NEUROCOMPUTER OPERATING IN THE RESIDUE CLASS SYSTEM
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Abstract
Objective. The aim is to justify the possibility of creating a data processing neurocomputer (NC) based on the use of one kind of non-positional machine arithmetic residue class system (RCS). Methodology. In the basis of research of the problem of NC creation there is a methodology based on the use of methods of synthesis of non-positional code representation structures (NPCRS), as well as on the realization of data processing methods in RCS. The totality of these methods is realized on the basis of using three basic principles of data processing in RCS: independence of processing of numerical values of the residue content; equality of functioning of data processing channels; low-digit data in the numerical representation of the residue content. Results. The results of the conducted research confirm the possibility of creation of NC using RCS as a basis for information processing. Formal (semantic) similarity of mathematical models, as well as analytical similarity of artificial neural systems representation with the basic formulas of data processing represented in RCS is presented. The correspondence of the operation of weighted summation in neuron to the operation of addition by modules in RCS is established. It is shown that the activation function of a neuron can be efficiently approximated using multiplication operations by modules in RCS. It is analytically shown that the representation of synapse weights in NPCRS elements allows to realize parallel computations similar to parallel information processing in the human brain. Scientific Novelty. For the first time, a comprehensive study of the influence of RCS on such key characteristics of NK neurocomputers as performance in processing large amounts of data, reliability of information storage and transmission, and overall fault tolerance has been carried out. A new approach to the construction of NC based on the use of neural network mathematical basis based on non-positional RCS codes is proposed. The introduction of this mathematical apparatus into the structure of neural networks provides the possibility of achieving higher accuracy and naturalness in modeling the hierarchical organization inherent in biological neural networks of the human cognitive system. Practical Significance. The prospects for further research are the development of specific hardware implementations of super-performance and highly fault-tolerant NC based on RCS, as well as the study of the possibility of applying this approach to solve specific problems of artificial intelligence, such as pattern recognition and natural language processing.
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