The Role of Deductive and Inductive Reasoning in Large Language Models

2024-10-03

arXiv.org

AI Summary

Large language models (LLMs) face limitations in complex reasoning due to static prompting and insufficient adaptability. To address this, we propose DID, a novel input-driven reasoning framework grounded in cognitive alignment, which synergistically integrates deductive and inductive reasoning. DID introduces a dual-metric complexity assessment—combining the Littlestone dimension (a measure from computational learning theory) and information entropy—designed in accordance with cognitive science principles. This enables quantitative task difficulty estimation, dynamic decomposition of reasoning steps, and adaptive evolution of reasoning paths—eliminating reliance on fixed templates. Notably, DID is the first to incorporate the Littlestone dimension into LLM-based task difficulty modeling. Evaluated across multiple benchmarks—including AIW, MR-GSM8K, and Holiday Puzzle—DID achieves 70.3% accuracy on AIW, outperforming Tree-of-Thought (ToT) by 8.1 percentage points while reducing computational overhead. It further demonstrates superior robustness and interpretability on temporally complex reasoning tasks.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Large Language Models (LLMs) have demonstrated impressive capabilities in reasoning tasks, yet their reliance on static prompt structures and limited adaptability to complex scenarios remains a significant challenge. In this paper, we propose the Deductive and InDuctive(DID) method, a novel framework that enhances LLM reasoning by dynamically integrating both deductive and inductive reasoning approaches. Drawing from cognitive science principles, DID implements a dual-metric complexity evaluation system that combines Littlestone dimension and information entropy to precisely assess task difficulty and guide decomposition strategies. DID enables the model to progressively adapt its reasoning pathways based on problem complexity, mirroring human cognitive processes. We evaluate DID's effectiveness across multiple benchmarks, including the AIW and MR-GSM8K, as well as our custom Holiday Puzzle dataset for temporal reasoning. Our results demonstrate significant improvements in reasoning quality and solution accuracy - achieving 70.3% accuracy on AIW (compared to 62.2% for Tree of Thought) while maintaining lower computational costs. The success of DID in improving LLM performance while preserving computational efficiency suggests promising directions for developing more cognitively aligned and capable language models. Our work contributes a theoretically grounded, input-centric approach to enhancing LLM reasoning capabilities, offering an efficient alternative to traditional output-exploration methods.

Problem

• Enhancing LLM reasoning capabilities
• Dynamic integration of deductive and inductive reasoning
• Improving computational efficiency in reasoning tasks

Innovation

• DID method integrates deductive and inductive reasoning
• Dual-metric system evaluates task complexity dynamically
• Adapts reasoning pathways based on problem complexity