# Conformalized Signal Temporal Logic Inference under Covariate Shift

arXiv: https://arxiv.org/abs/2603.27062 · HTML: https://mlsanity.com/paper/2603.27062/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 28 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Adaptive Conformal Prediction for Motion Planning among Dynamic Agents](https://mlsanity.com/paper/2212.00278/) (2022)
- [Analysis of KNN Density Estimation](https://mlsanity.com/paper/2010.00438/) (2020)
- [Mining Parametric Temporal Logic Properties in Model Based Design for Cyber-Physical Systems](https://mlsanity.com/paper/1512.07956/) (2015)
- [Learning Signal Temporal Logic through Neural Network for Interpretable Classification](https://mlsanity.com/paper/2210.01910/) (2022)
- [Information Theoretic Learning with Infinitely Divisible Kernels](https://mlsanity.com/paper/1301.3551/) (2013)
- [Classification of Time-Series Data Using Boosted Decision Trees](https://mlsanity.com/paper/2110.00581/) (2021)
- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Learning Temporal Logic Predicates from Data with Statistical Guarantees](https://mlsanity.com/paper/2406.10449/) (2024)
- [Conformal Prediction for Signal Temporal Logic Inference](https://mlsanity.com/paper/2509.25473/) (2025)
- [Time-aware Motion Planning in Dynamic Environments with Conformal Prediction](https://mlsanity.com/paper/2511.18170/) (2025)

## Built on by (most cited first, 1 of 1)

- [SCP-NL2TL: Selective Conformal Prediction with Semantic Verification for Natural Language to Temporal Logic Specifications](https://mlsanity.com/paper/2608.05439/) (2026)

## Abstract (arXiv)

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.