mlsanityData to 14 Oct 2026

Harder Is Better: Boosting Mathematical Reasoning via Difficulty-Aware GRPO and Multi-Aspect Question Reformulation

arXiv 2601.20614 ↗First posted 28 Jan 2026cs.AI cs.CLcited by 19

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

  1. 2025AdaCuRL: Adaptive Curriculum Reinforcement Learning with Invalid Sample Mitigation and Historical Revisiting12 Nov
  2. 2025LaSeR: Reinforcement Learning with Last-Token Self-Rewarding16 Oct
  3. 2025Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR19 Aug
  4. 2025Geometric-Mean Policy Optimization28 Jul
  5. 2025Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs17 Jun
  6. 2025S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models12 May
  7. 2025GRPO-LEAD: A Difficulty-Aware Reinforcement Learning Approach for Concise Mathematical Reasoning in Language Models13 Apr
  8. 2025VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks7 Apr
  9. 2025GPG: A Simple and Strong Reinforcement Learning Baseline for Model Reasoning3 Apr
  10. 2025Understanding R1-Zero-Like Training: A Critical Perspective26 Mar
  11. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scale18 Mar
  12. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning22 Jan
1 more
  1. 2017Proximal Policy Optimization Algorithms20 Jul

Other references · 21

  1. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  2. 2025Qwen3 Technical Reportcited by 8,820
  3. 2025Qwen2.5-VL Technical Reportcited by 5,587
  4. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  5. 2025Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilitiescited by 3,796
  6. 2024OpenAI o1 System Cardcited by 1,244
  7. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,136
  8. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
  9. 2025Group Sequence Policy Optimizationcited by 835
  10. 2023WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instructcited by 625
  11. 2025Kimi K2: Open Agentic Intelligencecited by 567
  12. 2021GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoningcited by 228
9 more
  1. 2024Common 7B Language Models Already Possess Strong Math Capabilitiescited by 109
  2. 2025Tree Search for LLM Agent Reinforcement Learningcited by 79
  3. 2023MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoningcited by 45
  4. 2025Detection and Mitigation of Hallucination in Large Reasoning Models: A Mechanistic Perspectivecited by 34
  5. 2025GHPO: Adaptive Guidance for Stable and Efficient LLM Reinforcement Learningcited by 34
  6. 2025HS-STaR: Hierarchical Sampling for Self-Taught Reasoners via Difficulty Estimation and Budget Reallocationcited by 18
  7. 2025DeepCritic: Deliberate Critique with Large Language Modelscited by 17
  8. 2026Thinking with Map: Reinforced Parallel Map-Augmented Agent for Geolocalizationcited by 9
  9. 2024PersonaMath: Boosting Mathematical Reasoning via Persona-Driven Data Augmentationcited by 7

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 19.

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  1. 2026Code2World: A GUI World Model via Renderable Code Generationcited by 29
  2. 2026Visually-Guided Policy Optimization for Multimodal Reasoningcited by 11
  3. 2026FASA: Frequency-aware Sparse Attentioncited by 8
  4. 2026MobilityBench: A Benchmark for Evaluating Route-Planning Agents in Real-World Mobility Scenarioscited by 8
  5. 2026Unveiling Implicit Advantage Symmetry: Why GRPO Struggles with Exploration and Difficulty Adaptationcited by 7
  6. 2026Learning Agentic Policy from Action Guidancecited by 4
  7. 2026Leveraging Error Diversity in Group Rollouts for Reinforcement Learningcited by 3
  8. 2026Policy Improvement Reinforcement Learningcited by 2
  9. 2026Ace-Skill: Bootstrapping Multimodal Agents with Prioritized and Clustered Evolutioncited by 2
  10. 2026Restoring the Sweet Spot: Pass-Rate Weighted Self-Distillation for LLM Reasoningcited by 2
  11. 2026RODS: Reward-Driven Online Data Synthesis for Multi-Turn Tool-Use Agentscited by 2
  12. 2026PrAg-PO: Prompt Augmented Policy Optimization for Robust and Diverse Mathematical Reasoningcited by 1
7 more
  1. 2026expo: Exploration-prioritized policy optimization via adaptive kl regulation and gaussian curriculum samplingcited by 1
  2. 2026fg-expo: Frontier-guided exploration-prioritized policy optimization via adaptive kl and gaussian curriculumcited by 1
  3. 2026RISE: Reliable Improvement in Self-Evolving Vision-Language Modelscited by 1
  4. 2026Unlearnable, or Unmeasured? On the Reliability of Difficulty Labels in RLVRcited by 1
  5. 2026D2Evo: Dual Difficulty-Aware Self-Evolution for Data-Efficient Reinforcement Learningcited by 0
  6. 2026Frontier Learning: Training LLM Reasoners at the Edge of Capabilitycited by 0
  7. 2026DART-ES: Difficulty-Aware Reweighting and Targeted Replay for Fine-Tuning LLMs with Evolution Strategiescited by 0

Similar, not cited

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  1. 2026The Easy, the Hard, and the Learnable: Confidence and Difficulty-Adaptive Policy Optimization for LLM Reasoning
  2. 2025QuestA: Expanding Reasoning Capacity in LLMs via Question Augmentation
  3. 2025MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy
  4. 2025Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models
  5. 2025Think Smarter not Harder: Adaptive Reasoning with Inference Aware Optimization
  6. 2025RIDE: Difficulty Evolving Perturbation with Item Response Theory for Mathematical Reasoning
  7. 2026Transformation-Augmented GRPO for Enhancing Exploration in Reasoning of Large Language Models
  8. 2026Are complicated loss functions necessary for teaching LLMs to reason?