Neural networks with quadratic decision functions have been introduced as alternatives to standard neural networks with affine linear ones. They are advantageous when the objects or classes to be identified are compact and of basic geometries like circles, ellipses 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：二次决策函数神经网络作为标准仿射线性神经网络的一种替代方案被提出。当待识别对象或类别具有紧凑且基本几何形状（如圆形、椭圆等）时，该模型具有显著优势。本文研究了此类试探函数在分类任务中的应用。特别地，我们在MNIST手写数字数据集和亚种分类任务上对该算法进行了测试与比较。同时，我们证明了该实现可分别基于Tensorflow和Keras软件中的神经网络架构构建。