[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83975-en":3,"doc-seo-83975-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83975,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","From Graphs to Gradients: Physics-Inspired Structural Attribution for Cyber-Physical IoT Systems and Beyond","Interpretable AI explanation methods aim to reveal underlying causes and their effects, moving beyond correlation-focused explainability toward causal, intervention-aware reasoning. Directed causal structure recovery is often infeasible in large hybrid cyber-physical IoT systems with feedback loops and partial observability. The proposed framework models dependencies using an undirected, energy-based representation inspired by statistical mechanics, enabling rigorous dependency-aware attribution via energy-landscape variations and reliable explanations of abnormal behaviors. Extensive simulations on an industrial IoT testbed show higher attribution accuracy, improved perturbation robustness, and better scalability than graph-based explainability.","From Graphs to Gradients: Physics-Inspired Structural Attribution for  \nCyber-Physical IoT Systems and Beyond  \nSpyridon Evangelatos, Christos Diou, Member, IEEE, Georgios Th. Papadopoulos, Member, IEEE, Evangelos Markakis, Member, IEEE, and Panagiotis Sarigiannidis, Member, IEEE  \narXiv :2607 .05563v 1 [ cs .AI] 6 Jul 2026  \nAbstract—Interpretable explanation methods in Artificial Intelligence aim to uncover the underlying causes and their effects, enabling a deeper understanding of why a system behaves ina certain way under different inputs. In contrast to traditional explainability methods, which mainly highlight correlations between input variables and their corresponding output variables, causal explanation focuses on answering interventional questions. By doing so, it provides more robust insights, assisting users in better understanding automated decisions, especially in high-risk domains.  \nRecovering an explicit directed causal structure, however, is often impractical in large-scale, hybrid cyber-physical systems characterised by feedback loops and partial observability. This paper introduces a novel framework inspired by concepts drawn from the field of 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 within the system, without requiring the recovery of a directed causal graph. In addition, it also supports reasoning about the effects of perturbations across hybrid interactions, providing reliable explanations of abnormal behaviours.  \nOur framework was empirically examined through extensive simulations on an industrial IoT testbed that consists of hybrid continuous and discrete variables, demonstrating higher attribution accuracy, improved robustness to perturbations and substantially better scalability compared to state-of-the-art graphbased explainability approaches. While the resulting attributions are not intended to fully recover or explain the system’s underlying generative dynamics, they provide valuable, dependencyaware explanations that support both human interpretation and downstream predictive and diagnostic tasks. Although it is demonstrated in industrial IoT security, our framework is also applicable to other high-dimensional cyber-physical and sociotechnical systems that require principled, structural explanations.  \nImpact Statement  \nModern cyber-physical systems, such as industrial IoT infrastructures and water treatment plants, are increasingly exposed to complex and often hidden failure mechanisms. When incidents occur, operators need clear explanations of what caused them and how they propagate across interconnected  \nS. Evangelatos is with the Research & Innovation Development Department, Netcompany S.A., Luxembourg (email: sevangelatos@netcompany.com) .  \nC. Diou and G. Papadopoulos are with the Department of Informatics and Telematics, Harokopio University of Athens, Greece,(emails: [cdiou@hua.gr](cdiou@hua.gr)and [g.th.papadopoulos@hua.gr](g.th.papadopoulos@hua.gr)).  \nE. Markakis is with the Department of Electrical and Computer Engineering, Hellenic Mediterranean University, Greece,(email: [emarkakis@hmu.gr](emarkakis@hmu.gr)).  \nP. Sarigiannidis is with the Department of Electrical and Computer Engineering, University of Western Macedonia, Greece, (email: psarigianni[dis@uowm.gr](dis@uowm.gr)).  \ncomponents. The framework introduced in this paper provides such explanations without relying on hard-to-obtain directed causal graphs or opaque model-specific techniques, making it suitable for systems with many interacting variables.  \nExperimental results on the SWaT testbed show that the proposed method approaches perfect identification of root causes, while competing approaches remain close to zero. In addition, our method maintains higher at","cbCaidpZUu3EmvHf","https://ap.wps.com/l/cbCaidpZUu3EmvHf","pdf",634811,1,13,"English","en",105,"# Abstract\n# Impact Statement\n# Index Terms\n# Introduction","[{\"question\":\"What problem does the paper address in AI explainability?\",\"answer\":\"The paper addresses the limitation of traditional explainability that emphasizes correlations, by proposing an approach aligned with causal questions about how interventions affect system behavior.\"},{\"question\":\"Why is recovering a directed causal graph difficult for cyber-physical IoT systems?\",\"answer\":\"It is often impractical due to feedback loops, partial observability, and the challenges of identifying reliable directed structures from observational data at scale.\"},{\"question\":\"How does the proposed method produce attribution without a directed causal graph?\",\"answer\":\"It uses an undirected, energy-based representation inspired by statistical mechanics, analyzing how changes in the energy landscape reflect the influence of individual components and how perturbations propagate through hybrid 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problem does the paper address in AI explainability?","Question",{"text":75,"@type":76},"The paper addresses the limitation of traditional explainability that emphasizes correlations, by proposing an approach aligned with causal questions about how interventions affect system behavior.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is recovering a directed causal graph difficult for cyber-physical IoT systems?",{"text":80,"@type":76},"It is often impractical due to feedback loops, partial observability, and the challenges of identifying reliable directed structures from observational data at scale.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed method produce attribution without a directed causal graph?",{"text":84,"@type":76},"It uses an undirected, energy-based representation inspired by statistical mechanics, analyzing how changes in the energy landscape reflect the influence of individual components and how perturbations propagate through hybrid 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