# Analyzing the Narration Gap in LLM-Solver Loops

arXiv: https://arxiv.org/abs/2606.19588 · HTML: https://mlsanity.com/paper/2606.19588/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 33)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Not what you've signed up for: Compromising Real-World LLM-Integrated Applications with Indirect Prompt Injection](https://mlsanity.com/paper/2302.12173/) (2023)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Ignore Previous Prompt: Attack Techniques For Language Models](https://mlsanity.com/paper/2211.09527/) (2022)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [InjecAgent: Benchmarking Indirect Prompt Injections in Tool-Integrated Large Language Model Agents](https://mlsanity.com/paper/2403.02691/) (2024)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Agent Security Bench (ASB): Formalizing and Benchmarking Attacks and Defenses in LLM-based Agents](https://mlsanity.com/paper/2410.02644/) (2024)
- [Formalizing and Benchmarking Prompt Injection Attacks and Defenses](https://mlsanity.com/paper/2310.12815/) (2023)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Benchmarking and Defending Against Indirect Prompt Injection Attacks on Large Language Models](https://mlsanity.com/paper/2312.14197/) (2023)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Optimization-based Prompt Injection Attack to LLM-as-a-Judge](https://mlsanity.com/paper/2403.17710/) (2024)
- [Is LLM-as-a-Judge Robust? Investigating Universal Adversarial Attacks on Zero-shot LLM Assessment](https://mlsanity.com/paper/2402.14016/) (2024)
- [Baldur: Whole-Proof Generation and Repair with Large Language Models](https://mlsanity.com/paper/2303.04910/) (2023)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [NL2TL: Transforming Natural Languages to Temporal Logics using Large Language Models](https://mlsanity.com/paper/2305.07766/) (2023)
- [SpecGen: Automated Generation of Formal Program Specifications via Large Language Models](https://mlsanity.com/paper/2401.08807/) (2024)
- [Autoformalize Mathematical Statements by Symbolic Equivalence and Semantic Consistency](https://mlsanity.com/paper/2410.20936/) (2024)
- [Ranking LLM-Generated Loop Invariants for Program Verification](https://mlsanity.com/paper/2310.09342/) (2023)
- [Autoformalizing Euclidean Geometry](https://mlsanity.com/paper/2405.17216/) (2024)
- [Evaluating Autoformalization Robustness via Semantically Similar Paraphrasing](https://mlsanity.com/paper/2511.12784/) (2025)

## Abstract (arXiv)

Formal tools such as SAT and SMT solvers are increasingly embedded in language model reasoning pipelines when a safety or security critical question can be formulated in logic. Unlike chain of thought whose steps are sampled from the model distribution without formal guarantee, a solver produces a sound and independently verifiable answer. However, the soundness guarantee can be lost in the interaction between the solver and the model. The hybrid pipeline has three components: formalizing the question, deciding it, and narrating the result. Prior work has studied the formalization and decision, but not narration, which is the step that turns a formal tool's output into the user answer. To fill the narration gap, we first model the LLM-solver loop as a verified decision procedure. We further evaluate five open-sourced models under prompt injection, and we find certificate gating makes the solver verdict sound, while an adversary can invert a verified conclusion across phrasings and channels. We study the mitigation through hardened prompt that reduces injection significantly but cannot eliminate it and still suffers under adaptive attack. Combining the formal analysis and empirical studies, we show in the LLM-solver loop, robustness does not reach to the answer that the user finally reads.