# Guided by Stars: Interpretable Concept Learning Over Time Series via Temporal Logic Semantics

arXiv: https://arxiv.org/abs/2511.04244 · HTML: https://mlsanity.com/paper/2511.04244/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 74 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Builds on (most cited first, 30 of 32)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels](https://mlsanity.com/paper/1910.13051/) (2019)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Benchmarking Multivariate Time Series Classification Algorithms](https://mlsanity.com/paper/2007.13156/) (2020)
- [LSTM Fully Convolutional Networks for Time Series Classification](https://mlsanity.com/paper/1709.05206/) (2017)
- [HIVE-COTE 2.0: a new meta ensemble for time series classification](https://mlsanity.com/paper/2104.07551/) (2021)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Explainable Artificial Intelligence (XAI) on TimeSeries Data: A Survey](https://mlsanity.com/paper/2104.00950/) (2021)
- [A Time Series Forest for Classification and Feature Extraction](https://mlsanity.com/paper/1302.2277/) (2013)
- [Multivariate Time Series Classification with WEASEL+MUSE](https://mlsanity.com/paper/1711.11343/) (2017)
- [The Canonical Interval Forest (CIF) Classifier for Time Series Classification](https://mlsanity.com/paper/2008.09172/) (2020)
- [aeon: a Python toolkit for learning from time series](https://mlsanity.com/paper/2406.14231/) (2024)
- [Interpretable Time Series Classification using Linear Models and Multi-resolution Multi-domain Symbolic Representations](https://mlsanity.com/paper/2006.01667/) (2020)
- [Interpretable Classification of Time-Series Data using Efficient Enumerative Techniques](https://mlsanity.com/paper/1907.10265/) (2019)
- [Scalable Dictionary Classifiers for Time Series Classification](https://mlsanity.com/paper/1907.11815/) (2019)
- [A Survey of Explainable Artificial Intelligence (XAI) in Financial Time Series Forecasting](https://mlsanity.com/paper/2407.15909/) (2024)
- [A Robust Genetic Algorithm for Learning Temporal Specifications from Data](https://mlsanity.com/paper/1711.06202/) (2017)
- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Focusing on What is Relevant: Time-Series Learning and Understanding using Attention](https://mlsanity.com/paper/1806.08523/) (2018)
- [Graph Neural Networks for Traffic Forecasting](https://mlsanity.com/paper/2104.13096/) (2021)
- [Multi-Stage Prototype Learning for Interpretable Time Series Classification](https://mlsanity.com/paper/2106.09636/) (2021)
- [Retrieval-Augmented Mining of Temporal Logic Specifications from Data](https://mlsanity.com/paper/2405.14355/) (2024)
- [Societal, Economic, Ethical and Legal Challenges of the Digital Revolution: From Big Data to Deep Learning, Artificial Intelligence, and Manipulative Technologies](https://mlsanity.com/paper/1504.03751/) (2015)
- [Explainable Multivariate Time Series Classification: A Deep Neural Network Which Learns To Attend To Important Variables As Well As Informative Time Intervals](https://mlsanity.com/paper/2011.11631/) (2020)

## Abstract (arXiv)

Time series classification is a task of paramount importance, as this kind of data often arises in safety-critical applications. However, it is typically tackled with black-box deep learning methods, making it hard for humans to understand the rationale behind their output. To take on this challenge, we propose a novel approach, STELLE (Signal Temporal logic Embedding for Logically-grounded Learning and Explanation), a neuro-symbolic framework that unifies classification and explanation through direct embedding of trajectories into a space of temporal logic concepts. By introducing a novel STL-inspired kernel that maps raw time series to their alignment with predefined STL formulae, our model jointly optimises accuracy and interpretability, as each prediction is accompanied by the most relevant logical concepts that characterise it. This yields (i) local explanations as human-readable STL conditions justifying individual predictions, and (ii) global explanations as class-characterising formulae. Experiments demonstrate that STELLE achieves competitive accuracy while providing logically faithful explanations, validated on diverse real-world benchmarks.