LLM Reasoning Engine: Specialized Training for Enhanced Mathematical Reasoning (2025)

Abstract: Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical reasoning skills. Existing approaches to address this challenge often rely on ensemble methods and suffer from the problem of data scarcity in target domains. In this work, we present a novel method to enhance the capabilities of LLMs in mathematical reasoning tasks. Motivated by the need to bridge this gap, our approach incorporates a question paraphrase strategy, which aims to diversify the linguistic forms of mathematical questions to improve generalization. Additionally, specialized training objectives are employed to guide the model’s learning process, focusing on enhancing its understanding of mathematical concepts and reasoning processes. We conduct experiments on four datasets using different LLMs, and demonstrate the effectiveness of our approach in improving LLMs’ performance on mathematical reasoning tasks. Our findings underscore the significance of our methodology in advancing large language models and their potential implications for real-world applications that require mathematical reasoning abilities.

## introduction in recent years, large language models (llms) @xcite have emerged as powerful tools in the field of machine learning, demonstrating remarkable performance in a wide range of downstream benchmarks. their ability to understand and generate natural language text has revolutionized various applications, from language translation @xcite to question answering systems @xcite . central to their success is their ability to perform com-plex reasoning, enabling them to tackle complex problems with impressive accuracy and efficiency. however, while llms excel in many domains, they face challenges when it comes to solving mathematical problems. mathematical reasoning often requires intricate logical operations and a deep understanding of mathematical concepts @xcite , posing significant hurdles for conventional llm architectures. moreover, the scarcity of data in the mathematical domain @xcite further compounds these challenges, limiting the performance and generalization of these llms. some existing methods @xcite attempt to address these challenges by employing ensemble techniques, where multiple llms collaboratively solve mathematical problems. however, these methods can still be further improved, particularly in enhancing the performance of individual llms and mitigating performance degradation over extended reasoning steps. a major challenge when applying llms to complex mathematical problems is error propagation, especially in tasks requiring long reasoning chains. figure 1 illustrates this issue with an example from the gsm8k dataset @xcite , solved by the llama2-7b model @xcite . the problem involves multiple intermediate steps to reach the correct solution. however, the model makes an error in the initial steps, which cascades through subsequent stages of reasoning. this occurs because each reasoning step depends on the accuracy of preceding steps; even a minor initial error can compound, ultimately leading to significant deviations from the correct solution. this phenomenon highlights the limitations of current llms in maintaining accuracy across long reasoning sequences and underscores the need for improved methodologies to mitigate error propagation and enhance performance in mathematical tasks. in this paper, we propose novel approaches to address the limitations of existing methods in solving mathematical problems with llms. our contributions include the introduction of new training objectives designed to uncover underlying patterns in data, thus improving model performance. additionally, we leverage data augmentation techniques to maximize the utility of existing datasets to finetune llms, enhancing their effectiveness in mathematical reasoning tasks. to evaluate the efficacy of our proposed methods, we conduct experiments using four open-source llms-llama (touvron et al., 2023a), llama2 (touvron et al., 2023b), mistral (jiang et al., 2023), and mixtral (jiang et al., 2024)-on four widely used mathematical reasoning datasets: gsm8k @xcite , math @xcite , gsm8k_hard @xcite , and svamp @xcite . our results demonstrate significant performance improvements, underscoring the effectiveness of our methods in advancing the mathematical reasoning capabilities of llms. in summary, this paper presents novel contributions towards improving the performance of llms in solving mathematical problems, addressing the challenges posed by complex reasoning and data scarcity. our findings have implications for advancing the field of machine learning and expanding the applicability of llms to various problem domains. ## background the intersection of machine learning and mathematical reasoning has received significant attention from researchers seeking to enhance the capabil-ities of llms in solving complex mathematical problems. in this section, we review the previous literature exploring various approaches and methodologies to address the challenges posed by mathematical reasoning tasks and highlight the advances made in this domain. ## methodology the motivation for our methodology arises from the observation that while llms excel in various natural language processing tasks, their performance in mathematical reasoning remains suboptimal. this gap is primarily due to the inherent complexity of mathematical problems, which often requires intricate reasoning and logical deduction @xcite . furthermore, the limited availability of annotated data in the mathematical domain @xcite presents a significant obstacle to effectively training llms for such tasks. to overcome these challenges, we propose a novel approach that combines question paraphrasing techniques with tailored training objectives to strengthen the mathematical reasoning capabilities of llms. an overview of our proposed pipeline is illustrated in figure 2 . ## experiments mathematical reasoning challenges llms, requiring both natural language understanding and mathematical problem-solving skills. evaluating the effectiveness of llms in mathematical reasoning is crucial for advancing state-of-the-art nlp techniques and expanding their applicability across diverse problem domains. this study seeks to assess the performance of various llms on mathematical reasoning tasks through targeted experiments. ## analysis and discussion in this section, we delve into a comprehensive analysis and discussion of the experimental results, focusing on the effectiveness of our proposed method in enhancing llms' capabilities in mathematical reasoning tasks. we begin by dissecting the model's performance over varying numbers of reasoning steps, shedding light on the impact of our approach on problem-solving efficiency. subsequently, we present findings from an ablation study aimed at elucidating the importance of individual components within our proposed methods. finally, through a series of case studies, we illustrate both the successes and limitations of our approach, pro-viding valuable insights for future research directions. ## conclusion in this study, we addressed the challenge of enhancing llms' capabilities in mathematical reasoning tasks. our proposed method leverages innovative techniques to improve llms' understanding of mathematical concepts and reasoning processes. through rigorous experimentation, we demonstrated the effectiveness of our approach in improving llms' performance on various mathematical problems. our research advances the field of natural language processing by providing a comprehensive approach to enhancing llms' capabilities in mathematical reasoning tasks. by identifying key factors influencing model performance and proposing effective solutions, we bridge the gap between natural language understanding and mathematical reasoning. our study advances llms' reasoning capabilities, paving the way for broader applications in automated theorem proving, mathematical education, and ai-assisted research in scientific domains. future work could explore integrating symbolic computation with llms to further enhance mathematical reliability.