Analyzing the Nuances of Transformers' Polynomial Simplification Abilities
This work addresses a specific bottleneck in symbolic mathematical reasoning for AI research, offering incremental improvements in handling numeric operations.
The study investigated Transformers' difficulties with numeric multiplication in polynomial simplification tasks, finding that both Curriculum Learning and a Symbolic Calculator approach significantly improved performance over baseline models.
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.