Breaking the Data Barrier in Learning Symbolic Computation: A Case Study on Variable Ordering Suggestion for Cylindrical Algebraic Decomposition
This work addresses the efficiency bottleneck in symbolic computation for applications like formal verification and automatic theorem proving, though it is incremental as it builds on existing learning-based approaches.
The paper tackled the data scarcity problem in learning symbolic computation by designing connected tasks to generate abundant annotated data for pre-training a Transformer model, which after fine-tuning on CAD ordering datasets, produced variable orderings that significantly outperformed the best heuristic methods on average.
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations in high dimension. This creates a fundamental barrier on labelled data acquisition if leveraging supervised deep learning to accelerate symbolic computation. Cylindrical algebraic decomposition (CAD) is a pillar symbolic computation method for reasoning with first-order logic formulas over reals with many applications in formal verification and automatic theorem proving. Variable orderings have a huge impact on its efficiency. Impeded by the difficulty to acquire abundant labelled data, existing learning-based approaches are only competitive with the best expert-based heuristics. In this work, we address this problem by designing a series of intimately connected tasks for which a large amount of annotated data can be easily obtained. We pre-train a Transformer model with these data and then fine-tune it on the datasets for CAD ordering. Experiments on publicly available CAD ordering datasets show that on average the orderings predicted by the new model are significantly better than those suggested by the best heuristic methods.