The Analysis On Capabilities For Integer-weight Neural Networks

Artificial neural network (ANN) is partly inspired by biology and is a kind of simulation of the nature of biological neural network. There are two ways for the simulation:the first one is to simulat the structure and mechanism of the biological neural network, and implement the net shape structure of biological neural networks; the other one is to simulat some functions of biological neural networks, such as learning, controlling and recognition. ANN has been widely applied in pattern recognition, signal processing, data forecast, etc. And has achieved great success in these areas.With the rapid development of the application of Embedded Systems (ESs), various kinds of personal handheld devices, intelligent home appliances, car smart devices and other embedded systems play an more important role in our lives. The major intelligence technologies of these embedded systems include:voice recognition, fingerprint recognition, face recognition, temperarure control system, routing system etc. The learning ability, generalization ability and classify ability, of ANN have a congenital advantage in these intelligence applications. So, mapping of resultant ANN onto fast and compact ESs has potential value of applications and bright prospects. But the conventional ANN, which has float weights and non-linear continuous derivable activation function, need to do much float point computation to train the network to fulfill these applications.But ESs require the simplification of store, software and hardware, and need higher real-time capability. In a result, the conventional ANN can’t meet the reqirement of simplification and real-time capability. So, how to optimize the network in order to reduce the consumption of the resource and improve the speed become more importment. This paper has done deep researches on the structure and the operation mechanism of ANN, integer-weight neural network (IWNN), which have a better real time capability and need less resource, will be proposed to be used in the ESs.Recently, IWNN have many successful engineering application cases, but relative theoretical study of capability of IWNN still lags behind. In practical work, there are two ways frequently used to construct the network. The first technique is to forecast the number and precise of the neurons, then reduce or increase the number or precise to checkout the network, after several steps engineers can get a reasonable network structure; the second way is to discretize a real weight network directly. The disadvantages of the first method are the slow and complex construction, the difficulte estimation of initial parameter; by the second method, it is the hard to control the network error and lack theoretical guidance. But we have little material for these engineering problem. However, the domestic and international theoretical research is almost only on the real weight network, the theoretical research of the analysis of performance on the IWNN and the constructing method for IWNN is still few. This paper will study the density, complexity and learning performance of the IWNN base on the three-layer network model, and will offer some theoretical guidance for constructing method.This paper put emphasizes on studying the approximation performance of continuous functions by three-layer IWNN. This paper will give the answer of the question "Can an IWNN network approximat the continuous functions with arbitrarily small error", and also give some theoretical guidance to construct a good IWNN network. The purpose of this paper is to give some qualitative answers for the practical engineering problems and provide theoretical support for more widespread and more successful application of IWNN.