Machine Learning for Mathematical Software

Abstract

While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer Algebra Systems. We survey the authors own work and similar applications for other mathematical software. It may seem that the inherently probabilistic nature of machine learning tools would invalidate the exact results prized by mathematical software. However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it, and thus here, machine learning can have a significant impact.

To appear in Proc. ICMS 2018

References in corpus (7)

• Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition
• A Case Study on the Parametric Occurrence of Multiple Steady States
• Improving the use of equational constraints in cylindrical algebraic decomposition
• Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
• Speeding up Cylindrical Algebraic Decomposition by Gröbner Bases
• Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition With Groebner Bases
• Improve SAT-solving with Machine Learning

Cited by in corpus (9)

• Cylindrical Algebraic Decomposition with Equational Constraints
• Using Machine Learning to Improve Cylindrical Algebraic Decomposition
• Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition
• A Triumvirate of AI Driven Theoretical Discovery
• Algorithmically generating new algebraic features of polynomial systems for machine learning
• Improved cross-validation for classifiers that make algorithmic choices to minimise runtime without compromising output correctness
• A machine learning based software pipeline to pick the variable ordering for algorithms with polynomial inputs
• The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition
• Good pivots for small sparse matrices