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SAAS: Solving Ability Amplification Strategy for Enhanced Mathematical Reasoning in Large Language Models (2404.03887v4)

Published 5 Apr 2024 in cs.CL and cs.AI

Abstract: This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of LLMs. We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT) learning, hypothesizing that prioritizing the learning of mathematical reasoning ability is helpful for the amplification of problem-solving ability. Thus, the initial learning with CoT is essential for solving challenging mathematical problems. To this end, we propose a sequential learning approach, named SAAS (Solving Ability Amplification Strategy), which strategically transitions from CoT learning to PoT learning. Our empirical study, involving an extensive performance comparison using several benchmarks, demonstrates that our SAAS achieves state-of-the-art (SOTA) performance. The results underscore the effectiveness of our sequential learning approach, marking a significant advancement in the field of mathematical reasoning in LLMs.

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Authors (7)
  1. Hyeonwoo Kim (13 papers)
  2. Gyoungjin Gim (3 papers)
  3. Yungi Kim (13 papers)
  4. Jihoo Kim (9 papers)
  5. Byungju Kim (7 papers)
  6. Wonseok Lee (13 papers)
  7. Chanjun Park (49 papers)
Citations (1)
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Summary

Enhancing Mathematical Reasoning in LLMs with SAAS: A Novel Sequential Learning Approach

Introduction

LLMs have demonstrated exceptional capabilities across various domains, yet their proficiency in mathematical reasoning poses a challenge that necessitates further exploration. The paper under discussion introduces a novel sequential learning approach, dubbed Solving Ability Amplification Strategy (SAAS), aimed at enhancing both the mathematical reasoning and problem-solving skills of LLMs. By integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) learning in a strategic sequence, SAAS sets a new precedent in the advancement of LLM capabilities in the mathematical domain.

Background and Motivation

Previous efforts in incorporating mathematical reasoning into LLMs have been primarily based on CoT, PoT, fine-tuning, and continued pretraining approaches. While CoT enhances logical reasoning, it often falls short in computational accuracy when handling complex numerical data. Conversely, PoT, which translates reasoning steps into code, demands precise expression for effective computation, emphasizing the need for a combined strategy. Inspired by pedagogical methods that build problem-solving skills upon a foundation of logical reasoning, SAAS proposes a sequential learning strategy transitioning from CoT to PoT, aiming to leverage the strengths of both methods for improved performance.

SAAS: A Detailed Overview

The essence of SAAS lies in its sequential learning strategy, starting with CoT learning to establish a robust foundation of mathematical reasoning, followed by PoT learning that emphasizes computational accuracy. This approach is supplemented by a cognitive retention strategy, incorporating elements of CoT learning within the PoT phase to prevent the deterioration of reasoning skills. The synergy between these strategies is designed to address the limitations observed in standalone CoT or PoT learning methods, fostering a more holistic development of mathematical comprehension and problem-solving abilities in LLMs.

Experimental Validation

The effectiveness of SAAS was empirically validated through extensive benchmark comparisons and a strategic evaluation of its core components. Results demonstrated that SAAS outperforms existing models and approaches in solving complex mathematical problems, showcasing remarkable improvements, especially in tasks requiring sophisticated reasoning and computational precision. Analyzing the impact of sequential learning and cognitive retention strategies further elucidated their contribution to the overall performance, underscoring the importance of a structured learning progression and the balanced integration of reasoning and computational training.

Implications and Future Directions

The introduction of SAAS heralds significant implications for the advancement of LLM capabilities in mathematical reasoning, with practical applications that extend into coding, scientific analysis, and other domains where numerical and logical comprehension are crucial. The paper's findings encourage further exploration into sequential learning strategies and the optimization of cognitive retention mechanisms, aiming to enrich the problem-solving repertoire of LLMs beyond the mathematical domain. As LLMs continue to evolve, approaches like SAAS offer a blueprint for enhancing their proficiency in areas traditionally marked by human-like reasoning and complex decision-making processes.

Conclusion

The Solving Ability Amplification Strategy (SAAS) represents a substantial step forward in the quest to imbue LLMs with advanced mathematical reasoning and problem-solving skills. By thoughtfully sequencing CoT and PoT learning and incorporating cognitive retention strategies, SAAS not only achieves state-of-the-art performance but also opens new avenues for research into the development of more versatile and capable LLMs. The paper's insights into the synergistic potential of combined learning approaches pave the way for further advancements in the field, promising a future where LLMs can seamlessly navigate the complexities of mathematical reasoning and beyond.

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