# Neural Network for Weighted Signal Temporal Logic

arXiv: https://arxiv.org/abs/2104.05435 · HTML: https://mlsanity.com/paper/2104.05435/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 8 Apr 2021.

## Builds on (most cited first, 11 of 11)

- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Training Sparse Neural Networks](https://mlsanity.com/paper/1611.06694/) (2016)
- [Transfer of Temporal Logic Formulas in Reinforcement Learning](https://mlsanity.com/paper/1909.04256/) (2019)
- [STyLuS*: A Temporal Logic Optimal Control Synthesis Algorithm for Large-Scale Multi-Robot Systems](https://mlsanity.com/paper/1809.08345/) (2018)
- [Specifying User Preferences using Weighted Signal Temporal Logic](https://mlsanity.com/paper/2010.00752/) (2020)
- [Information-Guided Temporal Logic Inference with Prior Knowledge](https://mlsanity.com/paper/1811.08846/) (2018)
- [Event-Based Signal Temporal Logic Synthesis for Single and Multi-Robot Tasks](https://mlsanity.com/paper/2011.00370/) (2020)
- [Barrier Function-based Collaborative Control of Multiple Robots under Signal Temporal Logic Tasks](https://mlsanity.com/paper/2102.02609/) (2021)
- [Automatic Trajectory Synthesis for Real-Time Temporal Logic](https://mlsanity.com/paper/2009.06436/) (2020)

## 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)
- [Weighted Graph-Based Signal Temporal Logic Inference Using Neural Networks](https://mlsanity.com/paper/2109.08078/) (2021)
- [Multi-class Temporal Logic Neural Networks](https://mlsanity.com/paper/2402.12397/) (2024)
- [Learning Temporal Rules from Noisy Timeseries Data](https://mlsanity.com/paper/2202.05403/) (2022)
- [Time-Incremental Learning from Data Using Temporal Logics](https://mlsanity.com/paper/2112.14300/) (2021)

## Abstract (arXiv)

In this paper, we propose a neuro-symbolic framework called weighted Signal Temporal Logic Neural Network (wSTL-NN) that combines the characteristics of neural networks and temporal logics. Weighted Signal Temporal Logic (wSTL) formulas are recursively composed of subformulas that are combined using logical and temporal operators. The quantitative semantics of wSTL is defined such that the quantitative satisfaction of subformulas with higher weights has more influence on the quantitative satisfaction of the overall wSTL formula. In the wSTL-NN, each neuron corresponds to a wSTL subformula, and its output corresponds to the quantitative satisfaction of the formula. We use wSTL-NN to represent wSTL formulas as features to classify time series data. STL features are more explainable than those used in classical methods. The wSTL-NN is end-to-end differentiable, which allows learning of wSTL formulas to be done using back-propagation. To reduce the number of weights, we introduce two techniques to sparsify the wSTL-NN.We apply our framework to an occupancy detection time-series dataset to learn a classifier that predicts the occupancy status of an office room.