Conformalized Signal Temporal Logic Inference under Covariate Shift

2026-03-27

AI Summary

This work addresses the lack of reliability guarantees in existing signal temporal logic (STL) inference methods under covariate shift. The authors propose a conformal STL inference framework tailored for covariate shift scenarios: it first learns an initial STL formula via a template-free differentiable approach, then aligns the source and target distributions using limited deployment-time data, and finally incorporates a likelihood ratio–weighted conformal prediction mechanism to ensure the validity of the inferred logical specifications. This study is the first to integrate distribution weighting into conformal STL reasoning, significantly enhancing reliability during deployment while preserving the interpretability of logical rules. Empirical results on trajectory datasets demonstrate that the proposed method substantially improves the robustness and trustworthiness of STL symbolic learning under distributional shifts.

Abstract

Signal Temporal Logic (STL) inference learns interpretable logical rules for temporal behaviors in dynamical systems. To ensure the correctness of learned STL formulas, recent approaches have incorporated conformal prediction as a statistical tool for uncertainty quantification. However, most existing methods rely on the assumption that calibration and testing data are identically distributed and exchangeable, an assumption that is frequently violated in real-world settings. This paper proposes a conformalized STL inference framework that explicitly addresses covariate shift between training and deployment trajectories dataset. From a technical standpoint, the approach first employs a template-free, differentiable STL inference method to learn an initial model, and subsequently refines it using a limited deployment side dataset to promote distribution alignment. To provide validity guarantees under distribution shift, the framework estimates the likelihood ratio between training and deployment distributions and integrates it into an STL-robustness-based weighted conformal prediction scheme. Experimental results on trajectory datasets demonstrate that the proposed framework preserves the interpretability of STL formulas while significantly improving symbolic learning reliability at deployment time.

Problem

• Signal Temporal Logic
• Conformal Prediction
• Covariate Shift
• Distribution Shift
• Uncertainty Quantification

Innovation

• conformal prediction
• covariate shift
• Signal Temporal Logic
• differentiable STL inference
• weighted conformal prediction