# GraphMind: Theorem Selection and Conclusion Generation Framework with Dynamic GNN for LLM Reasoning

arXiv: https://arxiv.org/abs/2511.19078 · HTML: https://mlsanity.com/paper/2511.19078/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 12 of 12)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [Graph Neural Prompting with Large Language Models](https://mlsanity.com/paper/2309.15427/) (2023)
- [Theorem-of-Thought: A Multi-Agent Framework for Abductive, Deductive, and Inductive Reasoning in Language Models](https://mlsanity.com/paper/2506.07106/) (2025)
- [High Dimensional Robust Consensus over Networks with Limited Capacity](https://mlsanity.com/paper/2105.10823/) (2021)

## Built on by (most cited first, 2 of 2)

- [Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models](https://mlsanity.com/paper/2606.08831/) (2026)
- [Nazrin: An Atomic Neural Proof Automation Tactic in Lean 4](https://mlsanity.com/paper/2602.18767/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, including multi-step reasoning such as mathematical proving. However, existing approaches often lack an explicit and dynamic mechanism to structurally represent and evolve intermediate reasoning states, which limits their ability to perform context-aware theorem selection and iterative conclusion generation. To address these challenges, we propose GraphMind, a novel dynamic graph-based framework that integrates the graph neural network (GNN) with LLMs to iteratively select theorems and generate intermediate conclusions for multi-step reasoning. Our method models the reasoning process as a heterogeneous evolving graph, where nodes represent conditions, theorems, and conclusions, while edges capture logical dependencies between nodes. By encoding the current reasoning state with GNN and leveraging semantic matching for theorem selection, our framework enables context-aware, interpretable, and structured reasoning in a closed-loop manner. Experiments on various question-answering (QA) datasets demonstrate that our proposed GraphMind method achieves consistent performance improvements and significantly outperforms existing baselines in multi-step reasoning, validating the effectiveness and generalizability of our approach.