Symbolic Mathematical tasks such as integration often require multiple
well-defined steps and understanding of sub-tasks to reach a solution. To
understand Transformers' abilities in such tasks in a fine-grained manner, we
deviate from traditional end-to-end settings, and explore a step-wise
polynomial simplification task. Polynomials can be written in a simple normal
form as a sum of monomials which are ordered in a lexicographic order. For a
polynomial which is not necessarily in this normal form, a sequence of
simplification steps is applied to reach the fully simplified (i.e., in the
normal form) polynomial. We propose a synthetic Polynomial dataset generation
algorithm that generates polynomials with unique proof steps. Through varying
coefficient configurations, input representation, proof granularity, and
extensive hyper-parameter tuning, we observe that Transformers consistently
struggle with numeric multiplication. We explore two ways to mitigate this:
Curriculum Learning and a Symbolic Calculator approach (where the numeric
operations are offloaded to a calculator). Both approaches provide significant
gains over the vanilla Transformers-based baseline.

该研究旨在研究 Transformers 在多步骤的代数任务中的表现。作者提出了一个合成的多项式数据集生成算法，通过变化系数配置、输入表示、证明粒度和广泛的超参数调整，揭示了 Transformers 在数值乘法方面的困难，并针对此问题探索了课程学习和符号计算器两种方法，两种方法都比基准模型效果显著提升。