Cross‐Method Explanation Stability Under Prediction‐Preserving Perturbations in Explainable <scp>AI</scp>

ABSTRACT Post hoc explanation methods include Integrated Gradients (IG), SHAP, Vanilla Gradients, and Grad‐CAM, which are used to audit model decision‐making in high‐stakes domains. However, it remains unclear how explanations behave under prediction‐preserving perturbations. This paper aims to investigate how XAI methods can be stable across different explanation methods, provided they yield the same predictions. The outcomes were derived by carrying out experiments in a very confined perturbation regime (0.01) that had no change in predicted class despite measurable divergence in explanation maps for several XAI methods using a cosine‐based measure of similarity. Findings indicate that SHAP (mean = 0.6475), Vanilla Gradients (mean = 0.4647), and IG (mean = 0.3319) recorded significant variance, whereas Grad‐CAM was very stable (mean = 0.0058). The cross‐method analysis showed common vulnerability patterns across gradient‐based and perturbation‐based explainers, whereas Grad‐CAM demonstrated a specific ability to be resilient. Further discussion revealed that, before prediction changes with increasing ε, explanation divergence could already have commenced, indicating that further explanation is a more sensitive measure of model vulnerability than prediction. These results indicate that the explanation's reliability is highly method‐dependent and that when a particular explainer audits the case, one may be inclined to be misled. The paper presents a new criterion for robustness of cross‐method explanations as a prerequisite for reliable XAI and provides empirical evidence that supports multi‐explainer auditing and future defenses to promote consistency in explanations.