# Mitigating Forgetting Between Supervised and Reinforcement Learning Yields Stronger Reasoners

arXiv: https://arxiv.org/abs/2510.04454 · HTML: https://mlsanity.com/paper/2510.04454/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 38 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [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)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [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)
- [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)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [AdapterDrop: On the Efficiency of Adapters in Transformers](https://mlsanity.com/paper/2010.11918/) (2020)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)
- [Are All Layers Created Equal?](https://mlsanity.com/paper/1902.01996/) (2019)
- [What Would Elsa Do? Freezing Layers During Transformer Fine-Tuning](https://mlsanity.com/paper/1911.03090/) (2019)
- [SRFT: A Single-Stage Method with Supervised and Reinforcement Fine-Tuning for Reasoning](https://mlsanity.com/paper/2506.19767/) (2025)
- [AceReason-Nemotron 1.1: Advancing Math and Code Reasoning through SFT and RL Synergy](https://mlsanity.com/paper/2506.13284/) (2025)
- [UFT: Unifying Supervised and Reinforcement Fine-Tuning](https://mlsanity.com/paper/2505.16984/) (2025)
- [Step-wise Adaptive Integration of Supervised Fine-tuning and Reinforcement Learning for Task-Specific LLMs](https://mlsanity.com/paper/2505.13026/) (2025)

## Built on by (most cited first, 16 of 16)

- [Behavior Knowledge Merge in Reinforced Agentic Models](https://mlsanity.com/paper/2601.13572/) (2026)
- [Towards On-Policy SFT: Distribution Discriminant Theory and its Applications in LLM Training](https://mlsanity.com/paper/2602.12222/) (2026)
- [SFT-then-RL Outperforms Mixed-Policy Methods for LLM Reasoning](https://mlsanity.com/paper/2604.23747/) (2026)
- [Addressing Overthinking in Large Vision-Language Models via Gated Perception-Reasoning Optimization](https://mlsanity.com/paper/2601.04442/) (2026)
- [Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning](https://mlsanity.com/paper/2604.07941/) (2026)
- [InfoSFT: Learn More and Forget Less with Information-Aware Token Weighting](https://mlsanity.com/paper/2605.14967/) (2026)
- [Reasoning over Precedents Alongside Statutes: Case-Augmented Deliberative Alignment for LLM Safety](https://mlsanity.com/paper/2601.08000/) (2026)
- [WavAlign: Enhancing Intelligence and Expressiveness in Spoken Dialogue Models via Adaptive Hybrid Post-Training](https://mlsanity.com/paper/2604.14932/) (2026)
- [PACT: Privileged Trace Co-Training for Multi-Turn Tool-Use Agents](https://mlsanity.com/paper/2606.16215/) (2026)
- [DARE: Difficulty-Adaptive Reinforcement Learning with Co-Evolved Difficulty Estimation](https://mlsanity.com/paper/2605.09188/) (2026)
- [CopT: Contrastive On-Policy Thinking with Continuous Spaces for General and Agentic Reasoning](https://mlsanity.com/paper/2605.20075/) (2026)
- [Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO](https://mlsanity.com/paper/2608.27351/) (2026)
- [Boosting Reinforcement Learning with Verifiable Rewards via Randomly Selected Few-Shot Guidance](https://mlsanity.com/paper/2605.15012/) (2026)
- [Train4Merge: A Controlled Single-Teacher Study of RL vs. SFT Teachers for OPD-Based Model Merging](https://mlsanity.com/paper/2609.32303/) (2026)
- [TSRL: Trigger-based Supervised Reinforcement Learning for Continual Agent Training](https://mlsanity.com/paper/2610.17726/) (2026)
- [Geometric Calibration of Supervised Fine-Tuning](https://mlsanity.com/paper/2610.18634/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) show strong reasoning abilities, often amplified by Chain-of-Thought (CoT) prompting and reinforcement learning (RL). Although RL algorithms can substantially improve reasoning, they struggle to expand reasoning boundaries because they learn from their own reasoning trajectories rather than acquiring external knowledge. Supervised fine-tuning (SFT) offers complementary benefits but typically requires large-scale data and risks overfitting. Recent attempts to combine SFT and RL face three main challenges: data inefficiency, algorithm-specific designs, and catastrophic forgetting. We propose a plug-and-play framework that dynamically integrates SFT into RL by selecting challenging examples for SFT. This approach reduces SFT data requirements and remains agnostic to the choice of RL or SFT algorithm. To mitigate catastrophic forgetting of RL-acquired skills during SFT, we select high-entropy tokens for loss calculation and freeze parameters identified as critical for RL. Our method achieves state-of-the-art (SoTA) reasoning performance using only 1.5% of the SFT data and 20.4% of the RL data used by prior SoTA, providing an efficient and plug-and-play solution for combining SFT and RL in reasoning post-training.