# Off-Policy Merging Beats On-Policy Self-Distillation for Continual Learning

arXiv: https://arxiv.org/abs/2610.05872 · HTML: https://mlsanity.com/paper/2610.05872/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 49 of its 58 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 49)

- [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)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Branch-Train-Merge: Embarrassingly Parallel Training of Expert Language Models](https://mlsanity.com/paper/2208.03306/) (2022)
- [Patching open-vocabulary models by interpolating weights](https://mlsanity.com/paper/2208.05592/) (2022)
- [Towards Continual Knowledge Learning of Language Models](https://mlsanity.com/paper/2110.03215/) (2021)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)

## Abstract (arXiv)

A long-standing goal of AI is a model that can continually learn and improve itself. On post-trained models, supervised finetuning (SFT) on new data often causes poor generalization and catastrophic forgetting. As such, the conventional wisdom is that on-policy training is a prerequisite for continual learning. In practice, however, data containing new knowledge or capabilities are often off-policy. While methods such as on-policy self-distillation (OPSD) try to bridge this gap by converting off-policy data into on-policy signal, they have been shown to cause reasoning collapse. In this paper, we show that off-policy merging beats OPSD for continual learning. We first show that SFT learns a useful signal from new data, but naively applying its update interferes with existing capabilities. We reduce this interference with a simple recipe we term grafting, which changes where the update is learned and how it is applied: (1) learning the update on an earlier donor checkpoint, ideally even before the end of pretraining, and applying the weight update to the post-trained model; (2) scaling the weight update, equivalent to a form of model merging; and (3) optionally, masking the most sensitive update directions when the new data distribution is far from the post-trained model. Across continual learning settings including (1) distilling from expert traces, (2) self-improvement with STaR and Pedagogical RL, and (3) injecting knowledge after pretraining cutoff, grafting Pareto-dominates both SFT and OPSD in new-task and old-task performance, while avoiding expensive on-policy sampling. Therefore, our work challenges on-policy training as a necessity for continual learning on RL-trained models.