HCFNN: High-order coverage function neural network for image classification

Recent advances in deep neural networks (DNNs) have mainly focused on innovations in network architecture and loss function. In this paper, we introduce a flexible high-order coverage function (HCF) neuron model to replace the fully-connected (FC) layers. The approximation theorem and proof for the HCF are also presented to demonstrate its fitting ability. Unlike the FC layers, which cannot handle high-dimensional data well, the HCF utilizes weight coefficients and hyper-parameters to mine underlying geometries with arbitrary shapes in an n-dimensional space. To explore the power and potential of our HCF neuron model, a high-order coverage function neural network (HCFNN) is proposed, which incorporates the HCF neuron as the building block. Moreover, a novel adaptive optimization method for weights and hyper-parameters is designed to achieve effective network learning. Comprehensive experiments on nine datasets in several domains validate the effectiveness and generalizability of the HCF and HCFNN. The proposed method provides a new perspective for further developments in DNNs and ensures wide application in the field of image classification. The source code is available at https://github.com/Tough2011/HCFNet.git