Hilbert series, machine learning, and applications to physics
Hilbert series, machine learning, and applications to physics
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DOI：
10.1016/j.physletb.2022.136966
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发表时间：
2021-03
影响因子：
4.4
通讯作者：
Jiakang Bao;Yang-Hui He;Edward Hirst;Johannes Hofscheier;A. Kasprzyk;Suvajit Majumder
中科院分区：
文献类型：
--
作者：
Jiakang Bao;Yang-Hui He;Edward Hirst;Johannes Hofscheier;A. Kasprzyk;Suvajit Majumder
我们描述了简单的机器学习方法如何成功地预测希尔伯特级数（HS）的几何性质。回归器预测投影空间中的嵌入权重的平均绝对误差为0.01，而分类器预测维度和Gorenstein指数的准确率为> 90%，标准误差为0.5%。二进制随机森林分类器设法区分底层HS是否描述了一个完整的交叉点，准确率超过95%。神经网络（NN）表现出成功识别HS从Gorenstein环到相同的精度顺序，而生成的“假”HS证明微不足道的NN区分与那些相关的三维Fano品种考虑。
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to∼ 1 mean absolute error, whilst classifiers predict dimension and Gorenstein index to> 90% accuracy with∼ 0.5% standard error. Binary random forest classifiers managed to distinguish whether the underlying HS describes a complete intersection with high accuracies exceeding 95%. Neural networks (NNs) exhibited success identifying HS from a Gorenstein ring to the same order of accuracy, whilst generation of “fake” HS proved trivial for NNs to distinguish from those associated to the three-dimensional Fano varieties considered.