Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs
This work addresses a domain-specific challenge in symbolic integration for users of systems like Maple, offering an incremental improvement over current methods.
The paper tackled the problem of selecting sub-algorithms for symbolic integration in Computer Algebra Systems like Maple, using machine learning to improve output quality and runtime, with the TreeLSTM model outperforming both an LSTM and Maple's existing approach.
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.