Learning Reliable and Intuitive Temporal Logic Rules for Interpretable Time Series Classification

Recently, rule-based time series classification models are widely used in safety-critical scenarios demanding strong interpretability, through providing explicit and rigorous rationales. However, due to the discrepancy between discrete rules and continuous neural networks, the generated rules are not completely consistent with the actual decision-making process, rendering users hesitant to trust the model. Additionally, existing methods learn the role (weight) of each time point independently, which is not in line with human understanding and the consecutive nature of temporal properties. In this paper, we propose a novel neuro-symbolic model named TemporalRule, aiming to automatically learn Signal Temporal Logic (STL) rules for interpretable time series classification. Our model directly optimizes the neural networks representing discrete rules via gradient grafting, producing reliable rules that can exactly determine the classification results. Notably, a temporal logical layer is designed to simulate expressive temporal operators, including one 2-predicate operator (Until) and two 2-level composite operators (EA and AE), through adaptively learning the time bounds of involved intervals. That creates consistent weights for consecutive time points, enhancing the intuitiveness of derived rules. Extensive experiments on diverse real-world datasets in safety-critical domains show that TemporalRule achieves superior and stable classification accuracy compared to state-of-the-art rule-based approaches, and the learned rules can precisely and concisely explicate the classification results, leading to a trustable model.