# Recall-Extend Dynamics: Enhancing Small Language Models through Controlled Exploration and Refined Offline Integration

arXiv: https://arxiv.org/abs/2508.16677 · HTML: https://mlsanity.com/paper/2508.16677/

## Key facts

- Cited by 3 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 32 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Placed in

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

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

- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [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)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [GPG: A Simple and Strong Reinforcement Learning Baseline for Model Reasoning](https://mlsanity.com/paper/2504.02546/) (2025)
- [Small Models Struggle to Learn from Strong Reasoners](https://mlsanity.com/paper/2502.12143/) (2025)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)
- [SRFT: A Single-Stage Method with Supervised and Reinforcement Fine-Tuning for Reasoning](https://mlsanity.com/paper/2506.19767/) (2025)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning](https://mlsanity.com/paper/2506.17211/) (2025)
- [Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling](https://mlsanity.com/paper/2507.01679/) (2025)
- [Phi-4-Mini-Reasoning: Exploring the Limits of Small Reasoning Language Models in Math](https://mlsanity.com/paper/2504.21233/) (2025)
- [NFT: Bridging Supervised Learning and Reinforcement Learning in Math Reasoning](https://mlsanity.com/paper/2505.18116/) (2025)
- [GVPO: Group Variance Policy Optimization for Large Language Model Post-Training](https://mlsanity.com/paper/2504.19599/) (2025)
- [Step-wise Adaptive Integration of Supervised Fine-tuning and Reinforcement Learning for Task-Specific LLMs](https://mlsanity.com/paper/2505.13026/) (2025)
- [Making Small Language Models Efficient Reasoners: Intervention, Supervision, Reinforcement](https://mlsanity.com/paper/2505.07961/) (2025)
- [Reinforcement Learning vs. Distillation: Understanding Accuracy and Capability in LLM Reasoning](https://mlsanity.com/paper/2505.14216/) (2025)
- [UFT: Unifying Fine-Tuning of SFT and RLHF/DPO/UNA through a Generalized Implicit Reward Function](https://mlsanity.com/paper/2410.21438/) (2024)
- [Advantage-Guided Distillation for Preference Alignment in Small Language Models](https://mlsanity.com/paper/2502.17927/) (2025)
- [Harnessing Negative Signals: Reinforcement Distillation from Teacher Data for LLM Reasoning](https://mlsanity.com/paper/2505.24850/) (2025)

## Built on by (most cited first, 3 of 3)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [SFT-then-RL Outperforms Mixed-Policy Methods for LLM Reasoning](https://mlsanity.com/paper/2604.23747/) (2026)
- [From Trajectories to Prefixes: Reusing Teacher Trajectories via Replayed Prefixes and Online Continuation](https://mlsanity.com/paper/2607.19395/) (2026)

## Abstract (arXiv)

Many existing studies have achieved significant improvements in the reasoning capabilities of large language models (LLMs) through reinforcement learning with verifiable rewards (RLVR), while the enhancement of reasoning abilities in small language models (SLMs) has not yet been sufficiently explored. Combining distilled data from larger models with RLVR on small models themselves is a natural approach, but it still faces various challenges and issues. Therefore, we propose textitunderlineRecall-textitunderlineExtend textitunderlineDynamics(RED): Enhancing Small Language Models through Controlled Exploration and Refined Offline Integration. In this paper, we explore the perspective of varying exploration spaces, balancing offline distillation with online reinforcement learning. Simultaneously, we specifically design and optimize for the insertion problem within offline data. By monitoring the ratio of entropy changes in the model concerning offline and online data, we regulate the weight of offline-SFT, thereby addressing the issues of insufficient exploration space in small models and the redundancy and complexity during the distillation process. Furthermore, to tackle the distribution discrepancies between offline data and the current policy, we design a sample-accuracy-based policy shift mechanism that dynamically chooses between imitating offline distilled data and learning from its own policy.