Hierarchical Deconstruction of LLM Reasoning: A Graph-Based Framework for Analyzing Knowledge Utilization

TL;DR

This paper introduces a graph-based framework to analyze how large language models utilize different types of knowledge during reasoning, revealing discrepancies in performance across model sizes and question complexities.

Contribution

It proposes a hierarchical graph method and the DepthQA dataset to deconstruct questions into knowledge depths, providing new insights into LLM reasoning and performance discrepancies.

Findings

Smaller models show larger performance discrepancies.

Structured multi-turn interactions improve reasoning performance.

Distinct discrepancy patterns correlate with model size and training data.

Abstract

Despite the advances in large language models (LLMs), how they use their knowledge for reasoning is not yet well understood. In this study, we propose a method that deconstructs complex real-world questions into a graph, representing each question as a node with predecessors of background knowledge needed to solve the question. We develop the DepthQA dataset, deconstructing questions into three depths: (i) recalling conceptual knowledge, (ii) applying procedural knowledge, and (iii) analyzing strategic knowledge. Based on a hierarchical graph, we quantify forward discrepancy, a discrepancy in LLM performance on simpler sub-problems versus complex questions. We also measure backward discrepancy where LLMs answer complex questions but struggle with simpler ones. Our analysis shows that smaller models exhibit more discrepancies than larger models. Distinct patterns of discrepancies are observed across model capacity and possibility of training data memorization. Additionally, guiding models from simpler to complex questions through multi-turn interactions improves performance across model sizes, highlighting the importance of structured intermediate steps in knowledge reasoning. This work enhances our understanding of LLM reasoning and suggests ways to improve their problem-solving abilities.