Hierarchical Deconstruction of LLM Reasoning: A Graph-Based Framework for Analyzing Knowledge Utilization
This work provides insights into LLM reasoning for AI researchers, though it is incremental as it builds on existing analysis methods without introducing a new paradigm.
The study tackled the problem of understanding how large language models (LLMs) use knowledge for reasoning by proposing a graph-based framework to deconstruct questions into hierarchical depths, revealing that smaller models exhibit more performance discrepancies and that structured intermediate steps improve problem-solving across model sizes.
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.