# Beyond Math and Code: Lightweight Corpus-Grounded Process Rewards for Factual Question Answering

arXiv: https://arxiv.org/abs/2605.29648 · HTML: https://mlsanity.com/paper/2605.29648/

## 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 28 of its 33 references that are in the map.
- First posted on arXiv 28 May 2026.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [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)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Large Language Models Struggle to Learn Long-Tail Knowledge](https://mlsanity.com/paper/2211.08411/) (2022)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [Fine-tuning Language Models for Factuality](https://mlsanity.com/paper/2311.08401/) (2023)
- [Infini-gram: Scaling Unbounded n-gram Language Models to a Trillion Tokens](https://mlsanity.com/paper/2401.17377/) (2024)
- [R-Tuning: Instructing Large Language Models to Say `I Don't Know'](https://mlsanity.com/paper/2311.09677/) (2023)
- [FLAME: Factuality-Aware Alignment for Large Language Models](https://mlsanity.com/paper/2405.01525/) (2024)
- [Learning to Reason for Factuality](https://mlsanity.com/paper/2508.05618/) (2025)
- [KnowRL: Exploring Knowledgeable Reinforcement Learning for Factuality](https://mlsanity.com/paper/2506.19807/) (2025)
- [Impact of Co-occurrence on Factual Knowledge of Large Language Models](https://mlsanity.com/paper/2310.08256/) (2023)
- [Reasoning Models Hallucinate More: Factuality-Aware Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2505.24630/) (2025)
- [FoRAG: Factuality-optimized Retrieval Augmented Generation for Web-enhanced Long-form Question Answering](https://mlsanity.com/paper/2406.13779/) (2024)
- [QuCo-RAG: Quantifying Uncertainty from the Pre-training Corpus for Dynamic Retrieval-Augmented Generation](https://mlsanity.com/paper/2512.19134/) (2025)
- [On-Policy Self-Alignment with Fine-grained Knowledge Feedback for Hallucination Mitigation](https://mlsanity.com/paper/2406.12221/) (2024)
- [Stop Rewarding Hallucinated Steps: Faithfulness-Aware Step-Level Reinforcement Learning for Small Reasoning Models](https://mlsanity.com/paper/2602.05897/) (2026)

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

- [RSIAgent: Autonomous Exploration for Recursive Self-improvement in New Environments](https://mlsanity.com/paper/2609.15364/) (2026)
- [Agentic Commerce World: An Auditable and Verifiable Environment for Vibe Commerce](https://mlsanity.com/paper/2608.02441/) (2026)
- [Agent Step Value: Auditing Evaluation-Channel Sensitivity in Black-Box Agent Traces](https://mlsanity.com/paper/2607.04419/) (2026)
- [TRACE: Diagnosing Verifier Brittleness in Agentic Evaluation](https://mlsanity.com/paper/2610.11678/) (2026)

## Abstract (arXiv)

Process supervision during reinforcement learning (RL) post-training matters in factual question answering (QA) because responses receiving positive response-level rewards can still contain sentence-level factual errors. Unlike math and code, factual QA lacks inexpensive programmatic checks, making reward computation a bottleneck. Existing methods rely on neural verifiers to score individual sentences, requiring extensive model inference as RL repeats these checks across many sampled responses at every update. We therefore introduce CorVer (Corpus Verify), a lightweight training-time approach to process supervision that derives sentence-level rewards from corpus co-occurrence statistics. A 0.5B extractor identifies subject-object pairs, indexed corpus queries supply their co-occurrence counts, and the resulting sentence rewards are assigned to the corresponding tokens for RL. On Qwen3-4B and Qwen3-8B, CorVer reduces mean complete training time by 5.5-10.4 times relative to the four factuality-RL baselines. Across the four models evaluated against these baselines, CorVer achieves the highest accuracy in 17 of 20 model-benchmark settings. CorVer outperforms the unmodified models in all 30 standard factual-QA settings (six models from three families across five benchmarks) and remains effective on two additional multi-hop QA datasets.