Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems
This work addresses the need for interpretable heuristic optimization in computer algebra systems, though it appears incremental as it builds on existing human-designed heuristics.
The authors tackled the problem of optimizing variable ordering heuristics in cylindrical algebraic decomposition by representing human-designed heuristics as constrained neural networks and using machine learning to refine them, resulting in new heuristics of similar complexity.
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may be represented as a constrained neural network. This allows us to then use machine learning methods to further optimise the heuristic, leading to new networks of similar size, representing new heuristics of similar complexity as the original human-designed one. We present this as a form of ante-hoc explainability for use in computer algebra development.