Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs

Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the output integral, and the runtime. Choosing the right sub-algorithm for a given problem is challenging: we hypothesise that Machine Learning can guide this sub-algorithm choice. A key consideration of our methodology is how to represent the mathematics to the ML model: we hypothesise that a representation which encodes the tree structure of mathematical expressions would be well suited. We trained both an LSTM and a TreeLSTM model for sub-algorithm prediction and compared them to Maple's existing approach. Our TreeLSTM performs much better than the LSTM, highlighting the benefit of using an informed representation of mathematical expressions. It is able to produce better outputs than Maple's current state-of-the-art meta-algorithm, giving a strong basis for further research.

Generating Elementary Integrable Expressions

There has been an increasing number of applications of machine learning to the field of Computer Algebra in recent years, including to the prominent sub-field of Symbolic Integration. However, machine learning models require an abundance of data for them to be successful and there exist few benchmarks on the scale required. While methods to generate new data already exist, they are flawed in several ways which may lead to bias in machine learning models trained upon them. In this paper, we describe how to use the Risch Algorithm for symbolic integration to create a dataset of elementary integrable expressions. Further, we show that data generated this way alleviates some of the flaws found in earlier methods.