Prerequisites for the analysis of the neural networks functioning in terms of projective geometry

Vitulyova, Yelizaveta S.; Bakirov, Akhat; Shaltykova, Dina; Сулейменов, И. Э.

doi:10.1088/1757-899x/946/1/012001

Cited by 15 publications

(6 citation statements)

References 5 publications

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“…However, precisely the considerations of a philosophical nature force us to use an interpretation that based on the neural network model of the noosphere. Moreover, at present there are prerequisites for deciphering the code of neural networks [23,24]; in the future, this will make it possible to reveal those codes that are inherent in the global communication network -the noosphere.…”

Section: Discussionmentioning

confidence: 99%

Analysis of the statistics of information processes in telecommunication networks from the point of view of a neural-network model of the noosphere

Vitulyova,

Bakirov,

Shaltykova

et al. 2023

E3S Web Conf.

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It was found that the distribution of users of social networks by the number of contacts, as well as the statistics of telephone conversations by duration, obtained for different cities on the basis of experimental data, obey the same laws, expressed through a differential equation of the first order. This differential equation contains two phenomenological parameters, one of which is interpreted as the fractal dimension of the communication space, and the second is directly expressed through the Dunbar number or its analogue. Essentially, for all cities under investigation the numerical value of the parameter, interpreted as the fractal dimension of the communication space, remains constant with high accuracy. At the same time, the analogue of the Dunbar number, which describes the distribution of users of social online networks by the number of contacts, correlates with the population of the city. The results obtained are discussed from the point of view of the formation of a global communication network - the noosphere, which, due to the development of telecommunication technologies, is already de facto man-machine system. It is shown that the results obtained confirm the conclusion about the existence of objective laws describing the behavior of human-machine systems, made earlier on the basis of general philosophical considerations.

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Section: Discussionmentioning

confidence: 99%

Analysis of the statistics of information processes in telecommunication networks from the point of view of a neural-network model of the noosphere

Vitulyova,

Bakirov,

Shaltykova

et al. 2023

E3S Web Conf.

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“…Since 𝑒 𝑖 are mutually canceling idempotent elements. Expression (21) unambiguously shows that the result of calculating the product of the "higher" digits really does not completely depend on the result of calculating the product of the "lower" digits.…”

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

confidence: 98%

“…It is appropriate to emphasize that for decrypting algorithms according to which trained neural networks function, multivalued logic is also of interest [20,21].…”

Section: Introductionmentioning

confidence: 99%

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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“…Researchers in [12]- [14] it was shown that there is a very close relationship between the theory of error-correcting coding and the theory of neural networks, which are also often used for digital signal processing [15], [16]. This creates quite definite prospects for the practical use of multivalued logics, which are actively being developed at the present time [17], [18].…”

Section: Introductionmentioning

confidence: 99%

Algebraic fields and rings as a digital signal processing tool

Matrassulova

Vitulyova

Konshin

et al. 2022

IJEECS

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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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Prerequisites for the analysis of the neural networks functioning in terms of projective geometry

Cited by 15 publications

References 5 publications

Analysis of the statistics of information processes in telecommunication networks from the point of view of a neural-network model of the noosphere

Analysis of the statistics of information processes in telecommunication networks from the point of view of a neural-network model of the noosphere

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

Algebraic fields and rings as a digital signal processing tool

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