The occurrence of vacuum arcs or radio frequency (rf) breakdowns is one of the most prevalent factors limiting the high-gradient performance of normal conducting rf cavities in particle accelerators. In this paper, we search for the existence of previously unrecognized features related to the incidence of rf breakdowns by applying a machine learning strategy to high-gradient cavity data from CERN’s test stand for the Compact Linear Collider (CLIC). By interpreting the parameters of the learned models with explainable artificial intelligence (AI), we reverse-engineer physical properties for deriving fast, reliable, and simple rule–based models. Based on 6 months of historical data and dedicated experiments, our models show fractions of data with a high influence on the occurrence of breakdowns. Specifically, it is shown that the field emitted current following an initial breakdown is closely related to the probability of another breakdown occurring shortly thereafter. Results also indicate that the cavity pressure should be monitored with increased temporal resolution in future experiments, to further explore the vacuum activity associated with breakdowns.