# Feedback Makes Perfect: A Closed-Loop Framework for NL-to-STL Translation

arXiv: https://arxiv.org/abs/2609.33287 · HTML: https://mlsanity.com/paper/2609.33287/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [nl2spec: Interactively Translating Unstructured Natural Language to Temporal Logics with Large Language Models](https://mlsanity.com/paper/2303.04864/) (2023)
- [NL2TL: Transforming Natural Languages to Temporal Logics using Large Language Models](https://mlsanity.com/paper/2305.07766/) (2023)
- [Data-Efficient Learning of Natural Language to Linear Temporal Logic Translators for Robot Task Specification](https://mlsanity.com/paper/2303.08006/) (2023)
- [DeepSTL -- From English Requirements to Signal Temporal Logic](https://mlsanity.com/paper/2109.10294/) (2021)
- [Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challenges](https://mlsanity.com/paper/2402.13075/) (2024)
- [Enhancing Transformation from Natural Language to Signal Temporal Logic Using LLMs with Diverse External Knowledge](https://mlsanity.com/paper/2505.20658/) (2025)
- [Power Line Inspection Tasks with Multi-Aerial Robot Systems via Signal Temporal Logic Specifications](https://mlsanity.com/paper/2302.04691/) (2023)
- [ClarifySTL: An Interactive LLM Agent Framework for STL Transformation through Requirements Clarification](https://mlsanity.com/paper/2605.01209/) (2026)
- [ReasonSTL: Bridging Natural Language and Signal Temporal Logic via Tool-Augmented Process-Rewarded Learning](https://mlsanity.com/paper/2605.06483/) (2026)
- [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) enables rigorous verification and control of cyber-physical systems, but writing correct specifications requires expertise that most requirement holders lack. Large language models can translate natural-language (NL) requirements into STL, yet stronger translators alone approach an accuracy ceiling. We argue that this ceiling stems from how the task is posed: one-shot, open-loop translation is somewhat ill-defined. Natural language is ambiguous, and, more fundamentally, what a person writes may not always be what they intend, so the target specification is not fully contained in the input text. We therefore reformulate NL-to-STL translation as a closed-loop feedback process. Each generated formula is translated back into natural language for the user to check, and natural-language corrections drive revision until the user accepts the specification. Users never read or write formal syntax. This framework rests on an asymmetry familiar from feedback control theory. The forward path, from ambiguous language to formal logic, is hard and error-prone. The feedback path, from structured STL back to language, can be made highly precise, and a precise feedback path lets an imprecise forward path achieve precise closed-loop behavior. Experiments on 500 expert-authored requirements and seven LLMs support this view. Back-translated explanations agree with expert judgments in 99.5% of cases. Closed-loop refinement raises strong models from about 89% open-loop accuracy to 98.0--99.2%, and yields gains of over 30 percentage points for weaker models (e.g., 17.6%rightarrow48.0%). Ablations show these gains come from the semantic content of the feedback rather than from repeated attempts. An expert audit and a 280-session user study further confirm the reliability of the loop. We also identify a capability threshold above which feedback no longer helps.