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This paper addresses interpretable time series classification with Signal Temporal Logic, focusing on a gap that accuracy alone hides: a multiclass model can classify well while its inferred formulas fail to hold consistently for the true class. The authors propose satisfaction-based metrics, a two-stage training procedure, and class-conditional conformal calibration for finite-sample coverage guarantees. For ML readers, the useful takeaways are the explicit tradeoff between robustness margin and formula satisfaction and the finding that pooled calibration can hide per-class undercoverage. Evaluation is limited to naval, synthetic, and robot manipulation trajectories, so generalization beyond these domains remains untested.
Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes
arXiv:2610.14352v1 Announce Type: new Abstract: Signal Temporal Logic (STL) inference provides interpretable formulas for time series classification. For multiclass classification, however, accurate predictions do not necessarily ensure that the inferred formulas are satisfied consistently with the true class. We introduce the positive satisfaction rate and codeword satisfaction rate to quantify satisfaction of required formulas and consistency with the complete class codeword, respectively. We develop a two-stage procedure that first learns discriminative formulas using a margin-based objective and then refines predicate thresholds toward a small positive robustness target while fixing the formula structure and temporal intervals. Satisfaction and ranking penalties discourage violations of required formulas and loss of class separation. The decoding loss is used as a nonconformity score and calibrated separately for each class, providing finite-sample class-conditional coverage under intra-class exchangeability. Experiments on naval, synthetic, and robot manipulation trajectories demonstrate discrepancies between classification accuracy and formula satisfaction. The results further reveal a data-dependent tradeoff between robustness tightness and satisfaction, while class-conditional calibration mitigates undercoverage that can be hidden by pooled calibration.
Abstract:Signal Temporal Logic (STL) inference provides interpretable formulas for time series classification. For multiclass classification, however, accurate predictions do not necessarily ensure that the inferred formulas are satisfied consistently with the true class. We introduce the positive satisfaction rate and codeword satisfaction rate to quantify satisfaction of required formulas and consistency with the complete class codeword, respectively. We develop a two-stage procedure that first learns discriminative formulas using a margin-based objective and then refines predicate thresholds toward a small positive robustness target while fixing the formula structure and temporal intervals. Satisfaction and ranking penalties discourage violations of required formulas and loss of class separation. The decoding loss is used as a nonconformity score and calibrated separately for each class, providing finite-sample class-conditional coverage under intra-class exchangeability. Experiments on naval, synthetic, and robot manipulation trajectories demonstrate discrepancies between classification accuracy and formula satisfaction. The results further reveal a data-dependent tradeoff between robustness tightness and satisfaction, while class-conditional calibration mitigates undercoverage that can be hidden by pooled calibration.
Machine Learning (cs.LG)
arXiv:2610.14352 [cs.LG]
(or arXiv:2610.14352v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.14352 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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