# Neuro-symbolic Models for Interpretable Time Series Classification using Temporal Logic Description

arXiv: https://arxiv.org/abs/2209.09114 · HTML: https://mlsanity.com/paper/2209.09114/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 16 of 16)

- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels](https://mlsanity.com/paper/1910.13051/) (2019)
- [MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification](https://mlsanity.com/paper/2012.08791/) (2020)
- [Benchmarking Multivariate Time Series Classification Algorithms](https://mlsanity.com/paper/2007.13156/) (2020)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [HIVE-COTE 2.0: a new meta ensemble for time series classification](https://mlsanity.com/paper/2104.07551/) (2021)
- [TS-CHIEF: A Scalable and Accurate Forest Algorithm for Time Series Classification](https://mlsanity.com/paper/1906.10329/) (2019)
- [The Canonical Interval Forest (CIF) Classifier for Time Series Classification](https://mlsanity.com/paper/2008.09172/) (2020)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [The Temporal Dictionary Ensemble (TDE) Classifier for Time Series Classification](https://mlsanity.com/paper/2105.03841/) (2021)
- [Specifying User Preferences using Weighted Signal Temporal Logic](https://mlsanity.com/paper/2010.00752/) (2020)
- [Transparent Classification with Multilayer Logical Perceptrons and Random Binarization](https://mlsanity.com/paper/1912.04695/) (2019)
- [Census Signal Temporal Logic Inference for Multi-Agent Group Behavior Analysis](https://mlsanity.com/paper/1610.05612/) (2016)
- [Continuous-time Signal Temporal Logic Planning with Control Barrier Function](https://mlsanity.com/paper/1903.03860/) (2019)
- [Signal Temporal Logic Task Decomposition via Convex Optimization](https://mlsanity.com/paper/2103.06047/) (2021)

## Built on by (most cited first, 8 of 8)

- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Interpretation of Time-Series Deep Models: A Survey](https://mlsanity.com/paper/2305.14582/) (2023)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [A Study on Neuro-Symbolic Artificial Intelligence: Healthcare Perspectives](https://mlsanity.com/paper/2503.18213/) (2025)
- [Towards Interpretable Concept Learning over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2508.03269/) (2025)
- [Auditable Context-Aware HFMD Forecasting with Structured LLM Agents](https://mlsanity.com/paper/2511.23276/) (2025)
- [TimeSliver : Symbolic-Linear Decomposition for Explainable Time Series Classification](https://mlsanity.com/paper/2601.21289/) (2026)
- [Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes](https://mlsanity.com/paper/2610.14352/) (2026)

## Abstract (arXiv)

Most existing Time series classification (TSC) models lack interpretability and are difficult to inspect. Interpretable machine learning models can aid in discovering patterns in data as well as give easy-to-understand insights to domain specialists. In this study, we present Neuro-Symbolic Time Series Classification (NSTSC), a neuro-symbolic model that leverages signal temporal logic (STL) and neural network (NN) to accomplish TSC tasks using multi-view data representation and expresses the model as a human-readable, interpretable formula. In NSTSC, each neuron is linked to a symbolic expression, i.e., an STL (sub)formula. The output of NSTSC is thus interpretable as an STL formula akin to natural language, describing temporal and logical relations hidden in the data. We propose an NSTSC-based classifier that adopts a decision-tree approach to learn formula structures and accomplish a multiclass TSC task. The proposed smooth activation functions for wSTL allow the model to be learned in an end-to-end fashion. We test NSTSC on a real-world wound healing dataset from mice and benchmark datasets from the UCR time-series repository, demonstrating that NSTSC achieves comparable performance with the state-of-the-art models. Furthermore, NSTSC can generate interpretable formulas that match with domain knowledge.