Hierarchical Deconstruction of LLM Reasoning: A Graph-Based Framework for Analyzing Knowledge Utilization (2406.19502v2)

Abstract: Despite the advances in 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.

Investigating How LLMs Leverage Internal Knowledge to Perform Complex Reasoning

The paper "Investigating How LLMs Leverage Internal Knowledge to Perform Complex Reasoning" addresses the current gaps in understanding how LLMs utilize internalized knowledge for sophisticated reasoning tasks. The authors propose a novel method to dissect complex real-world questions into a hierarchical graph, where each question is a node linked to parent nodes representing necessary background knowledge.

Key Contributions and Methodology

1. DepthQA Dataset: The paper introduces DepthQA, a dataset constructed by deconstructing complex questions into three depth levels: recalling conceptual knowledge ($D_1$), applying procedural knowledge ($D_2$), and analyzing strategic knowledge ($D_3$). This dataset is derived from human-written scientific questions in the TutorEval dataset and is specifically designed to evaluate LLMs' problem-solving abilities through a structured reasoning process.
2. Forward and Backward Discrepancy:

The authors define two new metrics: - Forward Discrepancy: Measures the difference in LLM performance between simpler sub-problems and their associated complex questions. This metric highlights gaps in LLMs' ability to integrate simpler knowledge into more complex reasoning. - Backward Discrepancy: Captures instances where LLMs successfully answer complex questions but struggle with simpler sub-questions. This metric indicates possible inconsistencies or overfitting in how models leverage memorized knowledge.

1. Hierarchical Graph Structure: By structuring questions hierarchically, the approach emphasizes the gradual accumulation of knowledge. Each node (question) in the graph contributes incrementally to the resolution of deeper, more complex nodes. This structure is used to assess and quantify discrepancies at various levels of reasoning complexity.

Experimental Setup and Results

The authors evaluate several instruction-tuned LLMs, including LLaMA 2, LLaMA 3, Mistral, and Mixtral models with parameter sizes ranging from 7B to 70B. They find that smaller models generally exhibit larger discrepancies than larger ones. This analysis is supported by measuring depthwise discrepancies using the DepthQA dataset:

• Performance Trends:
  • Larger models like LLaMA 3 70B Instruct outperform smaller counterparts across all reasoning depths ($D_1$, $D_2$, $D_3$).
  • Smaller models, such as LLaMA 2 7B Chat, demonstrate higher forward and backward discrepancies, highlighting greater inconsistency in integrating and applying knowledge.
• Memorization Impact:
  • Smaller models tend to rely more on memorized knowledge, leading to significant performance drops when reasoning capabilities are required.
  • Forward discrepancies are more pronounced in models heavily reliant on memorization, while backward discrepancies are observed in larger models probed with less memorized complex questions.

Implications and Future Directions

Practical Implications

This research has significant implications for the development of more robust AI systems capable of handling real-world complex questions:

• Model Training:

Incorporating structured intermediate steps during model training can enhance the problem-solving capabilities of LLMs. Explicit reasoning processes, such as multi-turn interactions, improve performance even for larger models, highlighting an avenue for future fine-tuning techniques.

• Benchmarking Complex Reasoning:

DepthQA sets a new benchmark for evaluating complex reasoning in LLMs, providing a comprehensive testbed to measure both forward and backward reasoning capabilities. This can be extended to other domains to develop more generalized reasoning assessment tools.

Theoretical Implications

From a theoretical standpoint, the findings underscore the importance of structured knowledge integration:

• Knowledge Accumulation:

The hierarchical graph-based approach elucidates the importance of accumulating and synthesizing knowledge incrementally. This paradigm could inspire new architectures or training paradigms that explicitly model hierarchical knowledge structures within LLMs.

• Discrepancy Analysis:

The introduction of forward and backward discrepancies offers a nuanced understanding of LLM reasoning capabilities, shedding light on potential failure modes and areas for improvement in model design and training.

Conclusions

The paper provides a systematic approach to evaluating and understanding the reasoning capabilities of LLMs, emphasizing the integration of hierarchical knowledge structures. By proposing novel discrepancy metrics and introducing the DepthQA dataset, the research offers valuable insights into the strengths and limitations of current LLMs and sets the stage for future advancements in AI reasoning abilities. As AI continues to evolve, such in-depth analyses will be crucial in developing models that can effectively leverage internal knowledge to solve complex, real-world problems.