# Reasoning Error from Known Fact: Step-Level Self-Consistency Group Relative Policy Optimization for LLM

arXiv: https://arxiv.org/abs/2607.18915 · HTML: https://mlsanity.com/paper/2607.18915/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Hallucination detection and mitigation, one of 17 directions in LLM reasoning.
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Placed in

- LLM reasoning / [Hallucination detection and mitigation](https://mlsanity.com/lr/hallucination-detection-and-mitigation/)

## Builds on (most cited first, 20 of 20)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [SEED-GRPO: Semantic Entropy Enhanced GRPO for Uncertainty-Aware Policy Optimization](https://mlsanity.com/paper/2505.12346/) (2025)
- [Are Reasoning Models More Prone to Hallucination?](https://mlsanity.com/paper/2505.23646/) (2025)
- [The Hallucination Tax of Reinforcement Finetuning](https://mlsanity.com/paper/2505.13988/) (2025)
- [Detection and Mitigation of Hallucination in Large Reasoning Models: A Mechanistic Perspective](https://mlsanity.com/paper/2505.12886/) (2025)
- [CriticSearch: Fine-Grained Credit Assignment for Search Agents via a Retrospective Critic](https://mlsanity.com/paper/2511.12159/) (2025)
- [TruthRL: Incentivizing Truthful LLMs via Reinforcement Learning](https://mlsanity.com/paper/2509.25760/) (2025)
- [Chain-of-Thought Prompting Obscures Hallucination Cues in Large Language Models: An Empirical Evaluation](https://mlsanity.com/paper/2506.17088/) (2025)
- [FG-PRM: Fine-grained Hallucination Detection and Mitigation in Language Model Mathematical Reasoning](https://mlsanity.com/paper/2410.06304/) (2024)

## Abstract (arXiv)

With the rapid advancement of large language models (LLMs), modern systems not only possess strong foundational capabilities and extensive knowledge, but can also solve complex problems via long, multi-step reasoning. However, as reasoning traces become longer, LLMs may produce a substantial amount of hallucinated content during the reasoning process, which is often difficult to detect. In this work, we conduct a fine-grained analysis of hallucinations arising in LLM reasoning and find that the reasoning traces are particularly prone to Context-Sensitive Factual Hallucinations: cases where the model actually has the relevant knowledge, yet makes factual errors due to contextual interference during reasoning. To address this issue, we propose Step-level Self-Consistency Group Relative Policy Optimization (SSC-GRPO), which assigns step-level rewards to reasoning traces by computing self-consistency scores of individual steps across multiple rollouts. Compared with prior methods, SSC-GRPO achieves state-of-the-art performance on both mathematical reasoning benchmarks and hallucination leaderboards. Our results offer a new perspective for detecting and mitigating hallucinations in the reasoning process of large language models.