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Look Before You Leap: Problem Elaboration Prompting Improves Mathematical Reasoning in Large Language Models (2402.15764v2)

Published 24 Feb 2024 in cs.CL and cs.AI

Abstract: LLMs still grapple with complex tasks like mathematical reasoning. Despite significant efforts invested in improving prefix prompts or reasoning process, the crucial role of problem context might have been neglected. Accurate recognition of inputs is fundamental for solving mathematical tasks, as ill-formed problems could potentially mislead LLM's reasoning. In this study, we propose a new approach named Problem Elaboration Prompting (PEP) to enhance the mathematical capacities of LLMs. Specifically, PEP decomposes and elucidates the problem context before reasoning, therefore enhancing the context modeling and parsing efficiency. Experiments across datasets and models demonstrate promising performances: (1) PEP demonstrates an overall enhancement in various mathematical tasks. For instance, with the GPT-3.5 model, PEP exhibits improvements of 9.93% and 8.80% on GSM8k through greedy decoding and self-consistency, respectively. (2) PEP can be easily implemented and integrated with other prompting methods. (3) PEP shows particular strength in handling distraction problems.

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Summary

  • The paper introduces PEP, a method that enhances mathematical reasoning by decomposing and clarifying problem statements.
  • The methodology integrates with chain-of-thought prompting, achieving improvements up to 9.93% in zero-shot and few-shot learning scenarios.
  • PEP mitigates distraction by eliminating irrelevant details, leading to more accurate reasoning on datasets like GSM8k and GSMIC.

Problem Elaboration Prompting (PEP) in Mathematical Reasoning with LLMs

Introduction

The paper "Look Before You Leap: Problem Elaboration Prompting Improves Mathematical Reasoning in LLMs" addresses a critical challenge in the field of AI LLMs, specifically their application to complex mathematical reasoning tasks. The authors propose a novel method, Problem Elaboration Prompting (PEP), designed to enhance the reasoning capabilities of LLMs by improving the understanding of problem context before any reasoning process begins. This method aims to overcome the issue of distraction caused by irrelevant or poorly structured problem statements, a common pitfall in current LLM reasoning abilities.

Methodology

PEP is presented as an approach that emphasizes the decomposition and clarification of problem statements into smaller, comprehensible segments before engaging in any reasoning. The method adopts a human-like cognitive strategy: to thoroughly understand the problem's conditions and requirements (i.e., "look") before proceeding to solve it ("leap"). This preemptive clarity aims to prevent the model from being misled by spurious relationships within the problem context. Figure 1

Figure 1: We proposed Problem Elaboration Prompting~(PEP) for enhancing problem context, thereby improving subsequent reasoning. As depicted in the example, PEP decouples spurious relationships and refines statements, preventing downstream distraction errors.

PEP is straightforward to implement and can be easily integrated with other prompting methods like Chain-of-Thought (CoT) prompting. This integration capability suggests its potential utility in refining existing methodologies without extensive modifications to model architectures or training regimens.

Evaluation and Performance

Experimental evaluations were conducted across several mathematical reasoning datasets, such as GSM8k, SingleEq, AQuA, and SVAMP. The results demonstrate that PEP consistently outperforms standard prompting techniques in handling complex reasoning tasks, providing enhancements in both zero-shot and few-shot learning scenarios.

Notably, when applied to models like GPT-3.5, PEP delivered improvements of up to 9.93% and 8.80% using greedy decoding and self-consistency strategies, respectively. These improvements are significant, given the challenges in enhancing reasoning capabilities with existing techniques.

Dealing with Distraction

The effectiveness of PEP in mitigating distraction problems was particularly highlighted. By pre-processing problem statements to eliminate irrelevant details and clarify essential components, PEP bolsters the model's robustness against ill-formed problem inputs, an aspect often exploited to critique LLM performance. Figure 2

Figure 2: An overview of the proposed PEP and other problem-related methods. Rather than creating sub-questions or plans to guide subsequent reasoning, PEP focuses on clarifying and enriching the problem context, i.e., PEP can be integrated with these methods.

The paper reports that on the GSMIC dataset, which tests models' robustness against distraction, PEP achieved higher accuracies compared to other methods adapted with irrelevant instructional cues. This indicates that PEP's preprocessing phase enables models to maintain focus on relevant problem components and reasoning pathways.

Analysis of Components

An ablation paper in the paper further delved into the constituent strategies of PEP: decomposition and elucidation. It was revealed that both components contribute significantly to the method's success, with decomposition ensuring that the problem is broken into logical, manageable sub-parts, while elucidation aids the model in interpreting each sub-part comprehensively. This dual approach underscores the necessity of both structuring problem data and ensuring its interpretative clarity for improved reasoning. Figure 3

Figure 3: Breakdown accuracies w.r.t. irrelevant sentence factors~(T: Topic, RO: Role Overlap, NR: Num. Range). Lower accuracy suggests the model is more sensitive to that factor.

Conclusion

Problem Elaboration Prompting represents a pragmatic step forward in enhancing the problem-solving capabilities of LLMs for mathematical reasoning. By advancing the comprehension of problem context, PEP mitigates a common source of error in current models. Its adaptability and complementary nature, which allow for seamless integration with other prompting strategies, highlight its potential for broad application across various domains requiring advanced reasoning. Future work could explore the extension of PEP to other domains of complex task-solving beyond mathematical reasoning, potentially enhancing LLM performance in diverse, domain-specific applications.

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