Shapley Value

When an agent handling a payment exception loses money, the agent-step attribution methods this paper compares against will name one of its actions. They will do so even when a settlement message was dropped and the agent never had a chance: they intervene on agent actions and do not expose infrastructure faults as intervenable variables, so every dollar they explain is charged to a decision. We take a benchmark whose fault process is explicit and replayable, decompose each episode's realised delivery schedule into named, individually repairable messages, and intervene on both the agent's choices and the infrastructure's. A telescoping identity splits any policy's loss exactly three ways: an infrastructure effect, a policy differential against the best implementable policy, and a reference-policy residual. Two of the three can be negative, so none is a share; Shapley then divides the first into signed allocations over individual messages. One result is structural and needs no corpus: an agent-only baseline identifies no infrastructure cause, because its model contains no variable that could name one. What 545 planted episodes across 3 policies measure is the size of that consequence. It misfiles 100% of infrastructure episodes and charges $114,383.40 to the agent. Repairing what it names recovers 0.0% of the available loss; repairing a minimal sufficient set recovers 100.0%. Scoring messages one at a time is not merely imprecise: 27.8% (95% CI: 23.3--32.3%) of episodes do not decompose additively. We evaluate deterministic programmatic policies rather than language-model agents, which is what makes replay exact and which limits external validity to stochastic agents. The prevalence figures are properties of this generator, not field rates.

Explanations of machine learning models are usually judged by criteria that are hard to compare. We propose a simpler test: if an explanation really describes how a model uses its features, it should be possible to rebuild the model's predictions from it. We turn each explanation into a predictor by reading each feature's effect and adding them up, and measure how well that predictor reproduces the model on unseen data. Nothing is fitted, so the score reflects the explanation itself. The test applies to any explanation that can be written as a function of the features; we demonstrate it on partial dependence plots (PDP), accumulated local effects (ALE), SHAP and LIME. We prove that summing partial dependence curves gives the best possible additive summary of a model when its features are independent, and that this fails when they are dependent. Across 13 real datasets and 9 synthetic designs and four model families, which method scores best depends entirely on feature dependence: where features are independent SHAP is slightly worse than PDP, exactly as the theory predicts; on dependent real data SHAP leads. Some widely used quality metrics even prefer a damaged explanation to an intact one.

Deep learning models for dynamic survival analysis (DSA) achieve strong predictive performance by incorporating longitudinal patient data, but their black box nature limits clinical trust and adoption. Existing explainability methods cannot handle longitudinal, irregular inputs and functional survival outputs simultaneously, which limits their usability in DSA. We propose DynSHAP, a SHAP framework suited specifically for dynamic survival analysis. It extends common marginal SHAP estimators to this setting by treating time--feature pairs as players in the Shapley game. We further introduce Temporal DynSHAP, which learns linear dependencies in features over time and uses conditional sampling to address them in explanations. When applied to synthetic data with known ground-truth attributions, Temporal DynSHAP recovers temporally dependent features more accurately than marginal estimators for a given state-of-the-art model. Applied to two real-world clinical datasets and two DSA architectures, DynSHAP produces attributions faithful to model learning, allowing medical experts to see which patient information drove the prediction and when.

Shapley value (SV)-based methods are the prevailing framework for feature attribution in machine learning, yet existing population-level Shapley estimators generally assume that observations used to evaluate the coalitional game are fully observed under a common feature space. This assumption is routinely violated in multi-site studies across biomedicine, social science, and environmental monitoring, where institutions record different features under different protocols, producing systematic blockwise missingness across sources. We first show that the standard remedy of imputing missing features before computing Shapley values introduces systematic, coalition-dependent bias into the resulting attributions. We then propose \textbf{FUSHAP} (\textbf{Fu}sion \textbf{Sh}apley \textbf{A}ttribution from \textbf{P}artially-observed data), a method that leverages partially-observed auxiliary sites to reduce the variance of a preliminary single-site Shapley estimate without imputation. A permutation-based screening step detects and excludes sites whose data distributions are incompatible with the target population. In synthetic experiments, FUSHAP achieves $3$--$8\times$ lower MSE than the single-site estimator and $2$--$3\times$ lower MSE than imputation baselines without incurring imputation-induced bias, and the screening procedure identifies misaligned sites with $82\%$ power at moderate misalignment and $100\%$ for strong misalignment. On multi-site air quality and multi-center clinical data, FUSHAP reduces MSE by approximately $3$--$7\times$ relative to the single-site estimator; in the clinical application, standard imputation can increase MSE above the single-site baseline.

Explaining why a specific outcome occurred, and which inputs deserve the blame or credit, is central to philosophical, scientific, and policy analysis. Existing tools split into two camps. The theory of actual causality (AC) gives principled verdicts, but only for toy-sized models, because computing them requires enumerating counterfactual scenarios. Scalable attribution methods like SHAP (or even causal SHAP) at least partially ignore the causal structure that generated the data, and can give answers that conflict with a careful causal analysis. We close this gap with Probabilistic Causal Impact (PCI). PCI builds on actual causality and on Pearl's notions of probability of necessity and sufficiency, but recasts the question of explainability as an estimation problem on a probabilistic causal model that is easily approximated via Monte Carlo. By specifying a distribution over "candidate explanations," a distribution over counterfactual values, and a scoring function, PCI provides tractable, causally grounded, graded explanations, generalizing AC and Pearl's probability of causation as degenerate cases. We evaluate PCI in synthetic and real-world examples, spanning consistency checks with AC, scaling experiments, complex continuous-valued dynamical systems, and a real-world deployed causal machine learning model trained on millions of datapoints.

Agent skills are crucial external instructions that enable language agents to execute long procedural tasks such as coding or document processing. Existing agent skills are primarily created through human manual crafting or agent execution traces, with limited understanding of how each step contributes to overall skill performance on specific tasks; i.e., there remains an open problem in quantifying the contribution of individual steps within an agent skill. To address this issue, we first model skill-step attribution as a Shapley value-based contribution estimation problem, and then propose SkillShapley, a step-level attribution framework for agent skills. Notably, SkillShapley operates in two phases, motivated by key empirical insights, i.e., discretized benchmark rewards that create sharp performance cliffs, and step interactions that are largely additive rather than synergistic. Specifically, it first identifies informative coalitional regions, and then adaptively samples new coalitions that can yield reusable marginal evidence. Experiments on skills from the widely adopted SkillsBench demonstrate that our SkillShapley can effectively and efficiently identify high- or low-value skill steps, providing several key takeaways for agent skill creation.

Predictive explanation methods attribute a model output; they do not, by themselves, attribute an intervention effect on the real-world outcome. We introduce the Causal Attribution Score (CAS), a compact score architecture for causal explanation. CAS starts from an identified interventional coalition game, allocates the joint intervention contrast with causal Shapley contributions, and converts those raw outcome-scale effects into Local CAS, Signed Local CAS, and two complementary Global CAS summaries. The innovation is not a new Shapley formula, but a local-to-global causal reporting layer with an explicit intervention target. In the known-truth benchmark, eight repeated primary-interaction simulations (n = 2,200 each, three actions) gave mean Local CAS MAE of 0.107 for coalition-aware CAS, compared with 0.173 for one-at-a-time normalisation and 0.213 for a global normalised absolute ATE vector. The paired advantage over one-at-a-time normalisation increased from -0.003 under additivity to 0.091 under strong interactions. On both empirical DoubleML datasets, 401(k) eligibility/net financial assets (n = 9,915) and Pennsylvania reemployment bonus/unemployment duration (n = 5,099), predictive SHAP/TreeSHAP rankings differed materially from Feature-CAS rankings of treatment-effect modifiers. In Pennsylvania, dep1 (exactly one dependent) moved from predictive global rank 13 to Feature-CAS rank 2 and was the leading local Feature-CAS modifier. These results isolate the added value of separating what predicts the outcome from what explains heterogeneity in an estimated causal effect.

Machine learning pipelines commonly flatten relational data into single-table representations, discarding structural constraints. Widely used Shapley value-based feature attributions then rely on feature independence, evaluating the model on combinations that could never arise in the underlying data, producing misleading explanations. We propose RelShap, a framework that incorporates relational constraints and data provenance into Shapley value computation, restricting both background data and coalition evaluation to relationally valid configurations. The framework is estimator-agnostic and composes with Kernel SHAP, Monte Carlo, and Leverage SHAP without altering their sampling or weighting properties. Functional dependencies further induce equivalence classes over feature coalitions, which RelShap exploits to reduce runtime without changing Shapley values; we provide a combinatorial characterization of the expected speedup. Experiments across multiple datasets, models, and estimators show that RelShap produces explanations that are more faithful to the data-generating process, correctly identifying the dominant feature in controlled settings where existing methods, including Conditional SHAP and ManifoldShap, do not. Our code is available at: https://github.com/duneag2/relshap.

Intrusion detection systems (IDS) and automated systems for detecting and reporting cyber threats, are commonly handled via supervised machine learning methods. Though effective, these models struggle to effectively adapt to new attack types. This study proposes a novel approach by employing a reward-based, dueling Q-learning model for IDS, achieving an average accuracy of 99.68% across multiple attack classes. The proposed model has a dueling network architecture which separates its predictions into value and advantage streams. This has the benefit of improving learning efficiency and stability. The model was trained on the CIC-IDS2018, a benchmark dataset based on real-world intrusion detection scenarios, having multiple attack classes such as DDoS, botnets, and brute-force attacks. Furthermore, Explainable AI (XAI), specifically SHAP (SHapley Additive exPlanations), was also integrated into the training and evaluation process to provide interpretability into the model's predictions.

Prediction of post-wildfire debris flows is critical for mitigating hazards to communities, infrastructure, and resources during intense rainfall in recently burned areas. However, identifying reliable machine learning models is complicated by overlapping debris-flow and non-debris-flow events in feature space, the need for model interpretability, and limited training data. This paper addresses these challenges through a systematic evaluation of machine learning models in terms of predictive performance, feature importance, and synthetic data augmentation. Using basin-scale observations of post-wildfire debris-flow events across the western United States, we compare 15 models, including the Tabular Prior-Data Fitted Network (TabPFN). Repeated stratified cross-validation shows that TabPFN achieves the highest unaugmented performance with a threat score of 0.637, closely followed by the best tree-based models. SHapley Additive exPlanations (SHAP) are used to identify the features driving predictions, revealing that short-duration rainfall intensity and storm accumulation consistently rank highest, while burn severity and terrain features contribute less. We further evaluate synthetic data augmentation using TabPFN-generated samples to address the scarcity of debris-flow observations. Synthetic augmentation improves the performance of all models except CNN, with the largest mean threat score increase of +0.041 among the deep learning models. By combining rigorous model benchmarking, interpretable feature analysis, and synthetic data augmentation, this work provides a comprehensive framework for improving post-wildfire debris-flow prediction.

Agent skills are increasingly optimized by automated feedback loops, producing long structured artifacts whose internal value remains unclear. We study skill valuation: assigning credit to the internal units of a fixed skill, such as rules, examples, scripts, and heuristics, under a fixed agent and held-out task distribution. Skill valuation differs from data or prompt-span valuation because skill units are structured: they may depend on other units, belong to a document hierarchy, trigger agent behavior, and consume limited prompt context. We introduce SkillSV, a structure-aware Shapley-style framework for skill valuation. SkillSV compiles a skill into units, dependencies, and hierarchy, so that only valid counterfactual skills are evaluated. It uses paired deletion and length-neutral padding to separate content value from context cost, and estimates the resulting values with a rollout-budgeted estimator for noisy agent evaluations. On four agentic benchmarks, we assess the faithfulness, actionability, and explanation of SkillSV: it recovers unit interactions, preserves aggregate skill lift, and guides safe pruning and compression.

Most FDR-controlled feature selection methods are designed for coordinate-wise hypotheses, where each feature has a single weight or importance score. This abstraction fails in sequential and grouped models, where one original feature is represented by a block of sub-features, such as lags, recurrent states, or attention-based interactions. We propose a grouped-feature FDR control framework for such settings. For grouped linear models, we construct null-symmetric block-level mirror statistics with matrix-valued perturbations. For neural sequential models, we combine Permutation SHAP derivatives as model-agnostic block-level importance scores with kernel-based dependence measure. The framework is model-agnostic across network architectures, does not require specifying the covariate distribution, and reduces to Gaussian Mirror or Neural Gaussian Mirror when the block size is one. We prove FDR control for low- and high-dimensional grouped linear models and asymptotic symmetry of smoothed Permutation SHAP derivatives under fixed fitted nonlinear models. Experiments on simulated and real-world datasets show reliable FDR control and improved power under correlated grouped-feature signals.

This paper presents an interpretable machine-learning framework for predicting the splitting strength (ST) of asphalt concrete and supporting data-driven mixture design. A database consisting of 296 samples was established, and 14 input variables related to asphalt properties, aggregate gradation, and fiber characteristics were selected for modeling. Six machine-learning models, namely TabPFN, ANN, SVR, RF, XGBoost, and LightGBM, were developed and compared. Hyperparameter optimization was performed for five models using NSGA-II, while TabPFN was directly applied with its default configuration. The results show that all six models achieved satisfactory predictive capability, whereas TabPFN delivered the best overall performance on the testing set, with the lowest RMSE of 0.28, MAE of 0.21, MAPE of 18.01%, MAD of 0.14, the highest R^2 of 0.88, and the highest composite score of 0.91. SHAP analysis further revealed that nine dominant variables accounted for 92.0% of the total average contribution, among which Ag9.5, FT, Ag4.75, AC, and Du were the most influential. In addition, favorable parameter ranges for improving ST were quantified, such as Ag9.5 < 66.8%, Ag4.75 < 45.0%, AC < 5.4 wt.%, AV < 3.6%, and Du > 134.7 cm. Finally, a GUI platform integrating prediction and SHAP-based explanation was developed to improve the accessibility and practical applicability of the proposed framework.

Despite its many benefits, widespread access to individuals' personal data also causes severe privacy concerns for consumers, companies, and policymakers. This study proposes a novel framework that adapts the Shapley-value-based feature attribution approach to the problem domain of data privacy by capturing the two crucial dimensions of data privacy---disclosure risk and data utility. Our proposed framework takes a holistic view of data masking through a fair feature attribution approach based on Shapley values. Different from the existing literature that mostly focuses on the risk-utility tradeoff at the dataset level, the proposed framework addresses the tradeoff at the feature level. Furthermore, the proposed framework is agnostic to data masking methods, statistical and machine learning methods, and data utility and disclosure risk evaluation metrics. Experimental results show that our proposed method can effectively reduce disclosure risk while preserving data utility.

This work presents a comprehensive analysis and design of global sensitivity-based input shapers for a 3D Unmanned Aerial Vehicle-payload system, emphasizing robustness against uncertainties in payload mass and rope length. The proposed approach also leverages the Shapley value concept in controller design to systematically account for uncertainties, thereby reducing the controller's sensitivity to unknown parameters. To validate the effectiveness of the methodology, numerical simulations are conducted, comparing the proposed controller against non-robust, robust, and minimax designs. The results demonstrate that the standard global sensitivity or Shapley-based input shapers improve performance and offer a promising framework for uncertainty-aware control in aerial payload transport.

The alignment of Large Language Models (LLMs) is increasingly bottlenecked by data quality. As datasets scale, massive preference and instruction-tuning corpora inevitably accumulate hidden structural contradictions, safety risks, and systemic human annotation errors. Standard dataset auditing methods, such as semantic deduplication or LLM-as-a-judge, struggle to capture the actual predictive impact of individual records and often miss deep functional rule clashes. To address this, we introduce a scalable, inference-only data valuation pipeline that approximates the Shapley value without iterative model retraining. By mapping semantic k-NN neighborhoods into a directed graph, our framework evaluates data utility directly through a reference LLM's probability distribution using zero-shot and one-shot conditional log-likelihood shifts. Our pipeline then translates these predictive influence scores into localized advantage metrics to isolate gradient-conflicting records. We demonstrate the pipeline's efficacy in sanitizing two heavily vetted alignment datasets. First, applying our pipeline to the HelpSteer2 dataset reduced the manual audit search space by 99.1%, successfully uncovering falsely-labeled records across diverse failure modes. Second, applying our automated audit strategy to Anthropic's HH-RLHF training and evaluation splits identified thousands of hidden safety and factual preference inversions. Crucially, by extending this audit to the evaluation split, we expose severe vulnerabilities in current benchmark integrity: highly capable models frequently predict the safer or more helpful response, only to be penalized by objectively flawed human ground-truth labels. Overall, our work provides a mathematically grounded, highly efficient diagnostic tool to uncover human label failures, sanitize evaluation benchmarks, and ensure the integrity of LLM alignment data.

We study feature-level and node-level explanations for graph neural networks (GNNs) through the lens of Aumann-Shapley attribution. Path-integral methods such as Integrated Gradients provide an axiomatic formulation of attribution, but their practical use in deep GNNs typically relies on finite-sample numerical approximations to the path integral, requiring a trade-off between quadrature error and computational cost. This paper proposes APEX, a model-attribution co-design framework that makes the attribution integral exactly computable under a polynomial GNN architecture. The key component is PolyGIN, a GIN-style graph network whose message-passing, normalization, and transformation operations preserve a bounded multivariate polynomial form for scalar model scores, such as pre-softmax logits. We show that, for a PolyGIN with $L$ polynomial transformation blocks, the derivative along the attribution path has degree at most $2^L-1$. Therefore, Gauss--Legendre quadrature can evaluate the Aumann--Shapley path integral exactly, up to floating-point precision, with $2^{L-1}$ deterministic evaluation points. The resulting attributions can be computed at the feature level and then aggregated into node-level scores while preserving completeness. Experiments on synthetic and real-world graph benchmarks show that PolyGIN maintains competitive predictive performance, while the complete APEX framework achieves higher attribution fidelity than the compared baselines and substantially reduces the number of evaluations required for path integration.

Large Language Models (LLMs) excel at multi-step reasoning, yet current parallel reasoning approaches often fail to distinguish the contributions of individual reasoning paths. Many paths may be redundant, misleading, or even detrimental, but outcome-level rewards assign uniform reward, leading to ambiguous learning signals and unstable training. We propose Parallel Shapley, a reinforcement learning framework that attributes fine-grained, path-level contributions in multi-path reasoning. Treating each path as a player in a cooperative game, we leverage Shapley values to quantify marginal contributions, using a generative reward model to evaluate path utilities and Monte Carlo sampling for efficient approximation. Experiments on mathematical reasoning benchmarks show that Parallel Shapley outperforms existing baselines while providing more stable and interpretable training. Our framework effectively "fishes out the free riders," assigning reward proportionally and improving multi-path reasoning in LLMs.

This study contributes toward development of an Automated Data Processing (ADP) framework designed to evaluate and reinforce optimal machine learning model-feature combinations for predictive tasks in fused deposition modeling (FDM) process datasets. The methodology is centered around a reinforcement learning-inspired policy updating mechanism, where multiple machine learning models are trained on both full feature sets and feature subsets selected through Shapley-based Explainable AI (SHAP XAI) across 217 datasets. At each episode, the framework assesses the predictive accuracy and F1-scores of each model-feature pair, computes a scalar reward, and updates $Q$ values to guide future model selection. SHAP XAI feature importance was employed to generate reduced yet informative feature subsets to enable the framework to explore performance with dimensionality. The policy was shown to evolve over multiple episodes, with reward distributions used to visualize performance stability. Overall, results indicate that leveraging the ADP framework through XAI algorithms successfully converges toward optimal model-feature configurations with improved accuracy and stability. Specifically, the proposed framework improves the test-set AUC from 0.9248 to 0.9731 and increases the mean reward value by more than fifty percent compared with the baseline full-feature configuration.

Predictive process monitoring supports the optimization and control of operational business processes by forecasting the future state or outcome of ongoing cases. While deep neural networks have achieved strong performance for these tasks by modeling sequential dependencies in event logs, their black-box nature limits trust and practical adoption. Feature attribution methods are often used to address this, but applying them directly poses a dilemma: event-level attributions impose high computational complexity for long traces, while explanations based on aggregated trace representations often fail to capture the underlying control-flow dynamics. To address this issue, we propose a local post-hoc explainability method for deep neural networks in outcome prediction. The method relies on a control-flow-aware segmentation algorithm that partitions a trace into meaningful segments and supports the computation of segment-level SHAP explanations. This makes it possible to identify which parts of a trace influence a prediction and which change points steer the case toward the predicted outcome. We assess the proposed segmentation method on a synthetic dataset with known process logic, where meaningful change points can be explicitly verified, and we demonstrate its usefulness on real-world event logs from a loan application process and an administrative process of a Dutch municipality.

Jailbreak attacks on large language models are usually evaluated by attacker-centric metrics such as attack success rate (ASR), yet an attack that breaks a model is not necessarily useful for improving its safety. We propose a defender-centric view of jailbreak evaluation, where attacks are evaluated by the downstream safety improvements they enable when used as red-teaming data for safety training. Building on this view, we introduce A-MESS (Minimal Effective Attack-Subset Selection), a setting-agnostic framework for attributing and selecting jailbreak attacks from black-box subset utility observations. A-MESS estimates AttackSHAP, a Shapley-based score that attributes marginal utility to individual attacks and selects compact attack subsets under user-specified budgets via greedy or surrogate-based optimization. Across controlled utility landscapes and real LLM safety settings, we find that ASR rankings are weakly aligned with defender-centric utility, that AttackSHAP can be estimated accurately with limited utility queries, and that directly optimizing subsets yields stronger safety utility than attacker-centric or attribution-only selection. These results suggest evaluating jailbreak attacks as resources for improving safety, not only as tools for breaking models.

Air pollution and climate-related stressors are increasingly important concerns for respiratory health, especially in settings with unequal environmental exposure and healthcare capacity. This study evaluates an interpretable machine learning framework for predicting respiratory disease rates and air-quality status using structured country-level weekly data. Two supervised learning tasks were considered: regression of respiratory disease rate per 100,000 population and binary classification of air-quality status. Nine regression models and nine classification models were compared using nested cross-validation. Model interpretation was conducted using SHAP values, and subgroup analysis was performed across income levels and geographic regions. The results showed that PM2.5 concentration was the dominant predictor of respiratory disease rate, with linear and regularized linear models achieving the strongest regression performance. For air-quality classification, models achieved high balanced accuracy when PM2.5 was included, but performance decreased substantially when PM2.5 was removed, indicating strong dependence on pollutant-related information. SHAP analysis showed that, without PM2.5, socioeconomic and meteorological variables such as GDP per capita, precipitation, and healthcare access became more influential. Subgroup analysis showed similar aggregate regression error across income groups, but PM2.5 contributed more strongly to predictions in lower-middle-income countries. These results show that model accuracy alone is not sufficient for climate-health prediction. Interpretable models can help identify dominant pollution-related signals, test whether results depend on key pollutant variables, and show whether prediction patterns differ across socioeconomic groups.

This work presents a game-theoretic framework for interpretable hyperparameter-objective interaction analysis rather than proposing a new optimization algorithm. In the proposed framework, Shapley Effects are employed for global sensitivity analysis, while Pareto front sets are utilized to identify effective hyperparameter configurations and support early-stage model evaluation. The resulting analysis reveals which players (hyperparameters) are most influential with respect to different objectives in a given game (application). Consequently, the proposed framework provides interpretable insights into objective-aware hyperparameter interactions, enabling practitioners to guide subsequent optimization, reduce the search space, and perform early-stage model evaluation. The effectiveness of the proposed framework is demonstrated using three distinct neural network architectures across different problem domains under multi-objective settings.

Automated optimisation is increasingly adopted in industrial processes, yet a trust gap persists between engineers who design these algorithms and operators who must act on their recommendations. Explainable AI methods like SHAP (SHapley Additive exPlanations) have transformed interpretability for machine learning predictions; optimisation outputs could benefit from similar techniques. We present an approach that integrates Implicit Function Theorem (IFT) based sensitivity analysis with SHAP attribution and narrative generation via Large Language Models (LLM), producing explanations tailored for operators. Our approach leverages IFT to compute exact parameter sensitivities $\partial p^*/\partial x$ from the optimality conditions, enabling efficient GradientSHAP computation. For an industrial High Pressure Grinding Roll (HPGR) control optimisation problem with 22 features, we achieve equivalent SHAP attributions (correlation $>$0.99 with KernelSHAP) with over 40$\times$ speedup, enabling real-time natural language explanations. We validate on industrial scenarios and present feedback from domain experts on generated explanations.

Data Shapley is the standard principled answer to which training points are worth what, and its k-nearest-neighbor (KNN) specialization is the version deployed in practice: the exact estimator shipped by toolkits such as pyDVL and OpenDataVal. Exact algorithms are known for unweighted KNN and for weighted KNN classification, but weighted KNN regression and soft-label prediction have resisted: the only exact method is an O(N^K) brute force, exponential in neighborhood size K. The obstruction: the weighted regression prediction is a ratio of two coalition-dependent sums, whose normalization denominator breaks the additive, threshold, and duplication structures the prior polynomial algorithms rely on. We close this gap. We give (i) the first pseudo-polynomial-time exact algorithm (polynomial in N and K at fixed lattice precision) for weighted KNN-regression Data Shapley, a counting dynamic program over the joint integer state (sum of w, sum of w*y), verified against exhaustive enumeration with zero mismatch on 12,716 adversarial instances; (ii) a certified FPTAS for continuous weights and targets, with a machine-checkable per-value error certificate never violated across 86,400 checks; (iii) a complexity landscape, including an unconditional Omega(D_w) output-size lower bound and access-model hardness results; and (iv) a weighted soft-label multi-class extension. We release an open-source, CPU-only library and the first exact weighted-regression Data Shapley ground truth. On downstream mislabel detection our exact values are statistically equivalent to Monte-Carlo Data Shapley (dataset-level TOST, n=8, p<10^-4), the pre-registered outcome; the value of exactness is instead determinism, a certified error bound, and an exact reference for auditing estimators: Monte-Carlo did not reproduce the exact top-10% ranking at any budget tested, up to 3,000 permutations (~1.28e6 utility evaluations).

The Shapley value is a widely used concept in attribution problems, as it uniquely satisfies the axioms of linearity, consistency, equal treatment, and efficiency. Often, the inclusion AUC metric is used to evaluate the quality of player rankings, in order to identify positively participating players. However, it can be established that the Shapley value is not always reliable for this purpose. The core issue lies in its linearity: the Shapley value acts as a linear operator with an excessively large null space, which is likely to contain non-negligible perturbations that remain indistinguishable to the operator. To address this limitation, we explore the design of nonlinear axiomatic attribution methods. Inspired by the least core, which is a popular nonlinear substitute for the Shapley value, we introduce a class of nonlinear attribution methods that retain the remaining necessary axioms. Each method yields a contribution vector that is the unique optimal solution to a minimization problem, which aims to approximate utility functions as faithfully as possible. In terms of the inclusion AUC metric, our experiments demonstrate the potential effectiveness of these methods compared to Shapley value variants that relax only the efficiency axiom. Our code is available at https://github.com/watml/nonlinear-axiom.

The adoption of non-parametric machine learning models for regulatory capital estimation introduces a fundamental governance challenge: the inability to explain model outputs in a manner auditable by supervisory bodies. This 'black box' problem remains a major barrier to the adoption of Gaussian Process Regression (GPR) and related ML architectures in ICAAP and CCAR workflows despite their predictive advantages over traditional parametric approaches. This paper addresses this barrier through SHARC (SHAP for Regulatory Capital), an explainability framework for the Hybrid GPR-HS architecture and its stress-testing extension. SHapley Additive exPlanations (SHAP), derived from cooperative game theory and satisfying the properties of Local Accuracy, Missingness, Consistency, and Efficiency, are applied to Stressed Value-at-Risk (SVaR) outputs under three macro scenarios: West Asia War, Climate Risk, and AI Bubble/Regulatory Burden. SHARC decomposes SVaR into baseline, mean-driven, and volatility-driven components, enabling transparent linkage between scenario design and capital outcomes. Two findings emerge. First, SHARC consistently links non-linear SVaR outputs to underlying scenario inputs, confirming framework fidelity and providing auditable traceability of capital drivers. Second, under stress conditions, the mean return component (directional loss magnitude) dominates the variance component (volatility baseline) in determining capital levels, with implications for capital limit-setting, position management, and hedging strategy. The results establish SHARC as a regulator-aligned explainability layer that makes the Hybrid GPR-HS framework fully auditable and consistent with FRTB, ICAAP Pillar 2, and CCAR transparency requirements.

Shapley values are widely used to attribute value to training data based on their marginal contribution to performance on a validation set. Existing practice often assumes these values are stable once the training data and model are fixed. In this work, we uncover a systematic vulnerability: even modest changes to the validation set, such as introducing noises, cause directional shifts in Shapley distributions. As noises are added, Shapley values of training samples compress toward zero. We trace this to a noise-induced neighborhood reshuffling effect: perturbations alter the local rank order between validation and training samples, flattening the valuation landscape. Using the KNN-Shapley framework, we show through synthetic and real data that these shifts are consistent and reproducible. Our findings challenge the assumption of Shapley stability and reveal a new axis of fragility in data valuation. We propose normalization and boundary-aware validation strategies to mitigate these distortions and enable more robust, interpretable valuation in machine learning marketplaces.

In recent years, large language models have achieved remarkable success and have seen growing adoption in financial applications. At the same time, explainability remains critical in finance, a domain characterized by high stakes and strict regulatory requirements. Although numerous methods have been proposed to explain black box machine learning models, the majority of these approaches are designed for general purpose tasks and do not incorporate domain specific knowledge. In this work, we study the explainability of financial textual data modeled by large language models through the lens of the Shapley value. Specifically, we investigate whether Shapley based attributions align with established financial domain knowledge. Through rigorous theoretical analysis and extensive empirical evaluations, we demonstrate that Shapley values can yield explanations that are consistent with financial reasoning and can offer meaningful insights into the model's behavior in text based financial applications.

Predictive models are increasingly embedded in operational decision-making, yet standard explanation methods typically explain forecasts rather than the decisions those forecasts induce. This distinction is important in predict-then-optimize systems: large forecast changes may leave the optimizer's action unchanged, while small changes can alter the selected decision and its realized value. We propose Decision Value Attribution (DVA), a Shapley-based framework for attributing the value of a fixed prediction--optimization pipeline. The framework defines cooperative games whose payoff is the downstream decision value, allowing the players to be information sources, optimization or design parameters, or both. We present three variants: InfoDVA attributes value to features, DesignDVA attributes value to operational configurations, and Decision-Value Interactions (DVI) quantifies how information and design jointly create value. We further distinguish post-DVA, which evaluates decisions using realized outcomes, from pre-DVA, which evaluates decisions under the model's full prediction. This separation turns attribution into a decision-level diagnostic of whether the model's operational beliefs align with realized performance. The resulting attributions are expressed in the units of the operational objective and decompose the gain or loss relative to a baseline. Case studies in electricity storage arbitrage and emergency medical service coverage show that predictive explanations can be poor proxies for operational value, that DVA can guide targeted information-control interventions, and that optimization configurations determine when predictive information is decision-relevant.

Understanding model predictions is essential for physical applications, where outputs often inform safety-critical decisions, such as structural load assessment, weather warnings, and clinical diagnosis. Shapley values satisfy many desirable properties as an attribution method, but their computational cost during inference hinders their practical use. Current amortized explainers, such as FastSHAP, are limited to homogeneous inputs, which is problematic for physical applications where data often comes from irregular grids and geometries. We introduce OperatorSHAP, a grid-agnostic attribution method and training procedure that allows us to train FastSHAP-like explainers for neural operators. We establish a theoretical framework for attributions in function space, connecting to Aumann-Shapley values. We further show that OperatorSHAP's explanations are consistent with state-of-the-art discrete Shapley values across resolutions and transfer across grid sizes without retraining.

We address the problem of explainability in machine learning models through feature attribution methods. In particular, we consider a variant of Shapley values known as Asymmetric Shapley Values (ASV), which enables the incorporation of causal knowledge into model-agnostic explanations through the use of a causal graph. We show that in certain contexts in which the computation of SHAP is $\#P$-hard, the exact computation of ASV can be done in polynomial time. To extend this algorithmic result, we introduce a notion of equivalence classes over the topological orderings of the underlying causal graph, which is useful to reduce the time to compute ASV. In particular, we present a polynomial-time algorithm (in the number of equivalence classes) to compute it whenever the causal graph is a rooted directed tree. Finally, we develop an algorithm for approximating ASV in arbitrary causal DAGs which relies on a procedure to sample topological orderings uniformly at random. To implement this sampling mechanism we leverage known algorithms as well as simpler alternatives. Our experimental results demonstrate the practical viability of the proposed approach in realistic causal structures.

Location encoders transform geographic coordinates into high dimensional embeddings for downstream machine learning, but it is unclear how well these representations capture interpretable spatial effects. We benchmark whether GeoShapley, a game-theoretic explainer that treats all location features as a single joint player, can recover spatially varying coefficients from models built on location-encoder embeddings. Eleven encoders from the TorchSpatial framework are evaluated against a synthetic process with known coefficients, across three scales (grid, county, global), with and without raw coordinates alongside the embedding, and under untrained and contrastively trained conditions. Measuring recovery as the correlation between estimated and true coefficients, we report how it varies with scale and encoder architecture and compare the embeddings against a raw-coordinate baseline. Recovery of the primary coefficient is consistently high across encoders, whereas recovery of a secondary coefficient is more scale-dependent, differing most at the global scale; the raw-coordinate baseline remains competitive throughout.

As machine learning models grow more influential and opaque, algorithmic fairness and explainability are critical for ensuring accountability. However, we demonstrate that these auditing mechanisms are themselves vulnerable to subtle manipulation, camouflaging the influence of protected features. While prior work on data-agnostic attacks has exposed this vulnerability, they leave behind detectable artifacts that compromise their stealth. We introduce Targeted Identity Re-Association (TIRA) attacks, a novel family of attacks that iteratively and probabilistically manipulate a model's outputs without requiring access to the model's internals or feature representations. We formalize two algorithms: Probabilistic Micro-Shuffling (PMiS), which applies localized adjacent swaps, and Probabilistic Rank-Shift Micro-Perturbation (PRSMP), which introduces small, randomized rank shifts. We empirically demonstrate that TIRA attacks are highly effective at pushing fairness metrics towards ideal values. Crucially, TIRA attacks successfully confound SHAP-based explanations, leaving effectively zero residual attribution for protected features, a major improvement over prior work.

This article presents a complementary approach for integrating multimodal medical data in cancer classification, based on state space models represented by the Mamba architecture. To this end, a mixed multimodal fusion architecture, called Mixed Fusion, was employed and developed to enhance the interpretability of the decision-making process. The proposed approach explores two variants of Mamba: one dedicated to visual processing, responsible for classifying the lesion image and generating probabilities associated with the target classes, and another focused on tabular processing, which uses these probabilities together with clinical and/or sociodemographic data to produce the final diagnosis. The experiments were conducted on two medical datasets: PAD-UFES-20, composed of clinical images and information associated with skin lesions, and NDB-UFES, consisting of histopathological images and sociodemographic data related to oral cancer. The results indicate slightly lower performance in balanced accuracy, compared with Transformer-based approaches, on PAD-UFES-20, and superior performance on NDB-UFES. Additionally, substantial gains were observed in the recall metric. Furthermore, the adoption of the Mixed Fusion architecture enables the application of the Shapley Additive Explanations (SHAP) method, increasing the interpretability of the results. These findings indicate that Mamba-based models constitute a suitable alternative for multimodal classification in medical data, especially in scenarios in which sensitivity is a relevant requirement.

Signed pairwise interaction scores fundamentally conflate uniqueness (U), redundancy (R), and synergy (S). We prove this on a minimal 3-way XOR structural causal model: faithful indices such as Shapley-Taylor return zero per pair, whereas projective indices such as Shapley Interaction spread the third-order effect into pair scalars that conflate the three mechanisms. We introduce Stochastic Hi-Fi, a post-hoc, retraining-free predictability decomposition that estimates per-feature U/R/S profiles by interventional masked inference. The estimator provides exact interventional semantics, finite-sample Monte Carlo bounds, strict variance reduction from coupled diamond sampling, and uniform finite-vocabulary convergence. Across tabular SCMs, Stochastic Hi-Fi recovers structure missed by scalar baselines (up to 411x larger interaction-magnitude recovery ratios). It also separates redundant and synergistic heads in the GPT-2 IOI circuit. On NIH ChestX-ray14, Stochastic Hi-Fi matches GradCAM on Pointing Game and improves substantially on Deletion AUC.

Electricity markets are inherently complex systems characterised by strong nonlinearities, high-dimensional interactions, and increasing interdependence across regions. While deep neural networks (DNNs) have demonstrated strong predictive capabilities for electricity prices, their lack of interpretability limits their usefulness for understanding the underlying drivers of price formation. This paper addresses this gap by combining DNN models with explainable artificial intelligence (XAI) techniques to analyse the determinants of electricity prices across 39 European bidding zones. We employ SHAP (SHapley Additive exPlanations) to quantify feature contributions and apply and extend SSHAP, an aggregation framework to improve interpretability in high-dimensional settings. The analysis identifies that renewable energy sources, particularly solar, play a disproportionately important role in price formation despite their lower share in total power generation. Gas prices remain a dominant and consistent driver across electricity markets, while interconnections significantly shape price dynamics, highlighting the strong interdependence of European electricity systems. In addition, a synthetic EU-wide electricity market is constructed to explore the counterfactual scenario of a fully integrated market with a single price.

Hierarchical Federated Learning (HFL) enables scalable collaborative model training across distributed devices while preserving data privacy. However, existing HFL client selection mechanisms suffer from a fundamental strategic inefficiency. By prioritizing stability over Pareto efficiency (PE), they produce suboptimal resource allocations, and without strategy proofness (SP), participants are incentivized to misrepresent their true preferences, both failures degrading system overall welfare in the Pareto sense in practice. To address it, we propose SCOPE-FL (Strategy-proof Chain-based Optimal pareto efficient Federated Learning), a synchronous HFL framework that formulates client selection as a two-sided school choice problem solved through the Top Trading Cycle (TTC) algorithm that simultaneously guarantees PE and SP. For reward distribution, SCOPE-FL employs a scalable Shapley value approximation based on One-Round Reconstruction (OR), ensuring compensation proportional to each client's contribution. The entire mechanism executes via blockchain smart contracts, providing the tamper-proof environment required for the SP guarantees to hold in practice. A comprehensive evaluation on MNIST, Fashion-MNIST, and CIFAR-10 demonstrates that SCOPE-FL outperforms state-of-the-art approaches, including DA, IAS, and other methods across model accuracy, convergence rate, and reward efficiency, while achieving communication latency comparable to DA and blockchain overhead significantly lower than DA at scale.

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

This study examines whether machine learning (ML) models can outperform the naive random walk benchmark in forecasting the monthly USD/CAD exchange rate. Using daily data from the Bank of Canada spanning January 2017 to May 2026, resampled into 113 monthly observations, five ML models are evaluated: linear regression, random forest, gradient boosting, XGBoost, and AdaBoost. These models are benchmarked against the naive random walk model and exponential smoothing with Holt-Winters seasonality (ETS). All models are evaluated using an expanding-window framework to maintain strict out-of-sample integrity, and forecast-accuracy differences are assessed using the Diebold-Mariano (DM) test. Structural break detection identifies four significant breakpoints in the series, corresponding to the escalation of the US-China trade war in 2018, the COVID-19 economic recovery in 2020, the peak of the Bank of Canada rate-hiking cycle in 2022, and the start of the Bank of Canada rate-cutting cycle in 2024. SHAP, or Shapley Additive Explanations, analysis is applied to interpret the drivers of the best-performing ML model. The results show that the naive random walk model remains a formidable benchmark. Linear regression is the only model that statistically outperforms the naive random walk model, with a DM statistic of 3.0585 and a p value of 0.0071, whereas the ML ensemble models show only marginal differences. Random Forest with an expanding-window framework achieves the lowest MAPE of 1.17 percent among all models except the random walk. SHAP analysis confirms that short-term lags, particularly lag1 and lag2, and recent rolling means dominate predictions, consistent with the near-random-walk behavior of exchange rates.

Hierarchical multi-agent systems (MAS) are rapidly being deployed in high-stakes workflows across domains such as finance and software engineering. In these systems, safety and security are inherently distributed across role-specialized agents, significantly expanding the attack surface, particularly under coordinated adversarial behaviors such as privilege escalation and cross-agent collusion. Existing red-teaming approaches for MAS remain limited: they rely on heuristic selection of target agents and perturb isolated message streams, leaving critical questions unanswered as which agents are most responsible for system safety, and how compromised agents can coordinate to bypass defenses. We propose MAStrike, a closed-loop framework for collusive red-teaming in hierarchical MAS. We propose the first agent-level Shapley value analysis for MAS, quantifying each agent's marginal contribution to system robustness under task-specific distributions. GGuided by this attribution, MAStrike identifies vulnerable agent coalitions and generates coordinated, role-aware adversarial manipulations. These attacks are iteratively refined through structured causal diagnosis, attributing failure cases to uncompromised agents that block adversarial attempts. We further build a comprehensive MAS red-teaming benchmark and controllable environments spanning diverse hierarchical topologies and domains, including finance, software engineering, and CRM. Extensive experiments across MAS built on multiple frontier models show that MAStrike substantially outperforms heuristic baselines. Our analysis further uncovers non-trivial Shapley value distributions and higher-order interaction structures among agents, revealing critical vulnerabilities and coordination patterns that are overlooked by prior single-agent or template-based methods.

As artificial intelligence and machine learning (AI/ML) models become integral to network operations, their lack of transparency poses a significant barrier to operator trust. Existing explainable artificial intelligence (XAI) techniques often fail to bridge this gap for non-specialists, producing technical outputs that are difficult to translate into actionable insights. This paper presents a framework specifically designed to address this shortcoming. It leverages a moderately sized large language model (LLM) and extends beyond the standard use of SHapley Additive exPlanations (SHAP) feature influence values. The framework employs a structured prompt enriched with mutual feature interaction data to generate human-understandable natural language explanations. To validate our framework, we performed an empirical evaluation on an optical quality of transmission (QoT) estimation use case with human evaluators. We collected independent performance evaluations from specialists, which showed a high inter-evaluator agreement. Compared to a state-of-the-art baseline that uses only SHAP feature influence values in a straightforward prompt, our approach improves the explanation usefulness and scope by 12.2% and 6.2%, while achieving 97.5% correctness.

Agentic AI systems are increasingly being deployed as productive resources in organizational workflows, yet existing evaluation methods primarily measure isolated technical performance rather than economic contribution. This paper introduces \emph{Agentomics}, a workflow-based framework for valuing, attributing, and pricing human and artificial agents. The framework models a workflow as a configuration of heterogeneous agents whose collective performance determines gross value, deployment cost, reliability, and expected failure loss. Workflow value is treated as a team-level quantity that may include complementarities, substitution effects, bottlenecks, and nonlinear production; additive stage-level value is only a special case. Building on this workflow model, the paper formulates AI deployment as a coalition-formation problem and defines coalition value as the incremental net surplus generated relative to a benchmark human workflow. The Shapley value is then used to attribute economic surplus among participating AI agents, yielding a principled connection among valuation, accountability, and market pricing. The resulting Shapley pricing equilibrium provides a normative benchmark for assessing whether agent prices reflect expected marginal contribution. A security-operations case study illustrates how the framework accounts for productivity gains, deployment costs, reliability losses, and coalition-level complementarities in hybrid human--AI workflows.

Shapley values are a principled attribution measure widely used in interpretable machine learning, but their exact computation scales exponentially with the number of players, motivating a wide range of approximation methods based on value function evaluations of sampled coalitions. This raises the question of whether approximation accuracy can be improved by adaptively selecting coalitions for evaluation based on previous evaluations. This is particularly relevant in settings where the value function is costly and the number of evaluations is severely limited, such as retraining-based feature importance, data valuation, and hyperparameter importance. For this purpose, we propose ShaplEIG, a Bayesian experimental design approach that approximates the expensive value function using a Gaussian process surrogate and adaptively selects coalitions based on their expected information gain about the Shapley values. By the linearity of the Shapley values in the value function, we show that the expected information gain is available in closed form. Furthermore, we propose an efficient computation scheme that reduces the complexity from exponential to polynomial in the number of players via elementary symmetric polynomials. In extensive experiments across diverse costly applications, our method consistently improves sample efficiency in the low-budget regime over state-of-the-art baselines.

Estimating the economic contribution of a single patent inside a product that embodies tens of thousands of patents is a long-standing unsolved problem in intellectual property economics. We propose PatentXAI, a framework that treats patent valuation as a problem of explainable AI: given a characteristic function v(S) encoding the revenue achievable by patent subset S, a patent's Shapley value measures its fair share of product profit in a way that satisfies efficiency, symmetry, dummy, and additivity. To make computation tractable we restrict each patent's coalition to its Markov Blanket inside a knowledge graph, grounded in the C-SVE conditional independence theorem (Li et al., 2020). Scaling experiments from n=12 to n=100 patents using Pareto-distributed coverage graphs report median Markov Blanket size of 32.9 percent of n at n=100, with 90th-percentile blanket size of 55.2 percent of n, and runtime of 10 milliseconds per patent. Difference against exact ground truth at n=12 is 0.088; difference against a high-sample Monte Carlo reference at n=100 is 0.062 plus or minus 0.003. A dense-component experiment shows that when 80 percent of patents share one component, the blanket correctly expands to cover that dense cluster, and the difference versus reference falls to 0.039 because the pooled computation becomes more accurate on homogeneous portfolios. Profit allocation proceeds hierarchically: exact Shapley distributes total profit among macro-components, then centrality-weighted Shapley distributes each component budget among covering patents. Estimating v(S) from real data is the primary open problem; we distinguish this from the computational contribution and outline a concrete roadmap for empirical validation using public ETSI, USPTO, and Lens.org datasets.

Shapley values are a widely used tool for attributing importance and interactions among input variables in black-box models, but their computation involves a function defined over an exponentially large space of subsets. We propose TN-SHAP-G, a framework that exploits structure in graph-structured inputs to compute Shapley values and higher-order interaction indices efficiently. Given a predictor and a fixed masking scheme, TN-SHAP-G learns a compact, graph-aligned multilinear surrogate that approximates the masked-input behavior, represented as a tensor network whose topology mirrors the input graph. Once trained from a small number of oracle queries, the surrogate enables deterministic recovery of first- and higher-order Shapley indices via the multilinear extension, without additional model queries or Monte Carlo variance. Experiments on molecular benchmarks show that the learned factorization closely matches exact Shapley values on small graphs and scales efficiently to larger graphs where sampling-based methods become infeasible.

We propose a method combining Multi-Agent Deep Reinforcement Learning (MARL) and eXplainable Deep Learning (XDL) to reduce drag in wall-bounded turbulent flows. Taking as a baseline the results of training agents directly targeting wall-shear stress and opposition control, three SHAP-guided approaches are compared. In the first, the reward is computed from SHAP attributions of a U-net predicting the future velocity field; in the second, from SHAP attributions of a U-net predicting the skin-friction coefficient; in the third, from a combination of SHAP attributions of two U-nets predicting the skin-friction coefficient and the wall pressure fluctuations, respectively. The combined SHAP strategy based on skin-friction coefficient and wall-pressure fluctuations achieves the best overall performance, achieving a DR of 34.44% and a NES of 34.01% with only 0.43% normalized input power. Relative to opposition control, drag reduction and net energy saving increase by 49.41% and 48.52%, respectively. Compared with the direct wall-shear-stress baseline, the proposed strategy simultaneously improves performance while reducing the normalized actuation cost from 5.90% to 0.43%. Analysis of the results reveals that the energetically efficient policy is consistent with pressure-gated actuation, activating predominantly at near-zero wall pressure, and operates on a temporal timescale comparable to the lifetime of the near-wall turbulent structures.

Recent publications have suggested using the Shap- ley value for sensor anomaly/attack localization. We study the performance of such an approach by using mathematically de- fined optimum binary classifiers in the Shapley value calculation. To judge localization performance, we study the ability of the Shapley value of a given sensor observation to determine if that observation is anomalous. First, we prove that for cases with independent sensor observations, an optimized anomaly test using the Shapley value is equivalent to an optimized lower-complexity anomaly test using a single term in the Shapley value calculation, yielding the exact same probability of error. For some popular dependent observation cases involving two sensors, including correlated bivariate Gaussian/Laplacian probability density functions and constant/Gaussian at- tacks/anomalies, we prove that these two tests are fundamentally different, yielding different decision regions and error probabil- ities. Further, we prove that the Shapley value test is sometimes strictly inferior to the other (single term in Shapley calculation) test in certain statistically dependent bivariate Gaussian scenarios with large correlation magnitude and additive attacks/anomalies, while it is strictly superior in others, depending on the sign of the correlation. One can combine these two approaches to obtain a strictly better approach in these cases. These results, which provide the first theoretical statistical analysis of Shapley-based localization, seem very interesting based on the wide acceptance of the Shapley value by many researchers and should encourage further research on this topic. Numerical results are provided which illustrate our findings.

Interpretable machine learning requires models that are accurate and structurally faithful to the data. Existing explainability methods rely heavily on additive representations (e.g., Generalized Additive Models (GAMs), SHapley Additive exPlanations (SHAP), functional ANOVA), which can suffer from signal cancellation and off-support extrapolation in the presence of strong interactions. We propose Tensor Separation Learning (TSL), a regression model that learns a sum of rank-1 products of univariate per-feature functions via a stagewise greedy procedure with orthogonal refitting. By enforcing separability, TSL avoids the information loss inherent in additive projections caused by marginalizing higher-order interactions. The learned TSL model can be fully reconstructed from first-order partial dependence functions, up to constant factors. This stage-wise correspondence ensures that the resulting visualizations are faithful to the fitted components. We establish approximation-rate guarantees for functions with bounded mixed $p$-th order partial derivatives and demonstrate that TSL competes with black-box models on regression benchmarks.

Intrusion Detection Systems (IDS) in Internet of Things (IoT) environments face significant challenges due to data heterogeneity, lack of labeled data, and limited model interpretability. Federated Learning (FL) offers a privacy-preserving solution; however, existing approaches such as SOH-FL suffer from two key limitations: reliance on a manually tuned aggregation parameter γ and lack of explainability in model predictions. In this paper, we propose XAI-SOH-FL, an enhanced framework that integrates adaptive aggregation and explainable artificial intelligence into the SOH-FL paradigm. First, we introduce a dynamic γ selection mechanism based on similarity thresholding, enabling the aggregation process to adapt to evolving data distributions. Second, Bayesian Optimization is employed to automatically determine optimal γ values, eliminating the need for manual tuning. Third, SHAP (SHapley Additive exPlanations) is incorporated to provide feature-level interpretability for intrusion detection decisions. Experimental evaluation on the CICIDS2017 dataset demonstrates that the proposed approach achieves an accuracy of 94.12% and an F1-score of 0.92, outperforming the baseline SOH-FL model while converging in fewer communication rounds. Furthermore, SHAP-based analysis reveals that flow-level features such as Flow Duration and Packet Length significantly influence model predictions. These results indicate that XAI-SOH-FL provides an effective balance between accuracy, adaptability, and interpretability in heterogeneous IoT environments.

Federated learning is an emerging distributed paradigm that addresses the challenges posed by heterogeneous, privacy-sensitive data. It enables multiple clients to train a model collaboratively by aggregating their local updates at a server. However, conventional aggregation schemes typically use fixed weights that fail to reflect unequal and time-varying client contributions, leading to biased and unstable learning. To improve fairness and stability, we propose the Trajectory Shapley Value (TSV), a contribution metric that evaluates how each client influences the optimization trajectory of the global model using a validation-based, temporally consistent utility. Building on TSV, we design FedTSV, an adaptive aggregation method that converts per-round evaluations into dynamic client weights, allowing the server to respond to heterogeneous and adversarial participation in real time. Experiments on benchmark datasets show that FedTSV accelerates convergence, improves robustness, and yields more equitable contribution assessments, thereby providing a principled foundation for fairness-aware federated optimization.

As large language models (LLMs) are increasingly integrated into high-stakes decision-making, the ability to reliably quantify uncertainty has become a critical requirement for safety and trust. However, current uncertainty quantification methods primarily operate at the output level, often failing to distinguish whether uncertainty arises from the model's lack of knowledge or from ambiguity in the user's input. While input-centric uncertainty quantification has recently emerged as a promising direction, it remains relatively underexplored and typically relies on coarse, input-level information. Consequently, users are provided with scalar uncertainty scores that offer little actionable guidance on which parts of the input should be clarified to improve reliability. To address this limitation, we propose Shapley-based input uncertainty Quantification (ShaQ), a framework for span-level attribution of input-induced uncertainty. Our approach models ambiguous spans in the input as players in a cooperative game and quantifies their contributions using Shapley values, defined via the weighted average of marginal reductions in conditional entropy obtained by clarifying each span coalition. Unlike existing input-level approaches, our formulation captures complex interactions among spans and provides a principled decomposition in which individual attributions sum exactly to the total input-induced uncertainty. We evaluate ShaQ on the AmbigQA and AmbiEnt benchmarks, where it achieves state-of-the-art performance in ambiguity detection. We further demonstrate its utility on MediTOD, showing that ShaQ can localize under-specified clinical utterances and facilitate human-AI collaboration in high-stakes settings. Overall, ShaQ improves uncertainty estimation and provides actionable insights for targeted input clarification.

Electricity expense management presents significant challenges, as this resource is susceptible to various influencing factors. In universities, the demand for this resource is rapidly growing with institutional expansion and has a significant environmental impact. In this study, the machine learning models long short-term memory (LSTM), random forest (RF), support vector regression (SVR), and extreme gradient boosting (XGBoost) were trained with historical consumption data from the Federal Institute of Paraná (IFPR) over the last seven years and climatic variables to forecast electricity consumption 12 months ahead. Datasets from two campuses were adopted. To improve model performance, feature selection was performed using Shapley additive explanations (SHAP), and hyperparameter optimization was carried out using genetic algorithm (GA) and particle swarm optimization (PSO). The results indicate that the proposed cooperative ensemble learning approach named Weaker Separator Booster (WSB) exhibited the best performance for datasets. Specifically, it achieved an sMAPE of 13.90% and MAE of 1990.87 kWh for the IFPR-Palmas Campus and an sMAPE of 18.72% and MAE of 465.02 kWh for the Coronel Vivida Campus. The SHAP analysis revealed distinct feature importance patterns across the two IFPR campuses. A commonality that emerged was the strong influence of lagged time-series values and a minimal influence of climatic variables.

Multi-agent LLM decision systems for portfolio management still lack a principled way to assign credit across specialist agents, remain vulnerable to cold-start dominance under regime shifts, and offer limited transparency into how final allocations are formed. We propose Market Regime Council (MRC), a cooperative multi-agent decision system that computes exact Shapley credits across all single, pairwise, and Grand-coalition outputs for online agent weighting. Instantiated with N=3 specialist agents, at each trading period, MRC recomputes coalition-based Shapley weights from exponentially weighted performance histories, uses a Bayesian adaptive mixture to stabilize early periods, applies regime-dependent multipliers to adjust agent authority, and records each rebalance through a five-layer causal trace. Over 1,037 trading days across 13 crypto assets and five seeds, MRC achieves a Sharpe ratio of 1.51 and a cumulative return of 440.1%, ranking first on CR, SR, and IR among active baselines and attaining the lowest MDD among active methods. Ablation results show that the gains come from Shapley-weighted integration across coalition outputs rather than from any single stage in isolation. Code and demo data are included in the supplementary material.

Shapley additive explanations (SHAP) are widely recognised as computationally intractable for neural networks, since they induce an exponential search space over the input features. In this work, we take a first step towards scaling exact SHAP computation to larger search spaces by introducing an algorithm that leverages recent advances in neural network verification to compute arbitrarily tight exact lower and upper bounds on SHAP values for neural networks, ultimately recovering the exact SHAP values. We demonstrate that our approach scales to orders of magnitude larger search spaces than state-of-the-art exact methods. This provides an important first step towards exact SHAP computation and establishes a principled cornerstone for evaluating statistical approximation methods on larger search spaces.

Temporal knowledge-graph data marketplaces face three coupled failures in static designs: stale hybrid index shortcuts reduce recall as edges evolve, stationary Shapley pricing misattributes value after distribution shifts, and uncoordinated agents over-consume a shared differential-privacy budget. We present CHRONOS, a three-layer architecture providing a unified treatment of these challenges with explicit public and private separation. Layer one applies neural-ODE temporal decay to shortcut edges, providing a per-query expected recall-loss bound of Big-O of Pq lambda delta t, with a monotone-envelope guarantee reducing bound looseness to 1.8 to 3.2 times observed loss. Layer two conditions Shapley valuation on detected changepoints and provides finite-sample error guarantees under noise. Layer three uses EXP3-IX to achieve Big-O of the square root of T log T regret while enforcing epsilon and delta differential privacy via moments accounting. CHRONOS releases a privatized affinity matrix per epoch using the Gaussian mechanism; all retrieval and ranking are post-processing, incurring no extra privacy cost. We provide multi-epoch settlement, scalability analysis for 500 sellers, and comparisons against accelerated baselines. Across four benchmarks, CHRONOS shows 0.937 recall at ten, 2.74 queries per second, 161 ms latency, and total epsilon of 4.25 at delta of 10 to the power of negative 6 under zCDP composition. These results indicate a competitive operating point. A limitation is that at this privacy level, released valuations remain noise-dominated; utility derives primarily from public index routing and adaptive scheduling driven by low-sensitivity statistics.

Shapley and Banzhaf interactions capture the complex dynamics inherent in modern machine learning applications. However, current estimators for these higher-order interactions trade off between speed and accuracy. To overcome this limitation, we introduce ProxySHAP. ProxySHAP reconciles the high sample efficiency of tree-based proxy models with a principled path to consistency via residual correction. On a theoretical level, we derive a polynomial-time generalization of interventional TreeSHAP to compute exact interaction indices for tree ensembles, successfully bypassing exponential tree-depth dependencies in prior methods. Furthermore, we formally analyze the residual adjustment strategy, characterizing the specific conditions under which Maximum Sample Reuse (MSR) corrects proxy bias without its variance scaling exponentially with interaction size. Extensive benchmarking demonstrates that ProxySHAP sets a new state-of-the-art standard for approximation quality, including in large-scale applications with thousands of features. By achieving the lowest error in both small- and large-budget regimes, ProxySHAP significantly outperforms the prior best estimators ProxySPEX and KernelSHAP-IQ, while also delivering superior performance on downstream explainability tasks.

Shapley-based data valuation provides a principled way to quantify the contribution of training data, but its high computational cost makes it impractical in dynamic settings where tasks and training players evolve. Existing methods treat Shapley computation as a one-shot process and collapse contributions into aggregated scores, preventing reuse and requiring recomputation under any change. We introduce a new perspective that represents Shapley values as a player-by-task matrix and formulates dynamic valuation as a structured matrix maintenance problem. We exploit the fact that each task depends on a small subset of training players and that similar tasks yield similar valuations, leading to utility locality and coalition locality. Based on these insights, we propose D-Shap, a dynamic valuation framework that enables efficient updates by modifying only a small portion of the matrix: new task valuations are inferred via structure-aware interpolation, while updates induced by new players are confined to affected local matrix blocks. To eliminate the need for pre-specified evaluation tasks, we introduce self-valuation, which constructs the initial matrix directly from training data, supported by scalable subset reuse and coverage-aware anchor selection. Experiments across diverse models show that D-Shap performs task updates in milliseconds and reduces the cost of player updates by up to three orders of magnitude, while achieving valuation quality competitive with full recomputation.

Adaptive hierarchical systems accumulate routing state as they learn which components to select. We show that this state already defines a coherent attribution over the hierarchy. A leaf receives the product of the local routing weights on its path, while an internal node receives the corresponding prefix product. The same learned state can therefore be read consistently at group and component levels, and every finer readout sums exactly to its coarser counterpart. This attribution describes the preferences learned by the deployed router rather than an intrinsic or counterfactual value of a component. Across LLM, Census, agentic, and telecom-network hierarchies, the learned state contains meaningful structure at several levels, and the clearest organisation need not occur at the leaves. In the telecom study, Site- or Region-level readouts usually reveal clearer structure than Cell-level readouts. Comparison with Shapley attribution can then show whether the preferences learned in deployment match capabilities revealed by counterfactual coalitions. The result is a hierarchical explanation that requires no separate attribution model: the same routing state supports consistent explanations at several levels of the system.

Continual learning enables neural networks to learn tasks sequentially without forgetting previously acquired knowledge. However, neural networks suffer from catastrophic forgetting, where learning new tasks degrades performance on earlier ones. We address this problem with Shapley Neuron Valuation (SNV), a principled framework that quantifies Neuron importance in continual learning, grounded in cooperative game theory. SNV selectively freezes important Neurons while keeping others plastic, enabling buffer-free continual learning without expanding architecture. Experiments on ImageNet-1k show that SNV consistently outperforms existing buffer-free methods. In particular, SNV improves accuracy by +2.88% in the class incremental learning and +6.46% in the task incremental learning scenarios compared to the second baseline.