Classification with neural networks with quadratic decision functions

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, such as 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 Tensorflowand Keras, respectively.