# The Liouville Generator for Producing Integrable Expressions

arXiv: https://arxiv.org/abs/2406.11631 · HTML: https://mlsanity.com/paper/2406.11631/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 7 of 7)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level](https://mlsanity.com/paper/2112.15594/) (2021)
- [Can Neural Networks Learn Symbolic Rewriting?](https://mlsanity.com/paper/1911.04873/) (2019)
- [The Use of Deep Learning for Symbolic Integration: A Review of (Lample and Charton, 2019)](https://mlsanity.com/paper/1912.05752/) (2019)
- [Generating Elementary Integrable Expressions](https://mlsanity.com/paper/2306.15572/) (2023)
- [Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs](https://mlsanity.com/paper/2404.14973/) (2024)

## Built on by (most cited first, 2 of 2)

- [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)

There has been a growing need to devise processes that can create comprehensive datasets in the world of Computer Algebra, both for accurate benchmarking and for new intersections with machine learning technology. We present here a method to generate integrands that are guaranteed to be integrable, dubbed the LIOUVILLE method. It is based on Liouville's theorem and the Parallel Risch Algorithm for symbolic integration. We show that this data generation method retains the best qualities of previous data generation methods, while overcoming some of the issues built into that prior work. The LIOUVILLE generator is able to generate sufficiently complex and realistic integrands, and could be used for benchmarking or machine learning training tasks related to symbolic integration.