  Despite significant advancements, there is a limited understanding of how
large language models (LLMs) utilize knowledge for reasoning. To address this,
we propose a method that deconstructs complex real-world questions into a
graph, representing each question as a node with parent nodes 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, discrepancies
in LLMs' 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 have more
discrepancies than larger models. 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.
