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

arXiv: https://arxiv.org/abs/2404.14973 · HTML: https://mlsanity.com/paper/2404.14973/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 11 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 6 of 6)

- [Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks](https://mlsanity.com/paper/1503.00075/) (2015)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Can Neural Networks Learn Symbolic Rewriting?](https://mlsanity.com/paper/1911.04873/) (2019)
- [Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition](https://mlsanity.com/paper/1404.6369/) (2014)
- [Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition](https://mlsanity.com/paper/2304.12154/) (2023)
- [Generating Elementary Integrable Expressions](https://mlsanity.com/paper/2306.15572/) (2023)

## Built on by (most cited first, 3 of 3)

- [The Liouville Generator for Producing Integrable Expressions](https://mlsanity.com/paper/2406.11631/) (2024)
- [Transformers to Predict the Applicability of Symbolic Integration Routines](https://mlsanity.com/paper/2410.23948/) (2024)
- [Tree-Based Deep Learning for Ranking Symbolic Integration Algorithms](https://mlsanity.com/paper/2508.06383/) (2025)

## Abstract (arXiv)

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.