Neurons on Amoebae

06/07/2021

∙

by   Jiakang Bao, et al.

∙

0

∙

share

We apply methods of machine-learning, such as neural networks, manifold learning and image processing, in order to study 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 (e.g. lopsided amoeba with positive coefficients for F_0), it could even reach ∼99% accuracy. 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.