# stl2vec: Semantic and Interpretable Vector Representation of Temporal Logic

arXiv: https://arxiv.org/abs/2405.14389 · HTML: https://mlsanity.com/paper/2405.14389/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 50 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Embedding Symbolic Knowledge into Deep Networks](https://mlsanity.com/paper/1909.01161/) (2019)
- [Deep Learning with Logical Constraints](https://mlsanity.com/paper/2205.00523/) (2022)
- [Neuro-Symbolic Hierarchical Rule Induction](https://mlsanity.com/paper/2112.13418/) (2021)
- [DeepSTL -- From English Requirements to Signal Temporal Logic](https://mlsanity.com/paper/2109.10294/) (2021)
- [Improving Graph Neural Network Representations of Logical Formulae with Subgraph Pooling](https://mlsanity.com/paper/1911.06904/) (2019)
- [Embedding Symbolic Temporal Knowledge into Deep Sequential Models](https://mlsanity.com/paper/2101.11981/) (2021)
- [Learning Signal Temporal Logic through Neural Network for Interpretable Classification](https://mlsanity.com/paper/2210.01910/) (2022)
- [Metrics for Signal Temporal Logic Formulae](https://mlsanity.com/paper/1808.03315/) (2018)
- [STL2vec: Signal Temporal Logic Embeddings for Control Synthesis With Recurrent Neural Networks](https://mlsanity.com/paper/2109.04636/) (2021)
- [Learning Model Checking and the Kernel Trick for Signal Temporal Logic on Stochastic Processes](https://mlsanity.com/paper/2201.09928/) (2022)
- [Computing Probabilistic Bisimilarity Distances for Probabilistic Automata](https://mlsanity.com/paper/1907.01768/) (2019)
- [Towards Invertible Semantic-Preserving Embeddings of Logical Formulae](https://mlsanity.com/paper/2305.03143/) (2023)

## Built on by (most cited first, 3 of 3)

- [Bridging Logic and Learning: Decoding Temporal Logic Embeddings via Transformers](https://mlsanity.com/paper/2507.07808/) (2025)
- [Guided by Stars: Interpretable Concept Learning Over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2511.04244/) (2025)
- [Distilling Formal Logic into Neural Spaces: A Kernel Alignment Approach for Signal Temporal Logic](https://mlsanity.com/paper/2603.05198/) (2026)

## Abstract (arXiv)

Integrating symbolic knowledge and data-driven learning algorithms is a longstanding challenge in Artificial Intelligence. Despite the recognized importance of this task, a notable gap exists due to the discreteness of symbolic representations and the continuous nature of machine-learning computations. One of the desired bridges between these two worlds would be to define semantically grounded vector representation (feature embedding) of logic formulae, thus enabling to perform continuous learning and optimization in the semantic space of formulae. We tackle this goal for knowledge expressed in Signal Temporal Logic (STL) and devise a method to compute continuous embeddings of formulae with several desirable properties: the embedding (i) is finite-dimensional, (ii) faithfully reflects the semantics of the formulae, (iii) does not require any learning but instead is defined from basic principles, (iv) is interpretable. Another significant contribution lies in demonstrating the efficacy of the approach in two tasks: learning model checking, where we predict the probability of requirements being satisfied in stochastic processes; and integrating the embeddings into a neuro-symbolic framework, to constrain the output of a deep-learning generative model to comply to a given logical specification.