# Learning Model Checking and the Kernel Trick for Signal Temporal Logic on Stochastic Processes

arXiv: https://arxiv.org/abs/2201.09928 · HTML: https://mlsanity.com/paper/2201.09928/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 24 Jan 2022.

## Builds on (most cited first, 7 of 7)

- [Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics](https://mlsanity.com/paper/1904.11611/) (2019)
- [A Robust Genetic Algorithm for Learning Temporal Specifications from Data](https://mlsanity.com/paper/1711.06202/) (2017)
- [Metrics for Signal Temporal Logic Formulae](https://mlsanity.com/paper/1808.03315/) (2018)
- [Semantic Labelling and Learning for Parity Game Solving in LTL Synthesis](https://mlsanity.com/paper/1907.12157/) (2019)
- [Computing Probabilistic Bisimilarity Distances for Probabilistic Automata](https://mlsanity.com/paper/1907.01768/) (2019)
- [The 5th Reactive Synthesis Competition (SYNTCOMP 2018): Benchmarks, Participants & Results](https://mlsanity.com/paper/1904.07736/) (2019)
- [A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains](https://mlsanity.com/paper/1702.02528/) (2017)

## Built on by (most cited first, 7 of 7)

- [Retrieval-Augmented Mining of Temporal Logic Specifications from Data](https://mlsanity.com/paper/2405.14355/) (2024)
- [Towards Invertible Semantic-Preserving Embeddings of Logical Formulae](https://mlsanity.com/paper/2305.03143/) (2023)
- [stl2vec: Semantic and Interpretable Vector Representation of Temporal Logic](https://mlsanity.com/paper/2405.14389/) (2024)
- [ECATS: Explainable-by-design concept-based anomaly detection for time series](https://mlsanity.com/paper/2405.10608/) (2024)
- [Bridging Logic and Learning: Decoding Temporal Logic Embeddings via Transformers](https://mlsanity.com/paper/2507.07808/) (2025)
- [Towards Interpretable Concept Learning over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2508.03269/) (2025)
- [Distilling Formal Logic into Neural Spaces: A Kernel Alignment Approach for Signal Temporal Logic](https://mlsanity.com/paper/2603.05198/) (2026)

## Abstract (arXiv)

We introduce a similarity function on formulae of signal temporal logic (STL). It comes in the form of a kernel function, well known in machine learning as a conceptually and computationally efficient tool. The corresponding kernel trick allows us to circumvent the complicated process of feature extraction, i.e. the (typically manual) effort to identify the decisive properties of formulae so that learning can be applied. We demonstrate this consequence and its advantages on the task of predicting (quantitative) satisfaction of STL formulae on stochastic processes: Using our kernel and the kernel trick, we learn (i) computationally efficiently (ii) a practically precise predictor of satisfaction, (iii) avoiding the difficult task of finding a way to explicitly turn formulae into vectors of numbers in a sensible way. We back the high precision we have achieved in the experiments by a theoretically sound PAC guarantee, ensuring our procedure efficiently delivers a close-to-optimal predictor.