Feature Attribution

Feature attribution methods promise to identify which input features matter for a model output. In generative language models, however, it is often unclear what should count as a feature in the first place. In autoregressive language models, earlier generated tokens are both outputs of the model and inputs to later predictions. In diffusion language models, generation proceeds through iterative denoising or unmasking rather than fixed left-to-right prediction, so local explanation may target a state of diffusion rather than a next token. We argue that this ambiguity is not merely an implementation detail, but a conceptual limitation of carrying classifier-era feature attribution directly into generative language modeling. We introduce the Attribution Contract, a specification for feature-attribution claims that names what output is being explained, which features are eligible to receive attribution, what generative process is assumed, what is held fixed, and what model score is being attributed. The contract clarifies why the same attribution method can answer different questions depending on how it is instantiated. We argue that many disagreements about feature attribution in generative language models are not disagreements about attribution algorithms, but about unstated explanatory contracts. Using autoregressive and diffusion language models as case studies, we show when attribution to earlier generated tokens, intermediate states, or denoising stages is informative, when it is misleading, and why feature-attribution methods in generative language models should be evaluated as method-contract pairs.

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.

We observe that existing model interpretation methods generally ignore the baseline, and such neglect often results in imprecise or even incorrect interpretation. In this paper, we reformulate the task of model interpretation and the interpretation principles for model interpretation results to demonstrate the importance of the baseline. For the first time, we unify gradient-based methods, Integrated Gradients (IG), and Taylor expansion, clarify the relationships among the three, and explicitly identify the corresponding baseline for each method. This may have a significant impact on the further performance improvement of some gradient-based schemes. On this basis, we analyze the flaws and errors in related model interpretation methods (IG, LayerCAM, ODAM, Difference Map). We advocate evaluating the quality of model interpretation results precisely through the attribution error between the attribution result and the attribution target, rather than adopting flawed evaluation methods, such as those based on marginal-effect or the assumption of perfect model performance. We revise IG and develope a model interpretation method with a clear and reasonable baseline, achieving better results. Our method supports model interpretation based on features from any layer. Interpretation based on features from different layers are all reasonable, and the differences among these results reflect varying degrees of feature extraction at different feature extraction stages.

Explaining graph neural networks (GNNs) has become more and more important recently. Higher-order interpretation schemes, such as GNN-LRP (layer-wise relevance propagation for GNN), emerged as powerful tools for unraveling how different features interact thereby contributing to explaining GNNs. GNN-LRP gives a relevance attribution of walks between nodes at each layer, and the subgraph attribution is expressed as a sum over exponentially many such walks. In this work, we demonstrate that such exponential complexity can be avoided. In particular, we propose novel algorithms that enable to attribute subgraphs with GNN-LRP in linear-time (w.r.t. the network depth). Our algorithms are derived via message passing techniques that make use of the distributive property, thereby directly computing quantities for higher-order explanations. We further adapt our efficient algorithms to compute a generalization of subgraph attributions that also takes into account the neighboring graph features. Experimental results show the significant acceleration of the proposed algorithms and demonstrate the high usefulness and scalability of our novel generalized subgraph attribution method.

Transformer-based language models such as BERT having 110M+ parameters have revolutionized natural language understanding, yet their internal mechanisms remain largely opaque to researchers and practitioners. Traditional attention-based interpretability methods often emphasize structurally important but semantically weak tokens such as punctuation marks rather than meaningful semantic relationships. This work introduces a lightweight and model-agnostic framework for quantifying token-level representational importance using hidden-state activation strengths at Layer 8 of BERT. The proposed Activation Flow Network (AFN) framework computes Token Activation Strength using the L2 norm of Layer-8 hidden representations, enabling direct ranking of semantically salient tokens. The study further introduces a threshold-based activation bucket formulation that partitions tokens into HIGH-activation and LOW-activation groups using an empirical upper-quartile activation boundary. Experimental observations demonstrate that semantically meaningful content words consistently occupy the HIGH-activation bucket and dominate representational activation shifts, while structurally supportive tokens contribute comparatively less. The results suggest that Layer 8 acts as a critical semantic consolidation zone balancing structural and semantic information processing. By revealing how activation magnitudes concentrate around semantically informative tokens, this work provides an interpretable and computationally efficient alternative to attentioncentric analysis, contributing toward transforming BERT from a "black box" into a more transparent "glass box" model for natural language understanding.

Post-hoc explainable AI (XAI) methods typically produce deterministic attribution maps, whereas Bayesian neural networks (BNNs) induce a distribution over explanations. Capturing the variability of this distribution is important for uncertainty-aware decision-making. This paper formalises the \emph{explanation distribution} as the push-forward measure of the BNN posterior through any Lipschitz-continuous attribution operator. It further proposes the uncertainty-aware relevance attribution operator (UA-RAO), a general family of operators that summarises the explanation distribution using the mean, variance, coefficient of variation, quantiles, and set-theoretic aggregation measures. Theoretical support is provided through Monte Carlo accessibility and Wasserstein approximation bounds. The framework is evaluated on a 15-class power quality disturbance (PQD) classification benchmark, comparing three BNN approximations paired with three attribution operators using relevance mass accuracy and intersection-over-union as localisation metrics. Results show that deep ensembles with the mean UA-RAO improve localisation over the deterministic baseline, while other UA-RAO summaries reveal uncertainty patterns absent from point-estimate attributions. Qualitative results on measured signals further suggest that these patterns generalise beyond the synthetic training distribution. The framework is domain-agnostic and can be applied to any BNN paired with a Lipschitz-continuous attribution operator.

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.

We introduce B-cos GNNs, an inherently explainable class of graph neural networks whose predictions decompose exactly into per-node, per-feature contributions via a single input-dependent linear map. B-cos GNNs use linear (sum-based) aggregation and replace non-linear message and update functions with B-cos transforms. This induces meaningful, task-specific weight-input alignment that is directly accessible through the model's dynamic linearity. Instance-level explanations follow from a single forward and backward pass, requiring no auxiliary explainer, modified learning objective, or perturbation procedure. Instantiated as a GIN, our approach trades small losses in predictive accuracy for state-of-the-art explainability across diverse synthetic and real-world benchmarks, producing explanations orders of magnitude faster than post-hoc baselines.

Integrated Gradients (IG) is a widely adopted feature attribution method that satisfies desirable axiomatic properties. However, the choice of integration path significantly affects the quality of attributions, and the standard straight-line path introduces all input features simultaneously, often accumulating noisy gradients along the way. To address this limitation, we propose Spectral Integrated Gradients, which constructs integration paths based on singular value decomposition (SVD) of the baseline-to-input difference. By progressively activating singular components from largest to smallest, SIG introduces global structure before fine-grained details, naturally following a coarse-to-fine progression. Through extensive evaluation across diverse image classification datasets, we demonstrate that SIG produces cleaner attribution maps with reduced noise and achieves improved quantitative performance compared to existing path-based attribution methods. Our code is available at https://github.com/leekwoon/sig/.

The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition is explicit. It is closely connected to SHAP values, generalized additive models, and orthogonal polynomial expansions, and therefore constitutes a fundamental tool for additive explainability. In the more general and realistic dependent setting, however, obtaining a tractable representation and estimating the decomposition from data remain challenging. In this work, we address this problem for continuous inputs. By combining Hilbert space methods with the generalized functional ANOVA, we build an explicit decomposition Riesz Basis allowing to easily compute the decomposition. Our formulation recovers the classical independent case and its associated orthogonal decomposition. Building on this representation, we propose a simple but mighty algorithm to estimate the decomposition from a data sample in a model-agnostic setting and we compare it empirically with several state-of-the-art explanation methods, demonstrating the power of the approach.

We developed a tool for detecting domain shifts, namely subtle differences in the probability distributions of datasets. We identify these shifts using an algorithm designed to detect localised density anomalies in high-dimensional feature spaces. If an anomaly is present, we then identify the feature subspace in which the anomaly is most pronounced. This allows us to trace the domain shift to a small set of features, making the shift interpretable. Moreover, we provide a protocol for compensating domain shifts by extracting, from two unlabelled datasets, subsets of samples with no detectable residual distributional difference. We validate the framework on controlled 20-dimensional benchmarks with known ground truth, recovering both broad and localized shifts together with their supporting feature subspaces. We then apply it to healthy electrocardiogram (ECG) recordings represented by 782 features. In age- and sex-matched cohort comparisons differing in measurement-device composition, the method detects device-induced shifts, extracts representative subsets enriched in the imbalanced device components, and identifies ECG features associated with the acquisition contrast. These results suggest that density-shift detection and subspace attribution provide a practical framework for uncovering hidden cohort biases before downstream modelling.

Multimodal large language models (MLLMs) can produce fluent artwork emotion explanations, but they often suffer from attribute flooding: they enumerate many visible formal attributes without identifying which cues actually support the affective judgment. We therefore formulate artwork emotion understanding as Attribute-Grounded Selective Reasoning (AGSR), where predefined formal attributes serve as evidence units and only emotionally operative attributes should enter the final interpretation. To make this problem measurable, we extend EmoArt, originally introduced at ACM MM 2025 as a 132,664-artwork resource with content, formal-attribute, valence-arousal, and emotion annotations, by adding a 1,400-artwork human salience extension annotated by 15 art-trained annotators. This extension provides instance-level supervision for distinguishing attributes that are merely present from those that are emotionally salient. We further propose FAB-G (Formal-Attribute Bottleneck-Guided reasoning), a supervised multi-agent framework that first predicts attribute-level salience and then constrains downstream emotional analysis to the retained cues. Experiments show that FAB-G yields consistent gains in emotion, arousal, and valence prediction, achieves stronger agreement with human-marked salient attributes under Dice and Tversky metrics, and produces substantially more compact final explanations than prompting-based baselines. Cross-dataset evaluation further suggests that attribute-grounded salience selection transfers beyond the source distribution of EmoArt, while also revealing attribute-specific boundary cases. The dataset and project page are available at https://zhiliangzhang.github.io/EmoArt-130k/

Automated machine learning pipelines increasingly produce models whose predictions must be explained to end users, auditors, and downstream decision systems. The most widely used feature attribution methods (SHAP, Integrated Gradients, LIME) are typically chosen by convention rather than measured fidelity, because rigorous evaluation is impeded by the absence of ground-truth attribution on real data. We propose AGOP-IxG, a fast per-sample attribution method for tabular classifiers that pre-multiplies the per-sample gradient by a top-$K$ rank-truncated Average Gradient Outer Product matrix, and evaluate it against four widely-used baselines on a controlled tabular benchmark designed for AutoML practitioners. In Part 1, we construct three synthetic multi-class tabular tasks (linear, sparse nonlinear, interaction-based) where ground-truth attribution per sample is analytically or numerically derivable, and compare five methods: AGOP-IxG, SHAP (DeepExplainer), Integrated Gradients, InputXGradient, and LIME. AGOP-IxG leads on Spearman rank correlation and noise feature mass on all three synthetic datasets, and on top-$k$ precision on the interaction dataset. Across all settings, AGOP-IxG is approximately $350\times$ to $1{,}650\times$ faster than SHAP. In Part 2, we evaluate global faithfulness on Adult Income and Credit Card Default using the ROAR protocol; the methods cluster within $\sim 1.7\%$ relative AUC, consistent with AGOP-IxG being optimized for per-sample local attribution rather than global feature ranking.

Fully Connected Neural Networks (FCNNs) are often regarded as simple and intuitive architectures, yet they serve as the foundation for more complex models. Nonetheless, the lack of consensus on their interpretability continues to pose challenges, underscoring the enduring relevance of simpler, attribution-based approaches for understanding even the most advanced neural architectures. In this regard, we explore a novel idea for estimating feature attribution, by applying perturbation to the features' attached weights instead of their values. This method offers a fresh perspective aimed at mitigating common limitations in Occlusion techniques, such as Added Bias and Out-of-Distribution data. The application of this rule leads to the formation of a pair of novel attribution methods we call XWP and XWP_c. Founded on simple rules, our methods achieve competitive performance in identifying image signals for simple DNNs, competing with the most established attribution methods on standard baseline metrics. Our work thus contributes to the field of Explainability by introducing a robust framework that paves the way for addressing these long-standing vulnerabilities, and leads to more reliable and interpretable model explanations.

Feature attribution analysis is critical for interpreting machine learning models and supporting reliable data-driven decisions. However, feature attribution measures often exhibit stochastic variation: different train--test splits, random seeds, or model-fitting procedures can produce substantially different attribution values and feature rankings. This paper proposes a framework for incorporating stochastic nature of feature attribution and a robust attribution metric, RoSHAP, for stable feature ranking based on the SHAP metric. The proposed framework models the distribution of feature attribution scores and estimates it through bootstrap resampling and kernel density estimation. We show that, under mild regularity conditions, the aggregated feature attribution score is asymptotically Gaussian, which greatly reduces the computational cost of distribution estimation. The RoSHAP summarizes the distribution of SHAP into a robust feature-ranking criterion that simultaneously rewards features that are active, strong, and stable. Through simulations and real-data experiments, the proposed framework and RoSHAP outperform standard single-run attribution measures in identifying signal features. In addition, models built using RoSHAP-selected features achieve predictive performance comparable to full-feature models while using substantially fewer predictors. The proposed RoSHAP approach improves the stability and interpretability of machine learning models, enabling reliable and consistent insights for analysis.

Class attribution maps (CAMs) provide local explanations for the decisions of convolutional neural networks. While widely used in practice, the evaluation of CAMs remains challenging due to the lack of ground-truth explanations, making it difficult to evaluate the soundness of existing metrics. Independently, most commonly used CAM methods produce low-resolution attribution maps, which limits their usefulness for detailed interpretability. To address the evaluation challenge, we introduce a synthetic dataset with ground-truth attributions that enables a rigorous comparison of CAM evaluation metrics. Using this dataset, we analyze existing metrics and propose ARCC, a new composite metric that more reliably identifies faithful explanations. To address the low resolution issue, we introduce RefineCAM, a method that produces high-resolution attribution maps by aggregating CAMs across multiple network layers. Our results show that RefineCAM consistently outperforms existing methods according to the proposed evaluation.

The Average Gradient Outer Product (AGOP) governs feature learning in neural networks: the Neural Feature Ansatz states that weight Gram matrices at each layer align with the corresponding AGOP matrices computed over the training distribution. We ask a complementary question: can this same quantity serve as a post-hoc attribution method for explaining individual predictions? We introduce AGOP-Weighted: a novel attribution method that multiplies the per-sample gradient by sqrt(diag(M) / max diag(M)), a training-distribution prior that suppresses gradient noise and amplifies consistently important pixels -- a combination not present in any prior attribution method. We formalise two companion variants -- AGOP-Local (per-sample gradient, equivalent to VanillaGrad) and AGOP-Global (diag(M) directly as a zero-cost saliency map) -- and implement an efficient training-time accumulation hook; AGOP-Global then requires zero inference cost (disk lookup) while AGOP-Weighted requires only a single gradient pass. We conduct the first rigorous comparison of AGOP attribution against Integrated Gradients (IG), SmoothGrad, GradCAM, and VanillaGrad across two benchmarks with pixel-level ground truth: (i) the synthetic XAI-TRIS benchmark (four classification scenarios, 8x8 images, CNN8by8) and (ii) the photorealistic CLEVR-XAI benchmark (ResNet-18 fine-tuned from ImageNet). AGOP-Weighted achieves 44% higher mIoU than IG on linear tasks; AGOP-Global achieves 7x higher mIoU than IG on multiplicative tasks (where IG falls below random) at zero inference cost. Both findings generalise to ResNet-18 on CLEVR-XAI (+18% and +37% respectively). We further show that GradCAM fails on small-resolution images due to spatial resolution collapse, and that diag(M) quality improves monotonically throughout training even after classification accuracy has plateaued.

A critical step for reliable large language models (LLMs) use in healthcare is to attribute predictions to their training data, akin to a medical case study. This requires token-level precision: pinpointing not just which training examples influence a decision, but which tokens within them are responsible. While influence functions offer a principled framework for this, prior work is restricted to autoregressive settings and relies on an implicit assumption of token independence, rendering their identified influences unreliable. We introduce a flexible framework that infers token-level influence through a latent mediation approach for general prediction tasks. Our method attaches sparse autoencoders to any layer of a pretrained LLM to learn a basis of approximately independent latent features. Unlike prior methods where influence decomposes additively across tokens, influence computed over latent features is inherently non-decomposable. To address this, we introduce a novel method using Jacobian-vector products. Token-level influence is obtained by propagating latent attributions back to the input space via token activation patterns. We scale our approach using efficient inverse-Hessian approximations. Experiments on medical benchmarks show our approach identifies sparse, interpretable sets of tokens that jointly influence predictions. Our framework enhances trust and enables model auditing, generalizing to high-stakes domain requiring transparent and accountable decisions.

Machine learning algorithms in socially sensitive domains (e.g., credit decisions) often focus on equalizing predictive outcomes. However, satisfying these metrics does not guarantee that models use the same reasoning for different groups. We show that existing outcome-fair models can still apply fundamentally different reasoning to individuals, a hidden procedural bias'' missed by standard fairness metrics and algorithms. We propose Counterfactual Explanation Consistency (CEC), a framework that detects and mitigates this bias by aligning feature attributions between individuals and their counterfactual counterparts. Key contributions include a nearest-neighbor counterfactual generation method, a modified baseline for integrated gradient comparisons, an individual-level procedural fairness metric, and a corresponding training loss. We introduce a taxonomy identifying Regime B'' (same outcome, different reasoning) as a critical blind spot. Experiments on synthetic data, German Credit, Adult Income, and HMDA mortgage data demonstrate that outcome-fair baselines exhibit substantial hidden bias, while CEC substantially reduces it with modest utility cost.

Lack of transparency in AI systems poses challenges in critical real-life applications. It is important to be able to explain the decisions of an AI system to ensure trust on the system. Explainable AI (XAI) algorithms play a vital role in achieving this objective. In this paper, we are proposing a new algorithm for Explaining AI systems, FAMeX (Feature Association Map based eXplainability). The proposed algorithm is based on a graph-theoretic formulation of the feature set termed as Feature Association Map (FAM). The foundation of the modelling is based on association between features. The proposed FAMeX algorithm has been found to be better than the competing XAI algorithms - Permutation Feature Importance (PFI) and SHapley Additive exPlanations (SHAP). Experiments conducted with eight benchmark algorithms show that FAMeX is able to gauge feature importance in the context of classification better than the competing algorithms. This definitely shows that FAMeX is a promising algorithm in explaining the predictions from an AI system

Deep Learning has revolutionized machine learning, reaching unprecedented levels of accuracy, but at the cost of reduced interpretability. Especially in image processing systems, deep networks transform local pixel information into more global concepts in a highly obscured manner. Explainable AI methods for image processing try to shed light on this issue by highlighting the regions of the image that are important for the prediction task. Among these, Class Activation Mapping (CAM) and its gradient-based variants compute attributions based on the feature map and upscale them to the image resolution, assuming that feature map locations are influenced only by underlying regions. Perturbation-based methods, such as CorrRISE, on the other hand, try to provide pixel-level attributions by perturbing the input with fixed patches and checking how the output of the network changes. In this work, we propose Feature Activation Map Explanation (FAME), which combines both worlds by using network gradients to compute changes to the input image, manipulating it in a gradient-driven way rather than using fixed patches. We apply this technique on two common tasks, image classification and face recognition, and show that CAM's above-mentioned assumption does not hold for deeper networks. We qualitatively and quantitively show that FAME produces attribution maps that are competitive state-of-the-art systems. Our code is available: {\footnotesize https://github.com/AIML-IfI/fame.}

Attribution techniques explain the outcome of an AI model by assigning a numerical score to its inputs. So far, these techniques have mainly focused on attributing importance to static input features at a single point in time, and thus fail to generalize to sequential decision-making settings. This paper fills this gap by introducing techniques to generate attribution-based explanations for Markov Decision Processes (MDPs). We give a formal characterization of what attributions should represent in MDPs, focusing on explanations that assign importance scores to both individual states and execution paths. We show how importance scores can be computed by leveraging techniques for strategy synthesis, enabling the efficient computation of these scores despite the non-determinism inherent in an MDP. We evaluate our approach on five case-studies, demonstrating its utility in providing interpretable insights into the logic of sequential decision-making agents.

Graph neural networks (GNNs) are increasingly used to model biological systems, yet the reliability of post-hoc explanation methods for recovering meaningful molecular mechanisms remains unclear. Here, we systematically evaluate four widely used approaches: Saliency Attribution (SA), Integrated Gradients (IG), GNNExplainer, and Layer-wise Relevance Propagation (LRP) for identifying disease-relevant structure in breast cancer RNA-seq data projected onto a protein-protein interaction network. Using synthetic benchmarks with known ground-truth motifs, we show that explanation methods recover distinct signal organizations: SA performs best for sparse single-node drivers, whereas IG and LRP preferentially recover distributed pathway-like and cascade-like signals. In TCGA BRCA data, we identify a consistent topological signature of disease-associated hubs in which attribution peaks in the immediate 1-hop neighborhood and decays across successive network shells, a pattern most pronounced for IG and LRP and associated with strong enrichment of known cancer hubs. We further observe a trade-off between local hub enrichment and global gene ranking performance, with IG optimizing local enrichment and SA achieving superior global discrimination. Motivated by these complementary behaviors, we introduce a framework combining a shell-based hub score with consensus ranking across explainers. Consensus scores improve prioritization of canonical cancer genes (TP53, BRCA1, ESR1, MYC), reduce dependence on node degree, and, especially when tuned, outperform individual methods. Pathway enrichment further reveals improved recovery of biologically coherent cancer programs, including ERBB2, RTK, MAPK, immune, and cytokine signaling. Together, these results demonstrate that topology-aware integration of graph explanations can improve biological interpretability and biologically relevant molecular recovery.

Gradient-based attribution methods are model-faithful and scalable, but Integrated Gradients (IG) can be brittle because explanations depend on heuristic baselines, straight-line paths, discretization, and saturation. We propose Fisher--Rao Integrated Gradients (FRInGe), which defines both the reference and interpolation schedule in predictive distribution space. FRInGe replaces input baselines with a maximum-entropy predictive reference and follows a Fisher-Rao geodesic on the probability simplex. The corresponding input-space trajectory is realized through the pullback Fisher metric and stabilized by KL and Euclidean trust regions; attributions are obtained by integrating input gradients along this trajectory. Across six ImageNet architectures, FRInGe most clearly improves calibration-oriented attribution metrics, especially MAS scores, while remaining competitive on perturbation AUC and infidelity.

End-to-end autonomous driving models generate future trajectories from multi-view inputs, improving system integration but introducing opaque decisions and hard-to-localize risks. Existing methods either rely on auxiliary monitoring models or generate textual explanations, but are decoupled from the planning process and fail to reveal the visual evidence underlying trajectory generation. While attribution offers a direct alternative, planning differs from image classification by taking six-view camera images as input and predicting continuous multi-step trajectories, requiring attribution to capture both critical views and regions and their influence on outputs. Moreover, whether attribution maps can support risk identification remains underexplored. To address this, we propose a hierarchical attribution framework for end-to-end planning. Specifically, using L2 consistency with the original trajectory as the objective, we design a coarse-to-fine region attribution strategy that searches candidate regions across the full six-view input and refines attribution within them. We further extract three attribution statistics as predictive signals for planning risk, including attribution entropy to measure how concentrated the planner's reliance is over the joint visual space, within-camera spatial variance to characterize how spread out the attribution is within each view, and cross-camera Gini coefficient to quantify how unevenly attribution is distributed across the six cameras. Experiments on BridgeAD, UniAD, and GenAD show that these statistics correlate with planning risk, achieving Spearman correlations of $0.30 \pm 0.07$ with trajectory error and AUROC of $0.77 \pm 0.04$ for collision detection. The signal generalizes to held-out scenes with negligible degradation and remains stable under an alternative attribution baseline.

Attribution methods explain which input features drive a model's prediction, making them central to model debugging and mechanistic interpretability. Yet backward attribution methods, including gradients, LRP, and transformer-specific rules, lack a shared framework in which to compare the underlying backward calculations. We introduce such a framework by recasting backward attribution as a two-player game on an extended network graph, building on Gaubert and Vlassopoulos' ReLU Net Game. Gradients and the full alpha-beta-LRP family arise as integrals over game trajectories under specific equilibria, so attribution maps become projections of trajectory distributions rather than the primary object. Desired explanation properties, such as localisation focus, robustness to input noise, or stable attention routing, can be specified as game-theoretic concepts, including policy regularization, risk aversion, and extended action sets, and translate directly into novel adaptations of the well-known backward rules. On ViT-B/16, one such selected adaptation of alpha-beta-LRP outperforms prior transformer-specific backward methods across all considered localisation metrics.

We study the efficient computation of Shapley values for \emph{product games} -- cooperative games in which the coalition value factorizes as a product of per-player terms. Such games arise in machine learning explainability whenever the value function inherits a multiplicative structure from the underlying model, as in kernel methods with product kernels and tree-based models. Our key result is that the Shapley value of each player in a product game admits an exact one-dimensional integral representation: the weighted sum over exponentially many feature coalitions collapses to the integral of a degree-$(d-1)$ polynomial over $[0,1]$, where $d$ is the total number of features. This yields a Gauss--Legendre quadrature scheme that is \emph{provably exact} whenever the number of nodes satisfies $m_q \geq \lceil d/2 \rceil$, and otherwise provides a \emph{near-exact} approximation with error provably decaying geometrically in $m_q$. In practice, a few hundred nodes can achieve highly precise estimates even with thousands of features. Building on this formulation, we derive a numerically stable implementation via log-space evaluation, together with an efficient parallel implementation based on associative scan primitives that achieves $O(d\,m_q)$ total work and $O(\log d)$ parallel time. Experiments show that \textsc{QuadraSHAP} is the fastest numerically stable method across all tested configurations.

The main XAI attribution methods for deep neural networks -- GradCAM, SHAP, LIME, Integrated Gradients -- operate on separate theoretical foundations and are not formally comparable. We present GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley), a mathematical framework establishing a representation theory for attributions: every additive, linear, and continuous attribution functional on L^2(Q,mu) admits a unique canonical representation (Q, w, Delta), proved necessary by the Riesz Representation Theorem. This class encompasses SHAP, IG, LIME and linearized GradCAM, but excludes nonlinear functionals such as standard GradCAM or attention maps. Seven formal theorems provide simultaneous guarantees absent in any individual method: (T1) necessary canonical form; (T2) exact completeness; (T3) Monte Carlo convergence O(1/sqrt(m))+O(1/k); (T4) exact Shapley Interaction Values; (T5) Hoeffding ANOVA decomposition; (T6) Sobol sensitivity generalization; (T7) multi-scale extension (MS-GRALIS) with minimum-variance weights. An algebraic appendix justifies the GRALIS-SIV correspondence via the Mobius transform without circularity. GRALIS satisfies 13.5/14 axiomatic properties vs. 2.5-6/14 for individual methods, including completeness, sensitivity, locality, order-k interactions and optimal multi-scale aggregation simultaneously. Preliminary validation on BreaKHis (1,187 histology images, DenseNet-121) reports deletion faithfulness AUC +0.015 (malignant), 96% class-conditional consistency, SAL = 0.762+/-0.109 and sparsity index 0.39. Extended comparison with baseline XAI methods is planned for a companion paper.

Ascription of an image gives insights into the objects that influence the classification of the whole image or its pixels towards a specific category. These insights help radiologists to visualize deformities in medical imaging. Most of the existing visualization techniques are based on discriminative models and highlight regions of the input image participating in the decision-making of a classifier. However, these approaches do not take all noticeable objects into account as their objective is to classify the input by using a minimal set of discriminative features. To overcome the issue, a counterfactual explanation (CX) based class-oriented feature attribution method is proposed. A counterfactual explanation (CX) explicates a causal reasoning process of the form: "if X had not happened, then Y would not have happened". The method is built on generative adversarial networks (GANs) with a cyclical-consistent loss function. We evaluate our method on three datasets: synthetic, tuberculosis and BraTS. All experiments confirm the efficacy of the proposed method. This study also highlighted the limitations of existing counterfactual explanation techniques in producing plausible counterfactual instances (CIs). Accompanying CXs with believable CIs thus provides self-explanatory analogy-based explanations. To this end, a CI generation method is proposed. Also, a novel technique is used to evaluate the quality of CI. The baseline results are produced on the BraTS dataset.

The objective of this paper is to understand what characteristics and features of clinical data influence physician's decision about ordering laboratory tests or prescribing medications the most. We conduct our analysis on data and decisions extracted from electronic health records of 4486 post-surgical cardiac patients. The summary statistics for 335 different lab order decisions and 407 medication decisions are reported. We show that in many cases, physician's lab-order and medication decisions can be well predicted from a small subset of all features.