Imagine you are in a supermarket. You have two bananas in your basket and want to buy four apples. How many fruits do you have in total? This seemingly straightforward question can be challenging for data-driven language models, even if trained at scale. However, we would expect such generic language models to possess some mathematical abilities in addition to typical linguistic competence. Towards this goal, we investigate if a commonly used language model, BERT, possesses such mathematical abilities and, if so, to what degree. For that, we fine-tune BERT on a popular dataset for word math problems, AQuA-RAT, and conduct several tests to understand learned representations better. Since we teach models trained on natural language to do formal mathematics, we hypothesize that such models would benefit from training on semi-formal steps that explain how math results are derived. To better accommodate such training, we also propose new pretext tasks for learning mathematical rules. We call them (Neighbor) Reasoning Order Prediction (ROP or NROP). With this new model, we achieve significantly better outcomes than data-driven baselines and even on-par with more tailored models. We also show how to reduce positional bias in such models.

本文研究 BERT 语言模型是否具备数学能力，从而能够解决单词数学问题，提出了一种预训练任务 Neighbor Reasoning Order Prediction (ROPS)，针对数学过程提供了半正式的解释步骤，通过新的模型和预训练任务，实现了比数据驱动基线和结构更加优化的模型更好的结果，并且还展示了如何减少这种模型中的位置偏差。

通过预测推理顺序来衡量和提高BERT的数学能力