# Flow-DPO: Improving LLM Mathematical Reasoning through Online Multi-Agent Learning

arXiv: https://arxiv.org/abs/2410.22304 · HTML: https://mlsanity.com/paper/2410.22304/

## Key facts

- Cited by 12 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 19 of its 21 references that are in the map.
- First posted on arXiv 29 Oct 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/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 19 of 19)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark](https://mlsanity.com/paper/2405.12209/) (2024)
- [LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning](https://mlsanity.com/paper/2410.02884/) (2024)
- [Multi-step Problem Solving Through a Verifier: An Empirical Analysis on Model-induced Process Supervision](https://mlsanity.com/paper/2402.02658/) (2024)
- [Online Joint Fine-tuning of Multi-Agent Flows](https://mlsanity.com/paper/2406.04516/) (2024)

## Built on by (most cited first, 12 of 12)

- [From LLM Reasoning to Autonomous AI Agents: A Comprehensive Review](https://mlsanity.com/paper/2504.19678/) (2025)
- [Towards Scientific Intelligence: A Survey of LLM-based Scientific Agents](https://mlsanity.com/paper/2503.24047/) (2025)
- [A Survey of LLM-Driven AI Agent Communication: Protocols, Security Risks, and Defense Countermeasures](https://mlsanity.com/paper/2506.19676/) (2025)
- [Enhancing LLM Reasoning with Iterative DPO: A Comprehensive Empirical Investigation](https://mlsanity.com/paper/2503.12854/) (2025)
- [Neighbor GRPO: Contrastive ODE Policy Optimization Aligns Flow Models](https://mlsanity.com/paper/2511.16955/) (2025)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [MasHost Builds It All: Autonomous Multi-Agent System Directed by Reinforcement Learning](https://mlsanity.com/paper/2506.08507/) (2025)
- [GigaVideo-1: Advancing Video Generation via Automatic Feedback with 4 GPU-Hours Fine-Tuning](https://mlsanity.com/paper/2506.10639/) (2025)
- [GRLO: Towards Generalizable Reinforcement Learning in Open-Ended Environments from Zero](https://mlsanity.com/paper/2605.15464/) (2026)
- [LegalDrill: Diagnosis-Driven Synthesis for Legal Reasoning in Small Language Models](https://mlsanity.com/paper/2604.23809/) (2026)
- [STARE: Step-wise Temporal Alignment and Red-teaming Engine for Multi-modal Toxicity Attack](https://mlsanity.com/paper/2605.00699/) (2026)
- [The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes](https://mlsanity.com/paper/2606.11470/) (2026)

## Abstract (arXiv)

Mathematical reasoning is a crucial capability for Large Language Models (LLMs), yet generating detailed and accurate reasoning traces remains a significant challenge. This paper introduces a novel approach to produce high-quality reasoning traces for LLM fine-tuning using online learning Flows. Our method employs an incremental output production Flow, where component LLMs collaboratively construct solutions through iterative communication. We train the Flow using online Direct Preference Optimization (DPO) learning with rollouts, generating DPO pairs for each training example and updating models in real-time. We directly compare the quality of reasoning traces generated by our method with those produced through direct model inference, demonstrating the effectiveness of our approach in improving LLM performance in mathematical reasoning tasks.