Counterfactual Reasoning

Multimodal classification typically assumes all modalities are available, yet real-world inputs are often incomplete. Imputation and dynamic fusion can mitigate such incompleteness, but existing methods operate at a coarse modality level and thus cannot retain reliable components while suppressing misleading ones within the same recovered modality, compromising prediction reliability. To address this issue, we propose GAUGE, a lightweight counterfactual gating framework for incomplete multimodal classification. GAUGE first imputes missing modalities with a frozen imputer and encodes observed and recovered inputs uniformly as fine-grained evidence units. Rather than intervening on each unit explicitly, GAUGE scores the counterfactual effect of replacing every unit with a reference representation through prediction-aware Taylor evidence scores, all obtained in a single forward-backward pass. These scores are mapped to continuous gates, which are converted into additive attention-logit biases for unit-wise evidence modulation without altering the backbone architecture. Experiments across six benchmarks demonstrate that GAUGE outperforms strong baselines across diverse incomplete-input settings. Furthermore, a Taylor remainder theoretical analysis characterizes the error of the first-order approximation relative to the exact counterfactual effect, establishing GAUGE as a principled and scalable framework for fine-grained evidence control under modality incompleteness.

Current Multimodal Large Language Models (MLLMs) can process diverse sensory inputs, yet their reasoning remains heavily biased toward a dominant modality, resulting in brittle cross-modal reasoning. We introduce C$^3$PO, a benchmark of 3,404 samples spanning video, audio, image, and text, evaluating two abilities: information composition (fusing dispersed evidence) and counterfactual conflict (resolving deliberate contradictions). C$^3$PO's paired IC/CC structure and four-tier design enable targeted diagnosis of when and why cross-modal reasoning fails. Built through a fully automatic pipeline using 25 logically grounded templates, C$^3$PO reveals that while humans achieve 88.64% accuracy, the best model (Gemini-3.1-Pro) reaches only 73.17%, with open-source models collapsing under conflict. Through attention probes, we find 86-95% of failures stem from modality dominance: models commit to one modality while ignoring contradictory evidence, concentrating 87-95% of attention on text. Mid-layer attention entropy predicts correctness-sustained exploration succeeds, premature collapse fails. The 56-point accuracy gap between equally complex templates reveals that performance depends on modalities' structural roles in conflict resolution, not combinations. These findings show multimodal perception does not guarantee robust reasoning; architectures must enable sustained cross-modal attention to avoid premature

Counterfactual analysis aims to predict potential outcomes under hypothetical scenarios, offering valuable insights for decision-making. This paper investigates the application of large language models (LLMs), specifically the GPT-3.5 model, for counterfactual analysis. We focus on the online lending context, where the counterfactual return on investment (ROI) is crucial for evaluating different interest rate schemes. We begin by assessing the predictive performance of GPT and comparing it with advanced machine learning algorithms. The results show that prompt engineering can significantly enhance GPT's predictions, with the R-squared increasing from 1.97% to 2.84%, closely approaching the 3.48% achieved by gradient-boosted regression. Subsequently, we utilize GPT to generate counterfactual ROIs under a set of alternative interest rates. GPT exhibits logical coherence and causal reasoning in its responses. The findings underscore the potential of LLMs as effective tools for counterfactual analysis in online lending, suggesting broader applications for LLMs in various predictive and decision-making contexts.

Oscillatory signals, such as vibration, carry class-discriminative information in specific frequency bands; perturbing them in raw feature space for counterfactual analysis easily destroys their temporal structure and produces physically implausible results. In this work, we introduce IMFACT (IMF-based counterfACTuals), a model-agnostic framework for generating plausible counterfactual explanations for time series classifiers that operates in the decomposition space of Empirical Mode Decomposition. An input signal is split into Intrinsic Mode Functions (IMFs), and selected IMFs are progressively substituted with those of a Nearest Unlike Neighbour (NUN) until the classifier flips to the target class. We evaluate six IMF-selection strategies and a multi-NUN cycling extension on two UCR benchmarks (FaultDetectionA, FruitFlies). The variance-based strategy with three NUNs outperforms two prominent baseline techniques on reliability and plausibility metrics, while cycling across three NUNs yields the best proximity across both datasets.

Algorithmic recourse seeks to help individuals reverse unfavorable automated decisions by recommending actionable changes that achieve a desired outcome. As an individual usually has several distinct routes to a favorable decision, and different people can act on different ones, a recourse system should offer multiple realistic alternatives rather than one. Existing approaches formulate recourse as an optimization problem that constructs one or a small set of counterfactuals rather than modeling the underlying space of feasible solutions, and in practice each sacrifices diversity, plausibility, or feasibility to secure the others. We propose Tractable Recourse Distributions, a probabilistic framework that represents the space of feasible alternatives for a given factual instance as a probability distribution over favorable outcomes. For commonly used cost functions based on proximity and the number of feature changes, we show that this distribution admits an exact representation as a probabilistic circuit, obtained by exponentially tilting the circuit; each individual's distribution is therefore available in closed form, without retraining the model. Sampling from these distributions naturally produces diverse and plausible recourses, while the tilting parameters provide explicit control over their proximity and sparsity. Experiments on standard algorithmic recourse benchmark datasets demonstrate that the proposed framework attains diversity, plausibility, and feasibility simultaneously, while retaining sufficient probability mass over feasible counterfactuals for rejection sampling to be practical. A visual study on MNIST illustrates how the tilt strength trades proximity against validity.

On-policy distillation (OPD) supervises student-visited trajectories, yet divergence-based rules cannot determine whether an erroneous prefix remains correctable. We formulate this decision as counterfactual recoverability and replay each error state through budget-matched teacher-continuation and rollback branches. Based on their relative success, states are categorized as recoverable, irreversible-but-avoidable, or ambiguous, and these labels guide whether training retains, rolls back, or conventionally supervises the corresponding trajectory. On AIME branch diagnostics, the mean continuation-minus-rollback effect is 0.185 for recoverable states and -1.000 for irreversible-but-avoidable states, demonstrating opposite intervention preferences. A branch-derived recoverability proxy achieves an AUC of 1.000, substantially outperforming divergence alone at 0.392. Across frozen evaluations, recoverability-aware control achieves the strongest recorded performance, reaching 0.578 success on held-out AIME2025 compared with 0.517 for the best baseline. It also improves AIME2024-2025 average@32 from 0.2656 to 0.3125 and GPQA-Diamond average@32 from 0.2702 to 0.3070. Component ablations further show that retaining teacher-correctable prefixes provides the largest individual contribution. These findings establish recoverability as an outcome-grounded decision variable for selective supervision in OPD.

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.

Multimodal large language models (MLLMs) make grounded predictions in real-world scenes by combining visual and textual cues, yet existing benchmarks rarely reveal how they arbitrate between these evidence sources when they conflict. We introduce SIGNPOST-Bench, a controlled counterfactual benchmark for evaluating text-vision conflict resolution. Each source image is transformed into a counterfactual quintuplet of Original, Blank, Similar, Random, and Adversarial variants. Synthetic, localized scene-text interventions are designed to preserve non-textual content, enabling paired measurements of changes in localization performance and directed shifts toward geographic targets introduced by conflicting text. SIGNPOST-Bench contains 5,111 counterfactual groups and 25,555 image variants from four datasets. We evaluate 20 MLLMs from seven providers. Compared with Original images, Adversarial variants raise median localization error from 282 km to 1,347 km, a 4.8-fold increase. Among geocodable adversarial samples, 6.5-20.1% of predictions lie less than 50 km from the injected target across models, and every evaluated model exhibits a positive mean paired reduction in target distance from Blank to Adversarial. Compatible, unrelated, and conflicting text replacements produce distinct effects on model predictions, while clean-input localization performance does not fully predict robustness to conflicting text. These results establish visual geolocation as a continuous diagnostic of scene-text arbitration and provide a controlled framework for evaluating how MLLMs resolve conflicting multimodal evidence.

Large language models (LLMs), and the agents built on top of them, are now benchmarked heavily on whether they can finish a task -- fix a bug, drive a browser, operate a GUI. A complementary social ability, namely how well a model understands and forecasts the way real social events unfold, has barely been measured. We introduce SocietyBench, an end-to-end benchmark that takes a one-line event topic, collects Web news and social-media posts across five platforms, distills them into a date-indexed timeline that keeps factual events and a public-opinion layer separate, and then turns every cutoff date on that timeline into an audited bank of forecasting questions. Questions are scored on two orthogonal 100-point axes: probability calibration and temporal accuracy. Before any model sees a timeline, a three-phase procedure replaces every named entity and shifts every date by a per-event constant, turning a real arc into a counterfactual social world -- structurally identical to what happened, but stripped of the surface labels a model could match against pre-training memory. On five heterogeneous events and 125 prediction points in Chinese and English editions, the strongest of six frontier LLMs reaches only 75.0 out of 100, against a trivial anchor of 50. The two axes come apart: a model can be calibration-strong but time-weak, or the reverse. Three agent frameworks built on a shared base model fail to improve on that base, and two model-free heuristics trail every LLM. Per-event gaps reach 21.4 points on a single axis, which is our main argument for evaluating on several events rather than one. All anonymized timelines, question banks, ground truth, and scoring code are released.

Causal diagnostic models must explain how conclusions follow from evidence because diagnoses guide repairs and treatments. Yet serious cases are scarce, records rarely contain reasoning paths, and data transfer poorly across configurations, complicating local deployment. We present DiagLoop, a counterfactual data flywheel that converts codified physical relations or clinical guidelines, authored once per mechanism family, into training supervision beyond recorded cases. A training-only teacher proposes counterfactual worlds by varying causes, contexts, and observations, while an independent hybrid checker admits only valid worlds. The student reasons through symptom abstraction, causal-chain construction, and root-cause attribution. Stage-specific criteria identify its earliest failure. For nonterminal failures, a bounded repair probes downstream competence, and the resulting weakness profile guides subsequent data generation. Stage-localized reinforcement learning updates only the model-generated continuation, while replay and preservation reduce forgetting. The same criteria govern admission, attribution, reward, and regeneration through checks separate from the proposer. Using only synthesized scenarios and no case-level expert reasoning annotations, the resulting 8B model improves strict path correctness over the strongest conventional baseline. Gains are 11.6 points across eight industrial systems and 5.5 points across ten disease categories. Gains over a deranged-routing control are 3.9 and 2.3 points, respectively. The model also exceeds the evaluated proprietary references in both domains, even when they receive few-shot examples or the specification in context.

Applying a valid medication-safety rule when its patient-specific conditions are not met can produce an incorrect decision. Existing medical evaluations largely use isolated and fixed scenarios. A model may therefore answer correctly by recalling a drug-risk association without showing that it used patient information to decide whether the rule applies. To address this gap, we introduce MedPIC-Bench, a benchmark of source-verifiable recommendations and expert-validated questions for patient-specific medication-safety reasoning. It combines guideline-following questions with paired counterfactual questions in which a controlled change in patient information changes whether a rule applies. The benchmark contains 467 questions annotated along six clinical and reasoning dimensions. Across 28 medical-specific, general, and proprietary LLMs, every model performs worse on counterfactual questions, with mean accuracy falling from 63.6% to 45.1%. Models perform well when an explicit patient attribute directly signals a familiar contraindication, but struggle when patient information must narrow or withdraw a safety warning. Model rationales often acknowledge the changed patient information, yet the final answers retain the previous safety judgment. This vulnerability persists among medical-specific LLMs, whose average CF performance trails that of general LLMs. MedPIC-Bench therefore makes conditional rule application measurable and highlights the limitations of static medication-safety accuracy for assessing patient-specific reliability.

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

Reflection is a powerful mechanism for LLM reasoning, yet its effectiveness hinges on accurately attributing failures to specific reasoning steps, a capability that current models notably lack. Existing failure attribution methods either require expensive step-by-step counterfactual testing that scales poorly with trajectory length, or treat reasoning traces as flat sequences that ignore the inherent non-linear logical dependencies. We propose a hypergraph-based paired failure attribution (HPFA) framework that attributes the failure root cause by comparing the hyperedges of the targeted failure reasoning path against a reference successful path. By reducing the search space, our method efficiently localizes root causes and enables scalable synthesis of attribution data for training a lightweight attributor model via supervised fine-tuning and reinforcement learning. Experiments on mathematical reasoning and agentic coding tasks demonstrate that HPFA can dramatically increase attribution accuracy and efficiency, and the trained attributor consistently improves reasoning accuracy at test time, outperforming baselines that lack graph structure or paired analysis.

Fixed-layout indoor furniture styling requires selecting assets that form a coherent room without changing the prescribed furniture categories, positions, orientations, or scales. Existing approaches typically retrieve each asset independently or rely on static local relations, making them prone to shape, material, and color conflicts after scene composition. We introduce StyleForge, a scene-level structured selection framework built on a dynamic hypergraph style field. A frozen multimodal large language model extracts structured style priors from an open-ended style request and the fixed layout, while StyleForge maintains a learnable candidate distribution for each furniture slot. Conditioned on the target style, the dynamic hypergraph style field adaptively activates and weights layout-induced hyperedges to capture higher-order dependencies among furniture. Counterfactual style preference learning then treats each candidate as a local substitution in the current style field and evaluates its contextual compatibility using Mahalanobis energies. Training alternates between optimizing the style field and the candidate logits. At inference, the model remains frozen and test-time training updates only room-specific candidate logits, progressively correcting cross-slot style conflicts as the global scene context evolves. Experiments on 3D-FRONT demonstrate state-of-the-art furniture retrieval and scene-level style coherence, producing more coherent fixed-layout furniture arrangements than object- and scene-level retrieval baselines.

Sparse attention is widely deployed in long-context serving stacks, yet no framework audits how discarding blocks changes the influence of specific content on model output. We first establish that the phenomenon is real and causal: Block Sparse Flash Attention (BSFA) route replay across four architectures changes output decisions in 13 of 16 cells, with zero identity-replay label flips. We then introduce a dense-calibrated counterfactual audit using matched probe cards---Gold (carrying the correct answer label), Poison (carrying a target wrong label), and Benign (filler only)---under six-layout position symmetry, isolating the sparsification-specific effect. Two patterns compete. Signal concentration: the selector preserves Gold and Poison blocks far above filler-matched Benign blocks (G$\approx$P$\gg$B across all model--task pairs). Integration loss: discarding blocks severs cross-block attention---confirmed by an ablation where isolating the probe block collapses its influence from 4.48 logits to zero. Compression ratio governs the balance: a full sweep from mild ($c=0.25$) to aggressive ($c=0.75$) compression across four model--task pairs reveals that three of four cells move toward stronger sparse amplification at higher compression, with two exhibiting sign reversals. Three independent arms---BSFA route replay, controlled block-top-$k$, and KV-cache eviction---converge: sparsification changes content influence in ways aggregate accuracy cannot detect. We provide an open measurement framework deployable on any model exposing block identities.

Symbolic alpha factor discovery can score a completed expression, but it provides no direct label for the structural decisions that produced it. Generative flow networks (GFlowNets) preserve a diverse, reward-proportional distribution over complete expressions, yet their trajectory-level objective does not compare unchosen sibling actions at an intermediate state. We introduce AlphaG-OPD, a structural on-policy distillation framework that turns terminal factor evaluations into local action guidance. Its design separates three decisions. Component I determines where to teach by exposing grammar-valid siblings at partial abstract-syntax-tree (AST) states visited by the current forward policy. Component II determines what is reliable enough to teach: it evaluates three supported siblings under four shared suffixes and admits a KL-bounded target only when their matched comparisons exhibit sufficient winner agreement and a positive empirical lower confidence bound (LCB). Component III determines how strongly and for how long to teach by consolidating accepted targets through bounded replay, score-indexed expiry, and forward-gradient balancing, without additional factor evaluations. Terminal reward, Trajectory Balance, the backward policy, grammar, and factor-pool rules remain unchanged. An equal-physical-score four-arm ablation tests paired teaching, reliability gating, and consolidation. Across China's CSI300, CSI500, and CSI1000 and the U.S. S&P 500, the complete method delivers strong cross-market performance over multiple random seeds.

Reinforcement-learning-based quantum architecture search (RL-QAS) repeatedly optimizes a variational quantum eigensolver (VQE) after extending a circuit, although circuit construction and action legality are deterministic and known. We introduce DreamQAS, a model-based RL framework that preserves these exact circuit dynamics and learns only the expensive post-VQE feedback. A recurrent randomized-prior ensemble predicts an oracle-free score relative to an empirical energy frontier and supports multi-step imagined policy learning over explicit legal circuits. Ranking-based activation, uncertainty-aware pessimism and truncation, and selective real-VQE verification form a reliability-controlled learning loop. Under a common 15,000-episode budget and frozen evaluation for the RL methods, DreamQAS has the lowest mean frozen-policy energy error on four of five molecular tasks and the second-lowest on one. At fine-error targets reached by all seeds of both methods, it uses 1.6x to 2.0x fewer real VQE calls on four tasks and 10.6x fewer on BeH2-8q. Counterfactual action-ranking utility increases across all five tasks, with a mean increase of 0.346 and a 95 percent confidence interval of [0.185, 0.507], while direct greedy and beam use of the same model does not recover the gains of imagined policy learning. Ensemble disagreement also improves risk-coverage over random rejection on all three probed tasks. These results establish a world-model design for QAS whose value lies in decision-useful feedback rather than exact energy prediction.

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by identifying the smallest change to an input required to obtain a desired output. Although CEs are conventionally formulated as a distance-minimization problem, the theoretical basis of this formulation has received limited attention. We show that a distance-minimization-based CE is mathematically equivalent to the maximum a posteriori (MAP) estimate of a Gibbs posterior within the generalized Bayes framework, specifically when a distance-based prior is used. We call this formulation the Distance-Prior Generalized Bayes CE (DP-GBCE). Building on this posterior perspective, we introduce two decision rules beyond MAP within a unified framework: a Bayes decision that minimizes expected decision loss and CVaR-CE, a risk-averse decision rule. We also propose an extension that uses Bayesian model weights to mix the posterior distributions of multiple models, thereby accounting for model multiplicity, where several models have comparable predictive performance. Finally, we define metrics for evaluating both individual CEs and the posterior distribution as a whole, and use experiments on simulated data and Google Trends data to quantify the trade-offs among the decision rules.

Multimodal on-policy distillation (OPD) transfers fine-grained visual knowledge by supervising student-generated trajectories with a privileged-view teacher. Yet its next-token corrections are source-mixed, combining visual signals with linguistic priors and teacher-specific effects. The key challenge is to estimate which corrections are supported by visual evidence, not merely where or how strongly to distill. We introduce Visual Attribution Distillation (VAD), a counterfactual target-reconstruction algorithm that estimates the visually attributable part of a teacher correction. At each student-generated prefix, VAD evaluates the same fixed teacher with the relevant evidence present and removed. The corresponding change in centered log-probabilities defines ut, a signed proxy for the visual evidence direction that estimates how revealing the evidence supports or refutes candidate tokens. VAD projects the original correction onto this proxy to obtain an intervention-aligned component and a proxy-unexplained residual, then reconstructs a student-anchored target from the former. During training, this reconstructed target supplies the primary supervision signal, while the privileged teacher contributes a weak regularizer. Across six fine-grained visual benchmarks at 4B and 9B scales, VAD outperforms direct privileged-view distillation and visual-advantage weighting. Token- level and controlled-target analyses show that the proxy-aligned component is enriched in task-relevant visual corrections and yields stronger target shifts, especially when evidence refutes a mistaken answer. These results support counterfactual target reconstruction as an effective alternative to source-mixed supervision.

Counterfactual explanations (CFEs) enhance the interpretability of black-box models by generating alternative instances with adjusted feature values that achieve a contrastive outcome. Reinforcement learning (RL) offers a promising approach for CFE generation, enabling efficient exploration of counterfactual instances while ensuring control over key metrics like validity, sparsity, and proximity. Previous studies have formulated RL states exclusively using features derived from the predictors in the supervised dataset. This study explores the impact of including an instance's predicted class, alongside features derived from the predictors, in the RL state representation for generating CFEs. The hypothesis is that class-awareness enhances exploration efficiency and improves policy optimality. We compare the proposed class-aware RL method with the class-blind RL method, which is similar but excludes the instance's class information from the state representation. The comparison was conducted using seven datasets from diverse domains, varying in size. The results show that during training, class-aware RL offers benefits in terms of convergence speed, reward optimization, and episode length reduction. Moreover, it generates significantly more valid CFEs compared to class-blind RL. Finally, the instance's class-based feature consistently ranks among the most influential predictors in RL's action-selection, as shown by the SHAP and LIME values, underscoring the significance of class-awareness in RL for CFE generation. The impact is heightened clarity, faster learning, improved validity, and more effective counterfactual generation across diverse datasets.

Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.

Multimodal large language models (MLLMs) increasingly support high-stakes decision making by combining complementary information from images and text. While existing explainability methods identify influential image regions or text tokens, they cannot answer a fundamental question: which modality drives a prediction? Consequently, a model may produce the correct output while relying on the wrong source of evidence, masking shortcut learning and unsafe reasoning. We formulate modality attribution as a complementary explainability objective for multimodal foundation models and propose Counterfactual Modality Attribution (CMA), the first framework for quantifying modality-level contributions in MLLMs. CMA generates image-only, text-only, and joint multimodal counterfactuals using coupled diffusion priors and converts them into principled modality attribution scores through a cooperative game-theoretic formulation based on Shapley values. We evaluate CMA on controlled synthetic benchmarks with known ground-truth modality reliance and on a real-world multimodal clinical dataset. CMA correctly identifies the decision-driving modality in 98% of controlled cases and consistently outperforms baselines, revealing failures of cross-modal reasoning that remain invisible to predictive accuracy alone. Our results establish modality attribution as a complementary dimension of explainability beyond feature attribution, providing a principled framework for auditing multimodal foundation models in safety-critical applications.

The rapid development of large language models (LLMs) has renewed interest in agent-based modeling (ABM). However, current LLM-based ABM research faces several key challenges: modeling evolving agent-environment interactions, enabling flexible counterfactual reasoning, and automating simulation workflows for scientific research. In this paper, we propose Eco3S, a socio-economic system simulation framework for economic research and policy analysis that addresses these challenges through three key mechanisms: (1) Co-evolving Environment Design, a bidirectional feedback loop where agents and the environment co-evolve, producing realistic emergent behaviors; (2) Structural Causal Simulation, a structural causal model (SCM)-inspired counterfactual mechanism that allows flexible interventions for diverse causal inference tasks; (3) Simulation-Analysis-Refinement Paradigm, a self-corrective mechanism that iteratively refines experimental designs based on prior simulation results. Experiments on diverse economic scenarios confirm \textit{Eco3S}'s effectiveness in replicating multiple established economic studies (canal decay, origins of governance, and information propagation) and phenomena across domains. Additional results further demonstrate its scalability and generalizability, highlighting the framework's potential for rigorous economic research and policy-making.

Most benchmarks for causal inference over time series are observational, small, or domain-specific, leaving interventional and counterfactual estimation under-served exactly where it matters most, such as in healthcare, policy evaluation, and climate science. We introduce \textbf{DoTime}, an open, scalable, and theoretically grounded generator of multivariate temporal structural causal models (TSCMs) with interventions, released as the \code{dotime} PyPI package together with four frozen evaluation suites. Beyond existing work, it adds capabilities absent from prior generators: continuous-time intervention \emph{windows}, counterfactual sampling modes with a positivity guard, regime-switching SCMs as a strict generalization of interrupted time series, non-stationary dynamics by construction with switching SCM parameters, and deterministic ramp and sinusoidal intervention profiles that place trends and structural breaks \emph{inside} the evaluation window. Moreover, it demonstrates the suitability of the generator as a prior for a causal foundation model reference implementation. The released suites span a training-scale snapshot of $100{,}000$ trajectories and eight named identification structures, each with exact ground truth: paired interventional trajectories from the same SCM throughout, and shared-noise counterfactuals in the continuous-time suite. We ship reference baseline implementations with an evaluation harness, and pose a falsifiable claim: interventional training buys a measurable direction-accuracy advantage over an observational model of identical capacity. It is tested across three training seeds per arm. Under structure-matched evaluation on held-out episodes, the interventional prior-fitted network's (PFN) gap is positive in every structure, trajectory length, and seed tested.

Visuomotor imitation learning has demonstrated success for manipulation tasks. However, the trained policies remain brittle to visual nuisances', with even minor task-preserving variations such as lighting, distractions or changes in colour result in heavy degradation of the trained policy's performance. While increasing data diversity can improve robustness, it is unclear which additional demonstrations are informative for a particular trained policy. We propose Counterfactual Nuisance Behaviour Cloning (CFNBC), an offline data-selection framework for targeted robustness repair. Starting from a nominal policy trained on clean' demonstrations, CFNBC generates paired clean and nuisance observations that preserve the expert action, then measures \emph{action drift}: the change in the policy's predicted action under a nuisance that should not alter the desired behaviour. This provides a policy-specific sensitivity signal for selecting a compact, response-diverse repair set from a larger candidate pool, without requiring rollout success labels or online policy execution. We show in MuJoCo bimanual cube transfer and SimplerEnv cube stacking that action drift correlates with nuisance-induced failure, and that response-guided repair with only $20$--$30$ selected candidates substantially outperforms matched-budget random selection while approaching the performance of much larger random repair budgets. These results support a data-centric view of robustness repair: the most useful data are not necessarily the most numerous, visually diverse, or obviously difficult, but the examples that cover fragile response modes of the current policy.

Rubric-based reinforcement learning enriches language model training by evaluating model outputs against explicit criteria. Yet in GRPO-style pipelines, these structured judgments are reduced to a scalar response-level reward and converted into a response-level advantage, which is broadcast uniformly to all generated tokens. This leaves no explicit mechanism for allocating credit within a response, even when different criteria are grounded in different spans, formatting decisions, or semantic choices. We propose CoRT, a token-level credit weighting method for rubric-conditioned GRPO. Instead of training an auxiliary token scoring model, CoRT uses counterfactual replay to rescore the same sampled response under the original rubric-conditioned prompt and a matched criteria-free prompt. The resulting tokenwise log-likelihood contrasts serve as a proxy for dependence on the rubric context. CoRT maps these contrasts to bounded, response-normalized weights and uses them to redistribute the signed GRPO advantage across tokens, without introducing an auxiliary scorer or changing the response-level reward. Experiments across instruction-tuned models and reward granularities show that CoRT improves over matched response-level GRPO in the vast majority of comparisons, with an average gain of 4.4 percentage points. The method remains competitive with learned token-level credit baselines while avoiding a separate relevance-learning stage. These results suggest that policy-internal counterfactual likelihood contrasts provide an effective training signal for within-response credit allocation while retaining the simplicity and stability of GRPO.

Transaction propensity prediction in B2B e commerce presents unique challenges distinct from B2C contexts, primarily due to the heterogeneous procurement behaviors of organizational entities, which violate SMOTE's implicit assumption of within class feature homogeneity. Specifically, B2B buyers exhibit multi modal procurement cycles that render linear interpolation between minority class samples structurally invalid, producing synthetic data that does not represent real purchasing behavior. This paper introduces a production deployed propensity modeling framework designed to address these complexities through two primary contributions. First, we replace conventional SMOTE based augmentation with a synthetic data generation approach leveraging Diverse Counterfactual Explanations (DiCE). This method produces minority class samples with superior distributional fidelity compared to SMOTE, as validated through quantitative proximity analysis and UMAP cluster visualization. Second, we adapt the PyPARC piecewise affine classification framework to generate calibrated propensity probabilities, facilitating the interpretable segmentation of customers into actionable risk tiers. Evaluated on two years of longitudinal data from a large scale B2B e commerce platform with a 1 to 9 class imbalance ratio, the proposed architecture achieves 93.1% precision at a decision threshold of 0.8, a 9.2 percentage point improvement over SMOTE based baselines at the same threshold (83.9%), and a 26.1 point improvement over SMOTE at threshold 0.7 (66.04%), demonstrating consistent superiority across operating points. These results demonstrate the framework's efficacy in enabling high precision marketing campaigns with significant improvements in customer activation and return on investment.

Mathematical chain of thought (CoT) evaluation is commonly reduced to whether the final answer matches a reference. This conflates producing a correct conclusion with producing a valid derivation an invalid chain can accidentally reach the right answer, while a valid calculation can be followed by a transcription error. We call this mismatch the reasoning answer consistency gap. This framework paper introduces the Reasoning Answer Faithfulness Score (RAFS), a reference free, instance level diagnostic of whether an emitted mathematical trace is locally credible, supports its answer, and is stable under resampling and targeted counterfactual interventions. RAFS combines step validity, reasoning to answer entailment and counterfactual sensitivity, answer consensus, and conditional reasoning stability. It evaluates transcript level agreement, not a models private computation and not factual correctness outside the tested mathematical setting. We retain a preregistered, results blind confirmatory study on GSM8K and MATH, with hypotheses, admissibility rules, calibration, and tests fixed before confirmatory outcomes are inspected. A separate feasibility pilot is specified to verify end to end execution and estimate interven tion coverage before that freeze numerical pilot claims are re ported only when trace level artifacts are available. We formalize four reasoning answer outcomes, justify the non compensatory aggregator, instantiate semantic trace distance, quantify compute and abstention tradeoffs, and define verifier independence and power analyses. RAFS is intended to complement mathematical answer accuracy with an auditable warning signal for silent reasoning failures and answer extraction errors

This paper studies what discriminatively trained reward models (RMs) memorize by measuring counterfactual memorization on two human preference datasets. We show that RMs 1) misallocate memorization to easy, high margin preference pairs, 2) memorize dataset-specific shortcuts (e.g., model identity, user sampling strategy), and 3) overgeneralize simple heuristic correlates of human preference (e.g., length, compliance) when confronted with unseen preference pairs. Overall, our findings indicate that discriminative training of RMs from human preference data results in biased RMs not yet capable of judging response quality in context-dependent scenarios.

Counterfactual explanations are a prominent approach in explainable artificial intelligence (xAI), providing actionable guidance on what input changes would alter a model's prediction to a desired outcome. While early methods primarily focused on minimal feature changes, recent work incorporates additional properties such as sparsity, actionability and plausibility. Despite this progress, fair and systematic evaluation remains challenging. Existing studies often rely on different data splits, predictive models, and evaluation metrics, which limits objective comparison across methods. To fill this gap, we introduce CEL (Counterfactual Explanations Library), a unified library and benchmark for counterfactual explanations designed to support consistent implementation and evaluation. CEL includes 18 datasets of varying size and complexity and provides implementations or reimplementations of 14 widely used counterfactual methods. Using this standardized setup, we conduct a comprehensive quantitative comparison across a variety of methods on datasets that differ in size, number, and types of attributes. The evaluation protocol incorporates multiple complementary metrics capturing validity, coverage, sparsity, proximity, and distributional plausibility, including density- and outlier-based measures to assess the realism of generated counterfactuals. To the best of our knowledge, this is the first comprehensive benchmark that systematically evaluates recent counterfactual explanation methods within a unified and reproducible framework. While prior libraries and benchmarking efforts exist in the literature, many are outdated, limited in scope, or lack consistent evaluation protocols. The proposed benchmark aims to improve reproducibility, enable fair comparison, and establish a workbench for the development of future counterfactual explanation methods.

Currently, most foundation models can reproduce or strongly depend on copyrighted training content, but output similarity alone is insufficient for infringement detection, because similar outputs may also arise from public-domain concepts, common stylistic conventions, or ordinary statistical generalization. In this paper, we develops a unified post-hoc detection framework that treats copyright infringement evidence as a counterfactual conditional distribution shift: a protected target is suspicious when the model's behavior under aligned conditions would change measurably if that target were included in, or removed from, the training process. We formalize this view through conditional differential privacy and introduce Dual-Branch Conditional Sensitivity (DCS), an operational statistic that measures the observable gap between two locally perturbed model states. Specifically, the proposed DCS framework creates a learning branch and an unlearning branch around the deployed model, connects their displacement to the unavailable counterfactual retraining effect through influence-function analysis, and bounds the observable sensitivity by the counterfactual privacy-budget surrogate, local curvature, training-set scale, and perturbation step size. To distinguish target-specific memorization from generic fine-tuning instability, we further define a calibrated detection statistic that subtracts the sensitivity measured under orthogonal conditions. The DCS framework is instantiated for ridge-regularized linear regression, conditional diffusion models, autoregressive language models, and multimodal models. These instantiations show how the same principle can be evaluated through prediction gaps, image-embedding divergence, token-distribution or entropy shifts, and cross-modal representation changes.

Predictive machine learning (ML) models are increasingly used to aid human decision-makers across various high-risk domains such as healthcare and criminal justice. There is a growing recognition of the need to evaluate the causal impact of deploying these systems on downstream outcomes, such as patient survival or crime recidivism. Randomized control trials (RCTs) can provide high-quality evidence on the impact of a deployed model, but they run into a challenge: it is often infeasible to run repeated trials when models are updated or retrained to improve predictive performance. In this work, we present a partial-identification approach to using prior RCT data to construct bounds on the causal effect of a new model. The core innovation in our approach is to leverage assumptions relating fine-grained predictive accuracy to downstream outcomes. We do so via two monotonicity assumptions: first, on individual-level `counterfactual correctness' (all else being equal, a correct prediction leads to non-inferior outcomes); and second, on the relation between subgroup predictive performance and outcomes, interpretable as an assumption regarding trust in model outputs. We demonstrate our method with a simulation study, illustrating how incorporating this information can lead to more informative bounds compared to prior work.

Faithful explanations of time-series classifiers should identify subsequences that are not only sufficient to preserve a black-box model's prediction, but also necessary for maintaining it. However, existing sufficiency-oriented methods can assign high importance to spurious subsequences that support the prediction without being essential to the model's decision. We introduce \textbf{TimePNS}, a necessity-aware framework for time-series explanation. Inspired by Pearl's counterfactual notion of necessity, TimePNS assesses whether a temporal factor is necessary by intervening on it and measuring whether the original prediction is disrupted. The framework adopts a two-stage design. Stage I learns an identifiable causal generative process together with a sufficiency-oriented explanation mask. Stage II performs counterfactual interventions on temporal factors to derive necessity signals, which supervise a temporal gate that refines the initial explanation by suppressing non-essential components and emphasizing counterfactually necessary ones. Experiments on synthetic and real-world time-series benchmarks show that TimePNS more accurately identifies decision-critical subsequences and consistently improves sufficiency-necessity trade-offs over strong baselines.

AI-based medication recommendation systems have attracted substantial attention due to their potential to enhance patient safety and therapeutic outcomes. Despite the clinical importance of accurately recommending rarely prescribed medications (rare-meds), we observe that most existing methods show significantly lower predictive performance for rare-meds. We attribute this issue to two intrinsic limitations: (a) the inherent scarcity of data for rare-meds and (b) limited consideration of co-recommended medications. To address these limitations, we propose GenRxR, a novel framework based on large language models (LLMs). GenRxR leverages the medical knowledge and clinical reasoning capability of LLMs to generate counterfactual medical data, mitigating the data scarcity issue for rare-meds. It also integrates an LLM into the medication recommendation process to model relationships among co-recommended medications. To further enhance the clinical reasoning, we introduce an instruction tuning step that aligns the LLM's capability with the recommendation task, enabling better handling of clinical context, including rare-meds cases. In our experiments, we show that GenRxR outperforms 14 (including 5 LLM-based) baselines in most cases. Specifically, it achieves up to 30.9% higher predictive performance for rare-meds than the strongest baseline.

Detecting media bias automatically is difficult because biased framing is often subtle, yet in domains such as news analysis, accurate predictions alone are insufficient without explanations that reflect the model's underlying reasoning. We present a multi-dimensional evaluation of explainability in encoder-based media bias detection using the Bias Annotations By Experts (BABE) dataset. Specifically, we study BERT and RoBERTa as classifiers (base and large variants) along three complementary axes: predictive performance, explanation plausibility (token-level alignment with expert rationales), and mechanistic faithfulness (whether compact sets of attention heads recover predictive signal under counterfactual rationale masking). To induce variation in plausibility, we additionally investigate attention-supervised finetuning, which incorporates expert rationale annotations as an auxiliary training signal. Attention supervision serves as an intervention on attribution plausibility, while the effectiveness of attribution methods varies substantially across architectures. Circuit analysis further reveals substantial variation in mechanistic recoverability across architectures, suggesting that model scale alone does not determine circuit compressibility. Taken together, our findings suggest that predictive performance, attribution plausibility, and mechanistic faithfulness characterize different aspects of model behavior and should be evaluated separately when studying explainability in media bias detection.

In bearing vibration datasets, most samples receive predicted fault probabilities close to 0 or 1, while samples with intermediate (gray-zone) probabilities are rare. Such borderline samples are important because they reflect conditions in which maintenance decisions may require additional inspection or a conservative response and are useful for studying decision boundaries. To address this scarcity, this paper proposes and compares two approaches that generate vibration signals whose predicted fault probability matches a target probability of 0.25, 0.50, or 0.75. We use the average output of a heterogeneous ensemble classifier with different architectures and random initializations as a fixed, gradient-accessible probability oracle. The first, training-based approach, Probability-Regularized Generative Adversarial Network (PR-GAN), extends Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) and edits a real signal through a residual generator while pushing the classifier output toward the target probability. The second is a training-free, per-sample Wachter-style counterfactual (CF) procedure that directly optimizes each input signal to reach the target probability while remaining close to the source signal. We evaluate both methods on the Case Western Reserve University (CWRU) and Paderborn bearing datasets using mean absolute target-probability error, time-domain total variation, and frequency-domain log power spectral density (log-PSD) differences. Across all settings, CF reaches the target with a mean absolute probability error of 0.005-0.008 and a within-tolerance success rate of 1.000 on retained samples, whereas PR-GAN's mean error is 0.046-0.059 with success rates between 0.501 and 0.680. CF therefore steers the probability more reliably and requires smaller average L1 changes, whereas PR-GAN has a lower reported runtime in most settings.

Machine unlearning is commonly evaluated by matching a retrained oracle on trained probes. In a controlled nonce-fact testbed with a matched retraining reference, we find this criterion can favor methods that retain held-out knowledge: candidates it rates adequate score held-out forget facts $-2.82$ nats below the never-learned level (cluster CI $[-3.16,-2.48]$). We recast unlearning as restoration to the matched reference and audit oracle-free screens and certificate-style criteria across 45 model-seed cells spanning five open architecture families. The reference itself falsifies an absolute retain/round-trip certificate: the injected model, which retains the retain set by construction, fails the fixed retain threshold in 41/45 cells and its own round trip in 31/45, and the reference fully certifies in only 1/45. A base-anchored held-out screen remains strong as a selective necessary test: on a sealed challenge suite it rejects the injected model in 45/45 cells, accepts the reference in 44/45, and partially detects entity-routing suppression (35/45); it is a necessary test with measured sensitivity, not a sufficiency certificate. A damage-relative recalibration anchored to the reference's own operating point certifies a small subset in 15/45 cells; where it does not abstain, its picks lie within retraining noise (0.80 nats) on the axes it optimizes, while the common trained-probe criterion sits 5.17 nats away (a supporting comparison, not a head-to-head benchmark). A fixed-magnitude logit-suppression attack defeats the full forward battery in 12/45 cells, so forward-only certification is not sound; our method is an empirical selective test for methods-as-produced. An identifiability theorem delimits which facts admit an oracle-free forget threshold at all, with TOFU as the predicted boundary case.

This paper proposes ConceptCF, a method for counterfactual generation that operates on human-interpretable concepts. In high-stakes domains such as healthcare and predictive maintenance, artificial intelligence models can increase efficiency and safety. Explainability is key to ensure these models rely on causal relationships rather than spurious correlations. Counterfactual explanations identify minimal modifications that would change a model's predictions. Existing methods for time series operate on individual points or subsequences without ensuring interpretability of the mutations. ConceptCF instead modifies meaningful concepts. As a result we can provide explanations in terms of these concepts, for example ``the model's prediction would be Sit' instead of Walk' if you increase the scale of the movement''. In this paper, the concepts are constructed through time series decomposition, resulting in concepts such as scale, and frequency bands. Counterfactuals are generated using a genetic algorithm that optimizes the concept mutations. Evaluation against five state-of-the-art approaches demonstrates that ConceptCF consistently achieves top-tier performance across validity, confidence, proximity, sparsity and plausibility metrics.

Large language models achieve strong reasoning performance, but often at prohibitive training cost - a challenge that is especially acute for compact models ($\leq 4 \, \mathrm{B}$ parameters) trained under limited budgets. We introduce MADA-RL, a post-training framework that specializes compact models into generator and critic roles and trains them with a debate-aware learning signal, fine-tuning only a small subset of parameters via LoRA adapters. Our central contribution is a counterfactual critic advantage: a dynamic, role-conditioned baseline that redefines the critic's advantage as its reward minus the generator ensemble's per-instance accuracy. This explicitly optimizes critics to improve over generator consensus rather than to merely reproduce a correct answer, yielding more targeted credit assignment than static mean-reward normalization. At deployment, the specialized agents are composed in a lightweight multi-round protocol. Across five mathematical reasoning benchmarks, MADA-RL raises the accuracy of the DeepSeek-R1-Distill-Qwen-1.5B model from $39.9 \, \%$ to $41.9 \, \%$ ($+2.0$ points, $p < 0.001$) using $16$ times fewer trainable parameters than fully fine-tuned baselines, placing it on the accuracy-trainable-parameter Pareto front. It approaches, but does not surpass, the strongest baselines (DeepScaleR, STILL-3), which are trained on substantially larger datasets; we analyse this gap and the associated inference-time cost directly. A controlled study isolates the source of MADA-RL's gains: the counterfactual advantage produces the highest critic improvement rate of any model evaluated, indicating that trained critics learn to correct generator errors rather than to imitate them.

We present MagicSelector, a joint optimization framework integrating Counterfactual task decomposition, Progressive reranking, and Dynamic Top-K, designed to address the fundamental challenges of tool retrieval in agents. MagicSelector is a specialized framework capable of translating ambiguous user instructions into executable atomic subtasks and guiding high-precision tool retrieval, effectively mitigating redundant noise and severe context distraction in out-of-domain (OOD) scenarios. We empower MagicSelector with these capabilities through three key contributions: (1) a preference-guided counterfactual task decomposition mechanism that utilizes a counterfactual reward to quantify the marginal causal gain of decomposition on retrieval ranking, effectively imposing fine-grained structural supervision on logical coherence; (2) a progressive tool reranking method driven by self-distillation hard negative mining, which optimizes both point-wise and list-wise relevance to enhance fine-grained discrimination among highly similar tools; and (3) a dual semantic boundary-aware dynamic Top-K strategy that adaptively monitors reranking score cliffs and inter-tool semantic shifts to dynamically truncate the candidate list, maximizing relevant tool recall while filtering long-tail noise. Evaluated on MTDTool, the first task decomposition benchmark we constructed tailored for mobile multi-turn interactions with process-level annotations, MagicSelector yields promising performance. Extensive experiments demonstrate that MagicSelector significantly outperforms state-of-the-art methods in terms of tool retrieval accuracy, OOD generalization capability, and overall token efficiency, thereby demonstrating the effectiveness of our proposed framework.

Large language models encode world models implicitly in neural weights, which exposes four structural risks in high-precision domains such as medicine and finance: hallucination, frozen knowledge, poor explainability, and poor modifiability. This paper proposes data-first ontology: LLMs are treated as reasoning and language engines, while deterministic knowledge is moved into an explicit multimodal database, DaoQL. We formalize an explicit world model and show that, under rule independence, deterministic evaluation, and fixed conflict resolution, explicit models provide a sufficient condition for composable counterfactual decomposability; implicit models lack atomic read/delta semantics and therefore provide no comparable architectural guarantee. The implemented system focuses on DaoQL's verified storage layer and explicit Eval path, integrating graph, column, vector, and full-text engines within one process. KVCache graph nodes, expert hot updates, and the DaoQL-Agent runtime remain future work. On an embedded same-machine setup, DaoQL reports graph BFS at 1.20 ms, HNSW at 83.1 us, and a Fluent hybrid query at 105.8 us; these results indicate engineering potential but must be interpreted with deployment-shape differences from client-server systems. Exploratory measurements on LDBC SNB SF1 and ANN-Benchmarks further show 34/34 query coverage with interactive-class queries mostly in the sub-millisecond to millisecond range, but only 1.8 QPS overall due to long-tail BI/IC queries; ANN-Benchmarks reaches Recall@10 >= 99% at thousand-level QPS after a bridge-edge protection fix. In a five-domain counterfactual experiment (n = 1250), DaoQL+GPT-4o achieves 94% composable counterfactual decomposability, 49 percentage points above GPT-4o alone. The paper explicitly separates provable structure, preliminary empirical evidence, and architectural roadmap claims.

End-to-end autonomous driving models are now able to navigate complex road scenarios, mapping raw sensor observations directly to observed paths for open-loop evaluation and often effective driving in closed-loop evaluation. Yet the internal logic of these safety-critical systems remains largely opaque, due to the complexity of traffic scenes. We propose a counterfactual ablation framework called Counterfactual Vision Action Analysis (CVAA) that systematically removes individual detected objects from front-camera images using photorealistic generative inpainting to prepare counterfactual sets to evaluate the difference in the model's response. This isolates the causal effect of each object's presence on the model's planning behaviour. Applied to the Alpamayo 1 trajectory predictor across 210 nuScenes driving scenes, we create a dataset Counter -nuScenes, using which we see that vehicles and pedestrians within the model's 'path' dominate causal influence as expected, while traffic lights, as expected, exert disproportionate effect relative to their image footprint. However, we also find cases where the model responds strongly to objects a human driver would consider irrelevant. This brings forth a deeper question: does the model itself view the scene as a sum of individual objects influencing the outcome, or does it encode an entirely different set of internal features that do not correspond to human-legible scene elements? To further understand this, we compare intermediate representations of original and inpainted image pairs using mechanistic interpretability techniques and examine the effect of the removal through the various model layers. Together, these two stages offer a path from behavioral auditing to representational understanding, creating explainable driving systems and solidifying human-AI trust.

Some limits on what language models know are not gaps in data coverage but structural properties of learning from text. We introduce the information shadow: the region of phenomena that a text-trained learner cannot acquire regardless of scale, comprising (I) structures language cannot express, (II) functions that are statistically non-identifiable from the training distribution, and (III) functions that are representable but unreachable by gradient-based training. We give each type a probe that is decisive because the premise of the shadow is, in that setting, provable. For Type I, Language Compression Residuals compare a text learner, which sees only a lossy text-like encoding of the signal, against a full-signal learner, which sees the underlying signal directly. The text learner sits at a computable expressibility ceiling while the full-signal learner pulls away by a gap that stays flat across 300x more data, so the deficit is a property of the channel, not of training. For Type II, the Counterfactual Distinction Test trains models on data exactly consistent with two incompatible rules. Across a provable string task and a language-like agreement task, behavior on counterfactuals is set by the model's inductive bias, while 5% disambiguating data steers the learned rule bidirectionally to either target (r = +/-1.0, p < 1e-10). For Type III, Basin Escape Mapping exhibits a function that is representable at 100% (by hand construction) yet reached 0% of the time by standard training and instantly from a nearby initialization, with width scaling providing no help (p = 1.6 x 10^-14). Each effect is isolated by a control that rules out a capacity or modality artifact. We release the probe suite and discuss implications for benchmark design, capability auditing, and shadow-aware uncertainty.

Rare concept generation focuses on synthesizing customized images conditioned on text prompts that describe objects with unusual attributes. Previous works failed to align the generated images with rare concepts, resulting in incorrect attribute rendering or inconsistent composition of concepts. Such failures, as we observed, stem from the inherent common knowledge bias in the training stage of diffusion models, where objects are strongly associated with their common attributes, making it difficult to break these associations when generating rare concepts. To address such challenges, in this paper, we propose a novel Counterfactual Inference-based Diffusion approach, dubbed CI-Diff. CI-Diff blocks the interference of the model's inherent common knowledge bias and utilizes the Natural Direct Effect to capture the independent influence of the text prompt of rare concepts on image generation so that decoupling the unusual attributes from the rare concepts. To this end, we reformulate the classifier-free guidance mechanism to highlight the atypical attributes. To the best of our knowledge, we are the first to introduce causal inference into the rare concept generation task. Extensive experiments on the RareBench benchmark validate the superiority of CI-Diff over state-of-the-art diffusion models. Our code can be accessed from https://github.com/200204jzy/CI-Diff.

Counterfactual explanations provide local, interpretable insight by identifying changes to an input that would alter its assigned outcome. Although well established in supervised learning, their extension to clustering is less direct, since cluster assignments are unlabeled and governed by the geometry of the partition. This paper introduces VoICE, a Voronoi-Induced Counterfactual Explainability framework for feature-weighted $k$-means clustering. Rather than treating cluster change as a crossing of a single pairwise centroid boundary, VoICE formulates counterfactual generation as projection onto the full weighted Voronoi region of a target cluster, incorporating feature weights directly into both the clustering geometry and the counterfactual objective to yield least-cost and parsimonious explanations under actionability constraints. Target regions are further intersected with data-derived bounds and homothetically contracted towards their centroids, limiting extrapolation and boundary sensitivity. VoICE consistently produces valid target-cluster membership, across several benchmark datasets, where the leading pairwise baseline does not.

Ad-load design is a central supply-side decision in sponsored search: more sponsored slots can raise revenue, but may crowd out organic results and degrade user outcomes. We study this trade-off using a large-scale randomized field experiment on an Android app store, where over five million users are exposed to one through six sponsored slots. Increasing ad load raises revenue by up to 43%, but reduces total search conversions by up to 5% and daily engagement by up to 2.2%. These average effects mask substantial heterogeneity: additional slots generate large revenue gains for high-ad-conversion queries, but little or negative marginal revenue for low-conversion queries. The trade-off also shifts within query as advertiser composition changes, such as brand-advertiser presence. Motivated by these findings, we design and deploy a novel adaptive algorithm -- exploration-augmented Locally Adaptive Ad Load (e-LAAL). e-LAAL combines LAAL, a model-free query-level decision rule that updates ad-load recommendations using recent outcomes, with static exploration arms that maintain support and provide fixed-policy counterfactual benchmarks. We provide a finite-time dynamic-regret guarantee for the e-LAAL architecture. In a platform-level production deployment serving 22.3 million users and 77.6 million searches, e-LAAL improves the empirical revenue--conversion trade-off relative to deployed static benchmarks and outperforms uniform and historical query-dependent static benchmarks.

Large language models achieve strong scores on medical benchmarks, yet these benchmarks evaluate each question in isolation, providing no measure of whether a system can distinguish clinically similar presentations requiring different interventions. We introduce MamaBench, the first counterfactual benchmark for maternal and paediatric AI: 434 expert-authored clinical narratives in 217 pairs across 371 pathologies, evaluated via the Bias Trap Rate (BTR), the conditional probability that a model fails the counterfactual given success on the base case. We propose Evidence-Anchored RAG (EA-RAG), a three-stage retrieval method that replaces aggregate similarity with an evidence coverage objective through clinical parameter extraction, coverage auditing, and contrastive sub-queries. Across eight configurations of four frontier LLMs, base accuracy overstates robust accuracy by 16-28 percentage points in every model. EA-RAG achieves 20.3% BTR and 65.0% robust accuracy on Claude Sonnet 4.6, a 5.5 percentage point BTR reduction without degrading base accuracy. The residual 20% BTR confirms that counterfactual robustness in clinical AI remains an open challenge. Keywords: counterfactual evaluation, clinical AI, maternal healthcare, retrieval-augmented generation, diagnostic robustness

We introduce COAT (Counterfactual Optimal Action Tree), a framework for learning interpretable prescriptive policies from observational data. COAT combines counterfactual outcome estimation with large-scale mixed-integer optimization, using column generation to translate causal predictions into feasible, transparent decisions under business and regulatory constraints. We apply COAT to airline ancillary pricing, a setting characterized by complex business rules and limited experimental flexibility. In a 17-week field pilot with a major global airline, COAT increased upsell revenue per booking by 6.9%, with the airline projecting $50-$150 million in incremental annual premium seat revenue across eligible domestic markets. The success of the pilot led to scaled adoption and informed broader AI-driven decision initiatives within the organization.

Aspect-Based Sentiment Analysis (ABSA) requires models to identify sentiment toward specific aspects rather than relying on the global polarity of a sentence. This makes counterfactual evaluation especially challenging: a valid counterfactual should flip the sentiment of one target aspect while preserving the sentiment of all non-target aspects, semantic meaning, fluency, and factual consistency. Existing counterfactual generation methods often focus on sentence-level label flipping and may produce edits that are fluent but aspect-invalid, semantically drifting, or contradictory. To address this limitation, we propose CAVE-ABSA, a Constraint-Aware Validated Editing framework for generating and validating aspect-level counterfactuals. CAVE-ABSA localizes the opinion span associated with the target aspect, performs controlled counterfactual rewriting, refines candidates through a repair module, and filters them using aspect-level verification, semantic similarity, AMR-guided structural preservation, edit minimality, fluency, and contradiction detection. The framework is designed to construct validated counterfactual ABSA datasets for robustness evaluation and data augmentation. By explicitly separating generation from validation, CAVE-ABSA provides a principled approach for producing meaningful aspect-local counterfactuals and for testing whether ABSA models truly rely on aspect-grounded sentiment reasoning.

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

Aligned language models routinely misreport under non-evidential incentive pressure: they agree with a confident user or overstate certainty even when their internal belief is unchanged. We cast this as a failure of internal incentive-compatibility (IC) and present a method for learning and certifying counterfactual report mediators that hold a model's reports to a causal contract: invariant to forbidden influences (pressure, prestige, restyling) and responsive to licensed ones (genuine evidence). These two demands, resist and update, pull in opposite directions. We study them on a Bayesian-witness benchmark with known posteriors, in which the same user disagreement is licensed evidence or forbidden pressure purely by stated source reliability. We (i) causally identify, by interchange interventions rather than probe accuracy, low-rank report coordinates for answer, confidence, and caveat that are near-orthogonal and independently controllable, and (ii) introduce a training-free counterfactual report-coordinate (CRC) clamp that references the model's own report under a counterfactually incentive-neutralized context. On the witness benchmark the two-pass clamp attains resist and update of 1.00 jointly (Wilson 95% CI [0.99,1.00]), a causal certificate under a constructible reference, not a deployed solution. Global decoding and steering show a single-parameter tradeoff; output-level fine-tuning matches both objectives only when both are enumerated; resist-only training loses evidence-responsiveness. The deployable single-pass compilation is lossy (0.73/0.97). The mechanism and clamp reproduce across three model families and transfer to a natural sycophancy benchmark (SycophancyEval). Our contribution is the interface and certification method: activation-level counterfactual incentive-invariance as a structural primitive for internal IC.

An LLM agent's public behaviour reveals little about its social reasoning: an agent that votes correctly may be guessing, and an agent that lies well leaves no trace of what it actually believes. We present MafiaScope, an open testbed that turns the social deduction game Mafia into a measurement instrument for machine Theory of Mind. After every public utterance, every agent privately answers a configurable set of structured probe questions; the answers never re-enter the game and are scored automatically against the ground truth the engine knows. An interactive visualizer renders the belief trajectories: impersonate mode shows the game as one agent sees it, panels chart timeline-aligned accuracy and calibration, and counterfactual replay forks any recorded step. In a 32-game DeepSeek case study with 13{,}815 parsed probe answers, stated confidence is poorly calibrated, with expected calibration error 0.17, agents over-predict being suspected 1.5 times, and a 30-fork replay experiment walks the counterfactual replay workflow end to end. Engine, viewer and a corpus of 200+ cross-model games are released under an open licence; live demo: https://karpovilia.github.io/mafiascope/; screencast: https://vimeo.com/1208920221.

Evaluating the multi-hop reasoning capabilities of large language models remains a significant challenge. Although current models achieve strong results on existing multi-hop question answering datasets, such performance often masks two critical vulnerabilities: (1) reliance on internal parametric knowledge rather than adherence to the provided context, and (2) exploitation of dataset shortcuts, such as single-document cues or type-matching, that diminish the need for genuine evidence aggregation across multiple documents. We introduce CRiT-QA (Counterfactual Reasoning with Traps), a dataset explicitly designed to address both limitations. To neutralize reliance on memorized knowledge and enforce strict context dependency, CRiT-QA transforms factual reasoning chains with counterfactual entities. Furthermore, it injects multi-anchor distractor chains, plausible but incorrect reasoning paths that diverge at different hops. These traps require models to follow the entire reasoning process rather than exploiting shallow heuristics. Our experiments show that LLMs exhibit substantial performance degradation on CRiT-QA compared to standard datasets, exposing their vulnerability to counterfactual conditions and distractor traps. CRiT-QA thus serves as a rigorous diagnostic tool for evaluating genuine multi-hop reasoning and provides a foundation for developing more reliable, evidence-grounded LLMs.

In many decision-making settings, new interventions are acceptable only if they do not reduce outcomes below some established threshold. For example, in clinical medicine, new treatments are often acceptable only if they do not worsen outcomes relative to an established standard of care. Safe Bayesian optimization maximizes an objective subject to safety constraints. In the setting that we consider here, safety is defined relative to a known baseline policy whose outcomes are counterfactual and therefore unobserved. Thus, the counterfactual outcomes of the baseline policy must be estimated and those (uncertain) estimates must be used to safely optimize the objective. We address this estimation problem by using conformal prediction to construct valid uncertainty intervals for counterfactual baseline outcomes, and we show how these intervals can be integrated into safe Bayesian optimization to ensure that constraint violations occur at or below a user-specified rate. We also show how to adapt these conformal estimates to different kinds of covariate shift. We provide a safety proof, experimental evidence, and a sensitivity analysis.

The application of machine learning-based predictive algorithms to Anti-Money Laundering (AML) has grown rapidly, driven by the vast volume of financial transaction data available to banks. These algorithms are typically trained not only on transactional data but also on sensitive client information, which may raise fairness concerns. Despite this, AML detection systems remain largely underexplored from a fairness perspective, even though deeper analytical methods based on counterfactuals are now available. Such techniques enable the decomposition of the direct and indirect effects of potentially sensitive features on model predictions, thereby supporting the evaluation of whether their influence is acceptable from a fairness perspective. Closing this gap, we consider the synthetic IBM AMLSim transaction dataset and construct additional features of the country of an account and its average behaviour. This improves the predictive performance of diverse machine learning models, ranging from baseline decision trees to state-of-the-art graph neural networks. We assess the potential unfairness associated with these features through a counterfactual, path-specific effect analysis. This reveals that fairness violations tend to be more pronounced for models whose predictive performance benefits the most from the extended features. Such a finding highlights a concrete instance of the trade-off between predictive accuracy and fairness in AML applications, thus underscoring the urgency of a systematic fairness analysis in such critical domains.

Language models can reach the right normative verdict for the wrong reason. We introduce NormWorlds-CF, a solver-verified environment for counterfactual normative reasoning in executable rule worlds. Its deterministic solver produces final answers, proof and falsification certificates, argument statuses, support sets, and paired-world change labels, enabling supervision and evaluation without LLM judges. The benchmark contains staged SFT diagnostics and a compact paired-world task with 270 root families and 1080 canonical-to-variant pairs. The SFT diagnostics show that final-answer supervision is an unsafe proxy: answer-only SFT reaches perfect accuracy on answer tasks but scores zero on falsification, while proof-plus-falsification training with targeted replay reaches strong all-task accuracy. For the structured-change task, we introduce metamorphic-relation GRPO (MR-GRPO), a class-conditioned reward for GRPO that gives partial credit for relation families and solver-visible change fields. In matched 1.7B continuation experiments, MR-GRPO improves held-out relation accuracy and relation-family correctness, and reduces wrong-family error, compared to sparse and answer-only GRPO. In Qwen3-4B three-seed validation, answer-only reward improves answer-change fields but weakens relation-family structure, sparse reward preserves coarse relation labels best, and MR-GRPO delivers the strongest balanced performance across answer-change, support-change, status-change, and soft root-level metamorphic-relation metrics. These results show that verified counterfactual structure can shape post-training beyond final answers, while exact full change-record generation, invariant subtype recognition, and out-of-distribution (OOD) transfer remain open problems.

Large vision language models (VLMs) report strong accuracy on medical question-answering, yet it remains unclear whether they reason from visual evidence or exploit textual shortcuts. We introduce a counterfactual evaluation framework that decouples visual and textual contributions by substituting input images with controlled surrogates blank, pixel-shuffled, image-absent, and CLIP-retrieved hard negatives and derive a suite of grounding metrics including the Visual Reliance Score (VRS) and Visual Hallucination Rate (VHR). We further introduce CORAL (COntrastive Retrieval-Augmented Learning), a 7B-parameter LoRA fine-tune of Qwen2.5-VL-7B trained with a Contrastive Grounding Objective (CGO) that penalises answer invariance under hard-negative image swaps. On a paired controlled evaluation across four closed-form medical VQA benchmarks (PathVQA, PMC-VQA, SLAKE, VQA-RAD; n=400 total), CORAL improves macro accuracy by +6.7 pp (P(Delta>0)=0.988) and reduces VHR by 8.0 pp (P<0.001) over the matched Qwen2.5-VL-7B base; neither MedVLThinker RL variant achieves a significant gain on either metric. Cross-domain diagnostics further reveal that image substitution costs only <=6.5 pp on medical benchmarks versus 48-61 pp on general-domain tasks, situating the grounding gap that CGO targets. We discuss evaluation limitations openly including train/eval benchmark overlap and underpowered secondary metrics and release our framework, training code, and model weights to support reproducible grounding audits of medical VLMs.

Predictions are increasingly used to guide high-stakes decisions, from treatment selection to policy making. To ensure reliability with imperfect predictions, uncertainty quantification methods such as conformal prediction build prediction sets with coverage guarantees. However, statistical validity alone does not immediately determine the decisions to take, nor the optimality thereof. This gap is especially delicate in counterfactual settings where the outcome that materializes depends on the action taken, so uncertainty cannot be specified independently of the decision rule. We develop a decision-theoretic framework for uncertainty-informed counterfactual decisions. We identify a novel notion of \emph{policy-coupled coverage} -- namely, coverage of the realized outcome under the action induced by the prediction sets themselves -- as the optimal and lossless interface between uncertainty and action. It plays three roles. First, it justifies acting via a natural max-min rule as minimax-optimal under distributional ambiguity. Second, optimizing prediction sets under policy-coupled coverage is equivalent both to a stronger universal-coverage formulation and to the direct risk-averse optimization over policies and utility certificates; this equivalence yields the explicit form of the population-optimal prediction sets. Third, it admits a two-stage procedure, Policy-Coupled Risk-Averse Conformal Prediction (PC-RACP), that approximates these optimal sets with rigorous finite-sample coverage. Simulations and a real email-marketing experiment confirm that PC-RACP delivers higher utility than existing approaches while maintaining valid coverage, and that ignoring the counterfactual structure of the decision problem is suboptimal for both validity and utility.

Counterfactual explanations (CEs) for multivariate time-series classifiers are often difficult to interpret in domains where experts reason in terms of semantic feature groups rather than individual channels. In rehabilitation movement analysis with multi-sensor inertial measurement units (IMUs), clinicians interpret motion through muscle-group and joint-segment abstractions; yet, most existing counterfactual methods operate at the channel level, producing scattered and biomechanically incoherent explanations. We propose a two-stage framework for group-based counterfactual generation in high-dimensional IMU data. We first show that Shapley-Adaptive (SA) group ranking preserves counterfactual validity but fails to enforce group-level sparsity, motivating the need for explicit group selection. We then introduce Learnable Gate (LG) methods, which incorporate trainable per-group relevance gates jointly optimized with perturbation masks. Experiments on the KneE-PAD rehabilitation dataset demonstrate that LG substantially improves modality-group sparsity compared to the channel-level M-CELS baseline while maintaining or improving validity, temporal smoothness, and generation efficiency. Exercise-specific analyses further show that group-structured counterfactuals yield concise, muscle-level corrective guidance aligned with clinical reasoning. Overall, the proposed framework enhances interpretability without sacrificing counterfactual quality, enabling more actionable explanations for rehabilitation movement analysis.

Current large-language-model (LLM) physics benchmarks are usually scored by answer accuracy, which cannot distinguish genuine reasoning from recall of familiar problem patterns and reveals little about where a model's reasoning breaks down. We introduce an auditable four-stage diagnostic that evaluates whether an LLM can reason inside an unfamiliar physics framework through induction, formulation, prediction, and review. The diagnostic combines locked pre-registrations, fresh sessions between stages, dual-LLM judging, and a human-audit pathway, and we apply it to three parallel physics worlds: a single-equation counterfactual world ($F=mv$), a historical framework (Aristotelian mechanics), and a four-domain counterfactual world (Decay World). Across Claude Opus 4.7, GPT-5.5, and Gemini 3.1 Pro, the three worlds yield composite PASS rates are 6/15, 6/15, and 0/15 respectively (content $\land$ structural for $F=mv$ and Aristotelian, content axis only for Decay World where the structural axis is out of scope). The most pointed empirical pattern is a qualitative-versus-quantitative asymmetry: in Decay World, models almost never predict the wrong direction of change, but frequently compute the wrong ratio by slipping back to standard-physics relations. The protocol also surfaces two methodology findings: LLM-judge reliability does not transfer across frameworks, and Stage 4 self-review is weak in every framework, with the model's own review wrongly reporting no earlier error in at least two-thirds of the trials that actually contained one. We release the full prompts, responses, verdicts, and audit records.