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Tensor-matrix theory of Artificial Intelligence

Goal: Expand situation awareness about the current state of Tensor-matrix theory of Artificial Intelligence and evolving this theory

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Vadym Slyusar
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The article proposes ways to solve the problem of structural synthesis of neural networks architectures; based on non-traditional approaches to their analytical formalization and application of new ones data processing operations. The example of the CIFAR10 dataset proves the possibility of improving the accuracy of the solution image classification tasks within an alternative architecture with expandable input and narrowing structures of trained neural networks. The results of the application of input expanding image taken with Resizing and Conv2DTranspose layers at the input trained neural networks indicate the effectiveness of solving such classification problems by example CIFAR10 dataset. Achieved on the basis of the Xception neural network, the average classification accuracy of 10 classes CIFAR10 images are 97.3%. The side effect of pre-scaling images is leveling the accuracy of the classification of different classes, which allows us to consider such a change in size as an option data augmentation in the dataset. Tensor-matrix methods have been introduced for further development of this approach formalization of the description of neural networks on the basis of the penetrating end product of matrices and its block ones modifications. On this basis, a number of new convolution and maxpooling operations are proposed, as well as combinations on input of the narrowing segment not only symmetrically enlarged image, but also its variants obtained on the basis of a generalized penetrating product. It is about drawing images expanded by rows of pixels (horizontally) and columns (vertically), as well as a combination of several different options symmetrical image extensions on the principle of constructing a pyramidal segment of the PSPNet neural network.
Vadym Slyusar
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В работе предложена совокупность новых тензорноматричных операций для обработки данных в нейронных сетях.
Vadym Slyusar
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Vadym Slyusar
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In this article, the theory of tensor matrices U-net and GANs was proposed (in Russian, but all mathematical formulas will be understandable for any language)
Vadym Slyusar
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Detection and recognition of objects in images is the main problem to be solved by computer vision systems. As part of solving this problem, the model of object recognition in aerial photographs taken from unmanned aerial vehicles has been improved. A study of object recognition in aerial photographs using deep convolutional neural networks has been carried out. Analysis of possible implementations showed that the AlexNet 2012 model (Canada) trained on the ImageNet image set (China) is most suitable for this problem solution. This model was used as a basic one. The object recognition error for this model with the use of the ImageNet test set of images amounted to 15 %. To solve the problem of improving the effectiveness of object recognition in aerial photographs for 10 classes of images, the final fully connected layer was modified by rejection from 1,000 to 10 neurons and additional two-stage training of the resulting model. Additional training was carried out with a set of images prepared from aerial photographs at stage 1 and with a set of VisDrone 2021 (China) images at stage 2. Optimal training parameters were selected: speed (step) (0.0001), number of epochs (100). As a result, a new model under the proposed name of AlexVisDrone was obtained. The effectiveness of the proposed model was checked with a test set of 100 images for each class (the total number of classes was 10). Accuracy and sensitivity were chosen as the main indicators of the model effectiveness. As a result, an increase in recognition accuracy from 7 % (for images from aerial photographs) to 9 % (for the VisDrone 2021 set) was obtained which has indicated that the choice of neural network architecture and training parameters was correct. The use of the proposed model makes it possible to automate the process of object recognition in aerial photographs. In the future, it is advisable to use this model at ground stations of unmanned aerial vehicle complex control when processing aerial photographs taken from unmanned aerial vehicles, in robotic systems, in video surveillance complexes and when designing unmanned vehicle systems.
Vadym Slyusar
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In this paper, the tensor-matrix model of LeNet5 is proposed.
Vadym Slyusar
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This presentation is devoted to the tensor-matrix theory of the traditional approach to multichannel signal parameters measurements based analytical model of signals and the tensor-matrix theory of Neural Networks for Mechanical Measurements. This presents the basic concepts of matrix operations that can be used for ultrasonic, sonar, radar systems, wireless communications, and more systems with digital beamforming. It is intended for individuals in the field who wish to gain a general view of this area. For additional information, read the references on the final slides.
Vadym Slyusar
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In this paper proposed Data Farming methodology based on Pandemic models (SIR Model etc.)
Vadym Slyusar
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The versions of the mathematical formalization of neural hypernetworks based on the family of penetrating face products of matrices and tensors expanded to the block matrices are considered. As an example, the matrix A in the penetrating face product of matrix A and block matrix B can be considered as a picture pixels matrix on the input of a neural network. In this case, every block of matrix B corresponds to a block of weight coefficients for a few neurons in one layer of the neural network. Further steps of data processing in the considered neural network can be varied depending on the structure and type of layers of the neural network. In the case of convolutional neural networks the result of penetrating face products of matrices A and B has to be multiplied by a vector of one’s 1. This multiplication can produce a scalar, a vector-row, a vector, or a matrix. The result of such multiplication can be used as argument of an activation function. For the data processing in hierarchies of neural hypernetworks clusters, the generalized face-splitting products of matrices and block versions of these multiplications can be used. The operation of block penetrating Kronecker product of matrices has been introduced to simulate the input layer of a neural hypernetwork which processes multiple video streams from several video cameras in different spectral ranges in parallel by a set of several neural networks.
Vadym Slyusar
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This presentation is considered different aspects of the concept of the networked distributed engine control system (DECS) of future air vehicles. These aspects include the following: the structure of multiple networks similar to NATO Generic Vehicle Architecture (NGVA), the role of Artificial Intelligence (AI) in DECS, and the use Augmented Reality (AR) as Human-Machine Interface between AI and pilots. Deployment of AI solutions for monitoring equipment in on-board infrastructure can be provided on physical or virtual servers and in the clouds. In this case, it is possible to use various methods of alerting the pilot and ground personnel on the basis of AR. The use of AI allows covering an unlimited set of scenarios, to provide an assessment of the likelihood of equipment failure, classification alarm is normal, and recognition of the development of defects. To collect Big Data from sensors and the pre-processing of this data before a machine learning (ML) procedure it is proposed to form data sets with the help of the face-splitting matrix product. To decrease the time of reaction of Neural Networks it has been suggested the implementation of advanced tensor-matrix theory on the basis of penetrating face product of matrices. Other important results of the report are a possible version of the AR data format for DECS and a proposal about the use of non-orthogonal frequency discrete multiplexing (N-OFDM) signals to data transfer via fibre optics.
Vadym Slyusar
added a research item
This report is considered different aspects of the concept of the networked distributed engine control system (DECS) of future air vehicles. These aspects include the following: the structure of multiple networks similar to NATO Generic Vehicle Architecture (NGVA), the role of Artificial Intelligence (AI) in DECS, and the use Augmented Reality (AR) as Human-Machine Interface between AI and pilots. Deployment of AI solutions for monitoring equipment in on-board infrastructure can be provided on physical or virtual servers and in the clouds. In this case, it is possible to use various methods of alerting the pilot and ground personnel on the basis of AR. The use of AI allows covering an unlimited set of scenarios, to provide an assessment of the likelihood of equipment failure, classification alarm is normal, and recognition of the development of defects. To collect Big Data from sensors and the pre-processing of this data before a machine learning (ML) procedure it is proposed to form data sets with the help of the face-splitting matrix product. To decrease the time of reaction of Neural Networks it has been suggested the implementation of advanced tensor-matrix theory on the basis of penetrating face product of matrices. Other important results of the report are a possible version of the AR data format for DECS and a proposal about the use of non-orthogonal frequency discrete multiplexing (N-OFDM) signals to data transfer via fibre optics.
Vadym Slyusar
added a research item
The article discusses the possibilities of using the face splitting product of matrices for analyzing the topology of a multi-rank tactical network. As an example, a fragment of the communication network of a tactical unit is used, presented in the form of a graph consisting of 4 vertices and 5 edges. To analyze the structure of the graph, it is proposed to use secondary incidence matrices and cooccurrence matrices obtained using the face-splitting product of the original incidence matrices. This approach makes it possible to determine how many common vertices a particular pair or triple of edges has, how many edges in a given graph form a particular vertex in combination with other vertices, which pairs of vertices in the investigated graph form an edge, the number of vertices encountered in a route formed by a specific combination of pairs edges. In particular, it is possible to obtain information, important for analyzing the load in the network, about the number of edges with which this edge is connected by means of contact at the vertices of the graph bordering it. This makes it possible to formulate the requirements for the bandwidth associated with a specific edge of the communication line, which in case of critical situations (suppression of standard communication lines by interference or equipment failure) must have a stability margin for the data transmission rate.
Vadym Slyusar
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The preprint considers the method, which gives the answer to the question: How can one find out about "preferred" patterns based on the 1st preference, e.g. "if one chooses X as a first preference, then the second choice is likely to be..."? This method was proposed by the author by preparation of an answer to the discussion: https://www.researchgate.net/post/How_can_I_analyze_answer_patterns
Vadym Slyusar
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In this paper the tensor-matrix theory of Artificial Intelligency is considered and evolved.
Vadym Slyusar
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Vadym Slyusar
added 2 research items
Запропоновано удосконалений метод аналізу мультирангових мереж зв‘язку на основі теорії графів, який відрізняється формуванням торцевих добутків матриць інци-дентності. The improved method for the analysis of multi-rank communication networks based on graph theory is proposed, which differs in the formation of face-splitting products of incidence matrices.
Рассмотрены варианты применения торцевого произведения матриц инцидентности для решения задач анализа текстов, в частности, определения частоты встречаемости трех, четырех и более слов в предложениях отдельно взятого корпуса текста. Variants of using the face-splitting product of incidence matrices for solving problems of text analysis, in particular, determining the frequency of occurrence of three, four or more words in sentences of a separate text corpus are considered.
Vadym Slyusar
added a research item
Запропоновано удосконалений метод аналізу мультирангових мереж зв’язку на основі теорії графів, який відрізняється формуванням торцевих добутків матриць інцидентності. Моделювання та аналіз змін топології мобільної радіомережі й візуалізація результатів забезпечується за допомогою геоінформаційної системи ArcGIS-10.
Vadym Slyusar
added a research item
Запропоновано удосконалений метод аналізу мультирангових мереж зв’язку на основі теорії графів, який відрізняється формуванням торцевих добутків матриць інцидентності. Моделювання та аналіз змін топології мобільної радіомережі й візуалізація результатів забезпечується за допомогою геоінформаційної системи ArcGIS-10.
Vadym Slyusar
added a research item
Рассмотрены варианты применения торцевого произведения матриц инцидентности для решения задач анализа текстов, в частности, определения частоты встречаемости трех, четырех и более слов в предложениях отдельно взятого корпуса текста. Variants of using the face-splitting product of incidence matrices for solving problems of text analysis, in particular, determining the frequency of occurrence of three, four or more words in sentences of a separate text corpus are considered.
Vadym Slyusar
added a research item
In this paper the method of the face-splitting product of matrices for NLP is considered.
Vadym Slyusar
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Vadym Slyusar
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An improved method for the analysis of multi-rank communication networks based on graph theory is proposed, which differs in the formation of face-splitting products of incidence matrices.
Vadym Slyusar
added a research item
The article reveals an original approach to the organization of professional-oriented training and retraining of specialists in agrarian universities, which is based on the example of creating syllabuses and curriculum design in cooperation with business companies that are developers of information systems (IS). Cloud computing based IS, which were designed to automate the accounting of production and management processes in agrarian enterprises, allow students to attend training and perform a wide range of production tasks. The authors describe the main stages and results of the implementation of different ERP and CRM cloud computing systems in the training programs for bachelor and master courses in management, marketing, agronomy, as well as methods for organizing various forms of training for practicing professionals from agrarian enterprises.
Vadym Slyusar
added 9 research items
This lecture presents the basic concepts of a lot of matrix operations and related applications for digital beamforming, which was proposed by author in 1996-1998. This lecture can be used for radar system, smart antennas for wireless communications, and other systems applying digital beamforming. It's intended for individuals new to the field who wish to gain a basic understanding in this area. For additional information, check out the reference material presented at the end of this lecture.
The new concept of face-splitting and transposed face-splitting matrix products is determined; its main characteristics and modifications of the new types of products for module matrices are considered
When considering the multicoordinate digital antenna arrays (DAA) with mutual coupling of channels there arises a problem of the compact matrix record of the responses of the reception channels. For the solution of the given problem it is proposed to operate with a special type of the product of matrices, called the “face-splitting” and “transposed face-splitting” product (TFSP), respectively. With the aid of the TFSP it is possible to obtain the variant of the analytical model of a two-coordinate DAA with mutual coupling
Vadym Slyusar
added a project goal
Expand situation awareness about the current state of Tensor-matrix theory of Artificial Intelligence and evolving this theory