Counterfactual Routing Using Integer Programming with Constraint Generation

We present our submission to the IJCAI 2025 'Counterfactual Routing Competition' (CRC 25). The goal of the competition is to find counterfactual explanations for the shortest path problem. This requires deciding what the minimal changes to a road network would make a route chosen by the user the optimal route. This enables explanations such as "Your suggested route would indeed have been optimal, if road X were not a bicycle path." Our solution models the problem as an integer program, iteratively incorporating constraints until an exact solution is found. In the final evaluation on held-out test instances, our method ranked fourth in solution quality and obtained its solution fastest on every instance, with an average runtime of 9.0 seconds compared to 118.8 seconds for the next-fastest submission.

Taking the Whys Seriously: Limitations of Counterfactual Explanations in Justification and Recourse

Counterfactual explanations (CEs) are widely used in explainable artificial intelligence (AI) to show how a model's outputs would change if the input features were manipulated. This technique is used for a range of tasks such as debugging models, explaining predictions, justifying decisions, and providing algorithmic recourse. In this paper, we explore the normative legitimacy of employing counterfactuals in real-life model deployment settings. We discuss the different stakes involved in these different purposes for which CEs are commonly employed, and find stricter requirements for justification and recourse. In particular, we find that naive application of CEs for justification and recourse can lead to ignoring contestable choices made throughout the machine learning (ML) pipeline, thus obfuscating that decisions and counterfactuals for those decisions are also artifacts of an organization's materialized design and governance choices. We demonstrate this with four empirical experiments involving interventions at stages of the ML pipeline ``upstream" of the explanation itself, and show that these affect the generated counterfactuals. We find that an organization's choices on measurement models for feature and labels, business requirements, model validation, and the metric of model success have as much or more impact on the generated counterfactuals as the specifics of the generating method. Our findings underline the need to account for such choices upon providing justification and recourse, providing a stark reminder of the relational nature of these tasks. As putative justifications or recourse recommendations, CEs do not provide adequate answers to some important "why"-questions because they preclude consideration of whether the decision-maker ought to have acted differently.

Towards A Unified Information Bottleneck Framework for Time Series Explanations

Explaining deep learning models operating on time series data is crucial in various applications that require transparent and interpretable insights into model behavior. {Existing explanation methods generally fall into two categories: attribution-based explanations, which identify the temporal regions most responsible for a prediction, and counterfactual explanations, which reveal how an input should be modified to alter the model's decision.} {Despite valuable insights, these two fields are largely studied independently. This disconnect leaves attribution methods lacking causal validation, while counterfactual methods suffer from severe instability, producing adversarial-like noise instead of meaningful explanations.} In this work, we revisit time-series explainability from an information-theoretic perspective and show that existing explainers are vulnerable to trivial solutions and distributional shifts. To address these limitations, we propose a unified objective function for explainable time series learning that bridges attribution and counterfactual reasoning within a single framework. Building upon the Information Bottleneck principle, our formulation explicitly prevents trivial explanations and out-of-distribution counterfactuals. {Based on this objective function, we introduce {\modelname}, a novel explanation framework that learns a parametric transformation network to construct explanation-embedded instances, where preserved information yields attribution explanations and controlled information removal produces stable counterfactual explanations.} We evaluate {\modelname} on synthetic and real-world benchmarks against state-of-the-art baselines. Extensive quantitative and qualitative results show that {\modelname} consistently outperforms competing methods, yielding faithful attributions and stable counterfactual explanations.

Counterfactual Transition Graphs: Evaluating Cross-Class Transition Quality

Counterfactual (CF) explanations for time-series classifiers are usually evaluated one example at a time: what minimal edit flips this single window's prediction? We argue that the more informative question for diagnostic interpretability is structural: how does the classifier connect its own classes to each other? We propose a counterfactual transition graph (CGT) in which each node is a class and each edge weight is the CF reliability of the transition from one prototype to another under a proximity aware retrieval sweep. On a six-class hand-movement task, we induce a CGT that reveals a non-trivial topology, which is not predicted by the binary confusion matrix: it shows that counterfactual reachability does not align with classifier accuracy and even runs counter to it (Spearman $ρ=-0.37$ over the 15 pairs), i.e. the boundaries the classifier separates most confidently are among those an in-distribution edit can least often cross. Our framework is method agnostic, i.e. any CF-explainers can be used. Presently, we use it to juxtapose replacement-based CFs with gradient-based CFs; gradient-based methods reach almost any class by stepping off the data manifold, while replacement-based methods stay on it and fail on precisely the rigid boundaries.

Counterfactual Contrastive Analysis

Visual Counterfactual Explanations (VCEs) aim to explain image classifiers by generating minimally edited and realistic versions of an input image that change the classifier's prediction. Existing VCE methods are inherently classifier-dependent and therefore susceptible to classifier biases and failure modes, such as sensitivity to shortcut features and calibration errors. In this paper, we propose a classifier-free approach for visual counterfactual generation based on Contrastive Analysis (CA). Given two datasets corresponding to different classes (e.g., healthy and patients), we disentangle the generative factors that are common across the two datasets from those that are salient to each dataset, and generate counterfactual images by swapping only the salient factors. By operating directly on data distributions rather than decision boundaries, our method provides model-agnostic VCEs that are less sensitive to classifier biases. Our approach leverages the high-quality synthesis and well-structured latent space of StyleGAN2. We use the feature space F, instead than the usual W-space, to improve detail preservation. Unlike conventional CA approaches, which typically assume salient factors in only one dataset, we introduce an adapted framework and loss functions for VCE that allow multiple salient factors in each dataset. We evaluate our method on three medical imaging datasets and demonstrate superior counterfactual generation quality compared to existing approaches.

From Student Risk Prediction to SC2R: Semantics-Constrained Counterfactual Recourse for Educational Decision Support

Learning analytics models can identify students at risk of poor performance, but they do not directly indicate which interventions are feasible, actionable, and compatible with educational constraints. This paper introduces SC2R, a semantics-constrained counterfactual recourse framework for educational decision support. SC2R combines a calibrated predictive model, integer-programming-based recourse generation over discrete action variables, a lightweight RDF vocabulary for intervention-plan representation, and SHACL validation for enforcing timing, budget, immutability, and availability constraints. The framework is evaluated offline on the OULAD dataset using snapshots constructed relative to each assessment at two decision horizons. Results show that the predictive component provides strong performance, that compact intervention plans can be generated at scale, and that semantic validation reveals infeasible plans that lighter optimization-only settings would otherwise accept. Rather than claiming causal improvement in student outcomes, this work shows that counterfactual recourse becomes more operationally meaningful in education when recommendations are not only model-valid, but also semantically feasible and machine-checkable.

Command-Space Counterfactual Explanations for Pareto-Conditioned Reinforcement Learning

Pareto Conditioned Networks learn multiple multi-objective reinforcement learning behaviours by conditioning a single policy on a desired return command. However, the local mapping from command and state to action remains opaque. We propose command-space counterfactual explanations for PCNs: given a fixed state, original command, and foil action, we search, in a black-box setting, for a minimally changed desired-return command under which the same trained policy would choose the foil. Our contributions are threefold. First, we formulate PCN explanations as return-command interventions, using a return-only PCN variant that avoids the added ambiguity of horizon-conditioning. Second, we adapt adversarial machine learning methods to reinforcement-learning explanations. Third, we introduce a boundary-seeded directional search that improves over purely local optimization in the command-action landscape, resulting in our proposed approach CF-ZOO. The resulting explanations are actionable and intuitively expressed in the user's own preferences: "If your trade-off had shifted slightly towards X, the agent would have chosen Y."

Faithful, Sufficient and Understandable: Rethinking Graph Counterfactual Explanations via Discrete Diffusion Inversion

Graph Neural Networks (GNNs) achieve strong predictive performance on graph-structured data across domains such as chemistry, biology, and network analysis, yet they provide no intrinsic explanation of their predictions. This limits their adoption in high-stakes and safety-critical settings. Counterfactual explanations address this by revealing the minimal structural modifications that would change a model's prediction. On graphs, however, such a modification is hard to produce. The search space is discrete and combinatorial, and a valid answer must respect categorical node and edge types together with domain rules such as chemical valency in the case of molecular graphs. Existing explainers give up one of two things. Either edits are not held on the data manifold, or the search does not span the full edit space. We propose Graph Diffusion Counterfactual Explanation via Inversion (GDCE-I), which gives up neither. A discrete denoising diffusion model with a novel discrete inversion scheme enables distribution-aware edits leveraging the whole domain edit space. We further address the incomplete and inconsistent evaluation of graph counterfactuals by deriving a framework of explanation desiderata and applying it to every method under one shared protocol. Across four benchmarks, GDCE-I outperforms related work by a large margin on the defined framework. For the molecular domain, we further qualitatively show that GDCE-I attains interpretable in-distribution solutions.

COGENT: Counterfactual Gaussian Explanations for Volumetric Medical Images

Explainability is essential for deploying deep learning models in high-stakes medical applications. Existing explainability methods for volumetric imaging predominantly operate in voxel space, overlooking the structured representations introduced by recent advances in 3D scene modeling. We present COGENT (Counterfactual Gaussian Explanations), a framework that generates counterfactual explanations directly in the parameter space of Gaussian-based volumetric representations. Built upon MedGS and the Sybil lung cancer risk prediction model, COGENT optimizes selected Gaussian primitives through a differentiable rendering pipeline, enabling gradients from the downstream predictor to identify representation components that most influence model decisions. Unlike conventional pixel- or voxel-level attribution methods, our approach formulates explainability as a counterfactual optimization problem over an explicit 3D scene representation, producing sparse and spatially localized explanations while preserving anatomical consistency. We evaluate COGENT on lung CT scans using quantitative comparisons with existing explainability methods together with qualitative analysis by medical experts. The results demonstrate that representation-space counterfactual optimization provides clinically meaningful explanations while offering a new perspective on interpreting volumetric deep learning models.

FiRe: Fixed-Noise Refinement for Visual Counterfactual Explanations

Visual counterfactual explanations aim to change classifier decisions through realistic and localized edits while preserving decision-irrelevant content. Existing DDPM-based methods typically perform classifier-guided editing along a long reverse denoising trajectory. The changing noise levels make semantic editability and spatial control difficult to balance, and the editable state is noisy, whereas the target classifier is trained on clean images. As a result, these methods require either costly recursive denoising or low-quality one-step estimates to obtain classifier-facing clean images. We propose FiRe, a Fixed-noise Refinement framework for visual counterfactual explanations. Rather than following a reverse denoising trajectory, FiRe maps the input to a fixed noise level and iteratively refines the noisy state at that level. To provide clean images for classifier guidance, FiRe first adapts Pixel Mean Flow to visual counterfactual explanation, enabling direct clean-image prediction from noisy states. To make fixed-noise refinement produce minimal and localized counterfactual edits, FiRe introduces three FiRe-specific controls: a dynamic dual-mask strategy, adaptive guidance, and early stopping, which determine where edits accumulate, which changes become visible, and when refinement stops. Experiments on five tasks across three datasets show that, compared with the strongest recent baseline, FiRe achieves about 3$\times$ faster online inference and 8$\times$ fewer FLOPs while obtaining comparable or state-of-the-art counterfactual quality.

IMFACT: Counterfactual Explanations for Time Series via Intrinsic Mode Function Substitution

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.

Diverse and Plausible Algorithmic Recourse via Tractable Recourse Distributions

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.

A Generalized-Bayes Perspective on Counterfactual Explanations: Posterior-Based Decision-Making and Evaluation

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.

Class-Aware Reinforcement Learning for Counterfactual Explanation Generation

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.

SPARC Segmentation to Prediction via Affine Regression and Counterfactuals

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.

Counterfactual Explainability Framework With CycleGAN And Counterfactual-Classifier Alignnment Score for Retinal Disease Classification

Automated detection of vision impairing retina-based ocular conditions from fundus images is important for early screening, timely referral and reducing dependency on specialist-only assessment, for which neural network-based deep learning (DL) models have been widely utilized. However, explainability of the DL frameworks remains a major bottleneck for clinical adoption, particularly when model decisions are not linked to retinal regions that are clinically meaningful. To address this issue, this study presents CounterFundus, a novel CycleGAN-driven counterfactual explainability framework, integrating EfficientNet-B5-based retinal disease detection with visually interpretable disease-to-normal fundus image translation. For each pathological image, the counterfactual yielded by the CycleGAN generator represents an estimated healthy counterpart and the resultant difference map is utilized to localize disease-associated retinal changes. Unlike conventional post-hoc saliency methods, CounterFundus provides counterfactual explanations through visually plausible disease-to-normal retinal translation. Thereafter, to quantify the spatial agreement between counterfactual difference maps and classifier saliency, the Counterfactual-Classifier Alignment Score (CCAS) is introduced, embedding Spearman correlation, binary IoU and pointing accuracy into a single assessment protocol. To this end, EigenCAM-aligned evaluation demonstrates that the generated counterfactual explanations remain spatially consistent with classifier-relevant retinal evidence across all CCAS dimensions. Along with that, ablation studies further confirm that CCAS-filtered counterfactual augmentation improves the downstream classification performance in fundus images, establishing CounterFundus as a clinically-grounded, explainable artificially intelligence (XAI) framework for retinal disease detection.

ConceptCF: Concept-based Counterfactuals for the Explainability of Time Series

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.

SurvCF(t): Counterfactual Explanations for Survival Analysis in Predictive Maintenance Multivariate Time Series Data

Predictive maintenance relies on accurate Remaining Useful Life estimation, often formulated using survival analysis over multivariate time-series data. While modern deep survival models achieve strong predictive performance, their black-box nature limits their use in safety-critical settings where actionable insight is required. In this work, we introduce \textit{SurvCF(t)}, the first framework for generating counterfactual explanations for survival models operating on time-series data. \textit{SurvCF(t)} identifies minimal, plausible, and temporally consistent changes to an asset's operational history that increase its predicted life time, framing explanation as a constrained optimization problem combining validity, proximity, sparsity, and plausibility. We evaluate the method on multiple benchmarks, including C-MAPSS, N-CMAPSS, and a real-world case study of the Scania Component\_X dataset, demonstrating its ability to produce actionable and interpretable interventions. Our results show that \textit{SurvCF(t)} bridges the gap between survival prediction and prescriptive maintenance, enabling explainable and decision-oriented AI for maintenance strategies.

Counterfactuals for Feature-Weighted Clustering

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.

CausalGraphX: A Counterfactual Graph Neural Network Framework for Explainable Systemic Risk Assessment

The interconnected nature of global financial systems makes them vulnerable to systemic risks, where the failure of a few institutions can trigger catastrophic cascading defaults. Traditional risk models often fail to capture the complex, non-linear dynamics of these networks. While Graph Neural Networks (GNNs) have shown promise in modeling relational data, they primarily learn correlative patterns and function as black boxes, offering little insight into the causal mechanisms of shock propagation. This limitation is critical for regulators who require explainable models to perform stress tests and devise effective interventions. We introduce CausalGraphX, a novel framework that integrates GNNs with counterfactual reasoning to provide explainable assessments of systemic risk. CausalGraphX employs a Graph Attention mechanism to learn representations of institutional vulnerability and uses an adversarial regularization technique to ensure these representations capture causal drivers rather than spurious correlations. Furthermore, we propose an optimization-based approach to generate counterfactual explanations, answering questions such as, "What minimum capital injection would have prevented Bank A's default under a specific stress scenario?" We validate CausalGraphX on large-scale synthetic financial networks. Our results demonstrate that CausalGraphX significantly outperforms traditional and deep learning baselines in predicting cascading defaults while providing sparse, plausible, and actionable counterfactual explanations.

Explaining Reinforcement Learning Decisions in Self-adaptive Systems

Reinforcement Learning (RL) has been extensively used in autonomous and self-* systems, but RL policies, especially deep RL ones relying on neural networks, lack transparency and are difficult to understand. This can lead to diminished user trust, and makes for a more challenging verification of systems. To address this challenge, this paper introduces Explanations using Alternative Realities for Reinforcement Learning (EARL), a Python library to produce counterfactual explanations in RL settings. This library allows the user to produce explanations by exploring What-if scenarios to clarify agent behavior by comparing possible outcomes. Counterfactual explanations have been shown to be intuitive and user-friendly in psychology research, but have only recently been explored in RL, with existing implementations usually limited to toy examples and benchmarks. EARL supports counterfactual explanation generation in realistic RL-based self-adaptive systems. To demonstrate its applicability, we demonstrate its use in a simulation of CitiBikes, a self-adaptive bike-sharing system, and we provide evaluations showing how it performs in real applications.

Personalized Causal Recourse: A Human-In-The-Loop Approach

Algorithmic recourse addresses the challenge of providing tailored recommendations to users affected by unfavorable machine learning decisions, in potentially high-stakes scenarios. Traditional approaches to recourse often rely on the closest counterfactual explanations or assume a priori knowledge of a user's causal structure, resulting in interventions that overlook individual contexts and specific feature interactions. To overcome these limitations, we study a human-in-the-loop framework that iteratively approximates the user's structural causal model through interactive queries via Bayesian inference before producing recourse recommendations. This framework exploits humans' feedback to improve the identification of causal effects, allowing personalized recourse that is plausible, cost-effective, and aligned with the actual causal dependencies of each user. As a proof of concept, we evaluate this framework through simulated human responses. Our simulations across linear and non-linear causal models show promising results, though challenges remain in capturing complex, non-linear structures, emphasizing the importance of accurate approximations and robust noise distribution modeling.

Adaptive Group-Based Counterfactual Explanations for Time-Series Rehabilitation Data

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.

Profit-Based Counterfactual Explanations for Product Improvement: A Case Study of Manga Sales in Japan

Counterfactual explanation (CE) is widely used to enhance the interpretability of machine learning models and support data-driven decision-making based on model predictions. However, existing CE methods typically require two exogenously specified inputs: a desired output value (target) and a distance function that quantifies changes in explanatory variables. In regression settings, neither the validity of target specification nor the practical interpretation of the distance metric has been sufficiently addressed. Furthermore, most existing CE methods focus on altering predictions rather than optimizing a decision objective, even though real-world decision-making often requires explicit objective maximization. To address these limitations, we formulate CE as a profit maximization problem in management and marketing contexts and propose a framework termed profit-based counterfactual explanation (PBCE). PBCE eliminates the need for exogenous target specification by directly maximizing profit as the primary optimization objective. Concurrently, the distance term is reinterpreted as the cost of modifying product attributes, providing a clear and economically grounded interpretation.

PACE: A Neuro-Symbolic Framework for Plausible and Actionable Counterfactual Explanations

Counterfactual explanations explain machine learning predictions by identifying minimal input changes that would alter a model's decision. Although many existing methods successfully generate prediction-changing alternatives, they often produce unrealistic or infeasible recommendations due to a lack of explicit mechanisms for incorporating domain knowledge and intervention constraints. Neuro-symbolic AI offers a promising direction by combining data-driven predictive models with symbolic reasoning capable of representing human-understandable rules and feasible actions. This paper presents PACE, a modular neuro-symbolic framework for generating feasibility-aware counterfactual explanations. The framework separates prediction and reasoning into two components: a neural predictive model for classification and a symbolic reasoning layer that enforces domain-specific constraints during counterfactual generation. By explicitly modeling feasible interventions, the framework produces explanations consistent with domain knowledge while remaining interpretable and actionable. The approach is model-agnostic and adaptable to domains requiring realistic decision support. A case study is conducted on the Adult Income dataset, combining a multilayer perceptron classifier with Answer Set Programming (ASP) rules encoding feasible modifications to education, occupation, and working hours while preserving immutable attributes. Results highlight the trade-off between counterfactual validity and plausibility and show that symbolic constraints yield explanations that better satisfy domain-specific feasibility requirements, illustrating the potential of neuro-symbolic methods for transparent, feasibility-aware counterfactual explanation in explainable AI.

Introspective Coupling: Self-Explanation Training Tracks Behavioral Change Despite Fixed Supervision

When does training language models (LMs) to generate explanations of their predictions yield faithful introspection, rather than superficial imitation? We study LMs trained to explain which features of their inputs influenced their behavior, using models' counterfactual behavior on modified inputs as supervision. Surprisingly, we find that LMs trained on fixed counterfactual explanations derived from earlier checkpoints of themselves, or even from behaviorally similar models in different families, frequently produce explanations more faithful to their own current behaviors than to those of their training targets. This "introspective" coupling between LM explanations and behaviors occurs when training explanations remain sufficiently correlated with current behaviors over the course of training, even as behaviors themselves shift. We also show that introspective coupling tracks behavior shifts: when explanation training is provided concurrently with other post-training objectives, explanations track those shifts without requiring updated supervision. This phenomenon appears in multiple tasks, including sycophancy and refusal, and is robust to label noise. Overall, our results show that even fixed datasets of counterfactual explanations can provide scalable and generalizable post-training signal for introspection.

RECAST: Model Reconstruction via Counterfactual-Aware Wasserstein Geometry under Limited Data

Counterfactual explanations (CFs) help understand machine learning models by identifying minimal input changes that would lead to alternative model outcomes. Recent work demonstrates their utility for reconstructing black-box models, enabling third-party auditing of opaque decision systems for fairness and accountability. Still, CF-based reconstruction may suffer from decision boundary shifts, overfitting, and restrictive assumptions requiring online query access to target platforms. We propose REconstruction via Counterfactual-Aware waSserstein opTimization (RECAST) under limited data and restricted access, a behavioral surrogate model based on Wasserstein barycentric prototypes. Our approach addresses decision boundary shifts by incorporating CFs as informative, though less representative, samples for both classes, maintaining high surrogate fidelity in low-sample regimes without requiring online access during reconstruction. To enhance fairness auditing, our method enables systematic group fairness diagnostics. Experiments on real-world datasets and various setups show that RECAST effectively achieves high fidelity and query efficiency, as well as stable results even when the access is limited and noisy.

Target-confidence Recourse Using tSeTlin machines: TRUST

Counterfactual explanations are widely used to provide algorithmic recourse in high-stakes decision-making systems. Most existing methods seek the smallest change to an input that flips a model's decision. However, decision-makers often rely not only on predicted labels but also on confidence thresholds and risk margins. Counterfactuals that barely cross a decision boundary can be fragile and unstable under noise or model variation. In this paper, we propose Target-confidence Recourse Using tSeTlin machines (TRUST), a framework in which users explicitly specify the desired prediction confidence for recourse. Rather than generating counterfactuals and evaluating confidence afterward, TRUST directly searches for minimal changes that satisfy a user-defined confidence target, enabling comparison of recourse options in terms of cost, confidence, and robustness. We instantiate TRUST using a Probabilistic Tsetlin Machine (PTM) combined with Bayesian optimization. The probabilistic clause-based structure of PTM links prediction confidence to the stability of decision rules. We show that counterfactuals satisfying the same rules can still differ substantially in reliability depending on how securely they satisfy those rules, revealing whether decisions are supported by robust or fragile clause activations. Experiments on synthetic and real-world datasets demonstrate that target-confidence counterfactuals produce more robust and interpretable recourse than conventional boundary-based approaches. Across multiple benchmarks, TRUST achieves perfect robustness while maintaining low recourse cost, including an L2 distance of 0.10 on the Haberman dataset at 0.92 confidence. By explicitly controlling confidence and exposing rule-level stability, TRUST provides actionable recourse for high-stakes decision support.

P$^2$CE: Model-Agnostic Plausible Pareto-Optimal Counterfactual Explanations

The increasing use of machine learning algorithms in social applications has raised concerns about fairness and transparency, leading to the development of counterfactual explanations. These explanations supports individuals to understand and potentially alter unfavorable decisions in areas such as loan applications, job selections, and more, by providing actionable changes to input features that would lead to a desired outcome. Existing methods often struggle to balance feasibility, plausibility, and computational efficiency. To address this, we introduce P$^2$CE, an algorithm for generating plausible Pareto-optimal counterfactual explanations, offering users a diverse set of optimal trade-offs between different notions of feasibility. P$^2$CE employs an auxiliary isolation forest outlier detector to ensure that explanations are in accordance with the data distribution and leverages SHAP values to obtain optimal results with short computing times, regardless of the underlying model. Our algorithm was empirically evaluated on three datasets, demonstrating superior performance in terms of both solution quality and computational efficiency compared to related techniques.

ConTex: Reformulating Counterfactual Generation For Time Series Forecasting

Decision-making with deep learning-based time series forecasting requires not only accurate predictions but also actionable insights. However, current architectures do not inherently provide such information. Specifically, guidance is needed on how current conditions must be modified to shift from a predicted outcome to a desired future scenario. Counterfactual explanations provide a natural framework for this task, as they represent minimal input changes that alter the model's prediction, indicating when and how intervention is required. Existing approaches rely on instance-wise optimization, leading to inconsistency across instances, high computational costs, and limited applicability in real-time settings. To address these limitations, we reformulate counterfactual generation for time series forecasting as the problem of learning a globally consistent intervention strategy, allowing counterfactuals to be generated through a single shared function. We propose Counterfactual Time Series Explanations (ConTex), a model-agnostic, decomposed architecture comprising a temporal context encoder and a conditional encoder, followed by two heads that capture interventions in terms of temporal relevance and modification strength. This structure overcomes the instability and inconsistency of instance-based approaches by producing targeted, interpretable interventions across time and feature dimensions in a single forward pass, making it suitable for real-time applications. Across multiple forecasting architectures and benchmark datasets, ConTex achieves state-of-the-art validity while generating sparse counterfactuals that minimize the number of necessary interventions. Additionally, our approach reduces computational cost by at least 12-36x compared to instance-wise generation and supports real-time inference at approximately 0.007 seconds.