标题： 基于树的深度学习用于排序符号积分算法 显示英文标题

标题： Tree-Based Deep Learning for Ranking Symbolic Integration Algorithms

摘要： 符号不定积分在Maple等计算机代数系统中涉及从多种可用方法中选择最有效的算法。 并非所有方法都能解决给定的问题，当有多种方法可行时，尽管结果在数学上是等价的，但其呈现的复杂度可能有很大差异。 传统上，这种选择很少考虑问题实例，导致效率低下。 我们提出了一种机器学习（ML）方法，采用基于树的深度学习模型，在两阶段架构中：首先确定适用于给定实例的方法，然后根据预测的输出复杂度对它们进行排序。 此外，我们发现将数学表达式表示为树结构显著提高了性能，相比基于序列的表示，我们的两阶段框架优于其他ML公式。 使用由六个不同的数据生成器生成的多样化数据集，我们的模型在70,000个示例的保留测试集中几乎达到90%的准确率，以选择最优方法。 在Maple内部测试套件中的独立分布外基准测试中，我们的树变换器模型保持了强大的泛化能力，优于Maple内置的选择器和之前的ML方法。 这些结果突显了数据表示和问题框架在符号计算的机器学习中的关键作用，我们预计我们的方法能够有效地推广到数学软件中的类似优化问题。 显示英文摘要

摘要： 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.