Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
LCP
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"
Image for the paper "Neurons on Amoebae"

Neurons on amoebae

Machine learning

Machine-learning 2-dimensional amoeba in algebraic geometry and string theory is able to recover the complicated conditions from so-called lopsidedness.

Neurons on Amoebae

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\sim 99% accuracy, in particular for the lopsided amoeba of F0F_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.