# GFlowNet Fine-tuning for Diverse Correct Solutions in Mathematical Reasoning Tasks

arXiv: https://arxiv.org/abs/2410.20147 · HTML: https://mlsanity.com/paper/2410.20147/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 27 of its 35 references that are in the map.
- First posted on arXiv 26 Oct 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 27 of 27)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (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)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [DeepSpeed-Chat: Easy, Fast and Affordable RLHF Training of ChatGPT-like Models at All Scales](https://mlsanity.com/paper/2308.01320/) (2023)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [MathVC: An LLM-Simulated Multi-Character Virtual Classroom for Mathematics Education](https://mlsanity.com/paper/2404.06711/) (2024)
- [Weak-to-Strong Reasoning](https://mlsanity.com/paper/2407.13647/) (2024)

## Built on by (most cited first, 8 of 8)

- [GFlowVLM: Enhancing Multi-step Reasoning in Vision-Language Models with Generative Flow Networks](https://mlsanity.com/paper/2503.06514/) (2025)
- [Accurate and Diverse LLM Mathematical Reasoning via Automated PRM-Guided GFlowNets](https://mlsanity.com/paper/2504.19981/) (2025)
- [Loss-Guided Auxiliary Agents for Overcoming Mode Collapse in GFlowNets](https://mlsanity.com/paper/2505.15251/) (2025)
- [GFlowGR: Fine-tuning Generative Recommendation Frameworks with Generative Flow Networks](https://mlsanity.com/paper/2506.16114/) (2025)
- [Latent Thought Flow: Efficient Latent Reasoning in Large Language Models](https://mlsanity.com/paper/2606.16222/) (2026)
- [Stable-GFlowNet: Toward Diverse and Robust LLM Red-Teaming via Contrastive Trajectory Balance](https://mlsanity.com/paper/2605.00553/) (2026)
- [Interpretable epistemic uncertainty decomposition in sequential generative models via polynomial chaos surrogates](https://mlsanity.com/paper/2510.21523/) (2025)
- [Universality and Convergence of Generative Flows](https://mlsanity.com/paper/2610.05490/) (2026)

## Abstract (arXiv)

Mathematical reasoning problems are among the most challenging, as they typically require an understanding of fundamental laws to solve. The laws are universal, but the derivation of the final answer changes depending on how a problem is approached. When training large language models (LLMs), learning the capability of generating such multiple solutions is essential to accelerate their use in mathematical education. To this end, we train LLMs using generative flow network (GFlowNet). Different from reward-maximizing reinforcement learning (RL), GFlowNet fine-tuning seeks to find diverse solutions by training the LLM whose distribution is proportional to a reward function. In numerical experiments, we evaluate GFlowNet fine-tuning and reward-maximizing RL in terms of accuracy and diversity. The results show that GFlowNet fine-tuning derives correct final answers from diverse intermediate reasoning steps, indicating the improvement of the capability of alternative solution generation.