Abstract:We study certified runtime monitoring of past-time signal temporal logic (ptSTL) from visual observations under partial observability. The monitor must infer safety-relevant quantities from images and provide finite-sample guarantees, while being \emph{reusable}: once trained and calibrated, it should certify any formula in a target fragment without per-formula retraining. For fragments induced by a finite dictionary of temporal atoms, we prove that the \emph{semantic basis}, the vector of atom robustness scores, is the minimum prediction target within the class of monotone, 1-Lipschitz reusable interfaces: any formula is evaluated by a deterministic decoder derived from the parse tree, and a single conformal calibration pass certifies the entire fragment with no union bound. We also introduce a \emph{rolling prediction monitor} that predicts only current predicate values and reconstructs temporal history online; this is easier to learn but grows conservative at long horizons. On a pedestrian-crossroad benchmark, rolling achieves tighter certified bounds at short horizons while the semantic-basis monitor is up to 4-times tighter at long horizons. We validate the presented monitors on real-world Waymo driving data, where both monitors satisfy the conformal coverage guarantee empirically.
| Subjects: | Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV); Robotics (cs.RO); Systems and Control (eess.SY) |
| Cite as: | arXiv:2605.13923 [cs.LG] |
| (or arXiv:2605.13923v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13923 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Bardh Hoxha [view email]
[v1]
Wed, 13 May 2026 14:22:25 UTC (1,836 KB)