Vector Operations in Neural Network Computations

Vector Operations in Neural Network Computations

Naohiro Ishii (Aichi Institute of Technology, Toyota, Japan), Toshinori Deguchi (Gifu National College of Technology, Gifu, Japan), Masashi Kawaguchi (Suzuka National College of Technology, Suzuka, Japan) and Hiroshi Sasaki (Fukui University of Technology, Fukui, Japan)
Copyright: © 2013 |Pages: 13
DOI: 10.4018/ijsi.2013040104
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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.
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Asymmetric Biological Neural Network

First, we present the asymmetric neural network in the catfish retina, which was studied by Naka, et al (Sakuranaga & Naka, 1987; Naka, Sakai, & Ishii, 1988; Ishii et al., 2007) as shown in Figure 1. A biological network of catfish retina shown in Figure 1, might process the spatial interactive information between bipolar cells B1 and B2. The bipolar B cell response is linearly related to the input modulation. The C cell shows an amacrine cell, which plays an important role in the nonlinear function as squaring of the output of the bipolar cell B2.

Figure 1.

Asymmetric network with linear and squaring nonlinear pathways, which is extracted from catfish retinal network

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