Why Self-Inconsistency Arises in GNN Explanations and How to Exploit It

Abstract: Recent work has observed that explanations produced by Self-Interpretable Graph Neural Networks (SI-GNNs) can be self-inconsistent: when the model is reapplied to its own explanatory graph subset, it may produce a different explanation. However, why self-inconsistency arises remains poorly understood. In this work, we first identify re-explanation-induced context perturbation as the direct cause of score variation. We then introduce a latent signal assignment hypothesis to explain why only some edges are sensitive to this perturbation, and analyze how conciseness regularization affects latent signal assignment. Given that self-inconsistent edges do not provide stable evidence for the model's prediction, we propose Self-Denoising (SD), a model-agnostic and training-free post-processing strategy that calibrates explanations with only one additional forward pass. Experiments across representative SI-GNN frameworks, backbone architectures, and benchmark datasets support our hypothesis and show that SD consistently improves explanation quality while adding only about 4--6\% computational overhead in practice.

• The paper demonstrates that self-inconsistency in SI-GNN explanations originates from perturbations in local message-passing due to explanatory masking.
• It introduces a training-free self-denoising method that penalizes unstable, context-driven edges to enhance explanation plausibility with minimal computational overhead.
• Empirical evaluations across multiple datasets show that the self-denoising strategy improves explanation quality and sometimes task accuracy while preserving key signal integrity.

Mechanisms and Mitigation of Self-Inconsistency in SI-GNN Explanations

Introduction

Self-Interpretable Graph Neural Networks (SI-GNNs) have become the canonical framework for producing intrinsic explanations in graph learning, bypassing post-hoc interpretability pitfalls. Despite their architecture-level alignment with explanation generation, recent analyses have demonstrated a persistent phenomenon of explanation self-inconsistency: when an SI-GNN is reapplied to its own explanatory graph subset, it often produces divergent explanations. This instability challenges faithfulness, undermines practical reliability, and complicates downstream expert interpretation. The paper "Why Self-Inconsistency Arises in GNN Explanations and How to Exploit It" (2605.07527) delivers a mechanistic account of self-inconsistency and introduces a computationally efficient post-processing strategy for explanation denoising.

Causal Analysis of Self-Inconsistency

The primary insight is that self-inconsistency emerges from perturbations in local message-passing contexts induced by explanatory graph masking. SI-GNNs inherently couple prediction and explanation by extracting a subgraph, then using it for downstream classification. The initial explanatory mask alters node neighborhoods and edge weights, and when the model is reapplied, the message-passing trajectory changes—leading to substantial edge score variations, especially among contextually determined edges.

A "latent signal assignment" hypothesis is posited. The edge set is partitioned into:

• Positively signaled edges ($E_p$): edges supported by context-invariant latent signals, consistently high-scored.
• Negatively signaled edges ($E_n$): context-invariant but low-scored.
• No-signal/context-driven edges ($E_c$): reliance on local node neighborhoods.

Empirically, important (ground-truth-identified) edges are robust across passes, while unimportant edges are susceptible to contextual noise. Theoretical and empirical correlation analyses between edge score changes and neighborhood context variation validate this three-way structure and its evolution under conciseness regularization. As budget tightens, edge importance mass is reallocated, forcing some important edges into the context-driven regime and degrading downstream accuracy.

Self-Denoising: Explanation Calibration via Self-Inconsistency

The latent signal assignment model motivates the Self-Denoising (SD) strategy—a post-hoc calibration applied to SI-GNN explanations. SD penalizes edges exhibiting instability across repeated passes, downweighting context-amplified edges while preserving latent-signal-supported ones:

$$m_{ij}^{SD} = \max(0, (1 - n \Delta s_{ij}) m_{ij})$$

where $n$ is the denoising strength and $\Delta s_{ij}$ captures score instability.

SD is training-free, model-agnostic, and computationally lightweight, requiring at most one additional forward pass ($4$-$6\%$ overhead). The calibration introduces a tradeoff: increasing $n$ improves ranking correction (removing noisy edges) but risks prediction shift. The paper provides sufficient conditions for hyperparameter selection, bounding prediction drift via local differentiability and expectation bounds.

Classifier adaptation (fine-tuning the classifier on SD-calibrated explanations) is proposed as a lightweight remedy for induced OOD shifts, enabling validation-accuracy-based hyperparameter selection.

Empirical Evaluation and Complementarity

SD is benchmarked across four SI-GNN paradigms (attention-based, causal-based, size-constrained, MI-constrained), three GNN backbones, and four datasets (BA-2MOTIFS, 3MR, BENZENE, MUTAGENICITY). In all settings, SD improves explanation plausibility (AUC gains up to $3.9\%$), increases sparsity, and sometimes enhances task accuracy—with small or negligible fidelity loss by most metrics. Empirical distributions show SD maintains important edge scores while suppressing context-driven noise.

SD is further combined with Explanation Ensemble (EE), a cross-model calibration scheme based on explanation inconsistency across SI-GNN instances. Results indicate that SD and EE are complementary: SD efficiently removes context-driven instability, while EE targets cross-model variability. Their combination outperforms either strategy alone, yet SD is far less computationally intensive (one model vs. ensembles).

Theoretical and Practical Implications

The mechanistic characterization of self-inconsistency advances understanding of SI-GNN explanation dynamics under masking and regularization. The latent signal assignment framing clarifies how regularization budgets shape interpretability and why redundancy/noise persists. Practically, SD provides an efficient, universally applicable procedure for calibrating explanations, improving their alignment with model evidence.

The calibration reduces interpretability artifacts in high-stakes graph learning applications, mitigating risks in scientific and decision-critical tasks. Complementary strategies (SD+EE) expand the suite of trustworthiness interventions available to practitioners, with minimal deployment overhead.

Future Directions

Open theoretical questions remain regarding the identifiability of signal allocation and completeness of the latent signal model. SD cannot guarantee global explanation faithfulness—new criteria for trust assessment and hybrid strategies (e.g., integrating uncertainty quantification, adaptive signal estimation, or additional regularization mechanisms) are required. The methods proposed can be extended to other forms of self-explainable architectures, prototype-based GNNs, and non-instance-level explanation tasks.

Deeper investigation of the interplay between budget constraints, explanation entropy, and representational stability will be necessary for rigorous characterization and actionable guidance in SI-GNN deployment. The development of more reliable, user-adaptive, and provably faithful explanation frameworks remains an important avenue for graph machine learning.

Conclusion

By establishing context perturbation as the root cause of explanation self-inconsistency in SI-GNNs, and introducing the latent signal assignment hypothesis, the paper delivers both theoretical clarity and practical advances. The SD post-processing strategy leverages self-inconsistency signals for lightweight denoising, demonstrating improved explanation quality and broad applicability. Its complementarity with ensemble-based approaches, efficient operational profile, and robust empirical gains position SD as an important tool for advancing trustworthy graph learning and interpretability (2605.07527).