# BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning

arXiv: https://arxiv.org/abs/2506.17211 · HTML: https://mlsanity.com/paper/2506.17211/

## Key facts

- Cited by 63 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 44 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Placed in

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

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [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)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Leveraging Demonstrations for Deep Reinforcement Learning on Robotics Problems with Sparse Rewards](https://mlsanity.com/paper/1707.08817/) (2017)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [Small Models Struggle to Learn from Strong Reasoners](https://mlsanity.com/paper/2502.12143/) (2025)
- [CPPO: Accelerating the Training of Group Relative Policy Optimization-Based Reasoning Models](https://mlsanity.com/paper/2503.22342/) (2025)
- [Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning](https://mlsanity.com/paper/2504.13818/) (2025)
- [Kickstarting Deep Reinforcement Learning](https://mlsanity.com/paper/1803.03835/) (2018)
- [DUMP: Automated Distribution-Level Curriculum Learning for RL-based LLM Post-training](https://mlsanity.com/paper/2504.09710/) (2025)
- [Making Small Language Models Efficient Reasoners: Intervention, Supervision, Reinforcement](https://mlsanity.com/paper/2505.07961/) (2025)

## Built on by (most cited first, 30 of 63)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [Expanding the Capabilities of Reinforcement Learning via Text Feedback](https://mlsanity.com/paper/2602.02482/) (2026)
- [Scaf-GRPO: Scaffolded Group Relative Policy Optimization for Enhancing LLM Reasoning](https://mlsanity.com/paper/2510.19807/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [StepHint: Multi-level Stepwise Hints Enhance Reinforcement Learning to Reason](https://mlsanity.com/paper/2507.02841/) (2025)
- [RL Is Neither a Panacea Nor a Mirage: Understanding Supervised vs. Reinforcement Learning Fine-Tuning for LLMs](https://mlsanity.com/paper/2508.16546/) (2025)
- [Reuse your FLOPs: Scaling RL on Hard Problems by Conditioning on Very Off-Policy Prefixes](https://mlsanity.com/paper/2601.18795/) (2026)
- [Don't Tell the Answer, Truly Guide the Reasoning During RL Rollouts](https://mlsanity.com/paper/2510.09388/) (2025)
- [InT: Self-Proposed Interventions Enable Credit Assignment in LLM Reasoning](https://mlsanity.com/paper/2601.14209/) (2026)
- [Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment](https://mlsanity.com/paper/2601.14249/) (2026)
- [ADHint: Adaptive Hints with Difficulty Priors for Reinforcement Learning](https://mlsanity.com/paper/2512.13095/) (2025)
- [Learn Hard Problems During RL with Reference Guided Fine-tuning](https://mlsanity.com/paper/2603.01223/) (2026)
- [SFT-then-RL Outperforms Mixed-Policy Methods for LLM Reasoning](https://mlsanity.com/paper/2604.23747/) (2026)
- [Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning](https://mlsanity.com/paper/2605.02913/) (2026)
- [KnowRL: Boosting LLM Reasoning via Reinforcement Learning with Minimal-Sufficient Knowledge Guidance](https://mlsanity.com/paper/2604.12627/) (2026)
- [Selective Expert Guidance for Effective and Diverse Exploration in Reinforcement Learning of LLMs](https://mlsanity.com/paper/2510.04140/) (2025)
- [Off-Context GRPO: Learning to Reason on Hard Problems using Privileged Information](https://mlsanity.com/paper/2607.19313/) (2026)
- [Measuring Weak-to-Strong Legibility of Reasoning Models](https://mlsanity.com/paper/2603.20508/) (2026)
- [ICRL: Learning to Internalize Self-Critique with Reinforcement Learning](https://mlsanity.com/paper/2605.15224/) (2026)
- [Nudging Beyond the Comfort Zone: Efficient Strategy-Guided Exploration for RLVR](https://mlsanity.com/paper/2605.15726/) (2026)
- [Recall-Extend Dynamics: Enhancing Small Language Models through Controlled Exploration and Refined Offline Integration](https://mlsanity.com/paper/2508.16677/) (2025)
- [Think Outside the Policy: In-Context Steered Policy Optimization](https://mlsanity.com/paper/2510.26519/) (2025)
- [Training Reasoning Models on Saturated Problems via Failure-Prefix Conditioning](https://mlsanity.com/paper/2601.20829/) (2026)
- [Recycling Failures: Salvaging Exploration in RLVR via Fine-Grained Off-Policy Guidance](https://mlsanity.com/paper/2602.24110/) (2026)
- [Supervised Fine-Tuning versus Reinforcement Learning: A Study of Post-Training Methods for Large Language Models](https://mlsanity.com/paper/2603.13985/) (2026)
- [P^2O: Joint Policy and Prompt Optimization](https://mlsanity.com/paper/2603.21877/) (2026)
- [CoDistill-GRPO: A Co-Distillation Recipe for Efficient Group Relative Policy Optimization](https://mlsanity.com/paper/2605.08873/) (2026)
- [VISTA: View-Consistent Self-Verified Training for GUI Grounding](https://mlsanity.com/paper/2606.14579/) (2026)
- [Zone of Proximal Policy Optimization: Teacher in Prompts, Not Gradients](https://mlsanity.com/paper/2606.18216/) (2026)

## Abstract (arXiv)

Small language models (SLMs) struggle to learn complex reasoning behaviors, especially when high-quality traces are scarce or difficult to learn from. The standard training approach combines a supervised fine-tuning (SFT) stage, often to distill capabilities of a larger model, followed by a reinforcement learning (RL)stage such as Group Relative Policy Optimization (GRPO). In this paper, we investigate the fundamental limitations of this SFT + RL paradigm and propose methods to overcome them. Under a suitable theoretical model, we demonstrate that the SFT + RL strategy can fail completely when (1) the expert's traces are too difficult for the small model to express, or (2) the small model's initialization has exponentially small likelihood of success. To address these, we introduce BREAD: a GRPO variant that unifies the SFT and RL stages via partial expert guidance and branched rollouts. When self-generated traces fail, BREAD adaptively inserts short expert prefixes/hints, allowing the small model to complete the rest of the reasoning path, and ensuring that each update includes at least one successful trace. This mechanism both densifies the reward signal and induces a natural learning curriculum. BREAD requires fewer than 40% of ground-truth traces, consistently outperforming standard GRPO while speeding up the training by about 3 times. Importantly, we demonstrate that BREAD helps the model solve problems that are otherwise unsolvable by the SFT + RL strategy, highlighting how branched rollouts and expert guidance can substantially boost SLM reasoning.