# On the Non-decoupling of Supervised Fine-tuning and Reinforcement Learning in Post-training

arXiv: https://arxiv.org/abs/2601.07389 · HTML: https://mlsanity.com/paper/2601.07389/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 35 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [AceReason-Nemotron 1.1: Advancing Math and Code Reasoning through SFT and RL Synergy](https://mlsanity.com/paper/2506.13284/) (2025)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)
- [JustRL: Scaling a 1.5B LLM with a Simple RL Recipe](https://mlsanity.com/paper/2512.16649/) (2025)
- [Nemotron-Cascade: Scaling Cascaded Reinforcement Learning for General-Purpose Reasoning Models](https://mlsanity.com/paper/2512.13607/) (2025)
- [Beyond Two-Stage Training: Cooperative SFT and RL for LLM Reasoning](https://mlsanity.com/paper/2509.06948/) (2025)
- [Front-Loading Reasoning: The Synergy between Pretraining and Post-Training Data](https://mlsanity.com/paper/2510.03264/) (2025)
- [Beyond Scaling Laws: Understanding Transformer Performance with Associative Memory](https://mlsanity.com/paper/2405.08707/) (2024)
- [The Synergy Dilemma of Long-CoT SFT and RL: Investigating Post-Training Techniques for Reasoning VLMs](https://mlsanity.com/paper/2507.07562/) (2025)

## Built on by (most cited first, 6 of 6)

- [DeReason: A Difficulty-Aware Curriculum Improves Decoupled SFT-then-RL Training for General Reasoning](https://mlsanity.com/paper/2603.11193/) (2026)
- [GIFT: Reconciling Post-Training Objectives via Variational Finite-Temperature Gibbs Initialization](https://mlsanity.com/paper/2601.09233/) (2026)
- [TailSFT: Filtered Fine-Tuning Improves Post-Training Performance](https://mlsanity.com/paper/2608.25756/) (2026)
- [GAC: Noise-Aware Adaptive Mixing for Hybrid SFT-RL Post-Training](https://mlsanity.com/paper/2605.26184/) (2026)
- [Salesforce Koa: An Enterprise Language Model for Agentic Tool Use](https://mlsanity.com/paper/2609.15066/) (2026)
- [Reasoning-Preserving Fine-Tuning of Post-RL LLMs with Null-Basis LoRA](https://mlsanity.com/paper/2609.25618/) (2026)

## Abstract (arXiv)

Post-training of large language models routinely interleaves supervised fine-tuning (SFT) with reinforcement learning (RL). These two methods have different objectives: SFT minimizes the cross-entropy loss between model outputs and expert responses, while RL maximizes reward signals derived from human preferences or rule-based verifiers. Modern reasoning models have widely adopted the practice of alternating SFT and RL training. However, there is no theoretical account of whether they can be decoupled. We prove that decoupling is impossible in either order: (1) SFT-then-RL coupling: RL increases SFT loss under both distributional (KL-based) and landscape (PL-based) analyses; and (2) RL-then-SFT coupling: SFT lowers the reward achieved by RL under analogous conditions. Under the PL condition, we further derive the optimal RL duration that balances reward improvement against SFT degradation, identify the non-decoupling threshold governing when RL can improve SFT, and bound the gradient misalignment via spectral concentration. Experiments on Qwen3-0.6B confirm the predicted degradation, verifying that SFT and RL cannot be separated without loss of prior performance in the post-training pipeline.