Runtime Monitoring of Perception-Based Autonomous Systems via Embedding Temporal Logic

Runtime monitoring of autonomous systems traditionally relies on mapping continuous sensor observations to discrete logical propositions defined over low-dimensional state variables. This abstraction breaks down in perception-driven settings, where such mappings require additional learned modules that are often computationally expensive, brittle, and semantically misaligned. In this work, we propose Embedding Temporal Logic (ETL), a temporal logic that performs monitoring directly in learned embedding spaces. ETL defines predicates through distances between observed embeddings and target embeddings derived from reference observations. This formulation allows specifications to capture high-level perceptual concepts, such as similarity to visual goals or avoidance of semantic regions, that are difficult or impossible to express using traditional predicates. By composing these predicates with temporal operators, ETL naturally expresses temporally extended and sequential perceptual behaviors. We introduce ETL monitors for evaluating specifications over bounded embedding traces, along with a conformal calibration procedure that provides reliable and safety-oriented predicate evaluation. We evaluate our approach across multiple manipulation environments to show that ETL achieves strong empirical agreement with ground-truth semantics, including accurate monitoring of temporally composed behaviors.

Pretrained Embeddings as a Behavior Specification Mechanism

We propose an approach to formally specifying the behavioral properties of systems that rely on a perception model for interactions with the physical world. The key idea is to introduce embeddings -- mathematical representations of a real-world concept -- as a first-class construct in a specification language, where properties are expressed in terms of distances between a pair of ideal and observed embeddings. To realize this approach, we propose a new type of temporal logic called Embedding Temporal Logic (ETL), and describe how it can be used to express a wider range of properties about AI-enabled systems than previously possible. We demonstrate the applicability of ETL through a preliminary evaluation involving planning tasks in robots that are driven by foundation models; the results are promising, showing that embedding-based specifications can be used to steer a system towards desirable behaviors.