# Learning Signal Temporal Logic through Neural Network for Interpretable Classification

arXiv: https://arxiv.org/abs/2210.01910 · HTML: https://mlsanity.com/paper/2210.01910/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 4 Oct 2022.

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

- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Training Sparse Neural Networks](https://mlsanity.com/paper/1611.06694/) (2016)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Specifying User Preferences using Weighted Signal Temporal Logic](https://mlsanity.com/paper/2010.00752/) (2020)
- [Interpretable Classification of Time-Series Data using Efficient Enumerative Techniques](https://mlsanity.com/paper/1907.10265/) (2019)
- [Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications](https://mlsanity.com/paper/1903.05186/) (2019)
- [Mining Parametric Temporal Logic Properties in Model Based Design for Cyber-Physical Systems](https://mlsanity.com/paper/1512.07956/) (2015)
- [Classification of Time-Series Data Using Boosted Decision Trees](https://mlsanity.com/paper/2110.00581/) (2021)
- [Neural Network for Weighted Signal Temporal Logic](https://mlsanity.com/paper/2104.05435/) (2021)
- [Weighted Graph-Based Signal Temporal Logic Inference Using Neural Networks](https://mlsanity.com/paper/2109.08078/) (2021)
- [Interpretable Fault Diagnosis of Rolling Element Bearings with Temporal Logic Neural Network](https://mlsanity.com/paper/2204.07579/) (2022)

## Built on by (most cited first, 10 of 10)

- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Interpretable Imitation Learning via Generative Adversarial STL Inference and Control](https://mlsanity.com/paper/2402.10310/) (2024)
- [Multi-class Temporal Logic Neural Networks](https://mlsanity.com/paper/2402.12397/) (2024)
- [stl2vec: Semantic and Interpretable Vector Representation of Temporal Logic](https://mlsanity.com/paper/2405.14389/) (2024)
- [ClarifySTL: An Interactive LLM Agent Framework for STL Transformation through Requirements Clarification](https://mlsanity.com/paper/2605.01209/) (2026)
- [On Generating Explanations for Reinforcement Learning Policies: An Empirical Study](https://mlsanity.com/paper/2309.16960/) (2023)
- [A Safe Preference Learning Approach for Personalization with Applications to Autonomous Vehicles](https://mlsanity.com/paper/2311.02099/) (2023)
- [Conformalized Signal Temporal Logic Inference under Covariate Shift](https://mlsanity.com/paper/2603.27062/) (2026)
- [SCP-NL2TL: Selective Conformal Prediction with Semantic Verification for Natural Language to Temporal Logic Specifications](https://mlsanity.com/paper/2608.05439/) (2026)
- [Learning Optimal Signal Temporal Logic Decision Trees for Classification: A Max-Flow MILP Formulation](https://mlsanity.com/paper/2407.21090/) (2024)

## Abstract (arXiv)

Machine learning techniques using neural networks have achieved promising success for time-series data classification. However, the models that they produce are challenging to verify and interpret. In this paper, we propose an explainable neural-symbolic framework for the classification of time-series behaviors. In particular, we use an expressive formal language, namely Signal Temporal Logic (STL), to constrain the search of the computation graph for a neural network. We design a novel time function and sparse softmax function to improve the soundness and precision of the neural-STL framework. As a result, we can efficiently learn a compact STL formula for the classification of time-series data through off-the-shelf gradient-based tools. We demonstrate the computational efficiency, compactness, and interpretability of the proposed method through driving scenarios and naval surveillance case studies, compared with state-of-the-art baselines.