Causal

Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop \emph{Counterfactual Tucker Diffusion} (\CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, \CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.

In this paper, we study nonasymptotic $L^p$ error bounds for interval length and conditional coverage in split conformalized quantile regression (CQR). Our bounds rely on local regularity conditions and accuracy guarantees for the estimated quantiles. We further instantiate our bounds for quantile regression with sparse ReLU neural networks. We also consider covariate shift, where the calibration and test covariates have different distributions, and derive nonasymptotic bounds for this setting. We obtain matching minimax upper and lower bounds in expectation for two constructed fixed-score calibration benchmarks under known covariate shift. The bounds match for every $p\in[1,\infty]$ in the scalar problem and for finite $p$ in the $K$-threshold problem; for the latter, a high-probability minimax lower bound holds for every $p\in[1,\infty]$.

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).

Causal discovery from observational data is a fundamental yet challenging task in scientific research. While existing approaches are primarily based on conditional independence tests, structure scores, or restrictive functional assumptions, we propose Decoupled Causal Discovery (DCD), a novel decoupling-based perspective that does not rely on these methodologies. DCD directly identifies the Markov boundary (MB) by decoupling non-target variables via weighting functions, such that only variables within the MB preserve dependence with the target under the decoupled distribution. Building on this, DCD iteratively constructs the Completed Partially Directed Acyclic Graph (CPDAG) by exploiting structural asymmetries within the MBs. We establish the theoretical identifiability, soundness, and completeness of DCD. Empirical evaluations demonstrate that DCD achieves strong performance, particularly excelling in challenging noise regimes.

Structural causal models for time series recover contemporaneous and lagged effects, but most methods require complete observation windows and become misspecified when samples are missing. We introduce ITSY, the first continuous-optimization method for causal discovery from irregular time series under a linear model. ITSY reformulates the structural equation so that prediction uses the nearest available history rather than the possibly missing current slice, and jointly imputes missing values while learning both graphs. A weighted reconstruction objective corrects the noise transformation induced by this reformulation. Across synthetic regimes varying missingness, scale, graph density, and noise, and on a real world benchmark, ITSY consistently improves graph recovery over representative SCM-based baselines, demonstrating the effectiveness of the proposed method. The results establish a focused solution for irregular linear first-order dynamics and clarify the assumptions required for nonlinear or higher-order extensions.

Frontier coding agents are increasingly trusted to work autonomously for long periods of time, yet what they actually did is often hard to tell from their final response. We quantify the propensity of such agents to overclaim task completion, which may mislead the user. We operationalize overclaiming as a final response that reports work that the agent's own transcript shows it did not do, for example, claiming to have read a file it never opened. This criterion requires no inference about intent and does not depend on whether the delivered work is correct; it asks only whether the reported work was done. We introduce OverclaimBench, an evaluation suite of five file-review scenarios with transcript-based coverage measurements and registered planted defects. We evaluate eight proprietary frontier models in their own production command-line interfaces and four open-weight models under a single fixed harness, and find that 1) agents fail to read every file they were asked to review in 67.9% of runs; 2) among these incomplete runs, agents are misleading 80.4% of the time (59-96% per model), either falsely claiming a complete review or leaving the gap undisclosed; 3) requiring delegation to subagents increases coverage, but a large majority of reviews that remain incomplete are still misleading; and 4) agents that falsely claim a complete review miss planted defects at about 1.8 times the rate of agents that read every file, showing that claims of completion can conceal substantive failures. Together, these results show that agents' final responses are not reliable accounts of their actions.

Causal discovery from observational data is fundamental to statistics and machine learning, yet determining causal direction without interventions necessitates structural assumptions. Existing identifiability research primarily focuses on continuous variables under additive noise models, often neglecting mixed datasets containing ordinal scales, counts, and continuous measurements. This paper investigates causal discovery in Directed Acyclic Graphs (DAGs) where nodes follow either an ordinal distribution (via an ordered logit model) or a regular one-parameter exponential family distribution. We prove that the edge direction between an ordinal and an exponential family node is distributionally identifiable for generic parameter values. Our findings generalize previous Ordinal-Poisson results to the broader exponential family. Computationally, we introduce a score-based exhaustive search and a masked continuous optimization framework using DAGMA for larger graphs. Numerical results validate the theory, recovering edge orientations within a Markov equivalence class that are unidentifiable under classical structural equation models.

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.

Tool-augmented large language model (LLM) agents fail in a way no tool-selection or tool-security method addresses: they call tools that do not exist and pass arguments no schema declares. Existing defenses either pick the right tool (selection) or constrain what an agent may do with real tools (gating), both of which presuppose the emitted call refers to a real tool at all. We show this is a structural blind spot: a hallucinated call is by construction not a decision any gate made, so no gate can reject it. This paper is primarily a measurement and benchmark study. We give a five-class taxonomy of tool hallucination (H1-H5) and, as a reference point, the Resolution Rung: a training-free, closed-world resolver (registry membership plus a signature check) whose interest is where it must sit, not what it computes. We prove hallucination defense must precede any causal gate, and characterize the one irreducible residue (borrowed arguments schema-indistinguishable from a valid call). Across ten hosted models under two invocation surfaces we measure 322 genuine hallucinations; fabricated-tool calls concentrate on the unconstrained raw-JSON surface (34 vs. 3), and model scale does not help (a 675B model matches a 7-8B one). We then extend to the Model Context Protocol, where merging several servers into one namespace creates hallucination surfaces a single registry cannot express (a second taxonomy, M1-M5); on the live MCP surface we measure 154 hallucinations, including from frontier models that were clean on the single-registry surface, because collisions and shadowing are structural to the merge. We release the versioned Hallucinated-Tools Benchmark (HTB) so any resolver is comparable across submissions.

Causal discovery aims to recover causal relationships from observed data. In various fields, exploring causal relationships among variables remains an important topic, but this task becomes challenging due to the existence of latent confounders. Ignoring such confounders can lead to false associations and incorrect edge directions. In this paper, we study the linear structural equation model with latent confounders. We propose an algorithm that iteratively identifies terminal (observed) nodes and reconstructs the directed acyclic graph of the observed variables. To do this, we recover the precision matrix of the observed variables as a sparse plus low-rank matrix: a sparse matrix captures the conditional dependencies among observed variables, while a low-rank matrix captures the combined influence of a few latent confounders. We establish that for $p$ observed variables, $r$ latent confounders and $s$ edges, our procedure correctly identifies the directed causal relationship among observed variables, for $n \gtrsim \max\{s\log p,\ r p\}$ samples. Experimental results validate our theoretical contributions.

FastWAM-style world action models enable efficient action-only inference, but generalize poorly under visual distribution shifts. Their reconstruction-oriented representations emphasize appearance-specific details, limiting generalization to unseen scenes and objects. Without observation history, the model also lacks temporal evidence for robustly identifying task-relevant state changes and motion in unfamiliar visual conditions. To address these limitations, we present the Causal Semantic World Action Model (CSWAM), which augments FastWAM with a causal semantic expert built on V-JEPA 2.1. V-JEPA provides temporally grounded representations of semantic state changes and motion with less dependence on appearance-specific details. The expert learns their future evolution from a sparse history of current and past observations and shares the history-derived context with both the video and action streams through causal attention. At inference, CSWAM conditions action denoising on the current video state and observed semantic history, retaining efficient action-only inference. We conduct simulation and real-robot experiments to evaluate generalization under distribution shifts. With embodied pretraining, CSWAM raises Randomized success on RoboTwin 2.0 Clean-to-Randomized transfer from 10.16% to 45.18%, a gain of 35.02 percentage points over FastWAM. Across two real-robot tasks and three OOD difficulty levels, CSWAM improves average success over FastWAM by 42.5 percentage points, from 27.5% to 70.0%.

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.

Linear probes can decode safety-relevant concepts such as truthfulness from language-model activations, but probe accuracy may show only decodability, not that the features the probe weights causally drive model behavior. We demonstrate that this gap cannot be closed from the geometry of probe weights alone: the features geometrically aligned with probe direction need not be the ones the model uses, so causal relevance requires intervention. We introduce a feature-level diagnostic that decomposes a deployed True/False probe into sparse-autoencoder (SAE) features, ranks those features by both probe alignment and by gradient sensitivity of the model's behavior, and ablates the resulting shared, probe-only, and random feature sets under a coherence gate. On the truth probe of Buerger et al. (2024) (TTPD), applied in the instructed truth/deception setting of Long et al. (2025) for Gemma2-9B-Instruct, the two rankings overlap only weakly (about 12%, Spearman rho = 0.10), and ablation dissociates them sharply: features the probe shares with the model flip the output far more (up to 27%) than equally sized probe-only (6%) or random (1%) features at full coherence, while probe-only features instead perturb the probe's own readout. The dissociation holds across five seeds and a held-out split, and an activation-aware selection of features flips behavior nearly three times as often as the probe's geometric top features (17.6% vs. 6.1%). In this setting, therefore, the geometric projection of a probe's weight vector alone does not identify the features the model causally uses; however, combining probe information with feature activation statistics recovers substantially more behaviorally causal features, and coherence-gated SAE intervention is needed to separate them from probe readouts.

Model explainability is essential for understanding and trusting machine learning models. Existing explainable AI methods often explain predictions through feature importance, counterfactual explanations, or rules. However, a region-level characterization of when and only when a prediction behavior arises remains less explored. This paper proposes Causal Sufficient and Necessary Regional Explanations (SNRE), a framework that learns an input region $A$ and output region $B$ such that membership in $A$ is both sufficient and necessary for the model output to fall in $B$. Motivated by the classical Probability of Necessity and Sufficiency (PNS), we formulate a region-level PNS measure through stochastic interventions and derive a differentiable finite-sample estimator for optimization. SNRE parameterizes the input-output region pair with explicit and interpretable algebraic region families, together with a learnable feature mask, balancing expressiveness and interpretability. Experiments demonstrate that SNRE learns region pairs with strong sufficiency-necessity performance, robust explanation behavior, and practical utility for model analysis.

World-action models (WAMs) have emerged as a promising paradigm for robot manipulation by jointly modeling future visual dynamics and robot actions. However, existing WAMs are trained predominantly on successful trajectories, making them prone to failure when real-world execution diverges from the learned dynamics. This issue is amplified in autoregressive WAMs, where execution errors become part of the causal history and continue to influence subsequent predictions. To this end, we introduce \method{}, a training-free framework that reformulates failure recovery as \emph{test-time scaling over causal histories}. This formulation decomposes recovery into three coupled decisions: \emph{when} to revise the causal history, \emph{where} to recover a reliable history prefix, and \emph{which} history configuration best supports subsequent execution. Specifically, \method{} realizes these decisions through three stages: 1) \textbf{Progress-Aware Recovery Trigger} detects persistent non-progress and triggers recovery only when the current execution state permits intervention; 2) \textbf{History-Prefix Recovery} identifies the unreliable history suffix, retrieves a historical anchor matching the current physical state, and reconstructs the causal KV state from the retained prefix while conditioning on the latest real observation; and 3) \textbf{Hypothesis Verification} compares the future continuations induced by complete-history, recovered-prefix, and full-reset hypotheses, and commits the best-supported hypothesis. Experiments in both simulated and real-world manipulation settings demonstrate consistent improvements in task success, while ablations confirm the contribution of each recovery stage.

The problem of identifiability in linear parametric models (LPMs) whose nodes follow either an ordered logit model or a regular one-parameter exponential family is evaluated. The results go beyond classical structural equation models as well as results for nodes with observations from a homogeneous family of distributions. The main result establishes that the orientation of every edge joining an ordinal node to an exponential-family node is identifiable from the joint distribution alone at every parameter value, provided the ordinal node has at least three categories and the exponential-family node at least three points of support, with no restriction on the sufficient statistic. Converses show that both requirements are necessary: the three-category requirement is binding only for affine sufficient statistics, and the three-point requirement is binding under the canonical link. The guarantee extends to orienting every such mixed ordinal-exponential family edge of a given $d$-node undirected skeleton. Numerical experiments illustrate the theoretical results by successfully separating orientations within a Markov equivalence class, which are indistinguishable by conditional independence alone.

Who the judge is can affect an LLM-as-judge result, but measuring that effect without confusing it with candidate quality is difficult. We study four open-weight families (Llama 3.1, Qwen 2.5, Gemma 2, and Yi 1.5) in a fully crossed pairwise design with 9,312 judgments. A common per-family statistic is strongly confounded with candidate quality and correlates with Bradley-Terry ability at r = 0.95. We derive a corrected estimator that holds the candidate family fixed and compares judges. All four families then show a positive same-family lift (3.4-8.4 percentage points), with global FPS 0.067 (95% CI [0.053, 0.084], permutation p = 0.0002). The effect remains under panel-based quality controls, an independent human-consensus anchor, and a float16 judging replication. Judge-side likelihood is closely related to the effect: adding likelihood advantage reduces the controlled coefficient by 61%, which we treat as descriptive attenuation rather than causal mediation. Position is a separate failure mode. Across the panel, 55.4% of AB/BA pairs reverse, and reversal above 50% is incompatible with a simple independent content-noise model. Relative to a family-balanced reference, panel composition changes 18.5% of pairwise outcomes. A complete reproducibility archive has been prepared for public release.

AI and large language models can recover clinically meaningful features from electronic health records (EHRs), but predictive usefulness does not establish admissibility for causal inference. We introduce information set emulation: an AI typed lift attaches source evidence, clinical and recording times, decision-time availability, representation version, proposed causal roles, and unresolved ambiguity to extracted features under a locked target trial. Causal certificates record auditable evidence for those roles. Features with unresolved downstream roles are routed to compatible reporting or separate analyses. Typed evidence defines an observational fiber of causal worlds consistent with the observed law. The locked scalar estimand maps this fiber to a compatible image whose squared Chebyshev radius equals the residual minimax mean squared error when the image is nonempty and compact. This classical identity provides a target-specific measure of information ambiguity. The contribution is its integration with a joint EHR observation map and an auditable certificate architecture. Under explicit exchangeability, positivity, and nuisance-consistency conditions, we give identification and cross-fitted augmented inverse probability weighted estimation, distinguishing empirical and population targets. An EHR compression-drift identity separates the roles of frame presence, treatment assignment, and outcome observation. Artificial simulations and a common-law finite-world example illustrate estimation failures and information-radius reduction. Synthetic Phase 0 notes demonstrate audit diagnostics; a separate role-specific analysis spread illustrates routing and is not an exact fiber radius. All experiments are synthetic. The framework specifies when reconstructed information can support a point claim and when compatible reporting is required.

AI-generated covariates from notes, conversations, images, and wearable streams can change the causal question when their roles are left unspecified. A generated feature may represent a treatment version, pre-action state, history, design variable, mediator, outcome proxy, observation process, or intercurrent event; these roles are not interchangeable. We formulate a causal type discipline for sequential experiments: a versioned representation map, a causal role classifier, a claim-status filter, and an estimand lock. The lock fixes a standardized proximal effect before generated covariates enter the analysis. Under audit correctness and standard identification assumptions, admissible role assignments preserve this estimand. We apply the established conditional-covariance characterization of compression bias to substitution of generated representations for design-relevant states. A standardized decomposition separates compression, conditional-law, and standardization drift. Further results cover mediator adjustment, post-action leakage, marker-intervention conflation, outcome-guided discovery, and state-measurement error. Cluster-level orthogonal estimators distinguish empirical and superpopulation targets under repeated sessions and missing outcomes. Simulations show that refinement helps when it retains design-relevant information, whereas design erasure, leakage, and same-data marker selection can produce bias or undercoverage. The framework places causal semantics and claim status before confirmatory inference with generated representations.

Autonomous nano-UAV navigation requires accurate ego-motion estimation under stringent size, weight, power, and computing (SWaP-C) constraints, where visual sensors and LiDARs exceed payload limits, optical flow degrades in low-texture scenes, and inertial-only state estimation is susceptible to accumulated drift. While multi-zone time-of-flight (ToF) arrays provide a lightweight metric complement, 6-DoF estimation from merely 384 ranges per frame is challenged by invalid returns, anisotropic observability, and temporal computational scaling. We propose TIO-FORMER, a camera-free, optical-flow-free, and mapless range-inertial odometry framework driven by an IMU and an ultra-lightweight (15 g) payload of six orthogonal 8 x 8 ToF arrays. Our frontend pairs consecutive range grids with a bilateral gated difference, while IMU-guided cross-attention dynamically routes directional features conditioned on platform kinematics. A Streaming Causal Transformer couples an uncompressed Local KV cache with compressed Chunk-FIFO memory, maintaining bounded inference cost and memory footprint independent of flight duration. In real-flight evaluations, TIO-FORMER reduces open-loop position error by 54.4% compared to nano-UAV optical flow and by 66.4%-89.1% over learned inertial baselines. We also evaluate performance across multiple environments and robustness under severe sensing degradation. Deployed on an edge RISC-V companion computer, TIO-FORMER achieves a P95 latency of 10.466 ms and peak resident memory of 6.324 MiB (less than 5 percent system RAM), demonstrating that sparse range sensing provides practical geometric anchoring for resource-constrained micro-aerial robots. Code is available at https://github.com/Ly041021/TIO-Former.

In various fields, such as medicine and marketing, accurately predicting individual treatment effects holds significant promise. However, achieving reliable predictions alone is often insufficient for making informed decisions; it is equally important to understand why the treatment effect is higher for some individuals than for others. To address this two-fold challenge of prediction and interpretation, we introduce an algorithm based on decision trees and random forests for estimating individual treatment effects. Our algorithm is simple: it operates exactly like a standard random forest, but with a different splitting criterion, and requires no additional workarounds such as double machine learning or orthogonalization as used in Generalized random forests. It handles observational studies with varying treatment propensities without requiring separate estimation of the full propensity function. This is achieved by combining two splitting criteria---one targeting heterogeneity in the treatment effect, the other targeting bias correction for the average treatment effect---which together improve split point selection and automatically distinguish confounders from features responsible for heterogeneity. As a result, interpretation follows directly from the fitted tree structure itself, that is, from which features the trees split on and with which split statistics, without requiring separate post-hoc analysis. For the theoretical analysis of this algorithm, we consider a change point model with step functions for potential outcomes and treatment propensity and provide insights into the theoretical underpinnings of our approach. Simulation studies show that our simple algorithm achieves comparable, and often better, prediction accuracy than existing methods, while substantially improving interpretability.

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.

Diagnostic errors and mislabeling are common in biomedicine, which compromise the reliability of predictive models and data-driven outcomes. Stratifying unlabeled biomedical data based on complex relationships between features eliminates the need for data labels and overcomes the limitations of supervised learning. Traditional clustering methods assume restrictive data distributions, making them suboptimal for capturing complex dependencies in high-dimensional biomedical data. This paper introduces a novel cluster-friendly data presentation framework that integrates the non-Gaussian and non-linear feature dependence of copula models with an ensemble of causal structure discovery (CSD) methods based on Directed Acyclic Graphs (DAGs). While copulas model flexible multivariate distributions by relaxing assumptions related to multivariate normality, linear dependence, and symmetric relationships, an ensemble of DAG-based CSD methods identifies stable causal relationships between features. When clustered using K-means, the new data representation obtained by the proposed copula-adapted DAG (CopDAG) ranks first among the 12 methods in normalized clustering accuracy and adjusted Rand index across 16 biomedical datasets. Our CopDAG method predicts ground-truth class labels directly from feature relationships without data annotations and supervised learning, while also providing cluster visualizations and explainable causal structures of the biomedical data features.

When a video model generates physically incorrect motion, did it fail to learn the correct motion, or did it learn it but fail to use it? We show the latter: the correct motion remains available inside the model and can still be made to control the generated video. We train on videos where red masses oscillate slowly and blue masses oscillate quickly, then test a red mass with fast observed motion. Even when the model generates slow motion in this conflicting case, a low-dimensional edit predicted from simple physical variables restores the correct fast motion. We call this ability causal writability. At fixed strength, we find a sharp depth boundary: the same edit changes the video before the boundary but not after it. This closure marks commitment for that write. The motion signal nevertheless remains, and a stronger downstream write can restore physical motion, while excessive gain overshoots. Early causal writability predicts which errors training later corrects: those errors are writable at more network depths than errors that persist. We reproduce both causal writability and its sharp closure in a pretrained 1.3B video model, supporting generality across model scale and training regime.

Understanding and predicting wildlife movement is critical for ecology and conservation. While trajectory forecasting has advanced for human and vehicle movement, wildlife trajectories present distinct challenges: they are unconstrained in space, highly stochastic, and influenced by environmental conditions. We introduce MoveBench, the first large-scale benchmark for probabilistic wildlife movement forecasting, containing 2.6M GPS locations from 800+ individuals across 110 species in 127 countries, paired with 1.6B environmental raster tiles capturing 160 covariates known or hypothesized to influence movement. We propose a probabilistic evaluation protocol for movement trajectory forecasts, addressing limitations of point-prediction metrics for inherently stochastic phenomena. Through comprehensive empirical evaluation of four method families across multiple temporal and spatial scales, we reveal that: (1) existing predictive methods generalize better to future timepoints than to unseen individuals, (2) deep learning approaches do not consistently outperform simpler baselines, and (3) environmental covariate selection significantly impacts performance. MoveBench enables standardized evaluation of movement forecasting methods and provides a foundation for methodological advances on this ecologically important task.

Progress in inclusive household surveys has strengthened socioeconomic evidence for forcibly displaced populations, providing indispensable benchmarks on living conditions and welfare. However, these surveys remain resource-intensive and periodic, while conditions can change between rounds, particularly in settings affected by fragility, conflict, and violence. More frequently updated, spatially granular complementary evidence is therefore needed to identify where socioeconomic conditions may be changing between survey rounds and to inform operational prioritization. Earth observation and machine learning offer a scalable source of spatially explicit socioeconomic information. However, tools developed for general populations have not been systematically adapted and evaluated in forced displacement settings, where living conditions, settlement patterns, and displacement impacts may differ substantially. We address this gap by adapting a multimodal spatiotemporal vision transformer, pretrained on Demographic and Health Survey data from approximately 1.2 million households across 36 African countries, to forced displacement and host community settings in South Sudan, Cameroon, and Zambia. We develop and evaluate the updated, adapted model using socioeconomic indices derived from UNHCR FDS and RMS data. Our results show that satellite-derived geospatial covariates explain up to 66% of the variation in socioeconomic outcomes in camp-intersecting grids, with a mean absolute error (MAE) of 4.37 index points, and 41% in non-camp-intersecting areas, with an MAE of 5.41. The framework complements and adds value to periodic household surveys by filling critical spatial and temporal data gaps with regularly updated, model-based socioeconomic estimates. These estimates sustain insight between survey rounds and support timely humanitarian prioritization and field verification.

Large brains are metabolically costly, and associations with changing environments do not imply they evolved there, as the Cognitive Buffer Hypothesis (CBH) would suggest. They may instead evolve in stable conditions and later facilitate colonization of changing environments. Using neuro-evolution in an artificial seasonal foraging task, we compared agents evolving exclusively in changing environments to agents first evolved in static environments before transitioning. Results show that larger neural networks in dynamic environments arise mainly from prior static evolution, achieving superior performance under unpredictable changes. Our results challenge strict CBH predictions, provide agent-based (computational) support for a colonization-based account and highlight the role of evolutionary history in brain size evolution.

Urban region representation learning commonly combines heterogeneous data sources, such as mobility flows, points of interest, and land-use information, to support tasks including mobility analysis, public safety forecasting, and service demand estimation. Existing multi-view methods typically improve region embeddings by strengthening interactions across views. However, such methods often overlook view-specific regional structures and may propagate correlations induced by shared latent factors, which can reduce the stability of downstream predictions. To overcome this major limitation, we propose CURE, a confounder-aware framework for multi-view urban region representation learning. CURE first encodes each view with its regional graph structure, estimates a shared latent component, and then reduces its projected influence before cross-view interaction. A hierarchical graph-aware fusion module subsequently aggregates the residual view representations using local and global regional contexts Experiments on three real-world cities show that CURE improves predictive performance, remains robust under missing and noisy input views, and provides reliable cross-view integration through shared component separation and context-dependent view weighting.

Conformal counterfactual prediction constructs prediction sets with finite-sample coverage guarantees for counterfactual outcomes and individual treatment effects under the no-interference assumption. In this work, we relax this assumption by allowing each unit's potential outcomes to depend on other units' treatments and covariates. In this setting, propensity-score reweighting does not restore weighted exchangeability, and existing methods may fail to achieve valid coverage. To address this issue, we develop interference-adjusted weighted conformal prediction that accounts for interference by constructing an observable upper bound on the ideal and unobserved conformal $p$-value under the target intervention. The resulting prediction sets provide finite-sample marginal coverage guarantees for counterfactual outcomes and individual treatment effects in both transductive and inductive settings. We also derive a sharper construction when intervention-induced changes in nonconformity scores are bounded. Numerical experiments show that our methods preserve nominal coverage, whereas existing methods may not.

A medical claim's correctness often depends not on the claim alone, but on the clinical structure around it. A claim may require a lab reference range, a causal or conditional link, or patient-specific details to be judged correctly, and atom-level decomposition can fragment these dependencies, leaving the verifier with clinically incomplete claims. We reformulate medical fact-checking around snippet-level verification, where clause-grouped units preserve local clinical structure. We introduce MedSNIP-Bench, a human-annotated benchmark for snippet-level medical fact verification, and MedSNIP, an automatic snippet-generation pipeline. MedSNIP-Bench covers 276 consumer-health and clinical-vignette responses, segmented into 2,524 snippets with dual in-general and in-patient-context labels and six structural pattern codes. MedSNIP is evaluated against human snippet boundaries on MedSNIP-Bench and then used to generate snippet-level units for external corpora. Across MedSNIP-Bench, HealthFC, and MedHallu, snippet-level verification preserves or improves false-class F1, with gains concentrated where answers are long enough to fragment and where the verifier is strong enough to exploit the recovered structure. The largest merge-pattern gain is on causal-conditional clinical chains. It also reduces verifier calls by 24-73%, though the saving survives end-to-end only when decomposition is cheap, which an open-weight decomposer makes possible at no loss of chunking fidelity.

Vision-language models retain a substantial amount of pixel-decodable visual content in their visual key-value cache. We show, in our setting, that this retention is task-inert: across our preregistered tests, how much a unit retains never positively tracks whether the computation that answers the question causally relies on it. We measure retention with a learned pixel-inversion decoder and causal use with single-super-patch KV ablation, the teacher-forced drop in gold-answer log-probability, and relate the two within images under a preregistered, sign-calibrated, held-out design. Retention is decoupled from attention and, in a well-powered null, from causal utilization. Utilization is not inert to every proxy: attention weakly but significantly tracks it, the only signal we find that does and the design's positive control. We characterize pixel-decodable retention as an informational axis of the visual KV cache, orthogonal to the functional one. How much task-inert content a cache holds differs by architecture in our model pair: the encoder-free model retains 2.7 times more than the encoder-based one. The engineering consequence is a controlled negative result. At super-patch granularity, deconfounded pixel-decodable retention ranks KV eviction no better than random; at token granularity it acquires only a weak inverse-importance signal at larger budgets, dominated at every budget by attention magnitude. In our setting, pixel-decodable reconstructability is not a competitive KV-compression signal at any granularity we test.

Dashboard-mounted gaze trackers often lose sight of the driver's eyes during large head rotations, including shoulder checks, mirror glances, and intersection scanning. These maneuvers occur when information about the driver's visual attention is most useful. Offline gap-filling methods may reconstruct a missing interval using observations from both sides, but an online driver-monitoring system cannot rely on measurements that have not yet occurred. We therefore formulate causal gaze recovery: forecasting unavailable gaze at time t without target-tracker gaze at t or later. We introduce the Causal Context-Gated Forecaster (CCGF), which encodes a 60-frame pre-dropout history of gaze and head pose and combines it with DINOv3 scene features. A learned reliability gate controls the contribution of the history and scene representations as the dropout progresses. We evaluate two scene conditions: Live, in which the scene representation continues to update during tracker loss, and Frozen, in which the final pre-dropout representation is used throughout the missing interval. We evaluate CCGF on 2,047 eligible, naturally occurring GazeSense head_lost events drawn from 10.5 h of naturalistic driving by ten drivers. Across all recordings, head_lost accounts for 8.5 percent of GazeSense recording time. Synchronized gaze coordinates from a head-mounted Neon tracker provide supervision and evaluation targets but are never used as model inputs. Under leave-one-driver-out evaluation, CCGF achieves a mean per-driver median error of 175.7 px (10.5 deg) with Live scene updates, a 33 percent reduction relative to history-only causal forecasting. With Frozen scene input, the error increases to 210.8 px (12.9 deg), indicating that scene observations acquired during the dropout provide useful predictive information. We will release the dataset, evaluation protocol, and causal baselines.

Membership inference attacks (MIAs) are the standard tool for auditing the privacy risks of machine learning models. Given a query point, an MIA aims to determine whether that point was used to train the target model. In practice, such inference must rely on the statistical signals exposed by the model's outputs, such as confidence scores, logits, and intermediate feature representations. However, existing methods often fail to efficiently summarize and combine these statistical signals. To address this limitation, we propose Pairwise Likelihood MIA (PL-MIA), a unified method that combines a Gaussian likelihood-ratio (GLR) statistic with population calibration and the Cauchy combination test. We characterize theoretically how the GLR retains variance-contraction signals and establish conditions under which population calibration and Cauchy combination improve attack power. We obtain $p$-values from pairwise comparisons between the query point and reference points not used for training, and aggregate these continuous signals using the Cauchy combination test. This preserves the evidence strength that is discarded when each pairwise comparison is reduced to a binary vote. Extensive experiments demonstrate that PL-MIA outperforms strong baselines, improving the true positive rate (TPR) by over 25% in the critical low-false-positive regime, corroborating our theoretical findings. These results demonstrate how statistical principles can turn noisy model outputs into more powerful, calibrated, and reproducible evidence for membership privacy auditing.

Statistical data fusion combines two panels that share a block of covariates but observe disjoint outcome blocks, and in its traditional form no row observes both outcomes at once. That rules out the discriminative criterion one would rather train a Deep Boltzmann Machine with, since multi-prediction training needs ground truth for whatever it holds out. We propose observed-block multi-prediction, which restricts the multi-prediction objective to targets drawn from what each row actually observes. It is well defined for any missingness pattern and reduces to the original criterion when rows are complete. Having a discriminative criterion that survives the setting lets us ask whether the joint model is needed at all, by separating what it contributes into a representation part and an inference part. On two datasets of different kinds, a consumer purchase panel and public-domain census microdata, over grids in sample size and covariate width spanning 40 cells and 200 runs per method, almost none of the fine-tuned DBM's advantage comes from generative pre-training, which is confined to the smallest sample size on one dataset and absent on the other. It comes from conditioning on one outcome block when predicting the other. This term amounts to +0.19 and +0.36 percentage points, is positive in all 40 cells, never decays as the panels grow (it is flat on one dataset and grows on the other), and requires neither a second hidden layer nor more inference. Against baselines tuned on validation and given the same conditioning, the fine-tuned DBM is the best method in 37 of the 40 cells. The imputers that can also condition on the other outcome block mostly lose accuracy when they do, whereas the DBM gains in every cell; since fusion data cannot validate that choice, this is the property that matters.

Generative artificial intelligence changes how firms reach customers, but standard marketing data do not record how often users see and notice a firm's name in generated answers. We develop Generative Marketing Mix Modeling (GMMM) to estimate the causal effects of Generative Engine Optimization (GEO) and Generative Engine Marketing (GEM). For GEO, GMMM combines repeated generated answers with question counts, shares of use across generative systems, and notice probabilities. For GEM, it combines records of sponsored placements with notice probabilities. GMMM compares expected business responses under alternative treatment sequences and establishes sufficient conditions for identifying the resulting effects. We investigate the empirical performance of the proposed method using simulated answers to product recommendation in English and Japanese.

We post-train Qwen3.8-27B for Korean response style -- verbosity, list and markdown usage, discourse structure and register -- and measure two behaviours the objective never targets: abstention on ambiguous social questions in KoBBQ, where the benchmark-correct answer is UNKNOWN, and unprompted disclosure in securities guidance. Both move, and the changes are expressed primarily through the model's emission policy: how often it answers and how much it says. Matched target-form controls show that answer propensity depends on the training target, not the prompt set or recipe alone. Holding prompts, recipe, data volume and serving fixed and changing only the target text, three style seeds give positive answer-rate point estimates (mean +0.82 pp) and three neutral seeds negative ones (mean -1.53 pp); the observed seed ranges do not overlap and the means differ by 2.34 pp. A length-matched arm lies between them, and a fourth arm that stays short while preserving hedging is unstable across seeds, so which feature of the form is responsible is unresolved. For absolute stereotyped exposure the decomposition into an answer-propensity term and a conditional-composition term is an algebraic identity, not a finding; its empirical content is where the movement went. Across the trained checkpoints the changes are dominated by answer propensity while the composition term stays small, and because that term is evaluated on treatment-dependent answered subsets we do not read it as evidence about latent preference. Two measurement results follow. A between-arm contrast in conditional stereotyped share does not identify a change in conditional content preference when answer status is treatment-dependent. And agreement between two rule detectors for the same construct runs from 0.44 to 0.99 depending on which checkpoint produced the text -- observable without any reference labels.

Generalization under distribution shift remains a core challenge in modern machine learning, yet existing learning bound theory is limited to narrow, idealized settings and is non-estimable from samples. In this paper, we bridge the gap between theory and practical applications. We first show that existing definition of concept shift breaks when the source and target supports mismatch. Leveraging entropic optimal transport, we propose a key notion: $\gamma^{*}\!$-concept shifts, and derive a general error bound unifying covariate and $\gamma^{*}\!$-concept shifts, which applies to broad loss functions, label spaces, and stochastic labeling. We further develop estimators for these shifts with concentration guarantees, and the DataShifts algorithm, which can quantify distribution shifts and estimate the error bound in most applications - a rigorous and general tool for analyzing learning error under distribution shift.

We study the expressivity of spiking neural networks, which provide a natural framework for asynchronous, event-driven computation complementary to conventional feedforward neural networks. We consider the time-to-first-spike model in a setting for which the input-output map is continuous and piecewise linear, with affine pieces governed by causal feasibility constraints that determine which presynaptic spikes occur before a neuron fires. We first show that each neuron's firing time admits a maxout-like representation with exponentially many, highly constrained affine pieces. We then formalize causal regions as polyhedral regions with fixed causal sets and derive upper and lower bounds on the maximal number of causal regions in both shallow and multilayer feedforward spiking networks. Our theoretical and experimental results show that spiking networks can generate richer partitions of the input space than conventional feedforward ReLU networks.

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.

Average treatment effect (ATE) estimation in observational studies is a fundamental statistical tool used frequently in social science, medicine, and other fields. These fields often work with sensitive data where privacy protections are important, so a differentially private mechanism for ATE estimation is highly desirable. Here we present two propensity score-based algorithms for ATE estimation on observational data, one improving the inverse probability weighting (IPW) method used in prior work, and the other using blocking on the propensity score (BPS). Both show lower error and less bias than prior work, with the BPS-based algorithm frequently reducing error by 75% or more compared to prior work.

Fairness auditing of text-to-image diffusion models often requires generating large numbers of images across sampling configurations, making comprehensive evaluation computationally expensive. We propose a causal-abstraction-based audit instrument for efficiently evaluating fairness under interventions on the classifier-free guidance scale. Given a fixed prompt and a target feature function, we represent the diffusion process as a low-level structural causal model and construct a corresponding high-level model over abstract denoising states. We characterize the projected causal structure, establish identifiability of the fairness-relevant interventional query, and provide sufficient conditions under which the high-level model preserves this query. A probabilistic transformer implements the high-level model as an amortized predictor of target-feature distributions across guidance scales. Experiments evaluate distributional fidelity, fairness-query accuracy, and computational efficiency. We present two auditing demonstrations: one using standard Stable Diffusion 1.5 and another using StayFair, a fairness-enhanced Stable Diffusion model, to examine their behavior across guidance scales.

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.

Long-form instructional videos require automatic chaptering to support browsing, navigation, and knowledge access. Recent long-context language models can perform chaptering from textualized video inputs, but they remain costly and brittle for content-dense lecture videos with long transcripts, smooth topic transitions, and detailed chapter outputs. A scalable segment-then-caption paradigm reduces this cost, but introduces two new challenges: boundary error propagation and fragmented cross-chapter context. We propose \textbf{CausalChapter}, an intervention-inspired framework for long-video chaptering that estimates prediction-level influence through lightweight masking and removal interventions. For boundary localization, our Local Dependency Shift module detects drops in predictive dependency between adjacent temporal windows; for chapter description generation, our Cross-Segment Support Selection module reranks historical contexts according to their support for the current prediction. Experiments on long-video chaptering benchmarks show that CausalChapter improves boundary localization, chapter description quality, and cross-chapter coherence.

In this paper, we consider the scalar-on-function linear regression model under a realistic sampling scheme in which the functional covariates are observed on a regular grid and contaminated by additive noise. We propose a two-step estimation procedure: first, the underlying curves are reconstructed from the discrete noisy observations using a Fourier-based projection method; second, the slope function is estimated by a penalized least-squares criterion over finite-dimensional trigonometric spaces, with data-driven selection of the model dimension. We establish oracle-type inequalities for the prediction error, both with respect to the reconstructed curves and to the true latent curves. Under regularity assumptions on the slope function and polynomial decay of the eigenvalues of the covariate, we derive convergence rates for the prediction error and show that our estimator attains the minimax rate when the number of grid points is sufficiently large. Finally, the proposed method is illustrated on simulated data and on a real meteorological dataset.

In data-driven training, multivariate time-series forecasting is usually optimized with a scalar loss averaged over samples, variables, and horizons. This averaging is convenient, but the optimizer sees only the aggregated gradient, which does not reveal whether the variable-wise contributions align or oppose one another. To quantify how often this disagreement arises, we measure the variable-wise gradients directly and find that 30.6% of their pairwise cosine similarities are negative on average across seven datasets. However, conflict and harm are not the same thing. Under shared training 35 of the 64 variables do worse than a full-input single-target oracle, and the harmed fraction is not reliably predicted by how often gradients conflict. We propose Per-Variable Surgery (PV-Surgery), an optimizer-side training strategy for backbones with cache-compatible layers. One backward pass builds variable-wise gradient proxies from output-side signals and keeps the pointwise forecasting loss. Reliability-aware selection targets layers whose proxy sums closely approximate their shared-gradient slices. Conditional pooling forms anchor and conflict pools without dropping variables. Common-direction surgery aligns variable or pooled gradients with their normalized mean and restores input norms to avoid reweighting. In experiments across five backbones, seven datasets, and four horizons, PV-Surgery lowers MSE by 3.61% and MAE by 2.93% on average. For multivariate forecasting, this indicates that the variable-wise structure hidden by mean-loss training is a usable optimization signal.

Existing causal-inference benchmarks for LLMs mostly score method descriptions or whether generated code runs, not whether the executed workflow recovers the target causal estimate. CausalVerify studies this verification problem for structured econometric causal-estimation workflows by separating realistic interpretation from verifiable computation. It pairs 259 published economics papers (reconstructed research question, data description, institutional context) with 100 fixed-seed synthetic scenarios that realise CSV datasets for difference-in-differences, event study, instrumental variables, and regression discontinuity designs. Experiment A (real-paper text agreement) scores method-family and direction agreement against four-LLM consensus labels. Experiment B (synthetic execution) runs model-written R code and checks whether the extracted treatment-effect estimate matches a canonical estimator on the same realised dataset; this execution-grounded correctness layer is L2b+, distinct from L2b, which records only whether the code executes. A calibration arm asks whether self-reported confidence separates correct from incorrect workflows. On Experiment B, seven LLMs reach L2b+ pass rates of 10% to 88% at the default 50% tolerance, and 66 of the 426 workflows that execute (15.5%) return a wrong estimate. Execution ranking (L2b) agrees with L2b+ far better than text-direction scoring (L4): Kendall $τ=0.81$ and Spearman $ρ=0.93$, versus Kendall $τ$ between $-0.20$ and $0.10$ for L4. Llama-3.3-70B-Instruct shows the same qualitative gap, and reported confidence does not reliably separate correct from incorrect workflows. The claims are confined to standardized single-shot workflows in these four design families under the evaluated R backend and model panel; the benchmark does not measure general causal-inference ability. Code, data, cached outputs, and a datasheet are released.

In this paper, we propose ReactVAU, a Slow-Fast Decoupled Framework for real-time streaming Video Anomaly Understanding (VAU). Existing VAU methods rely on offline inference with global temporal sampling, which violates causality and prevents deployment in live surveillance streams. Conversely, general streaming video models satisfy causal access but dilute rare transient anomalies during memory compression and often invoke heavyweight MLLMs uniformly over long normal intervals. React VAU addresses this gap with three synergistic components: a lightweight Fast Detection Module based on Spatial Grid Folding (SGF) for continuous anomaly filtering; an Anomaly-Aware Persistent Memory (AAPM) that protects critical visual cues from temporal decay; and a heavyweight Slow Reasoning Module that remains dormant during normal streams and is awakened only by suspicious events for semantic verification and causal description. Extensive experiments on multiple benchmarks demonstrate that ReactVAU operates under strict streaming constraints while simultaneously achieving competitive performance in both anomaly detection and causal reasoning, alongside significantly enhanced computational efficiency by minimizing heavyweight MLLM invocations. Project page is available at https://huiyuiui.github.io/ReactVAU/

Multimodal large language models often capture visual-linguistic correlations but struggle to predict how local visual interventions propagate and affect downstream answers. We introduce InfluenceField, an intervention-aware latent field inserted between the visual encoder and language decoder. It lifts patch features into a continuous spatial representation, propagates directed influence over multiple steps, and predicts local intervention effects through a shared transition operator. Training jointly optimizes language modeling, cross-environment invariance, counterfactual rollout supervision, and structural regularization. For a nonlinear finite-basis population model, we show that target-aligned interventional supervision, together with a one-step separation condition on the transition, restricts admissible representations to within-location reparameterizations, so that the directed dependency graph of the full transition is recovered exactly. A linear specialization gives an exact partial-coverage characterization and a finite-loss stability bound, and the field analysis derives the spatial profile of coefficient interventions together with a shared-channel calibration result. On CausalVQA, InfluenceField improves overall accuracy over its backbone by 13.1 percentage points, with the largest gains on the planning and hypothetical categories. Capacity-matched baselines and structural controls attribute the gains in robustness and factual-counterfactual consistency to the causal objectives rather than to added capacity.

Demographic synthetic survey panels are often validated by matching aggregate answers to published surveys. We test what that certificate establishes across six multiselect batteries from four survey organisations in three countries. The headline analysis is restricted to three instruments whose synthetic cohort and human target share the stated population frame; three other batteries remain sensitivity analyses. The response contract dominates measured fidelity. In the aligned instruments, committed sets leave 66 of 128 model-battery option slots empty in panels of up to 500 respondents, versus 0 of 128 under per-option probability elicitation. Across eight uncapped model-instrument comparisons, probabilities reduce option-marginal MAE by 4.53 to 7.30 points. The capped instrument reverses on two models until the vectors are projected onto its stated maximum. These are measurement effects: human targets are realised check-all responses, whereas the vectors are latent inclusion propensities. Published marginal agreement also fails to discriminate respondent simulation from direct population estimation. On nine aligned model-battery pairs, a no-persona population-prevalence query averages 6.27 MAE versus 12.39 for committed panels and wins all nine comparisons. Constraint-aware probability vectors average 5.34 and beat the query on four of nine, so the baseline challenges the validation criterion rather than proving direct estimation uniformly best. On three unpublished demographic cells, neither approach beats reciting the national distribution. Population-marginal agreement is therefore evidence about an elicitation contract and an estimand obtainable without simulated respondents, not evidence of individual simulation.

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.

Research and news coverage of language-model deception increasingly attributes human-like mental-state concepts to language models. Such claims can blur the distinction between behavior that looks deceptive and a mechanism that is actually deceptive. We introduce a causal taxonomy separating prior commitment from retrospective report, model preference from realized output, false preference from sensitivity to the utility of misleading a recipient, and deceptive behavior from the provenance of the objective or strategy producing it. We test these distinctions in two open-weight model families. Across controlled guessing-game and stock-trading experiments, we find that deceptive-looking behavior can arise without the corresponding proposed mechanism, while other interventions provide direct evidence that recipient information state can causally affect deceptive preference. These results show that deceptive behavior can provide evidence for a deceptive mechanism. But even evidence for such a mechanism does not establish model agency in the deception.

Blackwell's 4-bit floating-point (FP4) tensor cores do not automatically make attention faster because softmax conversion and on-chip dependencies dominate once its matrix products shrink. We address this with \emph{Direct-P} for noncausal inference and a causal path that passes the forward quantization directly into backward. Direct-P maps scores directly to FP4 probabilities and reaches up to 2.13$\times$ the bfloat16 (BF16) forward throughput on an NVIDIA GB200. The causal path reconstructs probabilities from saved quantized queries and keys and uses 8-bit floating-point (FP8) gradient operands, accelerating a complete single-GPU 8-billion-parameter update by up to 1.14$\times$. Matched distributed training retains FP8 probabilities and values; every tested MXFP4 probability/value training trajectory diverges.

Quantile treatment effects (QTEs) measure the effect of a treatment on the distribution of an outcome, and their estimation at extreme quantile levels is of central interest in applications where the target quantiles lie far beyond the range of the data. For heavy-tailed potential outcomes, existing extremal QTE estimators rely on extrapolation combined with a causal extreme value index (EVI) estimator, but the resulting estimator is not invariant under a common location shift of the potential outcome distributions, even though the population QTE is. We address this issue in two steps. First, we adapt the location-invariant Fraga estimator of the EVI to the causal setting using inverse propensity score weighting. Second, we replace the original extrapolation formula with a difference-based scheme, under which the location parameter cancels when quantile differences are taken. The resulting QTE estimator is therefore location invariant. We establish the consistency and asymptotic normality of the proposed extremal QTE estimators, and provide a consistent variance estimator, leading to asymptotically valid inference. A simulation study confirms the location invariance, the stability with respect to the threshold, and the coverage of the proposed methods.

In this paper we study linear non-Gaussian acyclic models (LiNGAM) when used in federated environments. These causal models allow one to go beyond Markov equivalence. However, in many domains data are scarce, and increasing the sample size by centralising data from different clients is not advisable due to regulations such as the GDPR. The federated environment offers an attractive option to balance privacy and causal discovery accuracy. Unfortunately, the standard centralised estimator in the LiNGAM setting, i.e., DirectLiNGAM, cannot be straightforwardly federated. Higher-order cumulant tensors offer a way around this obstacle: they depend only on the joint distribution of the variables involved and add exactly across independent sample groups, so a single communication round suffices in horizontal, vertical, and hybrid partitions. However, FedISHC, i.e., the current federated method along these lines, breaks down under near-symmetric noise. To overcome the above limitation, we introduce the FedRCD family of causal discovery algorithms, and investigate three variants that trade off communication rounds against algebraic noise; two of them are exact federated counterparts of the centralised high-order cumulant (HC) and HC-LiNGAM algorithms, and the single-round variants further effectively support exact unlearning at any granularity, from a single observation to a whole client. Numerical experiments show that at sample sizes typical of real deployments, the entire cumulant-based federated family does not actually rank variables by the population asymmetry that the scores encode at zero. It ranks them by a variance ladder induced by the DAG along its directed paths, the cumulant counterpart of varsortability. Marginal standardisation collapses every cumulant method to near-random ordering, while scale-invariant DirectLiNGAM, not federable under this protocol, is unaffected.

In the natural sciences, symmetries and cause-effect relationships are ubiquitous. Yet for complex machine-learning tasks, like world-modeling in reinforcement learning, they appear difficult to harness. We propose a formal description of statistical systems based on symmetries in data leaving causal mechanisms invariant. The result is an abstract, simple and general mathematical language for causal reasoning. This paper provides formal descriptions of models and queries, setting up this language, and the formal infrastructure and strategies for their mathematically rigorous identification from data within this formalism. This approach reproduces and matches standard theoretical results on IID data and transport of experimental and non-experimental data. But its main purpose is to unify and substantially extend the scope of causal reasoning, in going beyond IID data and in approaching complex causal queries not captured by do- or soft-interventions. This new perspective on causally relevant aspects of data-modeling additionally sheds new light on well-known structures like c-components or hedges but also includes aspects of missing data and is inherently well-suited for the description of transfer and robustness properties.

Differentiable causal discovery methods increasingly encode expert priors as forbidden-edge constraints enforced by an Augmented Lagrangian (ALM) penalty, on the assumption that a data-adaptive relaxation mechanism will discount and eventually override a rule the data consistently contradicts. We show this design, which we call \emph{guide, not bind}, fails for two independent, precisely characterized reasons, and that directly repairing both restores it only partially. First, sequential penalty-ramping ALM suppresses a wrongly-forbidden true edge before any counterfactual check can detect it: we give three necessary conditions any adaptive relaxation must satisfy to avoid this (Proposition~\ref{prop:conditions}), prove that DADU---the natural relaxation rule this paper introduces as the object of study---violates all three (Corollary~\ref{cor:dadu_failure}), and confirm the failure across 3{,}072 training runs spanning graphs from 4 to 32 nodes, where a single wrong prior suppresses a true edge in 87--97% of trials under DADU. Second, and independent of any fix to the mechanism, we prove in closed form that the standard correlation-matching objective ties a true edge and its reverse to an identical cost of exactly $2r^2$ (Lemma~\ref{lem:tie}), not because the underlying equal-variance model is unidentifiable, but because normalizing to correlation discards exactly the variance information that would make it identifiable; covariance matching instead separates the two directions by a provable margin of at least $w_0^4$ (Lemma~\ref{lem:separation}).

Reasoning traces of large language models are widely read as containing "breakthrough" moments and early-legible fates. Both readings rest on measurements missing a counterfactual control at the level of the claim; we supply both controls. First, a restart-controlled truncation probe separates when a solution fits the continuation budget from when a prefix carries value that fresh computation cannot buy, comparing per-anchor continuation solve rates against from-scratch restart curves at matched total generated-token budget. Applied to 178 problem-model cells (89 MATH problems x two small open models, an outcome-blind but difficulty-targeted cohort), exactly 1 of 178 cells survives as prefix-limited; restart dose-response separates a compute-starved model from a capability-limited one; and wherever the matched budget lies inside the restart grid, continuing the model's own prefix beats restarting (9 of 9) -- predominantly compute compression rather than expanded reachability. Second, a pre-registered, difficulty-controlled test finds no detectable outcome information in early-window internal signals beyond a problem-difficulty baseline, and two generation-free analyses of public corpora show why this control is needed: a trace-blind difficulty proxy reaches AUROC 0.873 on 192K DeepSeek-R1 generations -- inside the published probe range -- and a closely matched reconstruction of the closest published early-window positive recovers a comparable pooled result (0.849) while within problem it is statistically indistinguishable from chance at all ten anchors (0.496 at t=4); a post-hoc within-targeted probe finds only a small average residual, concentrated in three low-failure problems. High pooled probe AUROCs cannot by themselves establish within-attempt information; a question-only baseline or within-problem evaluation is required.

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.

Causal inference is the practice of estimating the effect of a treatment or intervention from data. It traditionally requires a bespoke pipeline for every new problem: first proposing a causal mechanism, selecting a compatible estimator, and finally training it. Meanwhile, across diverse settings and modalities, much of machine learning has shifted to the paradigm of foundation models: networks pretrained once at scale and applied to new tasks without fine-tuning. Causal foundation models (CFMs) bring this paradigm to causal inference. CFMs are pretrained neural networks that estimate causal quantities, such as the average treatment effect, on entirely new datasets using in-context learning without requiring model updates. This work provides a practical introduction to this emerging area. We summarize the necessary background in causal inference and machine learning before discussing CFMs. Throughout, we include example code and Jupyter notebooks.

Post-training quantization (PTQ) is widely used to reduce the cost of serving large language models (LLMs), but its accuracy cost is uneven and is often tuned per model. We study where quantization damage occurs and how to allocate a small additional precision budget. Using causal mixed-precision intervention as ground truth (raise each layer to 8-bit in turn and measure the accuracy it recovers) across 9 open-weight models in 4 architecture families, we test 3 intuitive hypotheses: that quantization damage lives in task circuits, where the model computes, or in weight statistics. None of them predicts which layers benefit from restored precision. Recovery is instead diffuse: for 8 of 9 models, recovering 75% of the gap takes roughly half the layers; the lone exception, Qwen3-8B, is sharply concentrated. At a matched precision budget, spending it globally on finer quantization granularity beats locally repairing the most recoverable layers for all 8 group-128-compatible models (all but OpenLLaMA, whose width rules out group-128), by 21-52 points, including the concentrated Qwen3-8B. We report 2 secondary findings: the residual is budget-limited (8-bit is near-lossless in our evaluation across RTN, GPTQ, and AWQ), and the location of peak recovery correlates with architecture within a family, though not across families. Within this budget setting, global granularity is a better default than selectively protecting critical layers. More broadly, cheap signals that correlate with quantization damage do not necessarily identify where restoring precision improves accuracy; this must be tested with causal intervention.