Counterfactual Reasoning

Pearl's causal hierarchy shows that observational, interventional, and counterfactual queries are qualitatively distinct. We ask a quantitative version of this question: how many additional bits are needed to specify higher-rung causal answers once lower-rung answers are known? We formalize this via query-class description length, the Kolmogorov complexity of the answer oracle induced by an SCM for a class of queries. Our main construction gives binary acyclic SCMs whose observational distribution has constant description length, while the single-variable interventional answer oracle has description length $Θ(n^2)$. A degree-sensitive upper bound shows that finite-gate-schema SCMs of indegree $d$ have observational-interventional gap at most $O(nd \log(en/d) + n \log n)$, making the quadratic construction order-optimal in the dense regime and a rooted-tree construction order-optimal for bounded indegree. The quadratic separation persists under $\varepsilon$-accurate total-variation descriptions for every fixed $\varepsilon < 1/4$. At the next rung, the full hard-do interventional oracle can still leave a $Θ(n)$ counterfactual description gap. A general ambiguity-to-bits theorem and Shannon analogue show that these gaps equal the logarithm of residual higher-rung ambiguity up to lower-order terms.

Self-supervised learning methods learn high-quality visual representations, yet recent studies show that these representations often capture demographic biases present in the training data. Existing fairness-aware methods address this by redesigning the self-supervised objective itself, limiting portability across the rapidly evolving landscape of self-supervised learning (SSL) frameworks. We propose ProtoFair, a fairness-aware contrastive loss designed to work alongside existing SSL objectives without modifying them. ProtoFair leverages unsupervised prototype clustering to identify pseudo-counterfactual pairs: samples sharing the same cluster assignment but belonging to different sensitive groups. By pulling these content-matched, cross-group samples together in the embedding space, ProtoFair encourages the encoder to learn representations that are invariant to the sensitive attribute. The method requires only sensitive attribute annotations, no target labels, and integrates seamlessly with both SimCLR and SupCon. Experiments on CelebA and UTKFace demonstrate consistent fairness improvements while maintaining competitive accuracy.

The dominant noun-based modeling paradigm, grounded in probability theory and committed to pre-specified noun entities as primitive modeling units, is insufficient as a \emph{grammar of thought}: It leaves \emph{timing} outside the computational scope, precluding any adequate representation of the future as an open space of possibilities. This paper addresses three conceptual gaps absent from the existing literature: (1) possibility space -- a framework admitting multiple possible timelines for the same event; (2) timing computation -- the treatment of timing as a computable rather than observed dimension; and (3) causal factum -- the maximal causal efficacy recovered by reasoning backward from possible futures, rather than assumed in advance. Together, these definitions dissolve the confounding problem inherent to noun-based causal inference and provide the foundation for a spontaneously growing causal-reasoning world model. As proof of concept, we instantiate the framework and apply it to longitudinal EHR data from 3,276 breast cancer patients, demonstrating for the first time, to our knowledge, automatic trajectory discovery and counterfactual timing deduction (i.e., a What-If Machine) in a purely data-driven manner.

Counterfactual prompting (i.e., perturbing a single factor and measuring output change) is widely used to evaluate things like LLM bias and CoT faithfulness. But in this work we argue that observed effects cannot be attributed to the targeted factor without accounting for baseline ``meaning-preserving'' modifications to text that establish general model sensitivity. This is because every counterfactual edit is a compound treatment that bundles the variable of interest with incidental surface-form variation; this violates treatment variation irrelevance. We observe prediction flip rates on MedQA of 14.9% when we surgically change patient gender. However, this is statistically indistinguishable from the flip rates induced by simply paraphrasing inputs (14.1%). In this case, it would therefore be unwarranted to conclude that the LLM is especially sensitive to patient gender. To account for this and robustly measure the effects of targeted interventions, we propose a framework in which we compare (via statistical testing) differences observed under target interventions to those induced by paraphrasing inputs. We then use this framework to revisit a analysis done on the MedPerturb dataset, which reported evidence of model sensitivity to patient demographics and stylistic cues. We find that these effects largely dissipate when we account for general model sensitivity, with only 5 of 120 tests reaching statistical significance. Applying the same framework to occupational biography classification, we detect clearly significant directional gender bias, showing that the framework identifies real directional effects even when they are small. We evaluate a range of metrics -- aggregate, per-sample distributional, and regression -- and find that per-sample metrics are dramatically more powerful than aggregate metrics and regression powerfully and uniquely characterizes effect direction and magnitude.

Retrieval-Augmented Generation (RAG) models frequently produce answers grounded in parametric memory rather than the retrieved context, undermining the core promise of retrieval augmentation. A fundamental obstacle to fixing this unfaithfulness is the lack of training data that explicitly requires models to prefer context over internal knowledge. We introduce Faithfulness-QA, a large-scale dataset of 99,094 samples constructed through counterfactual entity substitution. Starting from two established extractive QA benchmarks--SQuAD and TriviaQA--we automatically identify answer-bearing named entities in each context, replace them with type-consistent alternatives drawn from a curated bank of 76,953 entities, and thereby manufacture controlled knowledge conflicts between context and parametric memory. Rigorous quality filtering ensures 100% pass rates across four automated checks on random 200-sample audits. We release the full dataset, the construction pipeline, and a typed entity bank covering eight named entity categories. Faithfulness-QA is designed as a training resource for attention-based faithfulness objectives and as an evaluation benchmark for measuring context-grounding behavior in RAG systems. Data and code are available at https://github.com/qzhangFDU/faithfulness-qa-dataset.

Single-arm trials accelerate study timelines by reducing the number of patients that must be recruited for a concurrent control group. However, these designs require an alternative comparator to estimate treatment effects. One approach is to construct a virtual control arm using a machine learning (ML) model trained on external control data to predict the counterfactual outcomes of the treatment arm. Our aim in this study was to leverage virtual controls by developing and evaluating ML-based counterfactual outcome models trained on IFX-treated patients to predict 1-year steroid-free clinical remission (SFCR ) and a composite of C-reactive protein remission plus steroid-free clinical remission (CRP-SFCR) for ADA-treated pediatric Crohn's disease patients, and to compare the resulting IFX-versus-ADA treatment effect estimates with those obtained using propensity score matching to external controls. Five ML models were used to train counterfactual models on the observed IFX cohort data. The resulting models were used to predict the counterfactual outcomes for the ADA arm patients. LGBM yields the best OR closest to the propensity score matched reference, and all 95% CI results align with the conclusion from the reference study that no statistical difference in the primary and secondary outcomes has been observed between the patients treated with ADA or IFX. Our study supports virtual controls as a viable and effective substitute for expensive, lengthy or unethical patient recruitment in an inflammatory bowel disease (IBD) trial. The developed gradient boosted prediction model can be used as a pretrained model to generate IFX counterfactual predictions in future studies, pending external validation and assessment of transportability.

Predicting the outcomes of prospective clinical trials remains a major challenge for large language models. Prior work has shown that both traditional correlational predictors, such as random forests and logistic regression, and strong commercial LLMs achieve limited performance on this task. In this paper, we propose DeepImagine, a framework for teaching LLMs biomedical reasoning through successive counterfactual imagining. The central idea is to approximate hidden causal mechanisms of clinical trials by training models to infer how observed trial results would change under controlled perturbations of experimental conditions, such as dosage, outcome measures, study arms, geography, and other trial attributes. To support this objective, we construct both natural and approximate counterfactual pairs from real clinical trials with reported outcomes. For settings where strict counterfactual supervision is available, such as paired outcome measures or dose-ranging study arms within the same trial, we train models with supervised fine-tuning. For broader settings where only approximate counterfactual pairs can be retrieved, we optimize models with reinforcement learning using verifiable rewards based on downstream benchmark correctness. We further augment training with synthetic reasoning traces that provide causally plausible explanations for local counterfactual transitions. Using this pipeline, we train language models under 10B parameters, including Qwen3.5-9B, and evaluate them on clinical trial outcome prediction. We aim to show that DeepImagine consistently improves over untuned language models and traditional correlational baselines. Finally, we aim to show that the learned reasoning trajectories provide interpretable signals about how models represent trial-level mechanisms, suggesting a practical path toward more mechanistic and scientifically useful biomedical language models.

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

Open-vocabulary scene graph generation (SGG) aims to describe visual scenes with flexible and fine-grained relation phrases beyond a fixed predicate vocabulary. While recent vision-language models greatly expand the semantic coverage of SGG, they also introduce a critical reliability issue: predicted relations may be driven by language priors or object co-occurrence rather than grounded visual evidence. In this paper, we propose an evidence-rounded open-vocabulary SGG framework based on counterfactual relation verification. Instead of directly accepting plausible relation proposals, our method verifies whether each candidate relation is supported by relation-pecific visual, geometric, and contextual evidence. Specifically, we first generate open-vocabulary relation candidates with a vision-language proposer, then decompose predicate phrases into soft evidence bases such as support, contact, containment, depth and state. A relation-conditioned evidence encoder extracts predicate-relevant cues, while a counterfactual verifier tests whether the relation score decreases when necessary vidence is removed and remains stable under irrelevant perturbations. We further introduce contradiction-aware predicate learning and graph-level preference optimization to improve fine-grained discrimination and global graph consistency. Experiments on conventional, open-vocabulary, and panoptic SGG benchmarks show that our method consistently improves standard recall-based metrics, unseen predicate generalization, and counterfactual grounding quality. These results demonstrate that moving from relation generation to relation verification leads to more reliable, interpretable, and evidence-grounded scene graphs.

Fair machine learning (ML) methods help identify and mitigate the risk that algorithms encode or automate social injustices. Algorithmic approaches alone cannot resolve structural inequalities, but they can support socio-technical decision systems by surfacing discriminatory biases, clarifying trade-offs, and enabling governance. Although fairness is well studied in supervised learning, many real ML applications are online and sequential, with prior decisions informing future ones. Each decision is taken under uncertainty due to unobserved counterfactuals and finite samples, with dire consequences for under-represented groups, systematically under-observed due to historical exclusion and selective feedback. A bank cannot know whether a denied loan would have been repaid, and may have less data on marginalized populations. This paper introduces a taxonomy of uncertainty in sequential decision-making -- model, feedback, and prediction uncertainty -- providing shared vocabulary for assessing systems where uncertainty is unevenly distributed across groups. We formalize model and feedback uncertainty via counterfactual logic and reinforcement learning, and illustrate harms to decision makers (unrealized gains/losses) and subjects (compounding exclusion, reduced access) of policies that ignore the unobserved space. Algorithmic examples show it is possible to reduce outcome variance for disadvantaged groups while preserving institutional objectives (e.g. expected utility). Experiments on data simulated with varying bias show how unequal uncertainty and selective feedback produce disparities, and how uncertainty-aware exploration alters fairness metrics. The framework equips practitioners to diagnose, audit, and govern fairness risks. Where uncertainty drives unfairness rather than incidental noise, accounting for it is essential to fair and effective decision-making.

Safety-critical traffic reasoning requires contrastive consistency: models must detect true hazards when an accident occurs, and reliably reject plausible-but-false hypotheses under near-identical counterfactual scenes. We present CCTVBench, a Contrastive Consistency Traffic VideoQA Benchmark built on paired real accident videos and world-model-generated counterfactual counterparts, together with minimally different, mutually exclusive hypothesis questions. CCTVBench enforces a single structured decision pattern over each video question quadruple and provides actionable diagnostics that decompose failures into positive omission, positive swap, negative hallucination, and mutual-exclusivity violation, while separating video versus question consistency. Experiments across open-source and proprietary video LLMs reveal a large and persistent gap between standard per-instance QA metrics and quadruple-level contrastive consistency, with unreliable none-of-the-above rejection as a key bottleneck. Finally, we introduce C-TCD, a contrastive decoding approach leveraging a semantically exclusive counterpart video as the contrast input at inference time, improving both instance-level QA and contrastive consistency.

Baseline estimation is critical to Demand Response (DR) settlement in electricity markets, yet existing machine learning methods remain limited in predictive performance, while methodologies from causal inference and counterfactual prediction are still underutilized in this domain. We introduce a Generalized Synthetic Control Method that builds on the classical Synthetic Control Method (SCM) from econometrics. While SCM provides a powerful framework for counterfactual estimation, classical SCM remains a static estimator: it fits the treated unit as a combination of contemporaneous donor units and therefore ignores predictable temporal structure in the residual error. We develop a generalized SCM framework that transforms baseline estimation into a dynamic counterfactual prediction problem by augmenting the donor representation with exogenous features, lagged treated load, and selected lagged donor signals. This enriched representation allows the estimator to capture autoregressive dependence, delayed donor-response patterns, and error-correction effects beyond the scope of standard SCM. The framework further accommodates nonlinear predictors when linear weighting is inadequate, with the greatest benefit arising in limited-data settings. Experiments on the Ausgrid smart-meter dataset show consistent improvements over classical SCM and strong benchmark methods, with the dominant performance gains driven by dynamic augmentation.

Simulating group-level user behavior enables scalable counterfactual evaluation of merchant strategies without costly online experiments. However, building a trustworthy simulator faces two structural challenges. First, information incompleteness causes reasoning-based simulators to over-rationalize when unobserved factors such as offline context and implicit habits are missing. Second, mechanism duality requires capturing both interpretable preferences and implicit statistical regularities, which no single paradigm achieves alone. We propose Policy-Guided Hybrid Simulation (PGHS), a dual-process framework that mines transferable decision policies from behavioral trajectories and uses them as a shared alignment layer. This layer anchors an LLM-based reasoning branch that prevents over-rationalization and an ML-based fitting branch that absorbs implicit regularities. Group-level predictions from both branches are fused for complementary correction. We deploy PGHS on Meituan with 101 merchants and over 26,000 trajectories. PGHS achieves a group simulation error of 8.80%, improving over the best reasoning-based and fitting-based baselines by 45.8% and 40.9% respectively.

Contextual bandit algorithms suffer from high regret during cold-start, when the learner has insufficient data to distinguish good arms from bad. We propose augmenting Disjoint LinUCB with LLM pseudo-observations: after each round, a large language model predicts counterfactual rewards for the unplayed arms, and these predictions are injected into the learner as weighted pseudo-observations. The injection weight is controlled by a calibration-gated decay schedule that tracks the LLM's prediction accuracy on played arms via an exponential moving average; high calibration error suppresses the LLM's influence, while accurate predictions receive higher weight during the critical early rounds. We evaluate on two contextual bandit environments - UCI Mushroom (2-arm, asymmetric rewards) and MIND-small (5-arm news recommendation) - and find that when equipped with a task-specific prompt, LLM pseudo-observations reduce cumulative regret by 19% on MIND relative to pure LinUCB. However, generic counterfactual prompt framing increases regret on both environments, demonstrating that prompt design is the dominant factor, more important than the choice of decay schedule or calibration gating parameters. We analyze the failure modes of calibration gating on domains with small prediction errors and provide a theoretical motivation for the bias-variance trade-off governing pseudo-observation weight.

LLM-empowered agent simulations are increasingly used to study social emergence, yet the micro-to-macro causal mechanisms behind macro outcomes often remain unclear. This is challenging because emergence arises from intertwined agent interactions and meso-level feedback and nonlinearity, making generative mechanisms hard to disentangle. To this end, we introduce \textbf{\textsc{CAMO}}, an automated \textbf{Ca}usal discovery framework from \textbf{M}icr\textbf{o} behaviors to \textbf{M}acr\textbf{o} Emergence in LLM agent simulations. \textsc{CAMO} converts mechanistic hypotheses into computable factors grounded in simulation records and learns a compact causal representation centered on an emergent target $Y$. \textsc{CAMO} outputs a computable Markov boundary and a minimal upstream explanatory subgraph, yielding interpretable causal chains and actionable intervention levers. It also uses simulator-internal counterfactual probing to orient ambiguous edges and revise hypotheses when evidence contradicts the current view. Experiments across four emergent settings demonstrate the promise of \textsc{CAMO}.

Counterfactual explanations (CE) explain model decisions by identifying input modifications that lead to different predictions. Most existing methods operate at the instance level. Distributional Counterfactual Explanations (DCE) extend this setting by optimizing an optimal transport objective that balances proximity to a factual input distribution and alignment to a target output distribution, with statistical certification via chance constrained bounds. However, DCE relies on gradient based optimization, while many real-world tabular pipelines are dominated by non-differentiable models. We propose DISCOVER, a model-agnostic solver for distributional counterfactual explanations. DISCOVER preserves the original DCE objective and certification while replacing gradient descent with a budgeted propose-and-select search paradigm. It exploits a sample-wise decomposition of the transport objective to compute per-row impact scores and enforce a top-k intervention budget, focusing edits on the most influential samples. To guide candidate generation without predictor gradients, DISCOVER introduces an OT-guided cone sampling primitive driven by input-side transport geometry. Experiments on multiple tabular datasets demonstrate strong joint alignment of input and output distributions, extending distributional counterfactual reasoning to modern black box learning pipelines. A code repository is available at: https://github.com/VALHALLA9/Discover.

Large Vision-Language Models (LVLMs) have grown increasingly powerful in recent years, but can also exhibit harmful biases. Prior studies investigating such biases have primarily focused on demographic traits related to the visual characteristics of a person depicted in an image, such as their race or gender. This has left biases related to cultural differences (e.g., religion, socioeconomic status), which cannot be readily discerned from an individual's appearance alone, relatively understudied. A key challenge in measuring cultural biases is that determining which group an individual belongs to often depends upon cultural context cues in images, and datasets annotated with cultural context cues are lacking. To address this gap, we introduce Cultural Counterfactuals: a high-quality synthetic dataset containing nearly 60k counterfactual images for measuring cultural biases related to religion, nationality, and socioeconomic status. To ensure that cultural contexts are accurately depicted, we generate our dataset using an image-editing model to place people of different demographics into real cultural context images. This enables the construction of counterfactual image sets which depict the same person in multiple different contexts, allowing for precise measurement of the impact that cultural context differences have on LVLM outputs. We demonstrate the utility of Cultural Counterfactuals for quantifying cultural biases in popular LVLMs.

Vision-Language-Action models (VLAs) promise to ground language instructions in robot control, yet in practice often fail to faithfully follow language. When presented with instructions that lack strong scene-specific supervision, VLAs suffer from counterfactual failures: they act based on vision shortcuts induced by dataset biases, repeatedly executing well-learned behaviors and selecting objects frequently seen during training regardless of language intent. To systematically study it, we introduce LIBERO-CF, the first counterfactual benchmark for VLAs that evaluates language following capability by assigning alternative instructions under visually plausible LIBERO layouts. Our evaluation reveals that counterfactual failures are prevalent yet underexplored across state-of-the-art VLAs. We propose Counterfactual Action Guidance (CAG), a simple yet effective dual-branch inference scheme that explicitly regularizes language conditioning in VLAs. CAG combines a standard VLA policy with a language-unconditioned Vision-Action (VA) module, enabling counterfactual comparison during action selection. This design reduces reliance on visual shortcuts, improves robustness on under-observed tasks, and requires neither additional demonstrations nor modifications to existing architectures or pretrained models. Extensive experiments demonstrate its plug-and-play integration across diverse VLAs and consistent improvements. For example, on LIBERO-CF, CAG improves $π_{0.5}$ by 9.7% in language following accuracy and 3.6% in task success on under-observed tasks using a training-free strategy, with further gains of 15.5% and 8.5%, respectively, when paired with a VA model. In real-world evaluations, CAG reduces counterfactual failures of 9.4% and improves task success by 17.2% on average.

Counterfactual explanations (CFEs) provide human-centric interpretability by identifying the minimal, actionable changes required to alter a machine learning model's prediction. Therefore, CFs can be used as (i) interventions for abnormality prevention and (ii) augmented data for training robust models. We conduct a comprehensive evaluation of CF generation using large language models (LLMs), including GPT-4 (zero-shot and few-shot) and two open-source models-BioMistral-7B and LLaMA-3.1-8B, in both pretrained and fine-tuned configurations. Using the multimodal AI-READI clinical dataset, we assess CFs across three dimensions: intervention quality, feature diversity, and augmentation effectiveness. Fine-tuned LLMs, particularly LLaMA-3.1-8B, produce CFs with high plausibility (up to 99%), strong validity (up to 0.99), and realistic, behaviorally modifiable feature adjustments. When used for data augmentation under controlled label-scarcity settings, LLM-generated CFs substantially restore classifier performance, yielding an average 20% F1 recovery across three scarcity scenarios. Compared with optimization-based baselines such as DiCE, CFNOW, and NICE, LLMs offer a flexible, model-agnostic approach that generates more clinically actionable and semantically coherent counterfactuals. Overall, this work demonstrates the promise of LLM-driven counterfactuals for both interpretable intervention design and data-efficient model training in sensor-based digital health. Impact: SenseCF fine-tunes an LLM to generate valid, representative counterfactual explanations and supplement minority class in an imbalanced dataset for improving model training and boosting model robustness and predictive performance

Early lane-change intention prediction is essential for autonomous driving and ADAS, but it remains challenging because lane-changing behavior depends on evolving traffic risk, surrounding-vehicle interactions, and target-lane feasibility rather than only instantaneous vehicle states. This study proposes an evolutionary physics-informed temporal fusion framework for three-class lane-change intention prediction, including left lane change, right lane change, and no lane change. Instead of using static physics-informed variables alone, the proposed method derives temporal descriptors from conventional traffic signals, including risk evolution, gap persistence, counterfactual lane utility, interaction pressure gradient, maneuver feasibility, and intent consistency. These descriptors are fused with temporal embeddings learned from raw trajectory sequences through a sequence encoder, and the fused representation is used for final classification. Experiments are conducted on the highD and exiD datasets under 1,s, 2,s, and 3,s prediction horizons. The proposed model achieves Macro F1-scores of 0.9514, 0.9256, and 0.8872 on highD, and 0.9386, 0.9070, and 0.8531 on exiD, respectively. The improvement is especially pronounced in exiD ramp-adjacent scenarios, indicating that temporal physical evolution is particularly useful in interaction-rich environments. These results demonstrate that combining evolutionary physics-informed descriptors with learned temporal representations provides a more dynamic and interpretable solution for early lane-change intention prediction.

Brain tumors induce complex structural deformations that obscure the patient' s original neuroanatomy, making it difficult to distinguish tumor-induced changes from inherent anatomical variability. Reconstructing a subject-specific pseudo-healthy brain can provide a critical reference for such analysis, but this task is inherently counterfactual, as paired pre-tumor scans and explicit healthy guidance are unavailable. We propose BrainNormalizer, a diffusion-based framework for subject-specific pseudo-healthy brain MRI reconstruction that enables anatomy-informed reconstruction without requiring paired data or explicit healthy references. The framework learns anatomical priors and edge-based structural conditioning through a two-stage training strategy consisting of inpainting-based diffusion fine-tuning and ControlNet-based edge conditioning. At inference, counterfactual pseudo-healthy reconstruction is achieved through a deliberate misalignment strategy, where tumorous inputs are paired with non-tumorous prompts and mirrored contralateral edge maps. This allows subject-specific anatomical guidance to be constructed from the patient's own anatomy, enabling anatomically consistent pseudo-healthy reconstruction that preserves individual structural characteristics. Experiments on the BraTS2020 dataset demonstrate that BrainNormalizer achieves improved distributional realism, symmetry-based structural consistency, and reduced false positive detection compared to existing methods. These results indicate that the proposed framework provides a principled approach for subject-specific counterfactual reconstruction and supports downstream analysis of tumor-induced deformation.

Large language models (LLMs) are now widely deployed in user-facing applications, reaching hundreds of millions of users worldwide. Despite their widespread adoption, growing reliance on their outputs raises significant concerns, particularly as users may be exposed to model-inherent biases that disadvantage or stereotype certain groups. However, existing bias benchmarks commonly rely on simple templated prompts or restrictive multiple-choice questions that fail to capture the complexity of real-world user interactions. In this work, we address this gap by introducing a counterfactual framework that automatically generates realistic, open-ended questions for LLM bias evaluation. Through iterative question mutation, our approach systematically explores areas where models are most likely to exhibit biased behavior. Beyond just detecting harmful biases, we also capture increasingly relevant response dimensions, such as asymmetric refusals and explicit bias acknowledgment. Building on this, we construct CAB, a diverse and human-verified benchmark for realistic and nuanced bias evaluations on current frontier LLMs. Our evaluation using CAB highlights the continued need for fairness research by showing that all examined models exhibit persistent biases across certain scenarios.

Large language models (LLMs) have transformed natural language processing (NLP), enabling diverse applications by integrating large-scale pre-trained knowledge. However, their static knowledge limits dynamic reasoning over external information, especially in knowledge-intensive domains. Retrieval-Augmented Generation (RAG) addresses this challenge by combining retrieval mechanisms with generative modeling to improve contextual understanding. Traditional RAG systems suffer from disrupted contextual integrity due to text chunking and over-reliance on semantic similarity for retrieval, often resulting in shallow and less accurate responses. We propose Causal-Counterfactual RAG, a novel framework that integrates explicit causal graphs representing cause-effect relationships into the retrieval process and incorporates counterfactual reasoning grounded on the causal structure. Unlike conventional methods, our framework evaluates not only direct causal evidence but also the counterfactuality of associated causes, combining results from both to generate more robust, accurate, and interpretable answers. By leveraging causal pathways and associated hypothetical scenarios, Causal-Counterfactual RAG preserves contextual coherence, reduces hallucination, and enhances reasoning fidelity.

We study operator relevance in data-driven partial differential equation (PDE) discovery. Sparse residual methods can select terms that improve residual fit, but residual contribution is not the same as functional necessity. We formalize this distinction through counterfactual operator interventions, where a candidate term is deleted or perturbed and the factual and intervened trajectories, or observables, are compared. The resulting theory gives six reusable results. A residual--counterfactual gap theorem shows that deletion effects are governed by the inverse linearized PDE map, not by residual magnitude alone. A certified decision theorem gives error margins for relevance, irrelevance, and abstention under neural or numerical surrogate error. An aliasing theorem characterizes experiment-dependent non-identifiability through the null space of the operator-evaluation design. A constraint-manifold theorem shows that operators vanishing on invariant constraint classes cannot be identified from trajectories restricted to those classes. A pruning-consistency theorem proves that sparse screening followed by counterfactual deletion recovers the functionally relevant support under a recall and margin condition. An observable-level adjoint theorem extends relevance testing from full-state deviations to scientific quantities of interest. Validation experiments test these mechanisms on synthetic PDEs with known support and on public geophysical fields from atmospheric reanalysis and NOAA OISST. The real-data results are reported as operator-surrogate diagnostics, not as unconditional recovery of physical laws. The framework provides a rigorous diagnostic layer for distinguishing residual usefulness from counterfactual operator relevance within a specified library, experiment class, norm, and tolerance.

We study counterfactual regression, which maps features to outcomes under hypothetical scenarios that differ from those observed in the data. This problem is central to decision-making under distribution shift, where treatment patterns may change at deployment. We develop a semiparametric framework for counterfactual regression along a prespecified incremental-intervention path. The target is a finite-dimensional constrained projection of counterfactual risk, estimated using cross-fitted influence-function representations of the program components. For smooth programs with fixed constraints and finite-dimensional programs with estimated linear constraints, we establish consistency and local stability of the optimizer under class-specific conditions, and derive pointwise and uniform first-order expansions. These results yield asymptotically valid inference, including simultaneous confidence bands for the counterfactual regression path. Simulations and an application to SMS reminders illustrate the finite-sample performance and practical applicability of the proposed approach.

When asked to explain their decisions, LLMs can often give explanations which sound plausible to humans. But are these explanations faithful, i.e. do they convey the factors actually responsible for the decision? In this work, we analyse counterfactual faithfulness across 75 models from 13 families. We analyze the tradeoff between conciseness and comprehensiveness, how correlational faithfulness metrics assess this tradeoff, and the extent to which metrics can be gamed. This analysis motivates two new metrics: the phi-CCT, a simplified variant of the Correlational Counterfactual Test (CCT) which avoids the need for token probabilities while explaining most of the variance of the original test; and F-AUROC, which eliminates sensitivity to imbalanced intervention distributions and captures a model's ability to produce explanations with different levels of detail. Our findings reveal a clear scaling trend: larger and more capable models are consistently more faithful on all metrics we consider. Our code is available at https://github.com/google-deepmind/corr_faith.

Churn models typically identify high-risk customers but do not specify which feasible retention action should be considered or why that action is appropriate. We present CARRE (Counterfactual Action Retrieval and Reason Evaluation), a three-stage framework that combines retrieval-augmented candidate generation, cost-aware counterfactual scoring, and large language model (LLM) reasoning. CARRE retrieves a predefined catalog of retention actions, estimates model-predicted churn-risk changes under explicit feature transformations, and generates a structured churn reason and a profile-grounded explanation for the selected action. On the IBM Telco Customer Churn dataset, CARRE achieves 79.8% greater mean model-predicted risk reduction than the plain SHAP baseline and 80.4% greater reduction than the cost-controlled SHAP+Cost baseline across 313 high-risk test cases; its cost-normalized efficiency is 10.5% higher than that of plain SHAP. On a 136-case reason-stratified evaluation sample, diagnosis-driven prompt refinement increases weak-label agreement from 79.4% to 90.4%, with no auxiliary-plan constraint violations; because the same sample was used for error diagnosis and re-evaluation, the post-refinement result is not an independent estimate of generalization. For 135 explanations generated using the pre-refinement v2 reason outputs, two cross-vendor LLM judges assign mean scores ranging from 4.02 to 5.00 out of 5, although one judge saturates on actionability, and a deterministic audit finds no contradictions among 66 verifiable profile claims. Retrieval ablations show that k=5 provides the best evaluated compromise between high candidate coverage and downstream reasoning agreement in this dataset. These results illustrate how retrieval, model-based counterfactual scoring, and language generation can be separated and jointly evaluated in a prototype churn-prescription pipeline.