Neurons on Amoebae

TL;DR

This paper employs machine learning techniques to analyze 2D amoebae in algebraic geometry and string theory, achieving high accuracy in classifying complex conditions and properties like genus and membership.

Contribution

It introduces the application of neural networks and manifold learning to study amoebae, providing efficient approximations for genus and membership classification.

Findings

Achieved up to 99% accuracy in certain amoeba classifications

Predicted genus with over 90% accuracy using machine learning models

Successfully applied image processing to analyze amoebae structures

Abstract

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 $\sim99\%$ 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.