Harder Is Better: Boosting Mathematical Reasoning via Difficulty-Aware GRPO and Multi-Aspect Question Reformulation
On the map: LLM reasoning → Reinforcement learning for reasoning
Abstract (arXiv)
Reinforcement Learning with Verifiable Rewards (RLVR) offers a robust mechanism for enhancing mathematical reasoning in large models. However, we identify a systematic lack of emphasis on more challenging questions in existing methods from both algorithmic and data perspectives, despite their importance for refining underdeveloped capabilities. Algorithmically, widely used Group Relative Policy Optimization (GRPO) suffers from an implicit imbalance where the magnitude of policy updates is lower for harder questions. Data-wise, augmentation approaches primarily rephrase questions to enhance diversity without systematically increasing intrinsic difficulty. To address these issues, we propose a two-dual MathForge framework to improve mathematical reasoning by targeting harder questions from both perspectives, which comprises a Difficulty-Aware Group Policy Optimization (DGPO) algorithm and a Multi-Aspect Question Reformulation (MQR) strategy. Specifically, DGPO first rectifies the implicit imbalance in GRPO via difficulty-balanced group advantage estimation, and further prioritizes harder questions by difficulty-aware question-level weighting. Meanwhile, MQR reformulates questions across multiple aspects to increase difficulty while maintaining the original gold answer. Overall, MathForge forms a synergistic loop: MQR expands the data frontier, and DGPO effectively learns from the augmented data. Extensive experiments show that MathForge significantly outperforms existing methods on various mathematical reasoning tasks. The code and augmented data are all available at https://github.com/AMAP-ML/MathForge.
Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 34 of its 42 references that are in the map. First posted on arXiv 28 Jan 2026.
Builds on
34 of 42 references.
Closest ancestors · 13
Same direction, newest first
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- 2025S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models12 May
- 2025GRPO-LEAD: A Difficulty-Aware Reinforcement Learning Approach for Concise Mathematical Reasoning in Language Models13 Apr
- 2025VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks7 Apr
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- 2025Understanding R1-Zero-Like Training: A Critical Perspective26 Mar
- 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scale18 Mar
- 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning22 Jan
1 more
- 2017Proximal Policy Optimization Algorithms20 Jul
Other references · 21
- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
- 2025Qwen3 Technical Reportcited by 8,820
- 2025Qwen2.5-VL Technical Reportcited by 5,587
- 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
- 2025Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilitiescited by 3,796
- 2024OpenAI o1 System Cardcited by 1,244
- 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,136
- 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
- 2025Group Sequence Policy Optimizationcited by 835
- 2023WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instructcited by 625
- 2025Kimi K2: Open Agentic Intelligencecited by 567
- 2021GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoningcited by 228
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- 2024Common 7B Language Models Already Possess Strong Math Capabilitiescited by 109
- 2025Tree Search for LLM Agent Reinforcement Learningcited by 79
- 2023MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoningcited by 45
- 2025Detection and Mitigation of Hallucination in Large Reasoning Models: A Mechanistic Perspectivecited by 34
- 2025GHPO: Adaptive Guidance for Stable and Efficient LLM Reinforcement Learningcited by 34
- 2025HS-STaR: Hierarchical Sampling for Self-Taught Reasoners via Difficulty Estimation and Budget Reallocationcited by 18
- 2025DeepCritic: Deliberate Critique with Large Language Modelscited by 17
- 2026Thinking with Map: Reinforced Parallel Map-Augmented Agent for Geolocalizationcited by 9
- 2024PersonaMath: Boosting Mathematical Reasoning via Persona-Driven Data Augmentationcited by 7
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Citing papers per year: 2026: 19.
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