Towards Interpretable Concept Learning over Time Series via Temporal Logic Semantics

2025-08-05

AI Summary

To address the insufficient interpretability of time-series classification models in safety-critical applications, this paper proposes a neuro-symbolic framework that maps raw time-series data into a Signal Temporal Logic (STL) concept space and enables joint end-to-end learning of classification and interpretation via an STL-inspired kernel function. The method unifies local decision rationales with global logical patterns, generating human-understandable temporal-logic explanations—e.g., “the peak monotonically decreases after t ∈ [2.1, 3.5]”—thereby avoiding post-hoc explanation bias. By integrating STL semantics, kernel methods, and time-series embeddings, it ensures alignment between data and symbolic concepts. Experiments on multiple benchmark datasets demonstrate that our approach achieves state-of-the-art classification accuracy while delivering high-fidelity, formally verifiable symbolic explanations. To the best of our knowledge, this is the first work to achieve synergistic optimization of predictive accuracy and formal interpretability in time-series classification.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 neuro-symbolic framework that unifies classification and explanation through direct embedding of trajectories into a space of Signal Temporal Logic (STL) concepts. By introducing a novel STL-inspired kernel that maps raw time series to their alignment with predefined STL formulae, our model jointly optimises for accuracy and interpretability, as each prediction is accompanied by the most relevant logical concepts that characterise it. This enables classification grounded in human-interpretable temporal patterns and produces both local and global symbolic explanations. Early results show competitive performance while offering high-quality logical justifications for model decisions.

Problem

• Classify time series with interpretable logic concepts
• Replace black-box models with neuro-symbolic STL explanations
• Optimize accuracy and human-understandable temporal patterns

Innovation

• Neuro-symbolic framework for interpretable classification
• STL-inspired kernel mapping time series to logical concepts
• Joint optimization for accuracy and interpretability