Exploring Energy Landscapes for Minimal Counterfactual Explanations: Applications in Cybersecurity and Beyond

Abstract

Counterfactual explanations have emerged as a prominent method in Explainable Artificial Intelligence (XAI), providing intuitive and actionable insights into Machine Learning model decisions. In contrast to other traditional feature attribution methods that assess the importance of input variables, counterfactual explanations focus on identifying the minimal changes required to alter a model's prediction, offering a ``what-if'' analysis that is close to human reasoning. In the context of XAI, counterfactuals enhance transparency, trustworthiness and fairness, offering explanations that are not just interpretable but directly applicable in the decision-making processes. In this paper, we present a novel framework that integrates perturbation theory and statistical mechanics to generate minimal counterfactual explanations in explainable AI. We employ a local Taylor expansion of a Machine Learning model's predictive function and reformulate the counterfactual search as an energy minimization problem over a complex landscape. In sequence, we model the probability of candidate perturbations leveraging the Boltzmann distribution and use simulated annealing for iterative refinement. Our approach systematically identifies the smallest modifications required to change a model's prediction while maintaining plausibility. Experimental results on benchmark datasets for cybersecurity in Internet of Things environments, demonstrate that our method provides actionable, interpretable counterfactuals and offers deeper insights into model sensitivity and decision boundaries in high-dimensional spaces.