Conformal Prediction for Signal Temporal Logic Inference

2025-09-29

AI Summary

Existing STL specification inference methods lack statistical confidence guarantees, undermining the reliability of interpretable rules. This paper introduces conformal prediction to STL inference for the first time, proposing an end-to-end differentiable framework: a robust nonconformity scoring function is designed, and conformal loss is integrated into training; smoothed STL semantics and gradient-based optimization jointly optimize both formula structure and prediction set quality. The method ensures statistical validity—achieving guaranteed (1−α) coverage—while significantly reducing prediction set size, improving coverage accuracy, and lowering misclassification rates. Experiments demonstrate consistent superiority over state-of-the-art approaches across multiple benchmark tasks. To our knowledge, this is the first deep learning framework for time-series interpretable reasoning that provides formal, distribution-free confidence guarantees.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Providing statistical guarantees for STL rule inference
• Enhancing reliability and interpretability of temporal logic formulas
• Reducing prediction uncertainty while improving classification accuracy

Innovation

• Differentiable conformal prediction for STL inference
• Robustness-based nonconformity score with smooth CP layer
• Single loss function optimizing accuracy and prediction sets