Fidelity as a scalar representation for post-hoc XAI: Toward uncertainty quantification and adversarial detection

Post-hoc explainable AI (XAI) methods, particularly those that produce explanations formed by feature-wise importance scores, have become central to interpreting opaque AI models. However, post-hoc explanations often suffer from instability arising from their inherent stochasticity and are also vulnerable to adversarial attacks. In this paper, we introduce the FISCAR (FIdelity as a SCAlar Representation) framework, which transforms feature-level importance scores within a given post-hoc explanation into a scalar quantity. Subsequently, by modeling this scalar as a random variable, FISCAR provides an anchor for quantitatively analyzing explanation processes in relation to the inherent randomness within post-hoc XAI. We develop two methods based on this FISCAR framework: a Bayesian quantification method that uses the inferred inverse gamma distribution of the random variable to measure uncertainty, and a detection method that identifies adversarial behavior by monitoring the empirical variance of the random variable. Simulations on real-world datasets show that FISCAR provides a practical and effective entry point for these downstream tasks, which would otherwise lack a numerical foundation for further analysis. FISCAR thus enables more accountable evaluation of post-hoc explainability and supports the development of more trustworthy AI systems.