge in industrial monitoring, as failures frequently arise from complex temporal dynamics and cross-sensor interactions. While recent deep learning models, including graph neural networks and Transformers, have demonstrated strong empirical performance, most approaches remain primarily correlational and offer limited support for causal interpretation and root-cause localization. This study introduces a causally-constrained probabilistic forecasting framework which is a Causally Guided Transformer (CGT) model for multivariate time-series anomaly detection, integrating an explicit time-lagged causal graph prior with deep sequence modeling. For each target variable, a dedicated forecasting block employs a hard parent mask derived from causal discovery to restrict the main prediction pathway to graph-supported causes, while a latent Gaussian head captures predictive uncertainty. To leverage residual correlational information without compromising the causal representation, a shadow auxiliary path with stop-gradient isolation and a safety-gated blending mechanism is incorporated to suppress non-causal contributions when reliability is low. Anomalies are identified using negative log-likelihood scores with adaptive streaming thresholding, and root-cause variables are determined through per-dimension probabilistic attribution and counterfactual clamping. Experiments on the ASD and SMD benchmarks indicate that the proposed method achieves state-of-the-art detection performance, with F1-scores of 96.19% on ASD and 95.32% on SMD, and enhances variable-level attribution quality. These findings suggest that causal structural priors can improve both robustness and interpretability in detecting deep anomalies in multivariate sensor systems.