General Backpropagation Algorithm for Training Second-order Neural Networks
This work addresses a method for training a specific type of neural network, which is incremental as it extends existing backpropagation techniques to a new neuron architecture.
The paper tackles the problem of training neural networks with second-order neurons by developing a general backpropagation algorithm, and numerical studies verify its effectiveness.
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 2nd 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 2nd order neurons already has a strong nonlinear modeling ability, such as implementing basic fuzzy logic operations. In this paper, we develop a general backpropagation (BP) algorithm to train the network consisting of 2nd-order neurons. The numerical studies are performed to verify of the generalized BP algorithm.