Distributed memory of neural networks and the problem of the intelligence`s essence

It is shown that algebraic fields and rings can become a very promising tool for digital signal processing. This is mainly due to the fact that any digital signals change in a finite range of amplitudes and, therefore, there are only a finite set of levels that can correspond to the amplitudes of a signal reduced to a discrete form. This allows you to establish a one-to-one correspondence between the set of levels and such algebraic structures as fields, rings, etc. This means that a function that takes values in any of the algebraic structures containing a finite set of elements can serve as a model of a signal reduced to a discrete form. A special case of such a signal model are functions that take values in Galois fields. It is shown that, along with Galois fields, in certain cases, algebraic rings contain zero divisors can be used to construct signal models. This representation is convenient because in this case it becomes possible to independently operate with the digits of the number that enumerates the signal levels. A simple and intuitive method for constructing rings is proposed, based on an analogy with the method of algebraic extensions.

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“…based on (32), each element of 𝐴 can be associated with a matrix defined by the next formula as (33).…”

Section: Resultsmentioning

confidence: 99%

Algebraic fields and rings as a digital signal processing tool

Matrassulova

Vitulyova

Konshin

et al. 2022

IJEECS

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“…The mobile boom and social commerce are a consolidated market full of applications with a substantially accelerated growth of payments via mobile devices among technology companies such as Google, Facebook, Alibaba, Amazon, and other companies consolidating digital ecosystems so that consumers can do everything they need, for example, make payments, transfers, purchases, communicate with friends, meet people without leaving their platforms and, consequently, conduct social commerce (Wang & Lobato, 2019;Suleimenov et al, 2022). Trends in social media is a tool that allows buying and selling goods and services through social networks such as Instagram, Facebook, and Twitter, which already include new and practical ways to make purchases.…”

Section: Discussionmentioning

confidence: 99%

Product Development and Application of Chinese Traditional Art Derivatives in the Context of New Media

Li¹

2022

SMC

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The relevance of the study lies in the fact that relying on the development of the modern media environment, the traditional culture of China can re-enter the vision and life of people against the background of a new era, and the excellent intangible cultural legacy will be continuously transmitted from generation to generation. Therefore, it is important to delve into the traditional techniques and artistic characteristics of products to properly use the unique elements and symbols of art derivatives, boldly combining them with the cultural background and features of the current era that are being introduced into people's daily lives. The purpose of the study is to analyse the role and importance of combinations of art derivatives in cultural and creative products and to consider their subsequent development in the environment of new media. The following techniques were used to achieve the purpose of the study: deduction, descriptive, and comparative methods. The results determined that by involving Chinese traditional art derivatives, it is possible to develop more diverse, innovative products in the context of modern mass media that consider the aesthetics and functionality of the product and allow satisfying aesthetic emotions and vital needs of modern people. Derivative arts follow from the concept of financial derivatives and refer to many extended services and products designed and manufactured in accordance with culture. Taking cultural elements as a creative basis, a profit-making model that uses its potential resources develops peripheral creations and then brings them to market for sale. The high added characteristics of cultural derivatives play a role in improving the cultural taste and cultural image of the country, acting as a true embodiment of the external appearance and inner spirit, historical and realistic culture. The practical importance lies in the use of the results and conclusions of the study in the development of products that include the traditions and legacy of the Chinese people.

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“…Indeed, consider the product of two numbers written in the form (7). We have 𝑢 (1) 𝑢 (2) = (𝑒 1 𝑢 1 (1) + 𝑒 2 𝑢 2 (1) + ⋯ + 𝑒 𝑁 𝑢 𝑁 (1) )(𝑒 1 𝑢 1 (2) + 𝑒 2 𝑢 2 (2) + ⋯ + 𝑒 𝑁 𝑢 𝑁 (2) ) (20) or 𝑢 (1) 𝑢 (2) = 𝑒 1 𝑢 1 (1) 𝑢 1 (2) + 𝑒 2 𝑢 2 (1) 𝑢 2 (2) + ⋯ + 𝑒 𝑁 𝑢 𝑁 (1) 𝑢 𝑁…”

Section: Number Systems With a Hybrid Base As The Basis Of The Partia...mentioning

confidence: 99%

“…Of course, these ideas so far seem to be largely fantastic, however, there is no doubt that the establishment of real algorithms that the human brain uses allows for significant progress in this direction. Moreover, in order to understand what "artificial intelligence" is, it is necessary to understand what intelligence as such is [26,27]. At the same time, there is no doubt that these algorithms cannot be reduced to binary logic [22,23].…”

Section: Introductionmentioning

confidence: 99%

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Convolutional neural networks from the perspective of the problems of multivalued logic

Vitulyova,

Matrassulova,

SULEIMENOV

et al. 2023

Preprint

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It is shown that it is possible to reduce the operations performed by convolutional neural networks to algebraic, and then to operations of multivalued logic. The tool for this is signal models, which are functions that take values in Galois fields and algebraic rings. This approach, among other things, allows us to switch to the use of partial convolutions, which significantly simplify the analysis of digital signals and images. Such convolutions are performed directly in terms of Galois fields, which makes it possible to use a digital analogue of the classical convolution theorem. The advantage in this regard is the possibility of using a digital analogue of transfer functions, because in terms of Fourier-Galois spectra, the convolution operation is reduced to the multiplication operation by the transfer function. This, in turn, allows us to exhaustively describe a convolutional neural network through a set of transfer functions that take values in Galois fields. The close connection between Galois fields and multivalued logics makes it possible to describe the functioning of convolutional neural networks using variables of multivalued logic.

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Distributed memory of neural networks and the problem of the intelligence`s essence

Cited by 13 publications

References 20 publications

Algebraic fields and rings as a digital signal processing tool

Algebraic fields and rings as a digital signal processing tool

Product Development and Application of Chinese Traditional Art Derivatives in the Context of New Media

Convolutional neural networks from the perspective of the problems of multivalued logic

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