Graph-Augmented Reasoning: Evolving Step-by-Step Knowledge Graph Retrieval for LLM Reasoning

2025-03-03

AI Summary

To address knowledge scarcity, hallucination propensity, and insufficient reasoning depth in small-scale frozen LLMs for mathematical reasoning, this paper proposes Graph-Augmented Reasoning (GAR), the first framework to jointly align knowledge graph retrieval with individual reasoning steps. Our method comprises: (i) process-oriented knowledge graph construction grounded in mathematical derivation chains; (ii) a hierarchical retrieval strategy that prioritizes step-relevant subgraphs; (iii) post-retrieval pruning (PRP) to distill contextually precise facts; and (iv) a lightweight reward model (RM) for stepwise confidence calibration. Crucially, GAR operates without fine-tuning—enabling zero-shot reasoning enhancement. Evaluated on Math500 and GSM8K, GAR boosts Llama-3B’s accuracy by 20.73% relatively on Math500, significantly mitigates hallucination, and enhances multi-step logical coherence.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Recent large language model (LLM) reasoning, despite its success, suffers from limited domain knowledge, susceptibility to hallucinations, and constrained reasoning depth, particularly in small-scale models deployed in resource-constrained environments. This paper presents the first investigation into integrating step-wise knowledge graph retrieval with step-wise reasoning to address these challenges, introducing a novel paradigm termed as graph-augmented reasoning. Our goal is to enable frozen, small-scale LLMs to retrieve and process relevant mathematical knowledge in a step-wise manner, enhancing their problem-solving abilities without additional training. To this end, we propose KG-RAR, a framework centered on process-oriented knowledge graph construction, a hierarchical retrieval strategy, and a universal post-retrieval processing and reward model (PRP-RM) that refines retrieved information and evaluates each reasoning step. Experiments on the Math500 and GSM8K benchmarks across six models demonstrate that KG-RAR yields encouraging results, achieving a 20.73% relative improvement with Llama-3B on Math500.

Problem

• Enhance small-scale LLMs' reasoning with step-wise knowledge retrieval.
• Address LLM limitations like hallucinations and limited domain knowledge.
• Improve problem-solving without additional training using graph-augmented reasoning.

Innovation

• Integrates step-wise knowledge graph retrieval
• Uses hierarchical retrieval strategy
• Implements universal post-retrieval processing model