Boost Math Skills in LLMs: Enhance Problem-Solving with Self-Evaluation System

The proposed self-critique pipeline aims to enhance the mathematical and linguistic abilities of large language models (LLMs) for practical deployment by utilizing a math critique model. Unlike existing approaches, the self-critique pipeline achieves a win-win solution by integrating mathematical enhancement into the feedback learning period during LLM alignment, thus improving overall performance on mathematical problem-solving tasks while maintaining general language capabilities. The pipeline consists of two stages: rejective fine-tuning (RFT) and direct preference optimization (DPO). Incorporating real-life scenario data and specialized mathematical data in the training process significantly improves the model’s performance in real-world applications and mathematical reasoning tasks, respectively. Limitations in handling graphic thinking, drawing abilities, and precision calculation capabilities provide insights for future work in integrating multimodal components and enhancing computational accuracy.

Key Takeaways πŸš€

  • The proposed self-critique pipeline aims to simultaneously enhance the mathematical and linguistic abilities of large language models (LLMs) for practical deployment in real-world scenarios.
  • The pipeline integrates mathematical enhancement into the feedback learning period during LLM alignment by utilizing a math critique model derived from the target LLM itself.
  • The self-critique pipeline consists of two stages: rejective fine-tuning (RFT) and direct preference optimization (DPO).
  • The M Aus Rval Benchmark data set is designed to evaluate the proficiency of LLMs in solving complex mathematical problems in real-world scenarios.
  • The self-critique pipeline improves the overall performance of LLMs on mathematical problem-solving tasks while maintaining their general language capabilities, enhancing their practical utility in real-world scenarios.

Introduction πŸ“š

The main motivation behind the proposed self-critique pipeline in the paper is to enhance both the mathematical and linguistic abilities of large language models (LLMs) for practical deployment in real-world scenarios. The pipeline aims to address the challenge of maintaining and improving both language and mathematical abilities in LLMs, unlike existing approaches that focus on either language or mathematical enhancement at the expense of the other.

Self-Critique Pipeline πŸš€

The self-critique pipeline seeks to achieve a win-win solution by integrating mathematical enhancement into the feedback learning period during LLM alignment. It utilizes a math critique model derived from the target LLM itself to provide judging feedback on the LLM’s generated solutions, focusing on generating mathematically accurate and logically consistent responses. This approach eliminates the need for additional external supervisory models and manual annotations, making the training process more efficient and effective.

The pipeline consists of two stages: rejective fine-tuning (RFT) and direct preference optimization (DPO). The RFT stage involves multiple sampling iterations, where certain responses are rejected based on predefined criteria, while the remaining responses are used for supervised fine-tuning. The DPO stage updates the model directly by learning from a pair of correct/incorrect answers, with a focus on challenging problems that were difficult to resolve in the RFT phase.

M Aus Rval Benchmark πŸ“Š

The M Aus Rval Benchmark data set is designed to evaluate the proficiency of LLMs in solving complex mathematical problems in real-world scenarios. It allows for the evaluation of LLMs’ mathematical reasoning abilities under both GPT-4 Turbo and the math critique scoring methods. The data set serves as a benchmark to assess the model’s performance in open-ended mathematical questions and to compare it against other models across various difficulty levels and categories.

Contributions of the Paper πŸŽ‰

The key contributions of the paper in terms of methodology include the development of the self-critique pipeline and the introduction of the M Aus Rval Benchmark data set. The proposed pipeline enhances both mathematical and linguistic abilities of LLMs through a two-stage process involving rejective fine-tuning (RFT) and direct preference optimization (DPO). The pipeline leverages a math critique model to provide judging feedback on generated solutions, focusing on improving mathematical accuracy and logical consistency.

In terms of results, the paper achieves state-of-the-art performance across various data sets, including M Aus Rval, AP 210k math, and the language subset of ALINE bench, surpassing similar-sized LLMs. The methodology significantly improves mathematical capabilities, particularly on open-ended math problems, and demonstrates competitive or superior performance compared to leading proprietary models like GPT-4 1106. Additionally, the paper addresses limitations in handling graphic thinking and drawing abilities and precision calculation capabilities, providing insights for future work in integrating multimodal components and enhancing computational accuracy.

Limitations and Future Work πŸ› οΈ

The limitations and future work mentioned in the paper

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