Latent Confounders

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.

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.

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.

In many settings, studying causal questions based on text data requires adjusting for confounding information within texts. Yet there is a tradeoff in constructing text representations for adjustment: they must be sufficiently large and/or dense to preserve the confounding variables necessary for unbiased effect estimation, but sufficiently small and/or sparse to satisfy finite-sample overlap and yield low-variance estimates. To address this tradeoff, we turn to sparse autoencoders (SAEs), and propose a novel causal adjustment pipeline that iteratively selects a minimal set of SAE features via conditional independence tests. We find that SAE representations achieve better adjustments (lower bias and and higher coverage) than alternative representations in standard semi-synthetic evaluations with binary confounders, and their interpretability offers opportunities for falsification. We also introduce a more realistic semi-synthetic evaluation that uses multi-label data as the unobserved confounders and find off-the-shelf adjustment methods require increased investigation for these more complex settings. Code: https://github.com/mianzg/sae-text-confounder

Representational similarity analysis (RSA) is increasingly used to ask which learning rules give convolutional networks brain-like representations. Because biologically plausible rules such as feedback alignment, predictive coding and STDP do not scale, studies that include them train small networks on small images (typically 32x32 CIFAR) and then compare them to brain responses modeled at much higher resolution. We find that a common result in this setting, that untrained or locally trained networks rival or beat backpropagation at early visual cortex, depends strongly on the resolution at which the network is evaluated. The V1 gap between an untrained network and a backpropagation-trained one widens from -0.001 +/- 0.007 at the 32px training resolution to +0.044 +/- 0.006 at 224px, growing monotonically across six resolutions (n=5 seeds). It holds in human fMRI and, directionally, in single-seed macaque electrophysiology, along the training trajectory, and for an ImageNet ResNet-50 and a Swin-Tiny transformer trained at 224px. Four candidate mechanisms are tested and none accounts for it: train/eval resolution matching, low-level Gabor and pixel structure, the normalization state of the untrained baseline, and convergence of the pooled descriptor toward a global brightness statistic; three are excluded by interventions holding the convolutional weights bit-identical. A fifth experiment locates the effect: capping image detail at the training resolution while letting the pooled positions grow 12-fold removes about 90% of it, so the dependence is carried by image detail rather than by pooling. Separately, a single scalar luminance value per image reaches rho = 0.075 against the V1 RDM, essentially matching the untrained network's 0.076, which bounds what this style of comparison can resolve. The one learning effect that holds across resolution is backprop above untrained, at LOC.

As Large Language Models (LLMs) are increasingly deployed as autonomous agents, accurately evaluating their latent values and biases is critical. The NLP community typically evaluates models using large, unstructured benchmarks. While effective for general capabilities, these datasets fundamentally conflate causal mechanisms: even when an aggregate bias is detected, unstructured evaluations cannot disentangle whether it stems from baseline traits, contextual confounders, or complex interactions. To address this, we introduce an analytically exact framework for the controlled behavioral evaluation of LLMs. We bridge human psychometrics with LLM mechanics by resolving gaps in design, measurement, and analysis. First, we replace unstructured prompting with fully crossed factorial experiments to systematically isolate causal main and interaction effects. Second, we eliminate Monte Carlo text sampling noise by operating directly on exact, token-level Probability Mass Functions (PMFs). Third, we derive a multivariate ordinal consensus metric and a distributional ANOVA to process these PMFs analytically. We validate our framework with a case study on consumer ethnocentrism across five LLMs, demonstrating how our approach isolates systemic country-of-origin biases that aggregate benchmarks otherwise obscure.

Large language models (LLMs) are increasingly reported to exhibit human-like neural and cognitive signatures, including concept cells, mental number lines, and cognitive maps. These claims often rely on linear probing and activation steering applied to a single model, yet both methods are highly sensitive to measurement choices. A reported parallel may therefore reflect the model, the measurement procedure, or both. We audit four representative neuroscience-inspired paradigms across 17 models from five families, spanning $0.6$B to $72$B parameters. Our main experiment examines the causal steerability of concept directions. With raw activation units and a fixed layer and coefficient, steerability appears to increase with model scale, resembling an emergent capability. However, this pattern is produced by an uncalibrated pipeline rather than by a claim established in the steering literature. The trend depends jointly on raw units, the readout metric, and the operating point; correcting any one of these removes it. With residual-norm-comparable interventions and held-out operating-point selection, concept steering remains significant at every scale, but shows no significant trend across the Qwen3 series, although the confidence interval does not rule out a moderate positive slope. The remaining results are mixed. A linear geographic world map is consistently decodable in every tested checkpoint up to $72$B. Number magnitude is strongly encoded, but whether individual neurons appear bell-shaped or monotonic depends on the selection criterion. Language-specific structure is localizable, but the direction of the cross-lingual asymmetry reverses under a different attribution method. These results suggest that the main constraint on AI neuroscience is not a lack of phenomena, but a lack of comparable measurements and adequate controls. We release the protocol, stimuli, and code.

Adaptive data-cleaning methods replace manual filtering thresholds with data-driven partitions. However, changing the partition granularity, the number of groups used to segment samples by estimated corruption risk, can implicitly shift the decision boundary and alter the overall number of removed samples. This creates a bias known as removal-budget confounding, where apparent gains in metrics like precision or false-positive rate reflect a smaller removal budget rather than superior corruption discrimination. To address this evaluation bias, we introduce an operating-point-aware evaluation framework that evaluates methods using matched-budget and matched-recall controls alongside threshold-independent metrics (AUROC and AUPRC). We test this framework on a multi-cue adaptive cleaner redesign featuring a reweighted learning-difficulty cue, an auxiliary Euclidean-distance cue, and increased partition granularity intended to isolate clean-but-difficult samples. While naive evaluations (assessing configurations at their own induced operating points) suggest substantial performance improvements for the redesign, these gains disappear once operating points are equalized. False-positive decomposition reveals that clean-but-difficult samples primarily drive error counts at low corruption rates, become threshold-dependent at moderate corruption, and contribute negligibly under severe corruption. Experiments on CIFAR-10 and ImageNet-100 demonstrate that most performance differences observed in naive evaluation shrink or vanish at low-to-moderate corruption when operating points are matched. True ranking advantages only remain in specific low-prevalence settings and in high-recall regions under severe corruption. These findings highlight that adaptive cleaning methods must be benchmarked at matched operating points to ensure performance gains reflect genuine corruption discrimination.

Vision-Language-Action (VLA) models have driven significant progress in robotic manipulation, yet they fundamentally struggle with the vision-override phenomenon. Driven by the severe modality imbalance between dense visual streams and sparse linguistic instructions, VLAs frequently fall prey to causal confusion. Instead of treating language as the primary causal driver, the policy entirely bypasses the original instruction by overfitting to spurious visual confounders, such as prominent objects or familiar layouts. To systematically alleviate this bias, we formalize the process of action generation as a Dual-path Deconfounding Graph (DDG) and propose CofactVLA, a novel causal intervention framework. By dynamically constructing a language-masked counterfactual branch within a single forward pass, CofactVLA isolates and neutralizes visual confounders through two synergistic mechanisms. First, Action-Level Orthogonal Projection Guidance (OPG) geometrically projects the factual velocity field away from the counterfactual visual bias during continuous flow matching, extracting the pure semantic intent. Second, Feature-Level Counterfactual Covariance Reduction (CCR) mathematically deconfounds latent representations by penalizing the positive eigenspace of the covariance difference, explicitly suppressing dominant visual shortcuts while preserving the causal language intent. Extensive experiments demonstrate that CofactVLA establishes a new state-of-the-art across diverse simulation benchmarks. Beyond simulation, real-world robot experiments demonstrate the causal efficacy of our method in bridging the generalization gap, yielding a 52.3% absolute success rate gain under out-of-distribution scenarios.

Estimating causal effects from real-world spatiotemporal data is challenging due to hidden confounders and interference. Standard causal identification methods assume conditional exchangeability given observed covariates, which fails whenever hidden confounders affect both treatment and outcomes - a common setting in domains such as climate, environmental policy, epidemiology, and regional economics. In this paper, we propose a novel spatiotemporal proximal causal inference framework that extends proximal identification theory to spatiotemporal settings. The proposed method jointly captures local and neighborhood-level confounding information by introducing treatment- and outcome-inducing proxies, and we derive a spatiotemporal outcome confounding bridge function that identifies the potential outcome without requiring direct recovery of the hidden confounder. We establish the identifiability of this bridge function under proxy exclusion restrictions and a spatiotemporal completeness condition, and show that the resulting estimator recovers the outcome through a proximal generalization of the g-computation formula. To operationalize this identification result, we propose a neural architecture that learns proxies via transformer-based spatiotemporal encoders - coupled with a conditional mutual information critic to enforce exclusion restrictions and a moment-matching network to guarantee that the learned bridge function satisfies the underlying identifying equation. We further introduce a stabilized weighting scheme to address treatment support imbalance. Experiments on synthetic datasets demonstrate that our approach achieves comparable performance to baseline causal inference methods, while providing, to our knowledge, the first theoretically grounded outcomes for the hidden confounding in the presence of spatiotemporal interference through a proximal causal inference framework.

Detecting when the statistical behavior of an engineered system changes, and identifying which component is responsible, are core problems in the monitoring of telecommunication networks, robotic platforms, security infrastructure, and multi-agent systems. In safety- and mission-critical deployments, such decisions must be accompanied by statistical reliability guarantees rather than by point estimates alone. Conformal changepoint localization (CONCH) and conformal root cause analysis (CROC) meet this need by returning confidence sets that contain the true changepoint, or the true root-cause stream, with a user-specified probability, without parametric assumptions on the data-generating process. In practice, however, observations are frequently corrupted, e.g., by outliers, sensor faults, or adversarial perturbations. While the finite-sample coverage of these procedures is preserved under contamination, the resulting confidence sets can become uninformatively large. Adopting a Huber-type contamination model, this paper proposes weighted CONCH (W-CONCH) and weighted CROC (W-CROC), which downweight observations that are likely to be corrupted with the goal of reducing confidence set size when data may be corrupted. The weighting mechanism, derived from a formal bound on the unknown corrupted data densities, leverages pre-existing second-order classifier-based uncertainty signals, such as those produced by evidential deep learning or Bayesian learning. W-CONCH and W-CROC are further generalized by introducing a meta-learning procedure for the weights that optimizes a differentiable surrogate of the confidence set size. Experiments on image-based and real-world changepoint and root-cause benchmarks show that uncertainty-based weighting substantially reduces confidence set size while maintaining the target coverage.

Estimating causal effects of linguistic properties from observational text is difficult because the same document can contain both the treatment of interest and the non-treatment textual attributes needed for adjustment. Existing approaches often learn representations from the full text to capture latent confounding, but when treatment status is itself encoded by words in the text, these representations can directly encode treatment. This creates a confounder trap: richer representations can make treated and control documents separable, inducing overlap violations even when the underlying causal problem satisfies overlap. We study latent text treatments that are encoded through lexicons or other treatment-defining lexical information, and propose masking-based adjustment representations that remove this lexical treatment signal before representation learning. We formalize representation-induced overlap failure, prove that deletion masking preserves overlap for bag-of-words/topic-model representations, and characterize replacement masking as a natural relaxation for large language models that hides treatment-defining tokens while preserving word order and context. Across simulations, masking improves overlap diagnostics, stabilizes treatment effect estimates, and reduces bias relative to adjustment methods that learn from the unmasked text.

Federated learning has emerged as a promising paradigm for spatio-temporal forecasting (STF), enabling collaborative model training without sharing raw observations. Existing federated STF methods primarily regard cross-client heterogeneity as an optimization challenge and mitigate it through personalized approaches. However, such heterogeneity fundamentally stems from diverse \emph{environmental conditions}, and these methods capture environment-specific forecasting patterns, hardly generalizing under environmental shifts. Our key insight is that the environmental diversity across federated clients should be exploited, as they provide \emph{complementary observations of the same underlying spatio-temporal system}. Based on this insight, we propose \method, a novel federated de-confounding framework that \textbf{treats clients as distinct causal environments}. \method leverages the client heterogeneity as distributed environmental evidence and learns a global prototype codebook to capture shared environmental regimes. We further derive a theoretical federated de-confounding bound that is linearly controlled by the averaged confounding strength. Extensive experiments demonstrate that \method consistently outperforms federated baselines, while providing transferable, interpretable, and communication-efficient environmental representations.

Phenotype-driven diagnostic benchmarks usually report the rank of the reference disease, but they rarely reveal which plausible alternatives are ranked above it or what evidence a tool-using model examines before making its decision. We introduce GraphRareBench, a provenance-preserving benchmark containing 2,365 ontology-derived cases and 18,093 target-confounder pairs. Each case includes a coarsened HPO query, a fixed candidate pool, graph-defined hard confounders, and source-linked evidence records. On the 237-case gene-component-disjoint test split, supervised rankers using a shared 21-feature interface achieved MRRs ranging from 0.640 to 0.740 and case-averaged target-over-confounder accuracies ranging from 0.898 to 0.916. Agents instantiated with Agents-A1 and DeepSeek-V4-Flash achieved MRRs of 0.746 and 0.718, respectively. Their paired MRR difference was not statistically significant, whereas their target-evidence coverage differed by 0.561. Together with the observation that 22.1% to 43.7% of selected Hit@10 successes still ranked at least one graph-defined hard confounder above the target, these results indicate that full-pool retrieval, hard-confounder discrimination, and observable evidence access capture complementary aspects of model behavior. GraphRareBench therefore provides a foundation for more transparent and evidence-aware evaluation of phenotype-driven diagnostic systems. Code and data are available at https://github.com/GUI0609/GraphRareBench.

Comparing CT reconstruction methods fairly is labor-intensive and largely manual, and many benchmarks use idealized data. We ask whether a large language model (LLM) agent can do the labor of reconstruction research on its own, and whether a ranking measured on ideal data predicts behavior under realistic noise. We built an agentic loop: the agent edits a solver, runs a short cluster job, reads one frozen metric, and revises. The metric is a calibrated headroom score against the FBP baseline, inside the field of view; every method shares the same differentiable fan-beam projector. We benchmarked 26 methods on Mayo low-dose CT (noise-limited) and a 128-view sparse-view breast task from the noiseless DL-Sparse-View Challenge, with validation-selected iterations scored on a held-out test set. Every trained breast model was then re-scored on noisy inputs (I_0 = 10^5 photons) without retraining, and separately retrained on matched noise. The agent independently implemented, tuned, and benchmarked all 26 methods, and recombined them into a compact solver of 969 parameters that ties the top Mayo tier at the 1% level using 0.4% of the champion's parameters. Benchmarking gives a tier of statistically indistinguishable top methods, not one winner. Mild input noise nearly inverts the breast ranking: the noiseless champion (a supervised image denoiser, hr 0.89) collapses to 0.00, while a learned primal-dual method rises to champion (0.72 to 0.93). An ideal-data leaderboard therefore does not predict robustness. The inversion is a transfer effect, not a permanent deficit: retraining on matched noise restores much of the clean ranking (Spearman rho 0.04 to 0.61). Noise is only the easiest confounder in an open-ended set (beam hardening, scatter, anatomy, disease), so no single-factor challenge certifies generality. Benchmarks should model a broad spectrum of realistic factors at once.

Modern recommender systems are typically based on deep learning (DL) models, where a dense encoder learns representations of users and items. As a result, these systems often suffer from the black-box nature and computational complexity of the underlying models, making it difficult to systematically enhance their recommendation capabilities. To address this problem, we propose Probabilistic Residual Learning (PRL), a causal Bayesian recommendation model that models the residual between ground-truth and base predictions, enabling targeted refinement of existing systems. Specifically, PRL (1) probabilistically groups users for localized residual modeling, (2) models domain-level confounders that influence user and item representations, and (3) aggregates cluster-specific residual predictions over the confounders using do-calculus. Experiments demonstrate that our plug-and-play PRL is compatible with various base deep learning recommender systems, improving their performance while automatically discovering meaningful user clusters.

AI systems increasingly retrieve from records that revise themselves: issue threads, encyclopedic histories, policy logs, and long conversations. The challenge is not only finding relevant evidence, but deciding which claims remain in force, which were superseded, and when to abstain. Structured memories promise to solve this with typed edges, temporal updates, and conflict status, yet evaluations often change mechanism and prompt presentation together. We study this as Evidence-State Revision, comparing flat retrieval, coarse edge invalidation, and fine-grained RevisionLedger on 2,907 high-agreement questions from GitHub, multi-repo issue histories, Wikipedia, and DyKnow-style temporal streams. A render-matched control (same layout, deprecation disabled) reveals the central confound: when a value is changed and later restored, RevisionLedger appears to beat a flat baseline by +0.182, but almost all the gain comes from easier presentation; the fine-grained mechanism residual is indistinguishable from zero (+0.021 to +0.025 across two judge families). After presentation is controlled, coarse invalidation is the only mechanism that pays for current-state queries, beating the fine ledger by 0.084; the same query-sufficiency principle says provenance mainly needs retained invalidated evidence, not richer typing. Memory evaluations should hold render fixed, and deprecation-aware systems should deploy the coarsest retained state that covers their queries.

We study causal inference under outcome interference for sequential, observational settings. Specifically, we consider settings where the binary outcomes over N units are Markovian across T time steps. At each time step, the outcomes of N units have dependencies captured through an Ising model; each outcome is also impacted through an external field capturing the effects of its treatment as well as latent confounders. Similar to panel data literature, these latent confounders are modeled to have a low-rank factor structure. Our data is a single sample from this high-dimensional distribution. To estimate causal quantities of interest, we provide a computationally efficient method based on Maximum Pseudo-Likelihood Estimation (MPLE) for learning the model parameters. Under mild assumptions, we establish non-asymptotic consistency for parameter estimation and show this translates to faithful estimation of causal quantities of interest after sampling from the learned model. We demonstrate the efficacy of the method through synthetic experiments as well as a real-world case-study investigating causal effects of vaccine rates on COVID-19 death rates within US counties nationwide.

Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

Cross-model comparisons read divergence in value dispositions as evidence that language models hold individuated values. Under single-draw measurement this conflates two quantities: a difference in central tendency (a genuine value difference) and a difference in response determinism (how sharply a model commits to a forced choice). We introduce a separation protocol -- no-rule value dilemmas with counterbalanced, repeated forced-choice measurement and a determinism index -- and a determinism-corrected decomposition that splits an apparent cross-model distance into a direction-flip component (genuine disagreement) and a same-side-more-extreme component we label determinism. Across nine models, determinism varies substantially (0.66-0.95 among engaging models); whether it is a per-model trait or tracks provider and scale is a question our method makes measurable but our sample leaves open. Correcting for determinism shrinks apparent individuation, while a few cross-family disagreements survive a strict test. We then isolate a second confound: the access harness serving each model. Re-collecting the same models through raw provider APIs, we find the deployment client shifts a model's value profile substantially and client-specifically: one subscription CLI moves a profile by 0.31, flips four of eighteen items, and inflates the flagship's apparent softness (0.34 via CLI vs 0.66 via raw API), whereas another provider's client is clean, confounding provider family with access client. The harness is a value-shaping layer: a base model that refuses one-in-ten forced choices is made compliant by an agent system prompt, established causally in a white-box control. An audit ranking models by single-draw value distance thus ranks a determinism-inflated quantity, confounded further by the client used. We contribute the decomposition and identify the deployment harness as a distinct value confound.

Bayesian causal discovery is widely used for its ability to quantify epistemic uncertainty over directed acyclic graphs (DAGs) through posterior inference. However, its behaviour under latent confounding remains poorly understood, as existing work typically notes that confounding breaks identifiability without characterising how the posterior distribution over DAGs responds. In this work, we analyse posterior behaviour under latent confounding in linear Gaussian causal models, focusing on additive latent confounding between exactly two observed variables. We derive a critical correlation threshold above which the score function favours graphs with a spurious edge between the confounded variables, and show that this threshold decreases with sample size -- more data lowers the correlation required for the spurious edge to be favoured. Beyond this threshold, we characterize two distinct posterior failure regimes determined by the local structure around the confounded variables. Our findings are supported by exact posterior computations on multiple graph structures, demonstrating both the predicted failure regimes.

Flexible machine-learning methods can be sensitive to hidden confounding: they may learn associations induced by unobserved confounders rather than stable signals. Spectral deconfounding mitigates this problem by shrinking high-variance directions of the covariate matrix that, under dense confounding, carry latent confounder information. Existing work has largely focused on linear models. We develop a nonlinear spectral deconfounding framework for gradient boosting. Our approach replaces the ordinary squared-error loss by a spectral loss, which alters the boosting dynamics by slowing down learning in confounding-aligned directions. We show that deconfounding is not achieved by the spectral loss alone, but by the interaction between spectral shrinkage and regularization, especially in terms of early stopping. Moreover, we provide a mixed-model interpretation that connects LAVA-type shrinkage to random-effects adjustment and yields an empirical-Bayes procedure for tuning the spectral loss. We also extend the method to general likelihoods and nonlinear confounding using Laplace approximations and kernel random effects. Across synthetic and real-world experiments, spectrally deconfounded boosting improves estimation of the target function under hidden confounding and is substantially more scalable than existing nonlinear spectral deconfounding baselines.

Parameterized quantum circuits (PQCs) are increasingly used as policies and value functions in quantum reinforcement learning, yet it remains unclear when and why quantum policies generalize. We give a PAC-Bayesian account in which generalization is governed not by the raw number of circuit parameters, but by the effective dimension of the Fisher geometry induced by the circuit. This quantity is inflated by entanglement, making entangling connectivity an independent axis of complexity.In controlled experiments that fix the number of trainable rotations and vary only entanglement, we find that circuits with larger Fisher effective dimension exhibit larger train-test gaps, while parameter count is a weak predictor. The resulting bound acts primarily as a ranking certificate: it correctly orders circuits with identical parameter count, which parameter-counting bounds cannot do. We validate this mechanism across supervised classification, quantum contextual bandits, and value-function generalization, where entangled circuits consistently generalize worse than non-entangled circuits of equal parameter count, with gaps shrinking as sample size increases.Our strongest evidence comes from low-variance decision models, including single-observable classifiers, value heads, and one-step policies. In end-to-end multi-step policy learning, entanglement effects remain statistically significant but high return variance leaves the full ordering only partially resolved. Partial-correlation analysis shows that Fisher effective dimension screens off entangling pattern, and controls for training accuracy, readout, and optimizer rule out major optimization confounders. The effect also persists on an IBM Heron quantum processor under real noise. Overall, our results reframe quantum policy design around an entanglement--generalization trade-off rather than expressivity alone.

Recovering the exact directed acyclic graph (DAG) in linear non-Gaussian acyclic models with latent confounders (LvLiNGAM) remains a challenging problem. Although LvLiNGAM is identifiable only up to an observational equivalence class, each equivalence class is characterized by a unique sparsest DAG. Recovering the sparsest DAG from finite samples, however, remains difficult. Although existing methods are asymptotically consistent, they do not provide an explicit finite-sample procedure for recovering the unique sparsest DAG, nor do they handle models with an arbitrary number of latent confounders. In this paper, we propose a finite-sample method for recovering the sparsest DAG without imposing any restriction on the number of latent confounders. Simulation studies and real-data analyses demonstrate that the proposed method achieves superior finite-sample performance compared with existing approaches.

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

Agent memory systems are increasingly evaluated against RAG and full-context baselines, but reported gains often mix changes in the memory method with changes in the language model, embedding model, or retrieval pipeline, making it unclear what is actually being measured. We present MemDelta, a controlled evaluation protocol that varies one component at a time on LongMemEval-S (500 questions, 50+ sessions, three model families). Four findings emerge: (1) verbatim RAG matches full-context GPT-4o-mini (47.2% vs. 49.8%, p = 0.34), but the ranking reverses across models: Gemini gains +14pp from full context, while Sonnet gains +31pp from RAG, partly because it refuses 63% of full-context queries; (2) swapping only the embedding model in an identical pipeline shifts accuracy by +6.2pp at n = 500 (p = 0.004), and Mem0 beats MiniLM-RAG by +11pp but loses to cloud-RAG by 1.2pp, so one variable flips the conclusion; (3) agent self-memory (42%) underperforms basic retrieval (47%); (4) on 2 of 6 question types (n = 88), Mem0 matches cloud RAG (72.7% vs. 73.9%, p = 1.0) at 50x the cost, suggesting narrow rather than general gains. We recommend memory evaluations fix embedding models across comparisons, stratify by model family, and report write-path cost before attributing gains to architecture.

Uplift modeling, crucial for estimating individual treatment effects (ITE), faces dual challenges: flexibly leveraging inter-group similarity to enhance discriminative power and debiasing under unobserved confounding scenarios. In this paper, we propose the Cross-Head Attention Uplift Network (CHAUN) and Robust Adversarial Inverse Propensity Score (RA-IPS) method to address these limitations. CHAUN employs shared feature embeddings and cross-head attention mechanisms to dynamically integrate treatment-specific and control-specific representations, enhancing inter-group correlation modeling. Theoretically, we prove that access to the true propensity scores ensures ITE identifiability even with unobserved confounders. For practical scenarios lacking true propensity scores, RA-IPS adversarially optimizes propensity weights within constrained uncertainty sets to mitigate bias from unobserved variables. Experiments on public datasets (CRITEO-UPLIFT, LAZADA) and a production e-commerce dataset demonstrate CHAUN's superiority over state-of-the-art uplift models, achieving relative improvements of up to 25.6% in QINI scores. RA-IPS further enhances robustness, outperforming standard IPS by 5.4% under unobserved confounding. The results validate the effectiveness of our proposed methods in real-world causal inference tasks.

Pooled across five AI coding agents, pull requests (PRs) with a human Co-Authored-By trailer merge less often than purely-autonomous ones (53.8% vs. 79.8%) -- yet this aggregate finding is a textbook Simpson's Paradox. Stratifying 33,596 PRs from the AIDev dataset by agent identity reverses the conclusion: Copilot and Devin show large positive within-agent gaps (+41.2 and +33.5 pp, both p<0.001), while Cursor, Claude Code, and Codex show small effects whose cross-sectional 95% CIs span zero. The paradox is driven entirely by agent composition: Codex, which dominates 64.9% of the dataset, achieves high merge rates while rarely using co-authorship. But Simpson's Paradox is only the first layer of a cascade of confounders: within-repo controls eliminate Devin's gap (+33.5 to +1.6 pp, p=0.73); a commit-count control further halves Copilot's within-repo gap (+36.2 to +24.4 pp); restricted to multi-commit PRs, the Copilot within-repo effect dissolves to +4.8 pp (p=0.59). No agent retains a clear co-authorship effect once both repository selection and PR structure are controlled. Our findings caution against reporting agent-pooled statistics without stratification and demonstrate that cross-sectional co-authorship associations are largely selection and PR-structure artefacts rather than evidence of a causal benefit.

Modern data analysis usually gives a prediction without showing whether the evidence behind it is clear, conflicting, or stable. Two cases can have the same fitted confidence even when one has mostly agreeing evidence and the other has strong support and strong opposition. We propose Signed Evidence Flow (SEF), which combines a fitted prediction rule with signed feature attributions to measure support, opposition, conflict, and perturbation stability. We prove that confidence determines conflict exactly when it also determines total evidence mass, derive the remaining conditional variance, and state when conflict can improve loss prediction beyond confidence and other audit variables. We also connect conflict to geometric decision fragility. Across healthcare, Covertype, black-box, finance, and ten external data sets, conflict sometimes separates risk among predictions that already appear confident. Cross-fitted tests show added error-ranking information beyond confidence and attribution entropy on several data sets, including two large finance tasks. The direction is not universal: in some tasks, lowconflict cases are riskier. We therefore introduce ScopeGate, a held-out permutation diagnostic that checks the direction before SEF is used for review triage. SEF is consequently an audit tool rather than a universal risk score: it describes evidence structure, while an independent calibration sample determines whether that structure is useful in the target population.

The presence of confounding bias poses a key challenge in policy evaluation, as the target causal effects of actions are not identifiable (i.e., underdetermined) from observational data. On the other hand, existing confounding-robust evaluation strategies require detailed prior knowledge about the environment or apply only to discrete treatments and outcomes. This paper investigates causal effect evaluation over the continuous domain from confounded observations, while requiring only basic temporal ordering between the treatment and the outcome. We introduce a universal discretization of the exogenous domains that approximates the observational and interventional distributions of any causal model with arbitrary accuracy using a finite number of latent states. Building on this newfound universal approximation property, we develop a novel family of Causal Gaussian process (CGP) models that effectively approximate the observational and interventional distributions of any causal model with confounded observations.

Deep generative models reproduce the observational distribution of their training data, inheriting any spurious associations it contains. A common source is an unobserved confounder that shapes both an attribute the user wants to control at sampling time and an attribute expected to vary in response. Existing causal generative approaches resolve the resulting ambiguity by imposing structural assumptions strong enough to single out one interventional distribution; in image domains, such assumptions are rarely warranted, and the data is generally consistent with a set of distinct causal mechanisms -- a feasible region of interventional distributions. We propose CauVaDE (Causal Variational Deep Embedding), built on a canonical augmented SCM in which the unobserved confounder collapses, without loss of generality, into a discrete latent cluster of bounded support while continuous variation is absorbed into independent noises. We prove that this canonical class is dense, in both observational and interventional Wasserstein distance, in the class of augmented SCMs compatible with a given causal diagram, and instantiate it as a mixture variational autoencoder whose cluster variable plays the role of the canonical confounder. An entropy regularizer with weight $γ$ on the cluster posterior then traces a family of candidate causal effects that fit the observational data to comparable likelihood while spanning the feasible region. Experiments on image data benchmarks show that CauVaDE produces diverse interventional samples and improves FID against an unconfounded reference.

Finding the source of failures, known as Root Cause Analysis (RCA), is essential for identifying the root causes of anomalies and maintaining the reliability of complex systems. While causal theory has advanced data-driven RCA, existing frameworks assume causal sufficiency, failing to account for the unobserved latent variables prevalent in real-world environments. To address this gap, we propose PAG-RCA. This framework models system failures as parametric interventions over Partial Ancestral Graphs (PAGs) to perform RCA in the presence of latent variables. We use standard causal identification algorithms to find the source of failures by quantifying causal effects over the PAG. When an effect is identifiable, candidate root causes are ranked based on their exact intervention effects. When effects are structurally unidentifiable, our framework (for the first time in the RCA literature) integrates partial identification to evaluate and score candidates using analytical causal bounds. By integrating latent variables and partial identification at once our framework ensures robust RCA even under data scarcity and latent-variable scenarios where traditional methods degrade. Evaluations on synthetic data, microservice anomaly benchmarks and power-grid cascading failures demonstrate that PAG-RCA consistently outperforms state-of-the-art data-driven baselines. By improving data-driven RCA performance under data scarcity, this methodology advances reliable automated diagnostics in partially observable complex networks.

Causal discovery methods commonly assume that all data is independently and identically distributed (i.i.d.) and that there are no unmeasured variables affecting the system. In practice, these assumptions are often violated, leading to inaccurate inference. In this paper, we study how to identify hidden confounding and selection biases from causal mechanism shifts. In particular, we show that structural biases lead to dependent mechanism shifts. That is, by considering for which variables the mechanisms change given data from different environments, we can tell which variables are unbiased, which are subject to hidden confounding, and which are undergoing selection bias. We formalize this into an empirically testable criterion based on mutual information, and show under which conditions it identifies structural biases. To tell which nodes are subject to what kind of bias, we introduce the StruBI algorithm. Experiments on synthetic and real-world data show that StruBI works well in practice, accurately recovering affected variable sets and types of biases, outperforming the state-of-the-art by a wide margin.

Multi-cause observational studies contain information about unmeasured confounding through the dependence structure among causes. However, literal imputation of the unobserved confounder is often more complex than learning a lower-dimensional substitute score that preserves the shared assignment variation needed for stable causal adjustment. The deconfounder (Wang and Blei, 2019) and related substitute confounder methods exploit this idea, but flexible assignment models can fit the joint distribution of the causes while producing scores that over-encode the treatment vector, collapse overlap, or capture single-cause variation. We develop a Bayesian factor assignment framework for learning sparse substitute confounders that retain coarse multi-cause dependence with shrinkage priors. The theory is stated at the level of posterior concentration, factor score contraction, and overlap-preserving assignment geometry and therefore does not rely on a particular shrinkage prior. Under these conditions, the proposed regression-adjusted estimators are consistent for mean potential outcomes when the corresponding latent variable identification assumptions hold. Shrinkage priors provide a natural tool for latent structural learning: they favour low-dimensional factors supported by multiple causes, discourage effectively single-cause factors, and induce an ordering of the latent factors through progressive shrinkage. Synthetic experiments illustrate the roles of signal strength, outcome validity, and geometry-aware regularization. In an Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline analysis, sparse substitute scores recover much of the adjustment obtained by directly conditioning on invasive cerebrospinal-fluid biomarkers, while collapse diagnostics identify when fitted factors reduce to individual observed measurements.

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

Prior work treats structured output as a reasoning tax, but this framing is incomplete: the cost of formatting depends strongly on a model's spare capacity. Using information-matched prose controls and a four-level schema complexity gradient, we separate format-specific effects from prompt-length confounds across 4 models and 5 benchmarks with 0% parse failures on successfully generated responses. We find that structured formats are capacity-dependent. Models with sufficient headroom absorb JSON constraints without degradation (Sonnet: $88.7\pm4.0$% JSON vs. $89.3\pm1.7$% CoT on MATH-Hard). In contrast, formats severely degrade models operating near their limits through two distinct mechanisms. First, under standard token budgets, Haiku drops 36.2pp ($p < 0.0001$) largely due to truncation. Second, even with extended budgets eliminating truncation, GPT-4o-mini drops 28.0pp ($p < 0.001$), revealing pure capacity competition independent of token exhaustion. This format penalty scales with schema complexity (McNemar $p < 0.0001$) and cannot be explained by prompt length alone. Furthermore, these results qualify claims of frontier model immunity: on AIME competition math, Opus 4.7 drops from 96.2% to 91.0% under JSON ($-5.3$pp; the displayed percentages are independently rounded, exact difference is $7/133 = 5.26$pp $\approx 5.3$pp). A delayed-structure ablation -- reasoning freely before formatting -- recovers most of the lost accuracy (3-run mean: 80--87%), supporting the capacity competition mechanism. The practical implication is not to avoid structured output, but to match it to capacity: when a model is near its limits, think first, format later.

Real-world regression often exhibits shortcuts: attributes that are spuriously correlated with continuous targets in training, yet unreliable under deployment shifts; regressing targets using such shortcuts may fail catastrophically at test time. Existing studies on spurious correlations focus primarily on classification, where labels are categorical and groups are naturally defined. However, many real-world tasks require continuous prediction, where hard label boundaries or discrete group-label pairs do not exist. We define Deep Spurious Regression (DSR) as learning from regression data with attribute-label confounding, addressing continuous spurious correlations, and generalizing to all attribute-label combinations at test time. Motivated by the intrinsic difference between classification and regression shortcuts, we propose to exploit the similarity among spurious attributes in both label and feature spaces, thereby accounting for nearby targets and related groups while calibrating both label and learned feature distributions across attributes. Extensive experiments on common real-world DSR datasets that span computer vision, environmental sensing, and large language model (LLM) regression verify the superior performance of our strategies. Our work fills the gap in benchmarks and techniques for studying spurious correlations in continuous prediction.

Multimodal models in oncology can produce accurate predictions, but accurate prediction does not reveal whether the model has learned biology that is shared across modalities, biology confined to one modality, or spurious correlations that reflect confounders rather than genuine biology. We introduce DECAT, a model-agnostic post-hoc evaluation framework that classifies multimodal representations into four diagnostic scenarios for a given task and modality, using five null-referenced metrics and a rule-based decision procedure. The framework operates on learned representations, requires no knowledge of which specific confounder is present, and returns indeterminate when the evidence is insufficient. We validate DECAT on synthetic data across four multimodal model classes (over 2,500 trained representations) and on real data from 8,979 TCGA patients, evaluating both multimodal embeddings and five pretrained pathology foundation models. Entangled models (e.g., CLIP) achieve near-perfect shared biology detection but falsely claim shared biology in the majority of cases where it is absent on real foundation model embeddings. This false claim rate increases with confound strength so that larger cohorts and stronger representations produce more confident but still incorrect diagnoses. Applied to both multimodal TCGA embeddings and five pathology foundation models without paired RNA, DECAT detects confounding invisible to AUROC without requiring the confounder labels, as confirmed by post-hoc stratification.

Understanding the effects of interventions is central to scientific progress, with randomized controlled trials (RCTs) regarded as the gold standard for causal inference in many applied fields. However, RCTs are costly, time-consuming, and often constrained by ethical or practical limitations, motivating the need for causal methods able to draw conclusions from observational data. While such data is collected at ever larger scale, making its use for causal inference is often hindered by the fact that not all variables affecting treatment allocation and the outcome are observed: an issue known as unobserved confounding. In this paper, we introduce a new study design called confounder detection via treatment intent. The idea is to query a human expert who makes treatment decisions, and ask them to compare pairs of units proposed by a principled matching strategy, with the goal of eliciting unobserved variables that explain why treatment decisions differ. We provide a theoretical basis for such a procedure, ascertaining conditions under which such a study design may elicit unobserved confounders. Building on this newly established foundations, we study treatment effects of interventions in the intensive care unit (ICU). First, we show empirical evidence strongly indicating that electronic health records (EHRs) collected in ICUs are subject to unobserved confounding. By using clinical text notes as a proxy for physicians' knowledge and leveraging natural language processing, we provide a proof of concept for our methodology in a semi-synthetic environment with a known ground truth.

Recommender systems often rely on observational user--item interaction data, which is prone to selection bias due to users' selective interactions with items. Inverse propensity weighting and doubly robust estimators effectively mitigate selection bias under observed confounding, but are unreliable in the presence of hidden confounders. Existing approaches relying on randomized controlled trials (RCTs) or global sensitivity bounds are constrained in practice: RCTs demand costly experimental data, while global sensitivity bounds presume a uniformly bounded effect of unmeasured confounders on propensities through sensitivity analysis, thereby neglecting heterogeneity across user--item interactions. To overcome this limitation, we propose a novel framework, which estimates user--item level sensitivity bounds, thereby substantially relaxing the homogeneity assumption inherent in global sensitivity bounds named Personalized Unobserved-Confounding-aware Interaction Deconfounder (PUID). To ensure both robustness and predictive accuracy, we further develop an adversarial optimization strategy and propose a benchmark-guided variant (BPUID) that incorporates pre-trained models as stabilizing references. Extensive experiments on three real-world datasets demonstrate that our approach significantly outperforms global methods under hidden confounding, without requiring RCT data.

We study the problem of selecting covariates for unbiased estimation of the total causal effect.Existing approaches typically rely on global causal structure learning over all variables, or on strong assumptions such as causal sufficiency - where observed variables share no latent confounders - or the pretreatment assumption, which limits covariates to those unaffected by the treatment or outcome. These requirements are often unrealistic in practice, and global learning becomes computationally prohibitive in high-dimensional settings.To address these challenges, we propose a novel local learning method for covariate selection in nonparametric causal effect estimation that avoids both the pretreatment and causal sufficiency assumptions. We first characterize a local boundary that contains at least one valid adjustment set whenever one exists for identifying the causal effect, and then develop local identification procedures to efficiently search within this boundary.We prove that the proposed method is sound and complete. Experiments on multiple synthetic datasets and two real-world datasets show that our approach achieves accurate causal effect estimation while substantially improving computational efficiency.

Large language models (LLMs) show potential as simulators of human behavior, offering a scalable way to study responses to interventions. However, because LLMs are trained largely on observational data, interventions in experiments with LLM-simulated synthetic users can induce unintended shifts in latent user attributes, causing user drift where the implicit simulated population differs across treatment conditions, potentially distorting effect estimates. We formalize the confounding or selection bias that can arise due to user drift and show how intervention-dependent shifts can inflate or attenuate observed differences in user responses under intervention. To diagnose confounding, we propose using negative control outcomes--attributes that should remain invariant under intervention--to identify distribution shifts across intervention conditions, providing evidence of user drift. To mitigate drift, we study adjusting the persona specification by eliciting additional confounders, finding that targeted, setting-relevant confounders can substantially reduce bias across survey-style and multi-turn agent evaluations.

Age dependent performance disparities in medical image classification often arise because age acts as a confounder, linking imaging morphology with disease prevalence. In practice, disparities can manifest as overdiagnosis at ages where disease prevalence is higher and underdiagnosis at ages where prevalence is lower, and can worsen under train test shifts in the age distribution. Conventional mitigation approaches that enforce strict age invariance may suppress diagnostically meaningful information encoded in age. We therefore propose a robust framework that mitigates the effects of age-dependent confounding by targeting spurious age linked trends rather than enforcing invariance. Following a warm-up phase, we characterize sample difficulty and model its age-dependent trends in a label-conditioned manner. We decorrelate age from dominant age difficulty trends using robust, Huber weighted affinity weights, attenuating confounding-driven shortcuts while preserving clinically meaningful, nonlinear age information. We further introduce an Age Coverage Score that scales the decorrelation penalty by minibatch age variance to ensure stable optimization under limited age diversity. Across two radiology datasets, our approach reduces age dependent true and false positive disparities with minimal AUC impact and remains robust to increasing train test age distribution shifts.

Clinical decision-making is a feedback system where risk estimates influence treatment, which in turn changes disease trajectories, and both shape clinicians' measurement practices. Static prediction often fails clinically: models trained on observational care logs conflate disease biology with clinician behavior, particularly under treatment confounder feedback and irregular or informative observation. This Review focuses on intervention-aware disease trajectory modeling in clinical AI--methods estimating patient-specific longitudinal disease evolution and assessing trajectory changes under alternative treatments. We organize the field around six linked components: three decision tasks (factual forecasting, counterfactual estimation, policy evaluation) and three data-generating mechanisms (disease evolution, treatment assignment, observation process) that determine identifiability. We present the first unified framework bridging forecasting, counterfactual trajectories, and policy evaluation across discrete/continuous time, explicitly addressing treatment assignment, time-varying confounding, and observation bias. We synthesize key method families (multistate/joint models, temporal point-process, deep sequence architectures, longitudinal causal inference), map them to relevant components, and align evaluation with claim strength via overlap diagnostics, uncertainty quantification, off-policy robustness, and target-trial validation. This synthesis advances benchmark prediction to decision-grade clinical evidence, enabling treatment-sensitive individualized futures, pre-deployment policy stress-testing, and safer closed-loop learning health systems that adapt/abstain when evidence is insufficient.

Corruption studies, the standard tool for evaluating chain-of-thought (CoT) faithfulness, infer which steps are ``computationally important'' from accuracy loss when steps are corrupted. We show that when benchmark chains end with an explicit terminal answer line, as in GSM8K and MATH, these tests largely measure \emph{answer placement} rather than where intermediate computation is carried out. Using matched GSM8K examples, removing only the final answer statement while preserving all reasoning collapses suffix sensitivity by about $19\times$ for Qwen~2.5-3B ($N{=}300$, $p{=}0.022$). Conflicting-answer prompts, which contain correct reasoning but a wrong explicit final answer, drive accuracy to zero or near-zero at 7B across five open-weight model families; wrong-answer following is strong at 3B--7B and attenuates sharply at larger scales. Replications on MATH, within-stable comparisons at 7B, and suffix-free chains show the same pattern in different guises: corruption sensitivity tracks the location of explicit answer text, not a fixed computational depth in the reasoning. Generation-time probes indicate that final answers are rarely early-determined during generation (${<}5\%$ early commitment), yet consumption-time behavior systematically follows explicit answer text. The confound is therefore largely a readout effect when the chain is consumed. We propose a three-prerequisite protocol (question-only control, format characterization, and an all-position sweep) as a practical minimum for future corruption-based faithfulness studies.

Causal sensitivity analysis aims to provide bounds for causal effect estimates in the presence of unobserved confounding. However, existing methods for causal sensitivity analysis are per-instance procedures, meaning that changes to the dataset, causal query, sensitivity level, or treatment require new computation. Here, we instead present an in-context learning approach. Specifically, we propose an amortized approach to causal sensitivity analysis based on prior-data fitted networks. A key challenge is that the sensitivity bounds are not directly available when sampling training data. To address this, we develop a general prior-data construction that is applicable across the class of generalized treatment sensitivity models. Our construction involves a Lagrangian scalarization of the objective to generate training labels for the bounds through a tradeoff between causal effect min/max-imization and sensitivity model violation, which avoids model-specific analytical derivations. We further show that, under standard convexity and linearity conditions, our objective recovers the full Pareto frontier of solutions. Empirically, we demonstrate our amortized approach across various datasets, causal queries, and sensitivity levels, where our approach achieves a test-time computation that is orders of magnitude faster than per-instance methods. To the best of our knowledge, ours is the first foundation model for in-context learning for causal sensitivity analysis.

In causal inference, confounders are variables that influence both treatment decisions and outcomes. However, unlike as in randomized clinical trials, the treatment assignment mechanism in observational studies is not known, and it is thus unclear which covariates act as confounders. Here, we aim to generate insight for causal inference and answer: which of the observed covariates act as confounders? We introduce ConfoundingSHAP, a Shapley-based method for attributing confounding strength to individual covariates. Our contributions are twofold. First, we propose a Shapley game targeted to infer the confounding strength of the covariates. Our resulting Shapley values differ from the standard applications of SHAP explanations on causal targets, such as understanding treatment effect heterogeneity, which are ill-suited for our task. Second, as our task requires evaluating the value function over many adjustment sets, we provide a scalable TabPFN-based estimation that avoids exhaustive refitting. We demonstrate the practical value across various datasets, where ConfoundingSHAP provides informative explanations of which observed covariates drive confounding and thereby helps to provide more insight for causal inference in practice.

Estimating counterfactual distributions under interventions is central to treatment risk assessment and counterfactual generation tasks. Existing approaches model the counterfactual distribution as a standalone generative target, without exploiting its relationship to the observational data. In this work, we show that under standard assumptions, observational and counterfactual outcome distributions are tightly linked: they have identical support and tail behavior, remain statistically close under weak confounding, and share any features of high-dimensional outcomes which are invariant to confounders. These properties motivate learning counterfactual distributions not from scratch, but via a deconfounding flow from the observational distribution. We formulate this problem via flow-matching and derive a semiparametrically efficient estimator based on a novel efficient influence function correction. We subsequently extend our estimator to target minimal-energy flows in high-dimensions, which we show can be especially simple targets between observational and counterfactual distributions. In experiments, deconfounding flows outperform existing debiased counterfactual distribution estimators, while also mitigating known failure modes of flow-based methods.

Existing interventional causal discovery methods -- IGSP, DCDI, ENCO -- assume causal sufficiency (no latent confounders) and rely on virtual interventions in synthetic simulators. In AI-for-Science settings such as molecular design and materials science, latent confounders are ubiquitous and real interventions (e.g., physics-based simulations) require hours to days per data point. We propose CFM-SD (Causal Flow Matching with Simulation Data), which uses first-principles physical simulators as do-operators in Pearl's interventional calculus to simultaneously handle latent confounders and real interventional data. Theoretically, $d$-variable causal structure is identifiable with $O(d)$ single-variable interventions -- the minimum under physical realizability constraints. In Intrinsic Evaluation on synthetic data ($γ=0.2$--$0.8$), CFM-SD achieves average F1$=0.800$ vs. F1$=0.127$--$0.562$ for all baselines. In Extrinsic Evaluation on real scientific data, CFM-SD achieves 57--58% bias reduction in molecular toxicity prediction and battery electrolyte optimization, demonstrating practical value beyond synthetic benchmarks.

Language-model (LM) surprisal is widely used as a proxy for contextual predictability and has been reported to correlate with metaphor novelty judgments. However, surprisal is tightly intertwined with lexical frequency. We explore this interaction on metaphor novelty ratings using two different word frequency measures. We analyse surprisal estimates from eight Pythia model sizes and 154 training checkpoints. Across settings, word frequency is a stronger predictor of metaphor novelty than surprisal. Across training stages, the surprisal--novelty association peaks at an early stage and then falls again, mirroring a similarly timed increase in the surprisal--frequency association. These results suggest that the often-reported optimal LM surprisal settings may incorrectly associate contextual predictability with metaphor novelty and processing difficulty, whereas lexical frequency may be the major underlying factor.

Despite extensive research into mitigating distribution shifts, many existing algorithms yield inconsistent performance, often failing to outperform baseline Empirical Risk Minimization (ERM) across diverse scenarios and necessitating newer algorithms which can handle scenarios where existing algorithms currently underperform. Furthermore, high algorithmic complexity frequently limits interpretability and offers only an indirect means of addressing spurious correlations. We propose eXplaining to Learn (eX2L): an interpretable, explanation-based framework that decorrelates confounding features from a classifier's latent representations during training. eX2L achieves this by penalizing the similarity between Grad-CAM activation maps generated by a primary label classifier and those from a concurrently trained confounder classifier. On the rigorous Spawrious Many-to-Many Hard Challenge synthetic data benchmark, eX2L achieves an average accuracy (AA) of 82.24% +/- 3.87% and a worst-group accuracy (WGA) of 66.31% +/- 8.73%, outperforming the current state-of-the-art (SOTA) by 5.49% and 10.90%, respectively. Beyond its competitive performance, eX2L demonstrates that functional domain invariance can be enforced by explicitly decoupling label and nuisance attributes at the group level.

In classification tasks, models may rely on confounding variables to achieve strong in-distribution performance, capturing spurious features that fail under distribution shift. This shortcut behavior leads to substantial degradation in out-of-distribution settings. Task arithmetic offers a potential solution by removing unwanted signals via subtraction of secondary model updates, but it typically requires full fine-tuning, which is computationally expensive. Prompt tuning provides a parameter-efficient alternative by adapting models through a small set of trainable virtual tokens. Task arithmetic on the resulting prompts presents an appealing alternative to operations on entire models, but the extent to which this approach can limit reliance on spurious features remains to be established. In this work, we study whether composing soft prompts through task arithmetic improves robustness to confounding shifts. We propose Hybrid Prompt Arithmetic (HyPA), which combines task prompts with linearized confounder prompts to counteract spurious correlations. Across multiple benchmarks, HyPA consistently improves the robustness-performance trade-off relative to prompt-arithmetic baselines under distribution shift. We further analyze how HyPA affects hidden representations and find evidence consistent with it mitigating confounding either by reducing the influence of confounder signals on predictions or by suppressing them in the representation. These results establish HyPA as a parameter-efficient and promising approach for improving robustness under confounding shifts in the evaluated setting.

Causal effect estimation from observational data requires careful adjustment for confounding. Classical estimators such as inverse probability weighting and augmented inverse probability weighting are effective under favorable model specification, but may become unstable when treatment assignment and outcome mechanisms are complex, non-linear, and high-dimensional. Machine learning and representation learning approaches improve flexibility, yet joint training can allow outcome-related information to influence treatment-side representations, which is undesirable from a causal perspective. We propose MOCA (Modular One-way Causal Attention), a transformer-based framework that separates treatment and outcome modeling through a modular design, and performs confounder adjustment using a one-way attention mechanism. A cutting-feedback strategy, implemented via gradient detachment, prevents the outcome loss from updating the treatment module. This design preserves directional information flow while retaining the representational power of transformer architectures for causal inference. Across multiple simulated scenarios, including linear, nonlinear, heavy-tailed, hidden confounding, and high-dimensional settings, MOCA shows competitive or improved performance relative to IPW, AIPW, X-learner, TARNet, and DragonNet. We further illustrate the method on the Infant Health and Development Program dataset and the Dehejia-Wahba dataset as real-world benchmarks. These results suggest that modular attention with one-way information flow provides a promising and interpretable direction for causal inference with modern deep learning models.

Cost-per-click (CPC) in paid search is an auction-generated outcome shaped by a competitive landscape that is only partially observable from any single advertiser's history. From 1.66 billion Google Ads log records for a concentrated car-rental market (2021-2023), we construct a weekly panel of 1,811 keyword series over 127 weeks (218,924 keyword-week observations) and build competition-aware proxies from keyword text, CPC trajectories, and geographic market structure. The design combines (i) semantic neighborhoods and a semantic keyword graph from pretrained transformer-based keyword representations, (ii) behavioral neighborhoods from Dynamic Time Warping (DTW) alignment of CPC trajectories, and (iii) geographic-intent covariates capturing localized demand and marketplace heterogeneity. We evaluate these signals both as exogenous covariates and as relational priors in spatiotemporal graph forecasters, benchmarking them against statistical, neural, and time-series foundation-model baselines. The results reveal a clear horizon crossover. At one week, graph-based models achieve the lowest error, reducing sMAPE by 15.1% relative to the strongest classical/ML baseline; at the six- and twelve-week horizons, covariate-augmented foundation models dominate, reducing sMAPE by 22.5% and 27.6%, respectively. The gains concentrate in the high-CPC, high-volatility keywords where forecasting errors are most costly. A falsification battery supports the competition interpretation at the planning horizon: the semantic competition graph outperforms a confounder-matched non-competitive graph by 4.05 sMAPE points, and matched-neighbour and time-shuffled controls show the six-week gains are competition-specific rather than generic smoothing. Together, the findings establish a horizon-dependent competition-aware forecasting design for auction-driven advertising markets under partial observability.

Conventional image denoising models often inadvertently learn spurious correlations between environmental factors and noise patterns. Moreover, due to high-frequency ambiguity, they struggle to reliably distinguish subtle textures from stochastic noise, resulting in over-removed details or residual noise artifacts. We therefore revisit denoising via causal intervention, arguing that purely correlational fitting entangles intrinsic content with extrinsic noise, which directly degrades robustness under distribution shifts. Motivated by this, we propose the Teacher-Guided Causal Disentanglement Network (TCD-Net), which explicitly decomposes the generative mechanism via structured interventions on feature spaces within a Vision Transformer framework. Specifically, our method integrates three key components: (1) An Environmental Bias Adjustment (EBA) module projects features into a stable, de-centered subspace to suppress global environmental bias (de-confounding). (2) A dual-branch disentanglement head employs an orthogonality constraint to force a strict separation between content and noise representations, preventing information leakage. (3) To resolve structural ambiguity, we leverage Nano Banana Pro, Google's reasoning-guided AI image generation model, to guide a causal prior, effectively pulling content representations back onto the natural-image manifold. Extensive experiments demonstrate that TCD-Net outperforms mainstream methods across multiple benchmarks in both fidelity and efficiency, achieving a real-time speed of 104.2 FPS on a single RTX 5090 GPU.

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (C-VAE) with a spatial prior, then estimates causal effects with a flexible outcome model. We show that this enables nonparametric identification of direct and spillover effects under weak assumptions--without multiple treatment types or a known latent-field model. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world environmental health and social science datasets. By turning local interference into a multi-cause proxy for latent spatial confounding, our framework advances robust causal inference for spatial data.

Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a ``source'' which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying DAG. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.

Large language models are being widely used across industries to generate text that contributes directly to key performance metrics, such as medication adherence in patient messaging and conversion rates in content generation. Pretrained models, however, often fall short when it comes to aligning with human preferences or optimizing for business objectives. As a result, fine-tuning with good-quality labeled data is essential to guide models to generate content that achieves better results. Controlled experiments, like A/B tests, can provide such data, but they are often expensive and come with significant engineering, logistical, and ethical challenges. Meanwhile, companies have access to a vast amount of historical (observational) data that remains underutilized. In this work, we study the challenges and opportunities of fine-tuning LLMs using observational data. We show that while observational outcomes can provide valuable supervision, directly fine-tuning models on such data can lead them to learn spurious correlations. We present empirical evidence of this issue using various real-world datasets and propose DeconfoundLM, a method that explicitly removes the effect of known confounders from reward signals. In simulation experiments, DeconfoundLM more accurately recovers causal relationships and mitigates failure modes of methods that assume counterfactual invariance, achieving over 16% higher objective score than ODIN and other baselines, when entangled confounding is present. Please refer to the project page for code and related resources.