Learn Beyond The Answer: Training Language Models with Reflection for Mathematical Reasoning
Zhihan Zhang, Zhenwen Liang, Wenhao Yu, Dian Yu, Mengzhao Jia, Dong Yu, Meng Jiang
2024-06-19
Summary
This paper discusses a new method for training language models to improve their ability to solve mathematical problems. The authors introduce a technique called reflective augmentation, which helps models think more deeply about problems rather than just providing quick answers.
What's the problem?
While existing methods for training language models have focused on increasing the amount of data they learn from, they often only prepare the models for basic question-answering tasks. This approach can limit the models' ability to handle more complex problems that require deeper understanding and reflective thinking. As a result, these models may struggle with tasks that go beyond simple calculations or straightforward answers.
What's the solution?
To address this issue, the authors propose reflective augmentation, which involves embedding reflection into each training example. This means that during training, the model is encouraged to think about different ways to approach a problem and consider various perspectives. By engaging with abstractions and analogies, the model learns to understand the material more thoroughly. The authors conducted extensive experiments to show that this method improves performance not only in standard mathematical tasks but also in more challenging scenarios that require critical thinking.
Why it matters?
This research is important because it enhances how language models learn and solve problems, making them more capable of tackling complex mathematical reasoning tasks. By fostering reflective thinking, this approach could lead to better educational tools and AI systems that can assist students and professionals in understanding and solving difficult problems effectively.
Abstract
Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on broadening the training set with various data augmentation techniques, which is effective for standard single-round question-answering settings. Our work introduces a novel technique aimed at cultivating a deeper understanding of the training problems at hand, enhancing performance not only in standard settings but also in more complex scenarios that require reflective thinking. Specifically, we propose reflective augmentation, a method that embeds problem reflection into each training instance. It trains the model to consider alternative perspectives and engage with abstractions and analogies, thereby fostering a thorough comprehension through reflective reasoning. Extensive experiments validate the achievement of our aim, underscoring the unique advantages of our method and its complementary nature relative to existing augmentation techniques.