Tree-Based Deep Learning for Ranking Symbolic Integration Algorithms

TL;DR

This paper introduces a tree-based deep learning framework for selecting and ranking symbolic integration algorithms, significantly improving efficiency and accuracy over traditional methods and prior ML approaches.

Contribution

It presents a novel two-stage ML architecture using tree-structured representations for better algorithm selection and ranking in symbolic integration tasks.

Findings

Achieves nearly 90% accuracy on a large test set.

Maintains strong generalisation on out-of-distribution data.

Outperforms Maple's built-in selector and previous ML models.

Abstract

Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results, though mathematically equivalent, can differ greatly in presentation complexity. Traditionally, this choice has been made with minimal consideration of the problem instance, leading to inefficiencies. We present a machine learning (ML) approach using tree-based deep learning models within a two-stage architecture: first identifying applicable methods for a given instance, then ranking them by predicted output complexity. Furthermore, we find representing mathematical expressions as tree structures significantly improves performance over sequence-based representations, and our two-stage framework outperforms alternative ML formulations. Using a diverse dataset generated by six distinct data generators, our models achieve nearly 90% accuracy in selecting the optimal method on a 70,000 example holdout test set. On an independent out-of-distribution benchmark from Maple's internal test suite, our tree transformer model maintains strong generalisation, outperforming Maple's built-in selector and prior ML approaches. These results highlight the critical role of data representation and problem framing in ML for symbolic computation, and we expect our methodology to generalise effectively to similar optimisation problems in mathematical software.