# Understanding the Synergy between SFT, RLVR, and OPD in LLM Post-Training

arXiv: https://arxiv.org/abs/2609.31900 · HTML: https://mlsanity.com/paper/2609.31900/

## 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 34 of its 36 references that are in the map.
- First posted on arXiv 25 Sep 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 34)

- [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)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [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)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Knowledge Distillation from A Stronger Teacher](https://mlsanity.com/paper/2205.10536/) (2022)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [Small Models Struggle to Learn from Strong Reasoners](https://mlsanity.com/paper/2502.12143/) (2025)
- [Nemotron-Cascade 2: Post-Training LLMs with Cascade RL and Multi-Domain On-Policy Distillation](https://mlsanity.com/paper/2603.19220/) (2026)
- [The Many Faces of On-Policy Distillation: Pitfalls, Mechanisms, and Fixes](https://mlsanity.com/paper/2605.11182/) (2026)
- [Trust Region On-Policy Distillation](https://mlsanity.com/paper/2606.01249/) (2026)
- [KL for a KL: On-Policy Distillation with Control Variate Baseline](https://mlsanity.com/paper/2605.07865/) (2026)
- [On the Geometry of On-Policy Distillation](https://mlsanity.com/paper/2606.07082/) (2026)
- [Demystifying On-Policy Distillation: Roles, Pathologies, and Regulations](https://mlsanity.com/paper/2607.13399/) (2026)
- [Weak-to-Strong Generalization via Direct On-Policy Distillation](https://mlsanity.com/paper/2607.05394/) (2026)
- [OPD+: Rethinking the Advantage Design for On-Policy Distillation](https://mlsanity.com/paper/2606.01039/) (2026)
- [When RL Fails after SFT: Rejuvenating Model Plasticity for Robust SFT-to-RL Handoff](https://mlsanity.com/paper/2606.09932/) (2026)

## Abstract (arXiv)

Modern LLM post-training composes supervised fine-tuning (SFT), reinforcement learning with verifiable rewards (RLVR), and on-policy distillation (OPD) into multi-stage pipelines, yet these stages are typically designed and evaluated in isolation. We show that this composition is consequential: a stage that improves the current model can make the next stage less effective. Through controlled experiments with Qwen3 models on math and science reasoning, we first characterize OPD across nine student-teacher pairs spanning 2x to 53x parameter ratios and show that OPD effectiveness depends on student-teacher compatibility rather than teacher scale alone. The surrounding stages of OPD reshape this compatibility in three ways: (1) A brief SFT warm-up improves subsequent OPD, while an RLVR-strengthened student regresses under distillation from the same teacher. (2) Adapting the teacher with RLVR raises downstream OPD accuracy in proportion to the capability it adds. Following these two interventions, we find that combining teacher adaptation and student warm-up alone raise average OPD accuracy from 29.2% to 43.8% (50% relative improvement) after the same number of distillation steps, with additional preparatory training. (3) At comparable accuracy, OPD leaves a stronger initialization for downstream RLVR than SFT, with a gap that widens as RL compute scales. Our results suggest that each post-training stage should be chosen not only for the capability it adds, but for the learning interface it creates for the next stage.