# Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search

arXiv: https://arxiv.org/abs/2502.02508 · HTML: https://mlsanity.com/paper/2502.02508/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 41 of its 100 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Placed in

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

## Builds on (most cited first, 30 of 41)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Self-critiquing models for assisting human evaluators](https://mlsanity.com/paper/2206.05802/) (2022)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Go-Explore: a New Approach for Hard-Exploration Problems](https://mlsanity.com/paper/1901.10995/) (2019)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [Marco-o1: Towards Open Reasoning Models for Open-Ended Solutions](https://mlsanity.com/paper/2411.14405/) (2024)
- [Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers](https://mlsanity.com/paper/2408.06195/) (2024)
- [TableBench: A Comprehensive and Complex Benchmark for Table Question Answering](https://mlsanity.com/paper/2408.09174/) (2024)

## Built on by (most cited first, 30 of 53)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [Machine Mental Imagery: Empower Multimodal Reasoning with Latent Visual Tokens](https://mlsanity.com/paper/2506.17218/) (2025)
- [PersonaMem-v2: Towards Personalized Intelligence via Learning Implicit User Personas and Agentic Memory](https://mlsanity.com/paper/2512.06688/) (2025)
- [ReMA: Learning to Meta-think for LLMs with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2503.09501/) (2025)
- [Learning When to Think: Shaping Adaptive Reasoning in R1-Style Models via Multi-Stage RL](https://mlsanity.com/paper/2505.10832/) (2025)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [LLM-based Agents Suffer from Hallucinations: A Survey of Taxonomy, Methods, and Directions](https://mlsanity.com/paper/2509.18970/) (2025)
- [Hierarchy-of-Groups Policy Optimization for Long-Horizon Agentic Tasks](https://mlsanity.com/paper/2602.22817/) (2026)
- [RLVR-World: Training World Models with Reinforcement Learning](https://mlsanity.com/paper/2505.13934/) (2025)
- [RL Tango: Reinforcing Generator and Verifier Together for Language Reasoning](https://mlsanity.com/paper/2505.15034/) (2025)
- [S2R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning](https://mlsanity.com/paper/2502.12853/) (2025)
- [HarnessForge: Joint Harness and Policy Evolution for Adaptive Agent Systems](https://mlsanity.com/paper/2606.01779/) (2026)
- [Satori-SWE: Evolutionary Test-Time Scaling for Sample-Efficient Software Engineering](https://mlsanity.com/paper/2505.23604/) (2025)
- [Unveiling the Compositional Ability Gap in Vision-Language Reasoning Model](https://mlsanity.com/paper/2505.19406/) (2025)
- [Loong: Synthesize Long Chain-of-Thoughts at Scale through Verifiers](https://mlsanity.com/paper/2509.03059/) (2025)
- [AdapThink: Adaptive Thinking Preferences for Reasoning Language Model](https://mlsanity.com/paper/2506.18237/) (2025)
- [Reinforcement Learning Teachers of Test Time Scaling](https://mlsanity.com/paper/2506.08388/) (2025)
- [GPO: Learning from Critical Steps to Improve LLM Reasoning](https://mlsanity.com/paper/2509.16456/) (2025)
- [Behavior Injection: Preparing Language Models for Reinforcement Learning](https://mlsanity.com/paper/2505.18917/) (2025)
- [Do LLM Agents Know How to Ground, Recover, and Assess? A Benchmark for Epistemic Competence in Information-Seeking Agents](https://mlsanity.com/paper/2509.22391/) (2025)
- [Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learning](https://mlsanity.com/paper/2512.10534/) (2025)
- [One Model, All Roles: Multi-Turn, Multi-Agent Self-Play Reinforcement Learning for Conversational Social Intelligence](https://mlsanity.com/paper/2602.03109/) (2026)
- [Rethinking Reasoning Quality in Large Language Models through Enhanced Chain-of-Thought via RL](https://mlsanity.com/paper/2509.06024/) (2025)
- [Learning to Ponder: Adaptive Reasoning in Latent Space](https://mlsanity.com/paper/2509.24238/) (2025)
- [Divide-Fuse-Conquer: Eliciting "Aha Moments" in Multi-Scenario Games](https://mlsanity.com/paper/2505.16401/) (2025)
- [A Survey of LLM × DATA](https://mlsanity.com/paper/2505.18458/) (2025)
- [Tailored Primitive Initialization is the Secret Key to Reinforcement Learning](https://mlsanity.com/paper/2511.12429/) (2025)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated remarkable reasoning capabilities across diverse domains. Recent studies have shown that increasing test-time computation enhances LLMs' reasoning capabilities. This typically involves extensive sampling at inference time guided by an external LLM verifier, resulting in a two-player system. Despite external guidance, the effectiveness of this system demonstrates the potential of a single LLM to tackle complex tasks. Thus, we pose a new research problem: Can we internalize the searching capabilities to fundamentally enhance the reasoning abilities of a single LLM? This work explores an orthogonal direction focusing on post-training LLMs for autoregressive searching (i.e., an extended reasoning process with self-reflection and self-exploration of new strategies). To achieve this, we propose the Chain-of-Action-Thought (COAT) reasoning and a two-stage training paradigm: 1) a small-scale format tuning stage to internalize the COAT reasoning format and 2) a large-scale self-improvement stage leveraging reinforcement learning. Our approach results in Satori, a 7B LLM trained on open-source models and data. Extensive empirical evaluations demonstrate that Satori achieves state-of-the-art performance on mathematical reasoning benchmarks while exhibits strong generalization to out-of-domain tasks. Code, data, and models are fully open-sourced.