We construct neural network regression models to predict key metrics of complexity for Gr\"obner bases of binomial ideals. This work illustrates why predictions with neural networks from Gr\"obner computations are not a straightforward process. Using two probabilistic models for random binomial ideals, we generate and make available a large data set that is able to capture sufficient variability in Gr\"obner complexity. We use this data to train neural networks and predict the cardinality of a reduced Gr\"obner basis and the maximum total degree of its elements. While the cardinality prediction problem is unlike classical problems tackled by machine learning, our simulations show that neural networks, providing performance statistics such as $r^2 = 0.401$, outperform naive guess or multiple regression models with $r^2 = 0.180$.

翻译：我们构建神经网络回归模型，用于预测双项理想Gröbner基复杂性的关键指标。本研究阐明了为何基于Gröbner计算的神经网络预测并非简单直接的过程。通过采用两种随机双项理想的概率模型，我们生成并公开了一个能够充分捕捉Gröbner复杂性变异特征的大规模数据集。利用该数据训练神经网络，我们预测约化Gröbner基的势及其元素的最大全次数。尽管势的预测问题不同于机器学习所处理的经典问题，但模拟实验表明，神经网络（性能统计量如$r^2 = 0.401$）优于朴素猜测或多元回归模型（$r^2 = 0.180$）。