From Graphs to Gradients: Physics-Inspired Structural Attribution for Cyber-Physical IoT Systems and Beyond

2026-07-06

AI Summary

This study addresses the challenge of effective attribution in large-scale hybrid cyber-physical Internet-of-Things systems, where traditional causal explanation methods struggle due to their reliance on explicit directed graphs and difficulties handling feedback loops and partial observability. To overcome these limitations, this work proposes a statistical mechanics–inspired undirected energy-based modeling framework that captures dependency structures among variables and analyzes shifts in the energy landscape to enable structured attribution without reconstructing a causal graph. The approach introduces a novel energy-landscape–based dependency-aware mechanism capable of reasoning about perturbation effects in systems with mixed continuous-discrete variables. Experiments on an industrial IoT platform demonstrate that the method significantly outperforms state-of-the-art graph-based approaches in attribution accuracy, robustness, and scalability, making it well-suited for high-dimensional cyber-physical and socio-technical systems.

Abstract

Interpretable explanation methods in Artificial Intelligence aim to uncover the underlying causes and their effects, enabling a deeper understanding of why a system behaves in a certain way under different inputs. Unlike traditional explainability methods, which mainly highlight correlations between input and output variables, causal explanation focuses on interventional questions. By doing so, it provides more robust insights, helping users understand automated decisions, especially in high-risk domains. Recovering an explicit directed causal structure, however, is often impractical in large-scale, hybrid cyber-physical systems with feedback loops and partial observability. This paper introduces a novel framework inspired by statistical mechanics that instead models variable dependencies through an undirected, energy-based representation of cyber-physical IoT systems. Our approach enables rigorous dependency-aware attribution by analysing how variations in the energy landscape reflect the influence of individual components, without recovering a directed causal graph. It also supports reasoning about perturbation effects across hybrid interactions, providing reliable explanations of abnormal behaviours. We empirically examined our framework through simulations on an industrial IoT testbed with hybrid continuous and discrete variables, demonstrating higher attribution accuracy, improved robustness and better scalability than state-of-the-art graph-based approaches. While the attributions are not intended to fully recover the system's generative dynamics, they provide valuable, dependency-aware explanations supporting both human interpretation and downstream predictive and diagnostic tasks. Although demonstrated in industrial IoT security, our framework also applies to other high-dimensional cyber-physical and socio-technical systems requiring principled, structural explanations.

Problem

• causal explanation
• cyber-physical systems
• IoT
• partial observability
• attribution

Innovation

• energy-based modeling
• structural attribution
• cyber-physical systems
• interpretable AI
• statistical mechanics