Are We Merely Justifying Results ex Post Facto? Quantifying Explanatory Inversion in Post-Hoc Model Explanations

Post-hoc explanation methods provide interpretation by attributing predictions to input features. Natural explanations are expected to interpret how the inputs lead to the predictions. Thus, a fundamental question arises: Do these explanations unintentionally reverse the natural relationship between inputs and outputs? Specifically, are the explanations rationalizing predictions from the output rather than reflecting the true decision process? To investigate such explanatory inversion, we propose Inversion Quantification (IQ), a framework that quantifies the degree to which explanations rely on outputs and deviate from faithful input-output relationships. Using the framework, we demonstrate on synthetic datasets that widely used methods such as LIME and SHAP are prone to such inversion, particularly in the presence of spurious correlations, across tabular, image, and text domains. Finally, we propose Reproduce-by-Poking (RBP), a simple and model-agnostic enhancement to post-hoc explanation methods that integrates forward perturbation checks. We further show that under the IQ framework, RBP theoretically guarantees the mitigation of explanatory inversion. Empirically, for example, on the synthesized data, RBP can reduce the inversion by 1.8% on average across iconic post-hoc explanation approaches and domains.