# Reshaping Reasoning in LLMs: A Theoretical Analysis of RL Training Dynamics through Pattern Selection

arXiv: https://arxiv.org/abs/2506.04695 · HTML: https://mlsanity.com/paper/2506.04695/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 49 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [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)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence](https://mlsanity.com/paper/2406.11931/) (2024)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)
- [Reinforcement Learning from Human Feedback with Active Queries](https://mlsanity.com/paper/2402.09401/) (2024)
- [Optimal Design for Reward Modeling in RLHF](https://mlsanity.com/paper/2410.17055/) (2024)

## Built on by (most cited first, 12 of 12)

- [Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectories](https://mlsanity.com/paper/2511.07368/) (2025)
- [QUATRO: Query-Adaptive Trust Region Policy Optimization for LLM Fine-tuning](https://mlsanity.com/paper/2602.04620/) (2026)
- [Which Tokens Matter? Adaptive Token Selection for RLVR with the Relative Surprisal Index](https://mlsanity.com/paper/2606.31575/) (2026)
- [Select and Improve: Understanding the Mechanics of Post-Training for Reasoning](https://mlsanity.com/paper/2606.13125/) (2026)
- [Dual-Evolving Reinforcement Learning for Automated Reward Design](https://mlsanity.com/paper/2512.13399/) (2025)
- [Group Pattern Selection Optimization: Let LRMs Pick the Right Pattern for Reasoning](https://mlsanity.com/paper/2601.07238/) (2026)
- [How Post-Training Shapes Biological Reasoning Models](https://mlsanity.com/paper/2606.16517/) (2026)
- [A Survey of Reinforcement Learning for Large Language Models under Data Scarcity: Challenges and Solutions](https://mlsanity.com/paper/2604.17312/) (2026)
- [Not only where, But when: Temporal Scheduling for RLVR](https://mlsanity.com/paper/2605.25381/) (2026)
- [The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning](https://mlsanity.com/paper/2606.11918/) (2026)
- [Preference Tuning as Spectral Update Reorganization](https://mlsanity.com/paper/2607.20438/) (2026)
- [How RL Reshapes LLM Reasoning: Transferability, Coverage, and Scaling Laws](https://mlsanity.com/paper/2610.04158/) (2026)

## Abstract (arXiv)

While reinforcement learning (RL) demonstrated remarkable success in enhancing the reasoning capabilities of language models, the training dynamics of RL in LLMs remain unclear. In this work, we provide an explanation of the RL training process through empirical analysis and rigorous theoretical modeling. First, through systematic reasoning-pattern-level and token-level analysis across the RL training process, we show that while different reasoning patterns exhibit relatively stable success rates during training, RL primarily optimizes a sparse subset of critical tokens, thereby reshaping reasoning pattern distributions to affect model performance. Building on these empirical insights, we develop a theoretical framework to understand the training dynamics of RL with two typical rewards: verifiable reward (RLVR) and model's internal feedback (RLIF). For RLVR, we analyze the training dynamics under two special cases: one where models readily converge to optimal reasoning strategies, and another where optimization becomes challenging, revealing that the base model's reasoning quality is crucial for determining convergence behavior. For RLIF, we examine how internal rewards initially improve model performance but can potentially lead to degradation with continued training. Extensive experiments validate our findings, advancing both theoretical understanding and practical applications of RL in language model enhancement.