# Proof Flow: Preliminary Study on Generative Flow Network Language Model Tuning for Formal Reasoning

arXiv: https://arxiv.org/abs/2410.13224 · HTML: https://mlsanity.com/paper/2410.13224/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Placed in

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

## Builds on (most cited first, 8 of 8)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [TheoremLlama: Transforming General-Purpose LLMs into Lean4 Experts](https://mlsanity.com/paper/2407.03203/) (2024)
- [Flow of Reasoning: Training LLMs for Divergent Reasoning with Minimal Examples](https://mlsanity.com/paper/2406.05673/) (2024)

## Built on by (most cited first, 4 of 4)

- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [Loss-Guided Auxiliary Agents for Overcoming Mode Collapse in GFlowNets](https://mlsanity.com/paper/2505.15251/) (2025)
- [Universality and Convergence of Generative Flows](https://mlsanity.com/paper/2610.05490/) (2026)

## Abstract (arXiv)

Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely out of reach for open models. To address this gap, we examine the potential of Generative Flow Networks as a fine-tuning method for LLMs to unlock advanced reasoning capabilities. In this paper, we present a proof of concept in the domain of formal reasoning, specifically in the Neural Theorem Proving (NTP) setting, where proofs specified in a formal language such as Lean can be deterministically and objectively verified. Unlike classical reward-maximization reinforcement learning, which frequently over-exploits high-reward actions and fails to effectively explore the state space, GFlowNets have emerged as a promising approach for sampling compositional objects, improving generalization, and enabling models to maintain diverse hypotheses. Our early results demonstrate GFlowNet fine-tuning's potential for enhancing model performance in a search setting, which is especially relevant given the paradigm shift towards inference time compute scaling and "thinking slowly."