# Conformal Prediction for Signal Temporal Logic Inference

arXiv: https://arxiv.org/abs/2509.25473 · HTML: https://mlsanity.com/paper/2509.25473/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [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)
- [VIMA: General Robot Manipulation with Multimodal Prompts](https://mlsanity.com/paper/2210.03094/) (2022)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [Differentiable Ranks and Sorting using Optimal Transport](https://mlsanity.com/paper/1905.11885/) (2019)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Conformal Prediction for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Conformal prediction under ambiguous ground truth](https://mlsanity.com/paper/2307.09302/) (2023)
- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Differentiable Inference of Temporal Logic Formulas](https://mlsanity.com/paper/2208.05440/) (2022)
- [Multi-class Temporal Logic Neural Networks](https://mlsanity.com/paper/2402.12397/) (2024)
- [Learning Temporal Logic Predicates from Data with Statistical Guarantees](https://mlsanity.com/paper/2406.10449/) (2024)

## Built on by (most cited first, 3 of 3)

- [Conformalized Signal Temporal Logic Inference under Covariate Shift](https://mlsanity.com/paper/2603.27062/) (2026)
- [SCP-NL2TL: Selective Conformal Prediction with Semantic Verification for Natural Language to Temporal Logic Specifications](https://mlsanity.com/paper/2608.05439/) (2026)
- [Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes](https://mlsanity.com/paper/2610.14352/) (2026)

## Abstract (arXiv)

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.