Fast-Slow-Thinking: Complex Task Solving with Large Language Models

Nowadays, Large Language Models (LLMs) have been gradually employed to solve complex tasks. To face the challenge, task decomposition has become an effective way, which proposes to divide a complex task into multiple simpler subtasks and then solve them separately so that the difficulty of the original task can be reduced. However, the performance of existing task decomposition methods can be suboptimal when the task contains overly complex logic and constraints. In this situation, the solution generated by LLMs may deviate from the original purpose of the task, or contain redundant or even erroneous content. Therefore, inspired by the fact that humans possess two thinking systems including fast thinking and slow thinking, this paper introduces a new task decomposition method termed ``Fast-Slow-Thinking'' (FST), which stimulates LLMs to solve tasks through the cooperation of Fast Thinking (FT) and Slow Thinking (ST) steps. Here FT focuses more on the general and concise aspect of the task, and ST focuses more on the details of the task. In FT, LLMs are prompted to remove the constraints of the original task, therefore simplifying it to a general and concise one. In ST, we recall the constraints removed in FT, so that LLMs can improve the answer generated in FT to meet the requirements of the original task. Therefore, our FST method enables LLMs to consider a complex problem via a human-like cognition process from coarse to fine, the effectiveness of which has been well demonstrated by the experiments on three types of tasks.

Large Language Models as an Indirect Reasoner: Contrapositive and Contradiction for Automated Reasoning

Recently, increasing attention has been focused drawn on to improve the ability of Large Language Models (LLMs) to perform complex reasoning. However, previous methods, such as Chain-of-Thought and Self-Consistency, mainly follow Direct Reasoning (DR) frameworks, so they will meet difficulty in solving numerous real-world tasks which can hardly be solved via DR. Therefore, to strengthen the reasoning power of LLMs, this paper proposes a novel Indirect Reasoning (IR) method that employs the logic of contrapositives and contradictions to tackle IR tasks such as factual reasoning and mathematic proof. Specifically, our methodology comprises two steps. Firstly, we leverage the logical equivalence of contrapositive to augment the data and rules to enhance the comprehensibility of LLMs. Secondly, we design a set of prompt templates to trigger LLMs to conduct IR based on proof by contradiction that is logically equivalent to the original DR process. Our IR method is simple yet effective and can be straightforwardly integrated with existing DR methods to further boost the reasoning abilities of LLMs. The experimental results on popular LLMs, such as GPT-3.5-turbo and Gemini-pro, show that our IR method enhances the overall accuracy of factual reasoning by 27.33% and mathematical proof by 31.43%, when compared with traditional DR methods. Moreover, the methods combining IR and DR significantly outperform the methods solely using IR or DR, further demonstrating the effectiveness of our strategy.