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

TL;DR

STELLE introduces a neuro-symbolic framework that embeds time series into a temporal logic space, enabling accurate classification with human-readable explanations based on STL formulae.

Contribution

It presents a novel STL-inspired kernel and a unified approach for interpretable time series classification combining accuracy with logical explanations.

Findings

Achieves competitive accuracy on real-world benchmarks.

Provides local STL-based explanations for individual predictions.

Generates global class-characterising STL formulae.

Abstract

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.