# R2 Flow: Recursive Self-Improvement via Recursive Skill Evolution

arXiv: https://arxiv.org/abs/2609.33867 · HTML: https://mlsanity.com/paper/2609.33867/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Agent skill learning and evolution, one of 16 directions in LLM agents and tool use.
- Builds on 60 of its 71 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Placed in

- LLM agents and tool use / [Agent skill learning and evolution](https://mlsanity.com/agents/agent-skill-learning-and-evolution/)
- Synthetic data and self-improvement for LLMs / [Self-evolving LLM agents](https://mlsanity.com/synth/self-evolving-llm-agents/)

## Builds on (most cited first, 30 of 60)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [AFlow: Automating Agentic Workflow Generation](https://mlsanity.com/paper/2410.10762/) (2024)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [SkillRL: Evolving Agents via Recursive Skill-Augmented Reinforcement Learning](https://mlsanity.com/paper/2602.08234/) (2026)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Trace2Skill: Distill Trajectory-Local Lessons into Transferable Agent Skills](https://mlsanity.com/paper/2603.25158/) (2026)
- [A Comprehensive Survey of Self-Evolving AI Agents: A New Paradigm Bridging Foundation Models and Lifelong Agentic Systems](https://mlsanity.com/paper/2508.07407/) (2025)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Qwen3.5-Omni Technical Report](https://mlsanity.com/paper/2604.15804/) (2026)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [SkillOpt: Executive Strategy for Self-Evolving Agent Skills](https://mlsanity.com/paper/2605.23904/) (2026)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)

## Abstract (arXiv)

LLM-based agents can improve themselves across tasks by reusing and revising the skills they orchestrate into executable procedures. Flow-based training fits this loop: it samples procedures in proportion to reward, and the flow through each skill credits it for the next library revision. Three obstacles stand in the way of making this self-improvement reliable: flow training suffers strategy collapse over tree-structured histories; nonnegative flow-based credit rewards frequent use as if it were benefit; and library edits rest on the task reward the policy optimizes. We introduce R2 Flow, a recursive self-improvement framework that alternates policy learning, independent verification, and versioned skill-library updates on a shared-state orchestration graph. The graph merges histories that differ only in the order of independent steps, allowing flow training to pool evidence across equivalent executions. A flow-share readout of the trained flow, invariant to the backward policy, and a separate signed utility rank which skills to change, verifier evidence decides whether an edit is warranted, and a residual-variance plateau sets when to update. Committed edits reshape the graph the next policy learns on, realizing recursive skill evolution. Across question answering, mathematical reasoning, interactive decision making, and code generation, R2 Flow improves task accuracy and library-edit precision over heuristic orchestration, reinforcement learning, and skill-evolution baselines, and transfers across executors. Code is available at https://github.com/beita6969/r2flow.