{"id":742414,"date":"2021-04-26T21:23:42","date_gmt":"2021-04-27T04:23:42","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=742414"},"modified":"2021-10-29T08:46:45","modified_gmt":"2021-10-29T15:46:45","slug":"polysimp","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/polysimp\/","title":{"rendered":"Analyzing the Nuances of Transformers’ Polynomial Simplification Abilities"},"content":{"rendered":"

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<\/em> 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.<\/p>\n","protected":false},"excerpt":{"rendered":"

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 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