Large Language Models as an Indirect Reasoner: Contrapositive and Contradiction for Automated Reasonin (AI summary)

Key Points

1. Introduction: The paper addresses the limitations of direct reasoning (DR) methods in complex reasoning tasks and proposes a novel Indirect Reasoning (IR) approach using contrapositives and contradictions to enhance the reasoning power of Large Language Models (LLMs).

2. Prominence of Large Language Models: Large Language Models have shown success in various tasks, including language comprehension, content generation, and logical reasoning.

3. Framework of Indirect Reasoning: The proposed IR method involves two stages: rule augmentation and indirect reasoning. The rule augmentation leverages the logical equivalence of contrapositive to augment the data and rules, while the indirect reasoning process is designed to guide LLMs to perform reasoning based on proof by contradiction.

4. Experimental Results: Experimental results on popular LLMs, such as GPT-3.5-turbo and Gemini-pro, demonstrate that the IR method enhances the overall accuracy of factual reasoning by 27.33% and mathematic proof by 31.43% compared to traditional DR methods. Additionally, combining IR and DR significantly outperforms the methods solely using IR or DR.

5. Previous Research Efforts: The paper discusses previous research efforts to improve the reasoning ability of LLMs, such as fine-tuning-based methods, tool-based methods, and Chain-of-Thought (CoT) prompting approaches.

6. Implementation of IR: The paper details the implementation of IR, including the design of prompt templates for zero-shot and few-shot scenarios to guide LLMs to engage in indirect reasoning effectively.

7. Combination with DR: The proposed IR method can be combined with traditional DR methodologies to create a Direct-Indirect Reasoning (DIR) framework, which enriches the reasoning paths of LLMs and improves their overall reasoning ability.

8. Assessment of Method Effectiveness: The paper evaluates the effectiveness of the IR method on factual reasoning and mathematic proof tasks, demonstrating significant improvements over DR methods across different LLMs and prompt methods.

9. Impact of Rule Augmentation and IR: Ablative experiments demonstrate the impact of rule augmentation on both DR and IR, showing notable performance improvements, particularly in factual reasoning tasks. The paper also illustrates how IR can reduce the number of reasoning steps needed for LLMs to reach conclusions in complex reasoning scenarios.

Summary

The research paper proposes a novel Indirect Reasoning (IR) method to enhance the reasoning power of Large Language Models (LLMs). It highlights the limitations of Direct Reasoning (DR) frameworks and advocates for leveraging the logic of contrapositives and contradictions to tackle IR tasks such as factual reasoning and mathematical proof. The methodology involves augmenting data and rules using the logical equivalence of contrapositive and designing prompt templates to trigger LLMs to conduct IR based on proof by contradiction.

Experimental results on popular LLMs, such as GPT-3.5-turbo and Gemini-pro, illustrate that the IR method enhances the overall accuracy of factual reasoning by 27.33% and mathematical proof by 31.43% when compared with traditional DR methods. Additionally, the combination of IR and DR methods outperforms the use of either method alone. The paper also discusses the application of IR in practical problem-solving scenarios and its potential to complement DR approaches.

Furthermore, the study presents the enhancement of LLMs' reasoning paths and the effectiveness of the proposed DIR framework. The paper provides detailed assessments of IR effectiveness, including its impact on reasoning steps and the combinational effects of IR and DR methods. Ablative experiments on the impact of rule augmentation on IR are conducted, showing notable improvements in the reasoning ability of LLMs, particularly in factual reasoning tasks.

The paper concludes by emphasizing the versatility of the proposed IR method and its potential to integrate additional logical laws to further enhance LLMs' reasoning skills. The research anticipates that the proposed technique will expand the application scenarios of LLMs and inspire better utilization of AI technology in the future. However, it also acknowledges that the method may inherit limitations of popular LLMs, which could lead to incorrect and biased answers in some instances.

Reference: https://arxiv.org/abs/2402.03667