Transformers to Predict the Applicability of Symbolic Integration Routines

Abstract

Symbolic integration is a fundamental problem in mathematics: we consider how machine learning may be used to optimise this task in a Computer Algebra System (CAS). We train transformers that predict whether a particular integration method will be successful, and compare against the existing human-made heuristics (called guards) that perform this task in a leading CAS. We find the transformer can outperform these guards, gaining up to 30% accuracy and 70% precision. We further show that the inference time of the transformer is inconsequential which shows that it is well-suited to include as a guard in a CAS. Furthermore, we use Layer Integrated Gradients to interpret the decisions that the transformer is making. If guided by a subject-matter expert, the technique can explain some of the predictions based on the input tokens, which can lead to further optimisations.