Vector Operations in Neural Network Computations

Abstract

Nonlinearity is an important factor in the biological visual neural networks. Among prominent features of the visual networks, movement detections are carried out in the visual cortex. The visual cortex for the movement detection, consist of two layered networks, called the primary visual cortex (V1), followed by the middle temporal area (MT), in which nonlinear functions will play important roles in the visual systems. These networks will be decomposed to asymmetric sub-networks with nonlinearities. In this paper, the fundamental characteristics in asymmetric and symmetric neural networks with nonlinearities are developed for the detection of the changing stimulus or the movement detection in these neural networks. By the optimization of the asymmetric networks, movement detection Equations are derived. Then, it was clarified that the even – odd nonlinearity combined asymmetric networks, has the ability of generating directional vector in the stimulus change detection or movement detection, while symmetric networks need the time memory to have the same ability. Further, the vector operations in the neural network are developed. These facts are applied to two layered networks, V1 and MT.