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Abstract
Signal Temporal Logic (STL) inference offers an interpretable framework for symbolic reasoning over 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. Technically, the approach first employs a template-free, differentiable STL inference method to obtain an initial model, and subsequently refines it using a deployment-proxy 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.
Modern learning systems can achieve strong predictive performance, but deployment often introduces distribution shift that degrades both reliability and uncertainty calibration. Our work studies how to combine interpretable STL rules with deployment-aware adaptation and conformal prediction for more reliable decision-making under covariate shift.
ConfrTLIcs
Conformalized Signal Temporal Logic Inference under Covariate Shift is a framework for learning interpretable Signal Temporal Logic (STL) classifiers while improving deployment-time reliability under distribution shift. The method starts from a differentiable STL learner that infers symbolic temporal logic formulas from labeled trajectory data and uses robustness semantics to produce a real-valued decision score.
To address the mismatch between nominal training data and deployment trajectories, the framework refines the learned STL classifier using deployment-proxy data and then calibrates its robustness-based decisions with weighted conformal prediction. This yields an interpretable, shift-aware inference pipeline that combines symbolic structure, distribution-aware adaptation, and calibrated uncertainty.
Motivation & Method
STL inference provides human-readable decision rules over trajectories, which is appealing in robotics and control. However, an STL classifier learned only from nominal data may not remain reliable at deployment when the trajectory distribution changes. Under such covariate shift, both the learned decision boundary and the calibration threshold used for uncertainty quantification can become mismatched to the test environment.
Our framework addresses these issues jointly. It first learns an initial STL classifier from a core training set, then adapts the formula using deployment-proxy trajectories to better align the learned robustness scores with deployment-relevant behaviors, and finally applies weighted conformal prediction to calibrate the robustness-based decision rule under distribution shift.
Dataset Setup
We evaluate our method on three trajectory classification tasks spanning time-series monitoring, robotic manipulation, and motion planning under covariate shift.
(a) Naval Surveillance Scenario: multivariate trajectories labeled as normal or anomalous operational behavior.
(b) VIMA Block Placement:
robot manipulation trajectories for placing an object into a target region while satisfying task constraints.
(c) Motion Planning:
2D trajectories that must reach a goal while avoiding static obstacles.
Experiments
We evaluate the proposed framework on trajectory classification tasks under covariate shift. Our experiments aim to answer three questions:
How does shift-aware STL refinement affect misclassification under the deployment distribution?
How do weighted conformal prediction and standard conformal prediction compare under distribution shift?
Can the proposed framework maintain compact and interpretable STL decision rules while improving reliability?
Results
(a) Cassification results of our method and baseline methods on trajectory datasets
(b) Weighted CP with Covariate Shift
(c) Comparison across datasets with weighted CP
Conclusion
We present a shift-aware STL inference framework that adapts learned STL formulas with deployment-proxy data and calibrates uncertainty with conformal prediction. The result is an interpretable decision pipeline that improves deployment-time reliability under covariate shift.
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