Self-Explainable Multi-Label Graph Neural Network for Correlated Evidence Attribution

Multi-label graph learning intends to capture the intrinsic complexity of real-world applications, where one sample is often related to multiple groups or consists of multiple objects. To date, a handful of multi-label graph learning methods exist, but none of them integrate training-time interpretation capability. While post-hoc graph explainers have been developed, they do not explicitly model label-dependent evidence sharing in multi-label graph learners, especially when label pairs are weakly or negatively associated. As a result, post-hoc approaches may miss how evidence should be shared or separated across different labels. This paper advances a new end-to-end self-explainable multi-label graph neural network (SEMGNN), which aims to simultaneously classify multi-labeled nodes and identify edges significantly contributing to each target node w.r.t. predicted labels. Different from post-hoc methods, SEMGNN jointly learns a predictor and a sparse edge-mask explainer within a unified framework and training objective. Label-label correlations are used to improve multi-label node classification and enhance individual label explanations, so that different labels of a node can be supported by distinct yet coherent structural and/or correlated evidence. Experiments and comparisons on synthetic and real-world multi-label networks, in social networking, entertainment, and life sciences, show that SEMGNN achieves competitive or improved predictive performance while providing more faithful and compact label-conditioned explanations.

From Abductive Explanations to Global Logical Rules for Node Classification in SGCs

Graph Neural Networks (GNNs) have achieved remarkable performance in node classification tasks, motivating growing interest in methods capable of explaining their predictions. Recent logic-based approaches, such as LogicXGNN, derive global logical rules for Graph Neural Networks (GNNs) from collections of explanatory subgraphs. While informative, these subgraphs may contain redundant structural information that is specific to individual nodes, potentially limiting the generality of the extracted rules. In this work, we propose a logic-based framework for node classification in Simple Graph Convolution (SGC) networks that uses minimal abductive explanations as an intermediate representation for rule extraction. For each node, we compute a minimal set of node-feature pairs sufficient to preserve the predicted class. These explanations are then used to train decision trees from which global logical rules are extracted. Experiments on benchmark datasets show that the proposed framework produces compact global rules while maintaining high fidelity to the original SGC model.

NICE: Scale-Stable Perturbations for Graph Neural Network Explanations via Noise Corruption

Post-hoc Graph Neural Network (GNN) explainers commonly follow a Perturb-Query paradigm, inferring the importance of graph elements based on queried predictions to perturbed inputs. However, such perturbations often introduce substantial distribution shift, undermining the reliability of the queried predictions used to derive explanations. While existing efforts mainly improve perturbed graphs or stabilize model predictions on them, we revisit the perturbation mechanism itself. We show that the widely used Element-wise Masking(EM) suppresses edge-induced messages toward zero, causing deterministic scale contraction that accumulates across message-passing layers, a phenomenon we term Scale Drift. Consequently, prediction changes under EM may conflate information corruption with deviations in propagation scale. As a scale-stable alternative to EM, we introduce Noise Corruption (NC), which perturbs each message through matched-norm random-direction corruption while preserving the expected squared message norm. Building on NC, we propose NICE, a Noise Corruption-based explanation framework, which learns a Stochastic Restoration Boundary (SRB) under NC-induced uncertainty, balancing target-prediction restoration against compactness. Furthermore, Boundary-Integrated Gradient (BIG) converts this boundary into edge attributions by accumulating each edge's contribution to reducing restoration risk along the restoration path. Experiments across multiple benchmarks demonstrate stronger explanation performance and model faithfulness while confirming that NC substantially reduces the Scale Drift induced by masking.

Overcoming Shortcut Learning in Graph Neural Networks through Active Explanation Guidance

Graph Neural Networks (GNNs) can solve prediction tasks by unintentionally exploiting shortcuts---that is, edges, nodes, and features that correlate with but are not causal for the prediction---which compromise their reliability in out-of-distribution tasks. We introduce XIGL, an architecture-agnostic human-in-the-loop strategy for removing such shortcuts from GNNs. Our key insight is twofold. On the one hand, reliance on shortcuts can be detected by inspecting GNN explanations. On the other hand, once made aware of such shortcuts, sufficiently expert users can provide tailored corrective feedback, which helps deconfound the model. XIGL supports any query strategy; however, since corrective feedback can be expensive to acquire, we develop an active learning strategy for prioritizing explanations that are more likely to display shortcut behavior, lowering annotation and cognitive costs. We showcase the effectiveness of XIGL, including both existing and proposed explanation-based strategies, on several GNN architectures. Our implementation is available online.

Dual Spatial-Temporal Attribution: Architecture-Aligned Post-Hoc Explainability for Recurrent Graph Anomaly Detection

Deep learning detectors for anomalies in dynamic graphs have reached strong accuracy, yet they remain opaque: when an edge is flagged, the analyst receives a score but no reason. This opacity is untenable in the cooperative, regulated information systems where such detectors are deployed, where automated decisions must be auditable and trustworthy. We address this gap for AddGraph, the foundational GCN+GRU framework for edge-level anomaly detection in dynamic graphs, which to our knowledge has never been equipped with any form of explainability. We present a strictly post-hoc explainability framework, X-AddGraph, built on a Dual Spatial-Temporal Attribution (DSTA) mechanism whose three components are each aligned with one of AddGraph's architectural modules: a gradient-based relevance attribution over the current adjacency structure (spatial), a direct reading of the contextual attention weights already computed during inference (short-term temporal, at zero additional cost), and a gradient rollback through the recurrent hidden states (long-term temporal). Because the detector is frozen, detection performance is preserved exactly (Delta AUC = 0, verified empirically to ten decimal places). On the UCI Message benchmark, our trained AddGraph baseline reaches an average per-snapshot AUC of 0.8705, exceeding the originally published result; X-AddGraph reproduces every score identically while adding explanations where none existed. Evaluated across four edge populations - confident true positives, low-confidence true positives, false positives, and random samples - the long-term attribution identifies historical snapshots carrying significantly more counterfactual signal than random selection (0.127 vs. 0.074), a capability that no spatially-blind explainer can provide. We release our implementation for full reproducibility.

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.

Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks

A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of the input leaves every attribution invariant. Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array. We show this is a structural obstruction rather than an implementation slip. When no minimal valid explanation is fixed by the input's automorphism group, no rule can be single-valued, minimal and symmetry-respecting at once. For the exact-k reports used in practice we give a parameter-free criterion, mechanised in Lean 4 with no axiom dependencies, that decides from the graph alone whether every score-optimal report of that size must split an orbit. Across 21298 instance-budget decisions the criterion agrees with a mechanical model-equivalence check without exception, and no severing case we found admitted a neutral alternative. The obstruction is common. Nontrivial automorphisms occur in 93.4% of Mutagenicity, the dataset the seminal explainability papers use, so the measure-zero dismissal of symmetric inputs, sound on the continuous domains it was made for, collapses here. At the sparsity budget those papers report, 24.0% of molecules with two interchangeable nitro groups (6 of 25) surface exactly one of them, every one arbitrary under mechanical verification. A model's blindness also manufactures symmetry: every MUTAG molecule contains atoms chemistry separates and the network provably cannot, and a matched control shows the resolution is set by what the model reads rather than how it is parameterised. Reporting orbits removes the arbitrariness at 0.11 ms and 0.43 extra edges per graph.

Towards Faithful Graph Explanations with Synergistic Edge Effects via Granular Balls

Instance-level explanations aim to reveal the rationale behind a model's decisions for a specific graph. Previous methods explain graph neural networks (GNNs) by selecting important edges to induce subgraphs, where edge importance is assessed by perturbing each edge and observing changes in the model predictions. However, they often neglect the synergistic effects among edges, which are crucial for accurately characterizing edge importance. To address this issue, we propose SeeExplainer, a parameter-free explainer to interpret GNNs. Specifically, we first introduce a granular-ball graph refinement mechanism that decomposes a graph into several disjoint granular-balls with no fixed size, and utilize them as nodes to construct a structural graph. This process can better capture the synergistic effects among edges. Then, we perturb nodes and edges in the structural graph to generate explanatory subgraphs based on their respective contributions. Experiments on several graph classification datasets of different networks show that SeeExplainer outperforms state-of-the-art baselines.

Measuring What Matters: A Unified Evaluation Framework for GNN Explainability

Graph eXplainable AI (G-XAI) is increasingly important for making Graph Neural Networks interpretable and accountable. While a growing number of explainers are available, choosing the right method and assessing the trustworthiness of its outputs remains unclear. Consistent evaluation practices and actionable guidance are still missing, hindering practical adoption. In this paper, we introduce a unified, quantitative benchmarking framework for G-XAI that requires no ground-truth assumptions. We formalize tabular explainability metrics for graph data, evaluating topological structure and node features as independent components. Our large-scale benchmarking study identifies explainers that consistently lie on the Pareto front across metric pairs and tasks, establishing robustly non-dominated solutions - while confirming that no single explainer achieves universal superiority. We distill our findings into actionable G-XAI usability guidelines to support Machine Learning practitioners in evaluating and deploying trustworthy GNN-based pipelines.

Towards the Explainability of Temporal Graph Networks via Memory Backtracking and Topological Attribution

Temporal graphs are ubiquitous in real-world applications and Temporal Graph Networks (TGNs) have achieved superior predictive accuracy. Understanding which historical events drive model predictions can enhance trustworthiness of TGNs. Existing explanation methods overlook the memory module, the core component that records and updates node histories, leaving the influence of past events unexplored. To address this, we attribute TGNs predictions through the topology attribution tree and memory backtracking tree. The topology attribution tree captures the influence of neighbors and their memory vectors, then the memory backtracking tree quantifies how historical events shape node memory vectors. We apply the LRP in TGNs, ensuring that the total contribution of events equals the logits of model. Finally, top-k selection may be unfaithful due to the nonlinear mapping from logits to probabilities, we design optimization objectives to identify the important events. Experiments on nine temporal graph datasets, spanning node property prediction, link prediction tasks and graph classification tasks, show that our method provides faithful explanations and outperforms state-of-the-art baselines. The code is available at https://github.com/yazhengliu/MemExplainer

Explaining Temporal Graph Neural Networks via Feature-induced Information Flow

Event-based Temporal Graph Neural Networks (ETGNNs) have demonstrated strong performance across a wide range of applications, including social network analysis, epidemic tracing, recommender systems, and political event forecasting. However, their increasing complexity poses significant challenges for explainability. Existing explanation methods focus only on a subset of the information flow within ETGNNs, typically tracing contributions from the event-related embeddings to the output. Consequently, they overlook the important pathways through event-induced variables, which mediate interactions between nodes and thereby play a central role in capturing long-range temporal dependencies. To overcome this limitation, we propose a novel attribution method that analyzes the \emph{entire} information flow through all event-associated variables. Our method is built upon the recent Normalized Relevance Measure (NRM) framework, which enables explicit quantification of information flow originating from event embeddings as well as information flow passing through event-induced variables. It also ensures comparability of latent variables across layers, and supports higher-order analysis of interactions between events. To handle the architectural complexity of ETGNNs, we extend the NRM framework with a modular decomposition procedure that facilitates the systematic construction of relevance structure for complex neural architectures. We evaluate our approach on two synthetic datasets for epidemic tracing and social dynamics, as well as a real-world dataset of political event networks. Our qualitative and quantitative experiments show that our method consistently outperforms existing explanation approaches while producing more human-interpretable explanations.

A Completion-Aware Framework for Impactful Counterfactual Explainability in Graph Neural Networks

In this study, we propose a novel pipeline for generic, model-agnostic, local-level counterfactual explainability in graph neural networks (GNNs). Although counterfactual explainers capable of both adding and removing edges have emerged in recent years, the need for generic and efficient solutions remains unmet, particularly concerning qualitative explanation generation. Our approach couples progress in factual explainability with missing edge prediction models rooted in link prediction research, in order to enhance the quality, robustness and intuitiveness of explanations. A multi-faceted experimental analysis conducted on real-world and synthetic graph classification benchmarks, both binary and multi-label, demonstrates the advancements in comparison to state-of-the-art baselines across diverse metrics.

CIExplainer++: Generating Causal and Interpretable Explanations for Graph Neural Networks

Explainable Artificial Intelligence aims to make black-box models more trustworthy by presenting, in a human-understandable manner, the elements that lead to the model's output. This involves both (i) identifying components and connections with genuine causal influence on outputs and (ii) translating such structures into an interpretable representation. For the former, we introduce CIExplainer, a novel perturbation-based method grounded in causal inference for explaining Graph Neural Networks (GNNs). CIExplainer identifies the subgraph with the highest causal effects on GNN predictions using the Potential Outcome Framework. We evaluate and compare CIExplainer on various GNN architectures (GCN, GraphSAGE, GAT, GIN) and datasets. To bridge subgraph explanations with human interpretability, we further propose G2TeXplainer, a method that transforms causal subgraphs into natural language explanations that capture both feature-level and relational information.

Beyond Soft Masks: Hard-Perturbation Mixup Explainer for Robust GNN Explainability

Graph Neural Networks (GNNs) have demonstrated remarkable performance across a range of applications involving graph-structured data, particularly in high-stakes domains. However, the opaque nature of their decision-making processes limits their trustworthiness and broader adoption. Existing post-hoc explanation methods aim to improve explainability by identifying subgraphs that influence GNN predictions and adopt mixup strategies to alleviate the out-of-distribution (OOD) issue caused by using subgraphs for prediction. Yet, these approaches typically rely on soft masks, which are inherently unable to fully eliminate label-irrelevant information, allowing redundant structures to leak into the mixup process and hindering the resolution of the OOD problem, thereby degrading explanation fidelity. In this work, we propose HPME, a Hard-Perturbation Mixup Explanation framework grounded in a generalized Graph Information Bottleneck, which leverages graph pooling to extract discrete explanatory subgraphs and to yield an information-capacity bound to thoroughly compress label-irrelevant components. Furthermore, we introduce a novel mixup strategy built upon structure-level replacement, generating in-distribution explanations to effectively mitigate the distribution shift. Extensive experiments on diverse tasks demonstrate that HPME achieves state-of-the-art performance in generating robust and interpretable explanations across both synthetic and real-world datasets.

HiSE: A Lightweight Hierarchical Semantic Explainer for Heterogeneous Graph Neural Networks

Heterogeneous graph neural networks (HGNNs) have demonstrated remarkable performance in modeling complex relational data, however their interpretability in high-stakes applications remains a critical challenge. Existing explanation methods suffer from two major limitations: on the one hand, the generated explanations fail to reflect the inherent semantic hierarchy of HGNNs, resulting in a lack of fidelity to the model's internal decision-making mechanism; on the other hand, feature explanations often rely on complex search or perturbation mechanisms, leading to excessive computational complexity and poor efficiency. To address these issues, we propose HiSE, a lightweight feature-oriented interpretable model for HGNNs. HiSE achieves semantically aware feature explanations through hierarchical semantic modeling: at the semantic level, local surrogate models based on the Least Absolute Shrinkage and Selection Operator (LASSO) are employed to learn sparse feature representations under each semantic view; at the cross-semantic level, the contributions of different semantic views are adaptively characterized via KL divergence to produce a unified explanation. Extensive experiments demonstrate that HiSE outperforms existing methods in terms of fidelity, robustness, and cross-semantic explanation capability, while its lightweight framework incurs low computational overhead, enabling efficient application to large-scale, complex real-world heterogeneous graphs.

Efficient Higher-order Subgraph Attribution via Message Passing

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.

Explaining Temporal Graph Predictions With Shapley Values

Temporal Graph Neural Networks (TGNNs) have become increasingly popular in recent years due to their superior predictive performance by combining both spatial and temporal information. However, how these models utilize the information to make predictions is rather unexplored, leading to potentially faulty or biased models. This work introduces two novel model-agnostic explainers for local explanations of TGNNs based on Shapley and Owen values. The first method, an event-level (edge-level) Shapley explainer, applies the KernelSHAP algorithm to estimate contribution scores for individual temporal events, providing interpretable descriptions for model behavior. The second, a feature-level Shapley explainer, extends this framework by decomposing event-level Shapley values into Owen values, and thereby uncovers hierarchical dependencies of the event and its features. The explainers outperform SOTA explainers on different metrics and datasets. Additionally, the Feature Explainer reveals a faulty extraction of actual timestamps of a commonly used TGAT implementation, helping to further understand performance drops on very sparse explanations.