# Weighted Graph-Based Signal Temporal Logic Inference Using Neural Networks

arXiv: https://arxiv.org/abs/2109.08078 · HTML: https://mlsanity.com/paper/2109.08078/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Towards Verified Artificial Intelligence](https://mlsanity.com/paper/1606.08514/) (2016)
- [Expressivity of Deep Neural Networks](https://mlsanity.com/paper/2007.04759/) (2020)
- [Specifying User Preferences using Weighted Signal Temporal Logic](https://mlsanity.com/paper/2010.00752/) (2020)
- [Spatio-Temporal Neural Networks for Space-Time Series Forecasting and Relations Discovery](https://mlsanity.com/paper/1804.08562/) (2018)
- [Graph Temporal Logic Inference for Classification and Identification](https://mlsanity.com/paper/1903.09714/) (2019)
- [Neural Network for Weighted Signal Temporal Logic](https://mlsanity.com/paper/2104.05435/) (2021)
- [A graph-based spatial temporal logic for knowledge representation and automated reasoning in cognitive robots](https://mlsanity.com/paper/2001.07205/) (2020)
- [Robotic Swarm Control from Spatio-Temporal Specifications](https://mlsanity.com/paper/1609.06283/) (2016)

## Built on by (most cited first, 5 of 5)

- [Learning Signal Temporal Logic through Neural Network for Interpretable Classification](https://mlsanity.com/paper/2210.01910/) (2022)
- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Multi-class Temporal Logic Neural Networks](https://mlsanity.com/paper/2402.12397/) (2024)
- [On Generating Explanations for Reinforcement Learning Policies: An Empirical Study](https://mlsanity.com/paper/2309.16960/) (2023)
- [Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes](https://mlsanity.com/paper/2610.14352/) (2026)

## Abstract (arXiv)

Extracting spatial-temporal knowledge from data is useful in many applications. It is important that the obtained knowledge is human-interpretable and amenable to formal analysis. In this paper, we propose a method that trains neural networks to learn spatial-temporal properties in the form of weighted graph-based signal temporal logic (wGSTL) formulas. For learning wGSTL formulas, we introduce a flexible wGSTL formula structure in which the user's preference can be applied in the inferred wGSTL formulas. In the proposed framework, each neuron of the neural networks corresponds to a subformula in a flexible wGSTL formula structure. We initially train a neural network to learn the wGSTL operators and then train a second neural network to learn the parameters in a flexible wGSTL formula structure. We use a COVID-19 dataset and a rain prediction dataset to evaluate the performance of the proposed framework and algorithms. We compare the performance of the proposed framework with three baseline classification methods including K-nearest neighbors, decision trees, support vector machine, and artificial neural networks. The classification accuracy obtained by the proposed framework is comparable with the baseline classification methods.