A new type of neurons for machine learning

In machine learning, an artificial neural network is the mainstream approach. Such a network consists of many neurons. These neurons are of the same type characterized by the 2 features: (1) an inner product of an input vector and a matching weighting vector of trainable parameters and (2) a nonlinear excitation function. Here, we investigate the possibility of replacing the inner product with a quadratic function of the input vector, thereby upgrading the first-order neuron to the second-order neuron, empowering individual neurons and facilitating the optimization of neural networks. Also, numerical examples are provided to illustrate the feasibility and merits of the second-order neurons. Finally, further topics are discussed.