# How Much Backtracking is Enough? Exploring the Interplay of SFT and RL in Enhancing LLM Reasoning

arXiv: https://arxiv.org/abs/2505.24273 · HTML: https://mlsanity.com/paper/2505.24273/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 30 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [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)
- [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)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrapping](https://mlsanity.com/paper/2402.14083/) (2024)
- [An Empirical Study on Eliciting and Improving R1-like Reasoning Models](https://mlsanity.com/paper/2503.04548/) (2025)

## Built on by (most cited first, 13 of 13)

- [SRFT: A Single-Stage Method with Supervised and Reinforcement Fine-Tuning for Reasoning](https://mlsanity.com/paper/2506.19767/) (2025)
- [Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling](https://mlsanity.com/paper/2507.01679/) (2025)
- [RL-PLUS: Countering Capability Boundary Collapse of LLMs in Reinforcement Learning with Hybrid-policy Optimization](https://mlsanity.com/paper/2508.00222/) (2025)
- [The Geometry of Reasoning: Flowing Logics in Representation Space](https://mlsanity.com/paper/2510.09782/) (2025)
- [The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic View](https://mlsanity.com/paper/2510.04028/) (2025)
- [Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failures](https://mlsanity.com/paper/2601.19928/) (2026)
- [T2PO: Uncertainty-Guided Exploration Control for Stable Multi-Turn Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.02178/) (2026)
- [Conformal Certification of Reasoning Trace Prefixes](https://mlsanity.com/paper/2605.30085/) (2026)
- [Provable Benefits of RLVR over SFT for Reasoning Models: Learning to Backtrack Efficiently](https://mlsanity.com/paper/2606.22938/) (2026)
- [Soundness-Aware Level: A Microscopic Signature that Predicts LLM Reasoning Potential](https://mlsanity.com/paper/2510.15216/) (2025)
- [KEPO: Knowledge-Enhanced Preference Optimization for Multimodal Reasoning with Applications to Medical VQA](https://mlsanity.com/paper/2602.00400/) (2026)
- [Search, Fail, Recover: A Training Framework for Correction-Aware Reasoning](https://mlsanity.com/paper/2607.07492/) (2026)
- [Metacognitive Behavioral Tuning of Large Language Models for Multi-Hop Question Answering](https://mlsanity.com/paper/2602.22508/) (2026)

## Abstract (arXiv)

Recent advancements in large language models (LLMs) suggest that reinforcement learning (RL) effectively internalizes search strategies, yielding significant improvements on challenging reasoning tasks through extended chains of thought. While backtracking is widely viewed as the core mechanism enabling this improvement, its precise dynamics and how SFT and RL interact to optimize for it, remain poorly understood. In this work, we argue that backtracking, the ability to explicitly revisit and revise earlier reasoning steps, is a key operator that enables the transition from linear generation to non-linear tree search for LLMs, unlocking strong performance on combinatorially complex tasks. We motivate this claim by first studying the interplay between supervised fine-tuning (SFT) warm-up and RL across eight reasoning tasks: Countdown, Sudoku, Arc 1D, Advanced Geometry, Color Cube Rotation, List Functions, Zebra Puzzles, and Self Reference. We find that a regular SFT warm-up using self-sampled CoT sequences provides a modest boost to subsequent RL compared to training without any SFT warm-up; however, such gains saturate as tasks become more difficult. Motivated by this failure mode, we introduce a backtracking-centric training recipe. By synthetically varying the number of explicit backtracking steps in the SFT warm-up, we show that (i) longer CoTs containing backtracks stabilize and amplify RL, and (ii) the optimal backtrack depth scales with task difficulty: zero for Arc 1D, one for Countdown, and five or more for Sudoku. Our findings establish that principled backtracking is essential for improving the model's reasoning capability.