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

arXiv: https://arxiv.org/abs/2503.18185 · HTML: https://mlsanity.com/paper/2503.18185/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 55 references that are in the map.
- First posted on arXiv 23 Mar 2025.

## Builds on (most cited first, 19 of 19)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Explaining NLP Models via Minimal Contrastive Editing (MiCE)](https://mlsanity.com/paper/2012.13985/) (2020)
- [Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End](https://mlsanity.com/paper/2011.04917/) (2020)
- [Local Saddle Point Optimization: A Curvature Exploitation Approach](https://mlsanity.com/paper/1805.05751/) (2018)
- [Formalising the Robustness of Counterfactual Explanations for Neural Networks](https://mlsanity.com/paper/2208.14878/) (2022)
- [MACE: An Efficient Model-Agnostic Framework for Counterfactual Explanation](https://mlsanity.com/paper/2205.15540/) (2022)
- [Counterfactual Explanation for Fairness in Recommendation](https://mlsanity.com/paper/2307.04386/) (2023)
- [Thermodynamics-inspired Explanations of Artificial Intelligence](https://mlsanity.com/paper/2206.13475/) (2022)
- [Generative Perturbation Analysis for Probabilistic Black-Box Anomaly Attribution](https://mlsanity.com/paper/2308.04708/) (2023)
- [Enhancing Counterfactual Explanation Search with Diffusion Distance and Directional Coherence](https://mlsanity.com/paper/2404.12810/) (2024)

## Built on by (most cited first, 6 of 6)

- [Tabular Diffusion based Actionable Counterfactual Explanations for Network Intrusion Detection](https://mlsanity.com/paper/2507.17161/) (2025)
- [FR-GESTURE: An RGBD Dataset For Gesture-based Human-Robot Interaction In First Responder Operations](https://mlsanity.com/paper/2602.17573/) (2026)
- [Large-scale Photorealistic Outdoor 3D Scene Reconstruction from UAV Imagery Using Gaussian Splatting Techniques](https://mlsanity.com/paper/2602.20342/) (2026)
- [Open-Vocabulary vs Supervised Learning Methods for Post-Disaster Visual Scene Understanding](https://mlsanity.com/paper/2603.01324/) (2026)
- [From Graphs to Gradients: Physics-Inspired Structural Attribution for Cyber-Physical IoT Systems and Beyond](https://mlsanity.com/paper/2607.05563/) (2026)
- [HANSARD: A Reference Architecture for Forensic Readiness, Runtime Witnessing, and Graded Attribution in Autonomous Multi-Agent AI Systems](https://mlsanity.com/paper/2608.22512/) (2026)

## Abstract (arXiv)

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.