# Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting

arXiv: https://arxiv.org/abs/2510.18874 · HTML: https://mlsanity.com/paper/2510.18874/

## Key facts

- Cited by 94 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 42 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 30 of 36)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMs](https://mlsanity.com/paper/2406.18495/) (2024)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [WildTeaming at Scale: From In-the-Wild Jailbreaks to (Adversarially) Safer Language Models](https://mlsanity.com/paper/2406.18510/) (2024)
- [A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicity](https://mlsanity.com/paper/2401.01967/) (2024)
- [Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data](https://mlsanity.com/paper/2404.14367/) (2024)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Continual Learning for Large Language Models: A Survey](https://mlsanity.com/paper/2402.01364/) (2024)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)
- [What is in Your Safe Data? Identifying Benign Data that Breaks Safety](https://mlsanity.com/paper/2404.01099/) (2024)
- [Test-Time Training on Nearest Neighbors for Large Language Models](https://mlsanity.com/paper/2305.18466/) (2023)

## Built on by (most cited first, 30 of 94)

- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [Online Experiential Learning for Language Models](https://mlsanity.com/paper/2603.16856/) (2026)
- [Reinforcement World Model Learning for LLM-based Agents](https://mlsanity.com/paper/2602.05842/) (2026)
- [Adaptation of Agentic AI: A Survey of Post-Training, Memory, and Skills](https://mlsanity.com/paper/2512.16301/) (2025)
- [Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation](https://mlsanity.com/paper/2605.16826/) (2026)
- [Distribution-Aligned Sequence Distillation for Superior Long-CoT Reasoning](https://mlsanity.com/paper/2601.09088/) (2026)
- [Simple Recipe Works: Vision-Language-Action Models are Natural Continual Learners with Reinforcement Learning](https://mlsanity.com/paper/2603.11653/) (2026)
- [Learning to Reason in 13 Parameters](https://mlsanity.com/paper/2602.04118/) (2026)
- [PivotRL: High Accuracy Agentic Post-Training at Low Compute Cost](https://mlsanity.com/paper/2603.21383/) (2026)
- [Rethinking Generalization in Reasoning SFT: A Conditional Analysis on Optimization, Data, and Model Capability](https://mlsanity.com/paper/2604.06628/) (2026)
- [Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment](https://mlsanity.com/paper/2601.14249/) (2026)
- [Towards Long-Lived Robots: Continual Learning VLA Models via Reinforcement Fine-Tuning](https://mlsanity.com/paper/2602.10503/) (2026)
- [chi0: Resource-Aware Robust Manipulation via Taming Distributional Inconsistencies](https://mlsanity.com/paper/2602.09021/) (2026)
- [CORD: Bridging the Audio-Text Reasoning Gap via Weighted On-policy Cross-modal Distillation](https://mlsanity.com/paper/2601.16547/) (2026)
- [Good SFT Optimizes for SFT, Better SFT Prepares for Reinforcement Learning](https://mlsanity.com/paper/2602.01058/) (2026)
- [On-Policy Self-Distillation with Sampled Demonstrations Reduces Output Diversity](https://mlsanity.com/paper/2606.26091/) (2026)
- [Advancing General-Purpose Reasoning Models with Modular Gradient Surgery](https://mlsanity.com/paper/2602.02301/) (2026)
- [Matching Accuracy, Different Geometry: Evolution Strategies vs GRPO in LLM Post-Training](https://mlsanity.com/paper/2604.01499/) (2026)
- [How to Fine-Tune a Reasoning Model? A Teacher-Student Cooperation Framework to Synthesize Student-Consistent SFT Data](https://mlsanity.com/paper/2604.14164/) (2026)
- [Learning with Rare Success but Rich Feedback via Reflection-Enhanced Self-Distillation](https://mlsanity.com/paper/2605.12741/) (2026)
- [Backtracking When It Strays: Mitigating Dual Exposure Biases in LLM Reasoning Distillation](https://mlsanity.com/paper/2605.19433/) (2026)
- [On-Policy Replay for Continual Supervised Fine-Tuning](https://mlsanity.com/paper/2605.29495/) (2026)
- [Distilled Reinforcement Learning for LLM Post-training](https://mlsanity.com/paper/2607.17247/) (2026)
- [Do We Need Adam? Surprisingly Strong and Sparse Reinforcement Learning with SGD in LLMs](https://mlsanity.com/paper/2602.07729/) (2026)
- [LaViDa-R1: Advancing Reasoning for Unified Multimodal Diffusion Language Models](https://mlsanity.com/paper/2602.14147/) (2026)
- [On-Policy Distillation with Best-of-N Teacher Rollout Selection](https://mlsanity.com/paper/2605.09725/) (2026)

## Abstract (arXiv)

Adapting language models (LMs) to new tasks via post-training carries the risk of degrading existing capabilities -- a phenomenon classically known as catastrophic forgetting. In this paper, toward identifying guidelines for mitigating this phenomenon, we systematically compare the forgetting patterns of two widely adopted post-training methods: supervised fine-tuning (SFT) and reinforcement learning (RL). Our experiments reveal a consistent trend across LM families (Llama, Qwen) and tasks (instruction following, general knowledge, and arithmetic reasoning): RL leads to less forgetting than SFT while achieving comparable or higher target task performance. To investigate the cause for this difference, we consider a simplified setting in which the LM is modeled as a mixture of two distributions, one corresponding to prior knowledge and the other to the target task. We identify that the mode-seeking nature of RL, which stems from its use of on-policy data, enables keeping prior knowledge intact when learning the target task. We then verify this insight by demonstrating that the use on-policy data underlies the robustness of RL to forgetting in practical settings, as opposed to other algorithmic choices such as the KL regularization or advantage estimation. Lastly, as a practical implication, our results highlight the potential of mitigating forgetting using approximately on-policy data, which can be substantially more efficient to obtain than fully on-policy data.