# Unspoken Hints: Accuracy Without Acknowledgement in LLM Reasoning

arXiv: https://arxiv.org/abs/2509.26041 · HTML: https://mlsanity.com/paper/2509.26041/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 15 of 15)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [ChatGPT Outperforms Crowd-Workers for Text-Annotation Tasks](https://mlsanity.com/paper/2303.15056/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [The Impact of AI on Developer Productivity: Evidence from GitHub Copilot](https://mlsanity.com/paper/2302.06590/) (2023)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Walk the Talk? Measuring the Faithfulness of Large Language Model Explanations](https://mlsanity.com/paper/2504.14150/) (2025)
- [Dissociation of Faithful and Unfaithful Reasoning in LLMs](https://mlsanity.com/paper/2405.15092/) (2024)

## Built on by (most cited first, 4 of 4)

- [State over Tokens: Characterizing the Role of Reasoning Tokens](https://mlsanity.com/paper/2512.12777/) (2025)
- [Silence Is Endorsement: Verification-Status Laundering in LLM Agent Pipelines](https://mlsanity.com/paper/2609.20211/) (2026)
- [Forecasting Future Behavior as a Learning Task](https://mlsanity.com/paper/2606.11445/) (2026)
- [To Reason or to Fabricate: Reasoning Without Shortcuts via Hint-Anchored Pairwise Aggregation](https://mlsanity.com/paper/2606.29481/) (2026)

## Abstract (arXiv)

Large language models (LLMs) increasingly rely on chain-of-thought (CoT) prompting to solve mathematical and logical reasoning tasks. Yet, a central question remains: to what extent are these generated rationales faithful to the underlying computations, rather than post-hoc narratives shaped by hints that function as answer shortcuts embedded in the prompt? Following prior work on hinted vs. unhinted prompting, we present a systematic study of CoT faithfulness under controlled hint manipulations. Our experimental design spans four datasets (AIME, GSM-Hard, MATH-500, UniADILR), two state-of-the-art models (GPT-4o and Gemini-2-Flash), and a structured set of hint conditions varying in correctness (correct and incorrect), presentation style (sycophancy and data leak), and complexity (raw answers, two-operator expressions, four-operator expressions). We evaluate both task accuracy and whether hints are explicitly acknowledged in the reasoning. Our results reveal three key findings. First, correct hints substantially improve accuracy, especially on harder benchmarks and logical reasoning, while incorrect hints sharply reduce accuracy in tasks with lower baseline competence. Second, acknowledgement of hints is highly uneven: equation-based hints are frequently referenced, whereas raw hints are often adopted silently, indicating that more complex hints push models toward verbalizing their reliance in the reasoning process. Third, presentation style matters: sycophancy prompts encourage overt acknowledgement, while leak-style prompts increase accuracy but promote hidden reliance. This may reflect RLHF-related effects, as sycophancy exploits the human-pleasing side and data leak triggers the self-censoring side. Together, these results demonstrate that LLM reasoning is systematically shaped by shortcuts in ways that obscure faithfulness.