Learn Beyond The Answer: Training Language Models with Reflection for Mathematical Reasoning

TL;DR

This paper introduces reflective augmentation, a novel training technique for language models that embeds problem reflection into each instance, improving mathematical reasoning especially in complex, reflective scenarios.

Contribution

It proposes a new reflective augmentation method that enhances models' understanding by encouraging reflection and abstraction during training, beyond traditional data augmentation.

Findings

Improves performance on complex mathematical reasoning tasks.

Complementary to existing data augmentation techniques.

Validates effectiveness through extensive experiments.

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.