# RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMs

arXiv: https://arxiv.org/abs/2509.21128 · HTML: https://mlsanity.com/paper/2509.21128/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 53 of its 90 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 53)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [Thought Anchors: Which LLM Reasoning Steps Matter?](https://mlsanity.com/paper/2506.19143/) (2025)
- [OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling](https://mlsanity.com/paper/2506.20512/) (2025)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)

## Built on by (most cited first, 30 of 34)

- [F-GRPO: Don't Let Your Policy Learn the Obvious and Forget the Rare](https://mlsanity.com/paper/2602.06717/) (2026)
- [SFT-then-RL Outperforms Mixed-Policy Methods for LLM Reasoning](https://mlsanity.com/paper/2604.23747/) (2026)
- [Uniform-Correct Policy Optimization: Breaking RLVR's Indifference to Diversity](https://mlsanity.com/paper/2605.00365/) (2026)
- [Emergent Slow Thinking in LLMs as Inverse Tree Freezing](https://mlsanity.com/paper/2509.23629/) (2025)
- [Know When You're Wrong: Aligning Confidence with Correctness for LLM Error Detection](https://mlsanity.com/paper/2603.06604/) (2026)
- [Knowledge Graphs are Implicit Reward Models: Path-Derived Signals Enable Compositional Reasoning](https://mlsanity.com/paper/2601.15160/) (2026)
- [Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failures](https://mlsanity.com/paper/2601.19928/) (2026)
- [RL makes MLLMs see better than SFT](https://mlsanity.com/paper/2510.16333/) (2025)
- [Modeling Hierarchical Thinking in Large Reasoning Models](https://mlsanity.com/paper/2510.22437/) (2025)
- [DeReason: A Difficulty-Aware Curriculum Improves Decoupled SFT-then-RL Training for General Reasoning](https://mlsanity.com/paper/2603.11193/) (2026)
- [Reasoning Pattern Matters: Learning to Reason without Human Rationales](https://mlsanity.com/paper/2510.12643/) (2025)
- [Reasoning Core: A Scalable Procedural Data Generation Suite for Symbolic Pre-training and Post-Training](https://mlsanity.com/paper/2603.02208/) (2026)
- [Self-Trained Verification for Training- and Test-Time Self-Improvement](https://mlsanity.com/paper/2605.30290/) (2026)
- [On Advantage Estimates for Max@K Policy Gradients](https://mlsanity.com/paper/2606.06080/) (2026)
- [OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation](https://mlsanity.com/paper/2606.06096/) (2026)
- [Select and Improve: Understanding the Mechanics of Post-Training for Reasoning](https://mlsanity.com/paper/2606.13125/) (2026)
- [SFT Conflicts, RL Coexists: A Theoretical and Empirical Analysis of Multi-Task Learning for LLMs](https://mlsanity.com/paper/2608.03573/) (2026)
- [Beyond Token-level Supervision: Unlocking the Potential of Decoding-based Regression via Reinforcement Learning](https://mlsanity.com/paper/2512.06533/) (2025)
- [ReasonAny: Incorporating Reasoning Capability to Any Model via Simple and Effective Model Merging](https://mlsanity.com/paper/2601.05560/) (2026)
- [Decouple before Integration: Test-time Synthesis of SFT and RLVR Task Vectors](https://mlsanity.com/paper/2605.00610/) (2026)
- [PolyFact: Comparing Consistency-Driven Post-training Methods for Cross-Lingual Factual Recall](https://mlsanity.com/paper/2606.06586/) (2026)
- [Rewriting or Reweighting? A Geometric Account in Language Models](https://mlsanity.com/paper/2608.01835/) (2026)
- [Reasoning as State Transition: A Representational Analysis of Reasoning Evolution in Large Language Models](https://mlsanity.com/paper/2602.00770/) (2026)
- [Mi:dm K 2.5 Pro](https://mlsanity.com/paper/2603.18788/) (2026)
- [Fine-Tuning A Large Language Model for Systematic Review Screening](https://mlsanity.com/paper/2603.24767/) (2026)
- [Synthesizing Instruction-Tuning Datasets with Contrastive Decoding](https://mlsanity.com/paper/2604.13538/) (2026)
- [Reasoning Core: Designing Broad Procedural Data for Completion-Supervised Reasoning Training](https://mlsanity.com/paper/2608.05148/) (2026)
- [Is Next-Chunk Reasoning RL Really Better than SFT? Revisiting Training Strategies under no-CoT Data](https://mlsanity.com/paper/2608.23256/) (2026)
- [SHAPE of Chain-of-Thought in Math Reasoning](https://mlsanity.com/paper/2608.28600/) (2026)
- [Locked at the Entrance, Open Inside: Where RLVR Narrows the Solution Space](https://mlsanity.com/paper/2608.29188/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are typically trained by reinforcement learning (RL) with verifiable rewards (RLVR) and supervised fine-tuning (SFT) on reasoning traces to improve their reasoning abilities. However, how these methods shape reasoning capabilities remains largely elusive. Going beyond an accuracy-based investigation of how these two components sculpt the reasoning process, this paper introduces a novel analysis framework that quantifies reasoning paths and captures their qualitative changes under each training process (with models of 1.5B, 7B, and 14B parameters on mathematical domains). Specifically, we investigate the reasoning process at two levels of granularity: the trajectory-level, which examines complete reasoning outputs, and the step-level, which analyzes reasoning graphs whose nodes correspond to individual reasoning steps. Notably, clustering of unique reasoning trajectories shows complementary effects: RL compresses incorrect trajectories, whereas SFT expands correct ones. Step-level analysis reveals that RL steepens (about 2.5 times), while SFT flattens (reduced to about one-third), the decay rates of node visitation frequency, degree, and betweenness centrality distributions in the reasoning graph. This indicates that RL concentrates reasoning functionality into a small subset of steps, while SFT homogenizes it across many steps. Furthermore, by evaluating the reasoning graph topologies from multiple perspectives, we delineate the shared and distinct characteristics of RL and SFT. Our work presents a novel reasoning path perspective that explains why the current best practice of two-stage training, with SFT followed by RL, is successful, and offers practical implications for data construction and more efficient learning approaches.