We use ansatz neural network 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：我们采用拟设神经网络模型预测二项式理想的Gröbner基关键复杂性指标。这项研究阐明了为何利用神经网络从Gröbner计算中进行预测并非简单的过程。通过两种随机二项式理想的概率模型，我们生成并公开了一个能够充分捕捉Gröbner复杂性变异的大规模数据集。利用该数据集训练神经网络，我们预测简化Gröbner基的基数及其元素的最大总次数。尽管基数预测问题有别于机器学习处理的经典问题，但模拟结果显示，神经网络（性能统计指标如$r^2 = 0.401$）优于朴素猜测或多元回归模型（$r^2 = 0.180$）。