# Finetuning with Sampling: SFT Learns Better Than You Think

arXiv: https://arxiv.org/abs/2610.02140 · HTML: https://mlsanity.com/paper/2610.02140/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 33 of its 40 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 30 of 33)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [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)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs](https://mlsanity.com/paper/2412.18925/) (2024)
- [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)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting](https://mlsanity.com/paper/2510.18874/) (2025)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [UFT: Unifying Supervised and Reinforcement Fine-Tuning](https://mlsanity.com/paper/2505.16984/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening](https://mlsanity.com/paper/2601.21590/) (2026)
- [Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning](https://mlsanity.com/paper/2602.10273/) (2026)
- [QUEST: Quality-Aware Metropolis-Hastings Sampling for Machine Translation](https://mlsanity.com/paper/2406.00049/) (2024)
- [Anchored Supervised Fine-Tuning](https://mlsanity.com/paper/2509.23753/) (2025)
- [Blink of an eye: a simple theory for feature localization in generative models](https://mlsanity.com/paper/2502.00921/) (2025)
- [When does a predictor know its own loss?](https://mlsanity.com/paper/2502.20375/) (2025)
- [ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problems](https://mlsanity.com/paper/2506.10955/) (2025)

## Abstract (arXiv)

Introducing new capabilities to frontier models has long been the goal of posttraining, which predominantly employs supervised finetuning (SFT) and reinforcement learning (RL) to this end. Conventional wisdom dictates that RL enables strong generalization on new tasks without losing existing capabilities, while SFT is prone to weak generalization and catastrophic forgetting. At the same time, SFT can learn from off-policy expert data, whereas RL must rely on a model's ability to find successful trajectories with repeated sampling. In our work, we seek to leverage the strength of on-policy learning while utilizing the privileged information contained in off-policy data. However, rather than modifying the learning objective to accommodate this data, we instead tailor the data distribution to better suit the learner. We introduce a Markov chain Monte Carlo (MCMC) sampling algorithm that progressively transforms off-policy traces to be more on-policy given a reference model for finetuning. Across tasks like scientific skill acquisition, mathematical reasoning, and open-ended expertise, our sampling algorithm enables SFT to rival prevailing posttraining techniques, often generalizing better and forgetting less than strong on-policy baselines. In addition, the resulting finetuned models exhibit strong distributional performance and are capable of learning beyond sharpening the base model distribution. At a higher level, our approach presents sampling as a model-native operator that shapes data for learnability, offering broader utility as a general-purpose primitive throughout the posttraining stack.