# Stop Rewarding Hallucinated Steps: Faithfulness-Aware Step-Level Reinforcement Learning for Small Reasoning Models

arXiv: https://arxiv.org/abs/2602.05897 · HTML: https://mlsanity.com/paper/2602.05897/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 40 of its 55 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 40)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [NewsQA: A Machine Comprehension Dataset](https://mlsanity.com/paper/1611.09830/) (2016)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Are Reasoning Models More Prone to Hallucination?](https://mlsanity.com/paper/2505.23646/) (2025)
- [The FACTS Grounding Leaderboard: Benchmarking LLMs' Ability to Ground Responses to Long-Form Input](https://mlsanity.com/paper/2501.03200/) (2025)
- [MiniCPM4: Ultra-Efficient LLMs on End Devices](https://mlsanity.com/paper/2506.07900/) (2025)
- [Scaf-GRPO: Scaffolded Group Relative Policy Optimization for Enhancing LLM Reasoning](https://mlsanity.com/paper/2510.19807/) (2025)
- [Large Language Models Hallucination: A Comprehensive Survey](https://mlsanity.com/paper/2510.06265/) (2025)
- [Apple Intelligence Foundation Language Models: Tech Report 2025](https://mlsanity.com/paper/2507.13575/) (2025)
- [TruthRL: Incentivizing Truthful LLMs via Reinforcement Learning](https://mlsanity.com/paper/2509.25760/) (2025)
- [Mask-DPO: Generalizable Fine-grained Factuality Alignment of LLMs](https://mlsanity.com/paper/2503.02846/) (2025)
- [Reasoning Models Hallucinate More: Factuality-Aware Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2505.24630/) (2025)
- [LoVeC: Reinforcement Learning for Better Verbalized Confidence in Long-Form Generations](https://mlsanity.com/paper/2505.23912/) (2025)

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

- [Beyond Math and Code: Lightweight Corpus-Grounded Process Rewards for Factual Question Answering](https://mlsanity.com/paper/2605.29648/) (2026)
- [CLIR-Bench: Benchmarking Multimodal Question Answering over Irregular Clinical Time Series](https://mlsanity.com/paper/2607.09880/) (2026)
- [Hallucination Across the Reasoning Lifecycle: Interface Visibility, Causal Evidence, and Release Control in Large Reasoning Models](https://mlsanity.com/paper/2610.05472/) (2026)
- [Rethinking Faithfulness in LLMs: A Pairwise Context-Sensitive Perspective](https://mlsanity.com/paper/2610.07894/) (2026)

## Abstract (arXiv)

As large language models become smaller and more efficient, small reasoning models (SRMs) are crucial for enabling chain-of-thought (CoT) reasoning in resource-constrained settings. However, they are prone to faithfulness hallucinations, especially in intermediate reasoning steps. Existing mitigation methods based on online reinforcement learning rely on outcome-based rewards or coarse-grained CoT evaluation, which can inadvertently reinforce unfaithful reasoning when the final answer is correct. To address these limitations, we propose Faithfulness-Aware Step-Level Reinforcement Learning (FaithRL), introducing step-level supervision via explicit faithfulness rewards from a process reward model, together with an implicit truncated resampling strategy that generates contrastive signals from faithful prefixes, while also mitigating reward hacking from step-level rewards. Experiments across multiple SRMs and Open-Book QA benchmarks demonstrate that FaithRL consistently reduces hallucinations in both the CoT and final answers, leading to more faithful and reliable reasoning. Code is available at https://github.com/Easy195/FaithRL.