Neural network with quadratic decision functions have been introduced as alternatives to standard neural networks with affine linear one. They are advantageous when the objects to be identified are of compact basic geometries like circles, ellipsis etc. In this paper we investigate the use of such ansatz functions for classification. In particular we test and compare the algorithm on the MNIST dataset for classification of handwritten digits and for classification of subspecies. We also show, that the implementation can be based on the neural network structure in the software Tensorflow and Keras, respectively.

翻译：具有二次决策函数的神经网络已被提出作为标准仿射线性神经网络的替代方案。当待识别目标具有圆、椭圆等紧凑基本几何形状时，该类网络展现出显著优势。本文研究了此类基函数在分类任务中的应用，具体在MNIST手写数字分类数据集及亚种分类任务上对算法进行测试与比较。此外，我们证明了该实现可分别基于Tensorflow和Keras软件框架中的神经网络结构完成。