# RL Fine-Tuning Heals OOD Forgetting in SFT

arXiv: https://arxiv.org/abs/2509.12235 · HTML: https://mlsanity.com/paper/2509.12235/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 52 of its 76 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [PandaLM: An Automatic Evaluation Benchmark for LLM Instruction Tuning Optimization](https://mlsanity.com/paper/2306.05087/) (2023)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [Fine-Tuning Large Vision-Language Models as Decision-Making Agents via Reinforcement Learning](https://mlsanity.com/paper/2405.10292/) (2024)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)
- [Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process](https://mlsanity.com/paper/2407.20311/) (2024)
- [Revisiting Catastrophic Forgetting in Large Language Model Tuning](https://mlsanity.com/paper/2406.04836/) (2024)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)

## Built on by (most cited first, 30 of 31)

- [Good SFT Optimizes for SFT, Better SFT Prepares for Reinforcement Learning](https://mlsanity.com/paper/2602.01058/) (2026)
- [Debunk the Myth of SFT Generalization](https://mlsanity.com/paper/2510.00237/) (2025)
- [Posterior Behavioral Cloning: Pretraining BC Policies for Efficient RL Finetuning](https://mlsanity.com/paper/2512.16911/) (2025)
- [Knowledge Graphs are Implicit Reward Models: Path-Derived Signals Enable Compositional Reasoning](https://mlsanity.com/paper/2601.15160/) (2026)
- [Continual GUI Agents](https://mlsanity.com/paper/2601.20732/) (2026)
- [Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failures](https://mlsanity.com/paper/2601.19928/) (2026)
- [(How) Learning Rates Regulate Catastrophic Overtraining](https://mlsanity.com/paper/2604.13627/) (2026)
- [GeoRA: Geometry-Aware Low-Rank Adaptation for RLVR](https://mlsanity.com/paper/2601.09361/) (2026)
- [When RL Fails after SFT: Rejuvenating Model Plasticity for Robust SFT-to-RL Handoff](https://mlsanity.com/paper/2606.09932/) (2026)
- [Gradient Coupling: The Hidden Barrier to Generalization in Agentic Reinforcement Learning](https://mlsanity.com/paper/2509.23870/) (2025)
- [Probing RLVR training instability through the lens of objective-level hacking](https://mlsanity.com/paper/2602.01103/) (2026)
- [Rotation-Preserving Supervised Fine-Tuning](https://mlsanity.com/paper/2605.10973/) (2026)
- [Towards Robust Endogenous Reasoning: Unifying Drift Adaptation in Non-Stationary Tuning](https://mlsanity.com/paper/2604.15705/) (2026)
- [RL Forgets! Towards Continual Policy Optimization](https://mlsanity.com/paper/2607.04364/) (2026)
- [TailSFT: Filtered Fine-Tuning Improves Post-Training Performance](https://mlsanity.com/paper/2608.25756/) (2026)
- [RedOne 2.0: Rethinking Domain-specific LLM Post-Training in Social Networking Services](https://mlsanity.com/paper/2511.07070/) (2025)
- [TMS: Trajectory-Mixed Supervision for Reward-Free, On-Policy SFT](https://mlsanity.com/paper/2602.03073/) (2026)
- [GUI-AC: Enhancing Continual Learning in GUI Agents](https://mlsanity.com/paper/2606.10522/) (2026)
- [Rewriting or Reweighting? A Geometric Account in Language Models](https://mlsanity.com/paper/2608.01835/) (2026)
- [Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO](https://mlsanity.com/paper/2608.27351/) (2026)
- [Less is More: Denoising Knowledge Graphs For Retrieval Augmented Generation](https://mlsanity.com/paper/2510.14271/) (2025)
- [WinDOM: Self-Family Distillation for Small-Model GUI Grounding](https://mlsanity.com/paper/2606.25964/) (2026)
- [Where Do CoT Training Gains Land in LLM based Agents?](https://mlsanity.com/paper/2606.26935/) (2026)
- [Stop Thinking, Start Looking: Efficient Post-Training for Multimodal Document Question Answering via Reasoning-Free Alignment](https://mlsanity.com/paper/2607.14682/) (2026)
- [Reach or Solve? Attributing Agentic RL Gains with Checkpoint Handoffs](https://mlsanity.com/paper/2609.19636/) (2026)
- [GRRR: The Geometry of Reshaping, Rotation, and Routing in Decoder LLM post-training](https://mlsanity.com/paper/2609.22146/) (2026)
- [Rethinking Token Reweighting for SFT: Suppress, Reverse, and Extrapolate Learned Features](https://mlsanity.com/paper/2609.33463/) (2026)
- [Selecting Diverse SFT Traces Improves Post-RL Generalization](https://mlsanity.com/paper/2609.33780/) (2026)
- [Understanding Off- vs On-Policy Distillation: A Tale of Distinct Training Objectives](https://mlsanity.com/paper/2609.38666/) (2026)
- [Exploration-Preserving Policy Optimization](https://mlsanity.com/paper/2610.04011/) (2026)

## Abstract (arXiv)

Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL) is a standard post-training recipe for improving Large Language Models (LLM) reasoning, but why it works remains unclear. We revisit the common claim that ``SFT memorizes, RL generalizes'' through checkpoint-wise analyses of in-distribution (ID) and out-of-distribution (OOD) reasoning. We find that OOD performance often peaks early during SFT and then declines despite continued improvement in ID reasoning. RL typically does not surpass this early SFT peak; rather, it restores OOD capability lost during later SFT, and only from a bounded range of SFT checkpoints. Further spectral analysis shows that this forgetting-and-recovery pattern correlates with rotations of singular vectors, while singular values remain largely stable. These findings suggest a more precise view of post-training dynamics: SFT can forget, RL can recover, and controlling singular-vector rotation may improve OOD robustness. Code is available at hrefhttps://github.com/jinhangzhan/RLHealsSFT.githttps://github.com/jinhangzhan/RLHealsSFT.