The Role of Deductive and Inductive Reasoning in Large Language Models

Large Language Models (LLMs) have achieved substantial progress in artificial intelligence, particularly in reasoning tasks. However, their reliance on static prompt structures, coupled with limited dynamic reasoning capabilities, often constrains their adaptability to complex and evolving problem spaces. In this paper, we propose the Deductive and InDuctive(DID) method, which enhances LLM reasoning by dynamically integrating both deductive and inductive reasoning within the prompt construction process. Drawing inspiration from cognitive science, the DID approach mirrors human adaptive reasoning mechanisms, offering a flexible framework that allows the model to adjust its reasoning pathways based on task context and performance. We empirically validate the efficacy of DID on established datasets such as AIW and MR-GSM8K, as well as on our custom dataset, Holiday Puzzle, which presents tasks about different holiday date calculating challenges. By leveraging DID's hybrid prompt strategy, we demonstrate significant improvements in both solution accuracy and reasoning quality, achieved without imposing substantial computational overhead. Our findings suggest that DID provides a more robust and cognitively aligned framework for reasoning in LLMs, contributing to the development of advanced LLM-driven problem-solving strategies informed by cognitive science models.

$T^2$ of Thoughts: Temperature Tree Elicits Reasoning in Large Language Models

Large Language Models (LLMs) have emerged as powerful tools in artificial intelligence, especially in complex decision-making scenarios, but their static problem-solving strategies often limit their adaptability to dynamic environments. We explore the enhancement of reasoning capabilities in LLMs through Temperature Tree ($T^2$) prompting via Particle Swarm Optimization, termed as $T^2$ of Thoughts ($T^2oT$). The primary focus is on enhancing decision-making processes by dynamically adjusting search parameters, especially temperature, to improve accuracy without increasing computational demands. We empirically validate that our hybrid $T^2oT$ approach yields enhancements in, single-solution accuracy, multi-solution generation and text generation quality. Our findings suggest that while dynamic search depth adjustments based on temperature can yield mixed results, a fixed search depth, when coupled with adaptive capabilities of $T^2oT$, provides a more reliable and versatile problem-solving strategy. This work highlights the potential for future explorations in optimizing algorithmic interactions with foundational language models, particularly illustrated by our development for the Game of 24 and Creative Writing tasks.