Do Transformers Understand Polynomial Simplification?

Vishesh Agarwal, Somak Aditya, Navin Goyal

Abstract: Recently researchers have demonstrated that Transformers can be trained to learn symbolic tasks such as solving integration and differential equations in an end-to-end fashion. In these setups, for an input symbolic expression, the Transformer predicts the final solution in a single step. Since such tasks may consist of a sequence of logical steps, question remains whether such networks have understood and learnt individual steps to reach the solution. To take a deeper look, we consider the task of polynomial simplification. 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. For this task, we describe a synthetic Polynomial dataset generation algorithm which generates polynomials with unique proof steps. Then, we conduct an extensive analysis of the Transformer’s abilities to learn the polynomial simplification task along different dimensions.

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