# Recursive Introspection: Teaching Language Model Agents How to Self-Improve

arXiv: https://arxiv.org/abs/2407.18219 · HTML: https://mlsanity.com/paper/2407.18219/

## Key facts

- Cited by 165 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 56 of its 66 references that are in the map.
- First posted on arXiv 25 Jul 2024.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)
- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 30 of 56)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [Language Models as Zero-Shot Planners: Extracting Actionable Knowledge for Embodied Agents](https://mlsanity.com/paper/2201.07207/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)

## Built on by (most cited first, 30 of 165)

- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [AutoSkill: Experience-Driven Lifelong Learning via Skill Self-Evolution](https://mlsanity.com/paper/2603.01145/) (2026)
- [Inducing Programmatic Skills for Agentic Tasks](https://mlsanity.com/paper/2504.06821/) (2025)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thought](https://mlsanity.com/paper/2501.04682/) (2025)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [MAPoRL: Multi-Agent Post-Co-Training for Collaborative Large Language Models with Reinforcement Learning](https://mlsanity.com/paper/2502.18439/) (2025)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [A Self-Improving Coding Agent](https://mlsanity.com/paper/2504.15228/) (2025)
- [MALT: Improving Reasoning with Multi-Agent LLM Training](https://mlsanity.com/paper/2412.01928/) (2024)
- [Self-rewarding correction for mathematical reasoning](https://mlsanity.com/paper/2502.19613/) (2025)
- [The Death of Schema Linking? Text-to-SQL in the Age of Well-Reasoned Language Models](https://mlsanity.com/paper/2408.07702/) (2024)
- [Are Reasoning Models More Prone to Hallucination?](https://mlsanity.com/paper/2505.23646/) (2025)
- [Multi-Agent Verification: Scaling Test-Time Compute with Multiple Verifiers](https://mlsanity.com/paper/2502.20379/) (2025)
- [e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs](https://mlsanity.com/paper/2506.09026/) (2025)
- [From Reflection to Perfection: Scaling Inference-Time Optimization for Text-to-Image Diffusion Models via Reflection Tuning](https://mlsanity.com/paper/2504.16080/) (2025)
- [SETS: Leveraging Self-Verification and Self-Correction for Improved Test-Time Scaling](https://mlsanity.com/paper/2501.19306/) (2025)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification](https://mlsanity.com/paper/2502.01839/) (2025)
- [Self-Questioning Language Models](https://mlsanity.com/paper/2508.03682/) (2025)
- [A Survey on the Optimization of Large Language Model-based Agents](https://mlsanity.com/paper/2503.12434/) (2025)
- [Reflect-DiT: Inference-Time Scaling for Text-to-Image Diffusion Transformers via In-Context Reflection](https://mlsanity.com/paper/2503.12271/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [ChemAgent: Self-updating Library in Large Language Models Improves Chemical Reasoning](https://mlsanity.com/paper/2501.06590/) (2025)

## Abstract (arXiv)

A central piece in enabling intelligent agentic behavior in foundation models is to make them capable of introspecting upon their behavior, reasoning, and correcting their mistakes as more computation or interaction is available. Even the strongest proprietary large language models (LLMs) do not quite exhibit the ability of continually improving their responses sequentially, even in scenarios where they are explicitly told that they are making a mistake. In this paper, we develop RISE: Recursive IntroSpEction, an approach for fine-tuning LLMs to introduce this capability, despite prior work hypothesizing that this capability may not be possible to attain. Our approach prescribes an iterative fine-tuning procedure, which attempts to teach the model how to alter its response after having executed previously unsuccessful attempts to solve a hard test-time problem, with optionally additional environment feedback. RISE poses fine-tuning for a single-turn prompt as solving a multi-turn Markov decision process (MDP), where the initial state is the prompt. Inspired by principles in online imitation learning and reinforcement learning, we propose strategies for multi-turn data collection and training so as to imbue an LLM with the capability to recursively detect and correct its previous mistakes in subsequent iterations. Our experiments show that RISE enables Llama2, Llama3, and Mistral models to improve themselves with more turns on math reasoning tasks, outperforming several single-turn strategies given an equal amount of inference-time computation. We also find that RISE scales well, often attaining larger benefits with more capable models. Our analysis shows that RISE makes meaningful improvements to responses to arrive at the correct solution for challenging prompts, without disrupting one-turn abilities as a result of expressing more complex distributions.