Learn Beyond The Answer: Training Language Models with Reflection for
  Mathematical Reasoning
Authors: name: Zhihan Zhang, name: Zhenwen Liang, name: Wenhao Yu, name: Dian Yu, name: Mengzhao Jia, name: Dong Yu, name: Meng Jiang
Organization: University of Notre Dame DM2 Lab

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.