# SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning

arXiv: https://arxiv.org/abs/2506.08989 · HTML: https://mlsanity.com/paper/2506.08989/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 62 of its 79 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Placed in

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

## Builds on (most cited first, 30 of 62)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [From Generation to Judgment: Opportunities and Challenges of LLM-as-a-judge](https://mlsanity.com/paper/2411.16594/) (2024)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)

## Built on by (most cited first, 30 of 42)

- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR](https://mlsanity.com/paper/2508.14029/) (2025)
- [Reinforcement Learning Meets Large Language Models: A Survey of Advancements and Applications Across the LLM Lifecycle](https://mlsanity.com/paper/2509.16679/) (2025)
- [PolySkill: Learning Generalizable Skills Through Polymorphic Abstraction](https://mlsanity.com/paper/2510.15863/) (2025)
- [Locate, Steer, and Improve: A Practical Survey of Actionable Mechanistic Interpretability in Large Language Models](https://mlsanity.com/paper/2601.14004/) (2026)
- [Group-Relative REINFORCE Is Secretly an Off-Policy Algorithm: Demystifying Some Myths About GRPO and Its Friends](https://mlsanity.com/paper/2509.24203/) (2025)
- [Find Your Optimal Teacher: Personalized Data Synthesis via Router-Guided Multi-Teacher Distillation](https://mlsanity.com/paper/2510.10925/) (2025)
- [ToolPRMBench: Evaluating and Advancing Process Reward Models for Tool-using Agents](https://mlsanity.com/paper/2601.12294/) (2026)
- [Dynamic Generation of Multi-LLM Agents Communication Topologies with Graph Diffusion Models](https://mlsanity.com/paper/2510.07799/) (2025)
- [Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis](https://mlsanity.com/paper/2511.09907/) (2025)
- [SCALER:Synthetic Scalable Adaptive Learning Environment for Reasoning](https://mlsanity.com/paper/2601.04809/) (2026)
- [GuiLoMo: Allocating Expert Number and Rank for LoRA-MoE via Bilevel Optimization with GuidedSelection Vectors](https://mlsanity.com/paper/2506.14646/) (2025)
- [Residual Decoding: Mitigating Hallucinations in Large Vision-Language Models via History-Aware Residual Guidance](https://mlsanity.com/paper/2602.01047/) (2026)
- [Beyond Outliers: A Data-Free Layer-wise Mixed-Precision Quantization Approach Driven by Numerical and Structural Dual-Sensitivity](https://mlsanity.com/paper/2603.17354/) (2026)
- [QueST: Incentivizing LLMs to Generate Difficult Problems](https://mlsanity.com/paper/2510.17715/) (2025)
- [Training LLMs for Divide-and-Conquer Reasoning Elevates Test-Time Scalability](https://mlsanity.com/paper/2602.02477/) (2026)
- [A Deep Dive into Scaling RL for Code Generation with Synthetic Data and Curricula](https://mlsanity.com/paper/2603.24202/) (2026)
- [Breaking the Solver Bottleneck: Training Task Generators at the Learnable Frontier](https://mlsanity.com/paper/2606.18284/) (2026)
- [Libra: Large Chinese-based Safeguard for AI Content](https://mlsanity.com/paper/2507.21929/) (2025)
- [One Sample to Rule Them All: Extreme Data Efficiency in Multidiscipline Reasoning with Reinforcement Learning](https://mlsanity.com/paper/2601.03111/) (2026)
- [Question Begets Question: Self-Evolving Curriculum for Reinforcement Fine-Tuning on Competition Mathematics](https://mlsanity.com/paper/2608.01522/) (2026)
- [Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions](https://mlsanity.com/paper/2512.00097/) (2025)
- [Confidence-Aware Alignment Makes Reasoning LLMs More Reliable](https://mlsanity.com/paper/2605.07353/) (2026)
- [AcquisitionSynthesis: Targeted Data Generation using Acquisition Functions](https://mlsanity.com/paper/2605.13149/) (2026)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)
- [From Pixels to Digital Agents: An Empirical Study on the Taxonomy and Technological Trends of Reinforcement Learning Environments](https://mlsanity.com/paper/2603.23964/) (2026)
- [A Survey of Reinforcement Learning for Large Language Models under Data Scarcity: Challenges and Solutions](https://mlsanity.com/paper/2604.17312/) (2026)
- [D2Evo: Dual Difficulty-Aware Self-Evolution for Data-Efficient Reinforcement Learning](https://mlsanity.com/paper/2605.17037/) (2026)
- [REVES: REvision and VErification--Augmented Training for Test-Time Scaling](https://mlsanity.com/paper/2606.18910/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for training large language models (LLMs) on complex reasoning tasks, such as mathematical problem solving. A prerequisite for the scalability of RLVR is a high-quality problem set with precise and verifiable answers. However, the scarcity of well-crafted human-labeled math problems and limited-verification answers in existing distillation-oriented synthetic datasets limit their effectiveness in RL. Additionally, most problem synthesis strategies indiscriminately expand the problem set without considering the model's capabilities, leading to low efficiency in generating useful questions. To mitigate this issue, we introduce a Self-aware Weakness-driven problem Synthesis framework (SwS) that systematically identifies model deficiencies and leverages them for problem augmentation. Specifically, we define weaknesses as questions that the model consistently fails to learn through its iterative sampling during RL training. We then extract the core concepts from these failure cases and synthesize new problems to strengthen the model's weak areas in subsequent augmented training, enabling it to focus on and gradually overcome its weaknesses. Without relying on external knowledge distillation, our framework enables robust generalization byempowering the model to self-identify and address its weaknesses in RL, yielding average performance gains of 10.0% and 7.7% on 7B and 32B models across eight mainstream reasoning benchmarks.