First, a student model is trained to recover the classifier'spredictions andtomatch theexplanations givenbytheexplainer.

In recent years, explaining decisions made by complex machine learning models has become essential in high-stakes domains such as energy systems, healthcare, finance, and autonomous systems. However, the reliability of these explanations, namely, whether they remain stable and consistent under realistic, non-adversarial changes, remains largely unmeasured. Widely used methods such as SHAP and Integrated Gradients (IG) are well-motivated by axiomatic notions of attribution, yet their explanations can vary substantially even under system-level conditions, including small input perturbations, correlated representations, and minor model updates. Such variability undermines explanation reliability, as reliable explanations should remain consistent across equivalent input representations and small, performance-preserving model changes. We introduce the Explanation Reliability Index (ERI), a family of metrics that quantifies explanation stability under four reliability axioms: robustness to small input perturbations, consistency under feature redundancy, smoothness across model evolution, and resilience to mild distributional shifts. For each axiom, we derive formal guarantees, including Lipschitz-type bounds and temporal stability results. We further propose ERI-T, a dedicated measure of temporal reliability for sequential models, and introduce ERI-Bench, a benchmark designed to systematically stress-test explanation reliability across synthetic and real-world datasets. Experimental results reveal widespread reliability failures in popular explanation methods, showing that explanations can be unstable under realistic deployment conditions. By exposing and quantifying these instabilities, ERI enables principled assessment of explanation reliability and supports more trustworthy explainable AI (XAI) systems.

Explainable artificial intelligence (XAI) is concerned with producing explanations indicating the inner workings of models. For a Rashomon set of similarly performing models, explanations provide a way of disambiguating the behavior of individual models, helping select models for deployment. However explanations themselves can vary depending on the explainer used, and need to be evaluated. In the paper "Evaluating Model Explanations without Ground Truth", we proposed three principles of explanation evaluation and a new method "AXE" to evaluate the quality of feature-importance explanations. We go on to illustrate how evaluation metrics that rely on comparing model explanations against ideal ground truth explanations obscure behavioral differences within a Rashomon set. Explanation evaluation aligned with our proposed principles would highlight these differences instead, helping select models from the Rashomon set. The selection of alternate models from the Rashomon set can maintain identical predictions but mislead explainers into generating false explanations, and mislead evaluation methods into considering the false explanations to be of high quality. AXE, our proposed explanation evaluation method, can detect this adversarial fairwashing of explanations with a 100% success rate. Unlike prior explanation evaluation strategies such as those based on model sensitivity or ground truth comparison, AXE can determine when protected attributes are used to make predictions.