# TLINet: Differentiable Neural Network Temporal Logic Inference

arXiv: https://arxiv.org/abs/2405.06670 · HTML: https://mlsanity.com/paper/2405.06670/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [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)
- [On Robustness Metrics for Learning STL Tasks](https://mlsanity.com/paper/2003.06041/) (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)
- [Information-Guided Temporal Logic Inference with Prior Knowledge](https://mlsanity.com/paper/1811.08846/) (2018)
- [Learning Signal Temporal Logic through Neural Network for Interpretable Classification](https://mlsanity.com/paper/2210.01910/) (2022)
- [Classification of Time-Series Data Using Boosted Decision Trees](https://mlsanity.com/paper/2110.00581/) (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)
- [Interpretable Imitation Learning via Generative Adversarial STL Inference and Control](https://mlsanity.com/paper/2402.10310/) (2024)

## Built on by (most cited first, 9 of 9)

- [Conformal Prediction for Signal Temporal Logic Inference](https://mlsanity.com/paper/2509.25473/) (2025)
- [Towards Interpretable Concept Learning over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2508.03269/) (2025)
- [GradSTL: Comprehensive Signal Temporal Logic for Neurosymbolic Reasoning and Learning](https://mlsanity.com/paper/2508.04438/) (2025)
- [Conformalized Signal Temporal Logic Inference under Covariate Shift](https://mlsanity.com/paper/2603.27062/) (2026)
- [First-Order Temporal Logic Tensor Networks](https://mlsanity.com/paper/2606.29972/) (2026)
- [SCP-NL2TL: Selective Conformal Prediction with Semantic Verification for Natural Language to Temporal Logic Specifications](https://mlsanity.com/paper/2608.05439/) (2026)
- [Guided by Stars: Interpretable Concept Learning Over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2511.04244/) (2025)
- [Ask for Any Appliance: A Prompt-Programmable Foundation Model for Non-Intrusive Load Monitoring](https://mlsanity.com/paper/2609.23146/) (2026)
- [Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes](https://mlsanity.com/paper/2610.14352/) (2026)

## Abstract (arXiv)

There has been a growing interest in extracting formal descriptions of the system behaviors from data. Signal Temporal Logic (STL) is an expressive formal language used to describe spatial-temporal properties with interpretability. This paper introduces TLINet, a neural-symbolic framework for learning STL formulas. The computation in TLINet is differentiable, enabling the usage of off-the-shelf gradient-based tools during the learning process. In contrast to existing approaches, we introduce approximation methods for max operator designed specifically for temporal logic-based gradient techniques, ensuring the correctness of STL satisfaction evaluation. Our framework not only learns the structure but also the parameters of STL formulas, allowing flexible combinations of operators and various logical structures. We validate TLINet against state-of-the-art baselines, demonstrating that our approach outperforms these baselines in terms of interpretability, compactness, rich expressibility, and computational efficiency.