Conformal Prediction for Signal Temporal Logic Inference

• URL: http://arxiv.org/abs/2509.25473v3
• Date: Tue, 21 Oct 2025 19:50:01 GMT
• Title: Conformal Prediction for Signal Temporal Logic Inference
• Authors: Danyang Li, Yixuan Wang, Matthew Cleaveland, Mingyu Cai, Roberto Tron,
• Abstract summary: Signal Temporal Logic (STL) inference seeks to extract human-interpretable rules from time-series data.<n>Existing methods lack formal confidence guarantees for the inferred rules.<n>We introduce an end-to-end differentiable CP framework for STL inference that enhances both reliability and interpretability.
• Score: 13.843989967082031
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Signal Temporal Logic (STL) inference seeks to extract human-interpretable rules from time-series data, but existing methods lack formal confidence guarantees for the inferred rules. Conformal prediction (CP) is a technique that can provide statistical correctness guarantees, but is typically applied as a post-training wrapper without improving model learning. Instead, we introduce an end-to-end differentiable CP framework for STL inference that enhances both reliability and interpretability of the resulting formulas. We introduce a robustness-based nonconformity score, embed a smooth CP layer directly into training, and employ a new loss function that simultaneously optimizes inference accuracy and CP prediction sets with a single term. Following training, an exact CP procedure delivers statistical guarantees for the learned STL formulas. Experiments on benchmark time-series tasks show that our approach reduces uncertainty in predictions (i.e., it achieves high coverage while reducing prediction set size), and improves accuracy (i.e., the number of misclassifications when using a fixed threshold) over state-of-the-art baselines.

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