Neurons on Amoebae
Neurons on Amoebae
复制标题
DOI：
10.1016/j.jsc.2022.08.021
复制
发表时间：
2021-06
期刊：
影响因子：
--
通讯作者：
Jiakang Bao;Yang-Hui He;Edward Hirst
中科院分区：
文献类型：
--
作者：
Jiakang Bao;Yang-Hui He;Edward Hirst
我们应用机器学习的方法，如神经网络，流形学习和图像处理，以研究代数几何和弦理论中的二维变形虫。借助于嵌入流形投影，我们恢复了由所谓的不对称性所得到的复杂条件。在某些情况下，它甚至可以达到99%的准确度，特别是对于F 0的不平衡阿米巴，我们主要关注的是正系数。使用权重和偏差，我们也找到了很好的近似值，以较低的计算成本来确定属的阿米巴。一般来说，模型可以很容易地预测属超过90%的准确率。与类似的技术，我们也调查的隶属度问题，和图像处理的阿米巴直接。
We apply methods of machine-learning, such as neural networks, manifold learning and image processing, in order to study 2-dimensional amoebae in algebraic geometry and string theory. With the help of embedding manifold projection, we recover complicated conditions obtained from so-called lopsidedness. For certain cases it could even reach∼ 99% accuracy, in particular for the lopsided amoeba of F 0 with positive coefficients which we place primary focus. Using weights and biases, we also find good approximations to determine the genus for an amoeba at lower computational cost. In general, the models could easily predict the genus with over 90% accuracies. With similar techniques, we also investigate the membership problem, and image processing of the amoebae directly.