Generalized backpropagation algorithm for training second‐order neural networks - Fan, Fenglei; Cong, Wenxiang; Wang, Ge (International journal for numerical methods in biomedical engineering, 2018)
The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to second‐order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear quadratic operation. A single second‐order neurons already have a strong nonlinear modeling ability, such as implementing basic fuzzy logic operations. In this paper, we develop a general backpropagation algorithm to train the network consisting of second‐order neurons. The numerical studies are performed to verify the generalized backpropagation algorithm. The main contribution of this paper is to propose deep neural networks consisting of quadratic artificial neurons and an associated generalized backpropagation algorithm and illustrate such networks with a number of examples. Interestingly, each quadratic neuron can be interpreted as a fuzzy logic gate, and a neural network of quadratic neurons can be naturally interpreted as a deep fuzzy logic system. Hence, we suggest to understand and develop quadratic neural networks in light of fuzzy logic theory and techniques for applications in which fuzzy logic is relevant.