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.
翻译:我们运用机器学习方法,如神经网络、多重学习和图像处理等,以在代数几何学和弦理论中研究二维阿默巴。通过嵌入多重投影,我们从所谓的偏斜性中恢复了复杂的条件。对于某些情况,它甚至可以达到$sim99 ⁇ $的精确度,特别是偏斜的阿默巴(from $_0)和正系数,这是我们主要关注的重点。我们用权重和偏差,也能找到好的近似值,以较低的计算成本来确定阿默巴的基因。一般来说,模型可以很容易地以超过90美元的孔径预测这种基因。用类似的技术,我们还调查会员问题,直接处理阿默巴的图像。