Explaining Failures of Cyber-Physical Systems with Actual Causality

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.

Explaining why a specific outcome occurred, and which inputs deserve the blame or credit, is central to philosophical, scientific, and policy analysis. Existing tools split into two camps. The theory of actual causality (AC) gives principled verdicts, but only for toy-sized models, because computing them requires enumerating counterfactual scenarios. Scalable attribution methods like SHAP (or even causal SHAP) at least partially ignore the causal structure that generated the data, and can give answers that conflict with a careful causal analysis. We close this gap with Probabilistic Causal Impact (PCI). PCI builds on actual causality and on Pearl's notions of probability of necessity and sufficiency, but recasts the question of explainability as an estimation problem on a probabilistic causal model that is easily approximated via Monte Carlo. By specifying a distribution over "candidate explanations," a distribution over counterfactual values, and a scoring function, PCI provides tractable, causally grounded, graded explanations, generalizing AC and Pearl's probability of causation as degenerate cases. We evaluate PCI in synthetic and real-world examples, spanning consistency checks with AC, scaling experiments, complex continuous-valued dynamical systems, and a real-world deployed causal machine learning model trained on millions of datapoints.

Falsification searches for counterexamples to formal specifications in cyber-physical systems (CPS). With specifications written in Signal Temporal Logic (STL), falsification can be formulated as a robustness optimization problem, traditionally tackled with black-box search algorithms. In parallel, large language models (LLMs) have recently emerged as surprisingly effective optimizers when coupled with iterative prompting. In this work, we connect these ideas and introduce LLM-Falsifier, an LLM-based approach that falsifies specifications by minimizing the STL robustness degree. Beyond generic prompt-based optimization, our key idea is to expose the LLM to semantic information that is natural for language models but absent from standard numerical optimizers, including natural-language input and output names, output trajectories, and critical-time witnesses for the minimum robustness value. These additions enable smarter and more sample-efficient robustness search. On the ARCH-COMP falsification benchmarks, LLM-Falsifier is shown to outperform existing falsification tools based on a range of optimization paradigms, from surrogate-based and Bayesian optimization to search-based testing, on 14 of 21 specifications when measured by the average number of simulations required to find a counterexample.