This paper proposes a new type of parallel-hierarchical network - a machine learning technology based on the completion of G-transformations. The network contains horizontal and vertical branches, which create a hierarchical structure. Each vertical and horizontal branch undergoes Gtransformation, which functions by calculating the differences of its elements at every step, and on selected elements. The selected elements are multiplied by the quantity of received non-zero differences. Elements calculated in this way present input data for further network transformations. When the horizontal and vertical branches are formed, their elements shift in time, which determines the formation of tail and intermediate network elements. The risk of erroneous calculations is reduced in a parallel-hierarchical network because when processing information in the presented network, the sum of the resulting elements, i.e. tail elements, are equal to the sum of the input network elements. This presents the ability to lower the risk of erroneous calculations, which assists in controlling the equality of the sums of the tail elements and the sums of the input elements. The obtained results can be used to solve a wide range of problems in various systems that require complex operations and risk assessment, such as comparison between or partial searches of digital images.
The possibilities for computational facilities have reached that critical moment where theoretical and applied research have revealed constraints in their application for the solution of a number of serial arithmetic problems using computers of the first five generations. For the parallel processing of information, the concept of evolutional improvements in computing and micro processing facilities have turned out to be nonefficient.
Constantly changing requirements regarding real-time signal processing and operation rate of the equipment has shown the necessity of creating computational structures with new architecture, enabling the processing of enormous data arrays with a high processing rate. We can state that nowadays we are approaching a new and important stage in the development of engineering facilities intended for processing both one-dimensional signals, and images.
The progress of computational facilities comprises the evolutionary transition from conventional von Neumann computational structures to “expert systems” and intelligent neural engineering systems, simulating the brain activity of human beings, and the intelligent computational facilities of the sixth generation.
These latest achievements require the reconsideration of Charles Babbage’s idea regarding the logic structure of computers and the transition to other physicaltechnological fundamentals of information presentation, approaching natural parallel transformation and hierarchical processing.
Since electronic devices have closely approached the physical limit of operations, the solution of the problem of information parallel processing, namely, real-time image processing, completely depends on the development of fast-acting and parallel intelligent computational processes, operational algorithms and architectures which are oriented on neural-like principles of information processing and transformation.
The existing methods of designing conventional algorithms and the architecture of computers do not meet the requirements of those algorithmic and architectural solutions that were achieved while designing computational structures with high levels of parallelism. 2
The Fundamentals of PHCS theory are based on learning and creation of
mathematical models of PH transforms writing, transmission, processing and presentation of
machine information [
The requirements, regarding similar networking structure, that can find wide application in theory and practice of various branches of science and technology as universal tool for investigation of information fields, and include conventional (regarding software part) and non-conventional (including, on the one hand, requirements, concerning flexible reconfiguration of basic algorithmic structure for performing intellectual operations – preprocessing, analysis and synthesis of information fields, on the other hands – engineering, that realize PH transforms). To find mathematically substantiated connections between the quality level of concrete algorithms and architecture of PHCS with maximum possible efficiency of PH transform, we formulate the theorem of limiting compression of information.
Theorem 1.1. For PН transform in conditions of admissible choice of numerical information at each level of its processing, there exists minimum time of transform, where the amount of output coefficients of transformation with greatest probability meets the requirements of ideal model.
Let where = 1, 2, . .. is the time of selection of random element from information array, we denote by = 1 + 2 + ⋯ + the time of selection of all the elements from input array of information. If the elements of input array of information are independent random values, distributed according to a definite rule, then, due to identify of operations, performed in each cycle, 1, 2, … are equally distributed independent values.
Let ( ) be the function of random value distribution , i.e., ( ) = ( ≥ ). We denote by ( ) the number of cycles of input array elements selection, – is the number of similar elements in input array of information.
We can find probabilities distribution of this random value, using function ( ). { ( ) = − } = − ≤ − { ≤ }. The difference ( ) − − ( ) we will denote as { ( ) = − }. We investigate time = − of element selection, at which the probability { ( ) = − } will be the greatest, in case, if value has the density , then it is not difficult to find − . It is sufficient to solve the equation:
Actually event { ( ) = } = − ≤ ≤ = − ≤ ∩ { ≥ } , then − − = 0 (1.1) Hence, to investigate the process of information transformation it is important to find the function − ( ) – the probability of the fact, that during time the selection occurs of − of various elements from input data array by − steps and value − – the time, at which probability { ( ) = − } will be the greatest.
To find − ( ) it is necessary to make assumption regarding the distribution of random value , = 1, 2, . .. It is quite natural to assume, that obeys to normal distribution. Let us consider in details this assumption. Let random value 1, 2, … have normal distribution law with parameters and , then is also distributed normally, but according to parameters and √ .
, − = ( − ) 2 − 2 ( 1 −
), − 1 ), (1.3) rithmic facilities. computational structures.
If we assume in the expression (1.3) = 0, then − = . In the given case time of transformation is maximum and is defined by the number of input elements. If element and does not depend on the dimensionality of input array, what was to be proved. ─ Corollary 1. The maximum speed of PH read/write of information is achieved by quantization of optimum criteria time by a number of serially formed coefficients (tail elements) of PH transformation. ─ Corollary 2. To achieve real-time scale at minimum complexity of parallelhierarchal algorithmic and engineering facilities, the operands of numerical field must be writing, storing and reading of information is performed by means of PH codes. Known serial logic-time codes – are codes, oriented on achieving processed on the basis of the method of PH transformation; and while maximum possible speed at minimal possible consumption of power for their preservation, PH codes for parallel writing-reading of information are codes, oriented at obtaining maximum possible compression and algorithmic speed at minimum complexity of algo─ Corollary 3. PH transformation allows to realize the principle of distributed networking processing, that is very important while realization of uniform neural-like 3
Special software However, network
were more or less uniform environment, as it is in classic form in acoustics and optics, then we would deal with wave, generated by point source. In case of
network the situation will be different. If for any non-zero elements propagating at great values differs greatly from the metrics of physical space in the network, then the results will be passages from one area into another and behavior will differ by far less regularity than phenomena of the wave type, used in classical physics. That is why, while modeling such processes, new approaches, taking into account non-uniformities of network space, are required. In this case, we come to the conclusion that natural neural networks are non-uniform and have a characteristic 3D architecture. At the same time, it is known, that N networks do not take into account non-uniformity and 3D dimensionality of natural neural networks. Further, these very ideas, regarding non-uniformity, S-dimensionality and presence of signal delay in the network laid the foundation of construction PH network. As we will see in the following sections, the topology of PH network, unlike the known artificial neural networks is not accidental. The topology of natural neural networks, that assigns the method of network cells connection, is, probably defined genetically, on the global level, that is why connections are not absolutely accidental.
The presentation of this dynamic structural complex on a semantic level is one of the chapter's tasks.
The basis of notions about such complex forms the following provisions. This, first of all, refers to addition of excitations at the moment of combining of various stimulations. First, the fact, that the cortex of cerebral hemisphere contains a great number of nervous cells, where afferent impulses converge (they carry excitations to central nervous system), these impulses arrive from various receptors- visual, auditory, thermal, muscle, etc. This proves the availability of complex mechanism of interaction between various cortex zones.
The availability of such mechanism of interaction assumes such characteristic
features of computation organization in the cortex: topographic character of video
image, simultaneity (parallelism) of signals actin, mosaic structure of the cortex [
On structural level, the organization of cortex zones in the form of interacting neural networks can be presented, as it is suggested in Fig. 1. Here, each layer of cortex zones is presented in the form of neural network as neurobiological process of hierarchically interdependent interaction of convergent-divergent structures. However, outputs of the neural networks of the same name of each of cortex zones form corresponding inputs for the next cortex zone. The term outputs of the name means the availability of multiple correlative process of coincidence of these inputs signals in time-neural networks are, probably, the ideal tool that can operate in a steady-state mode in conditions of uncertainty. Neural networks, functioning on the principle of dynamic multifunctionality, include interaction of convergent-divergent structures in horizontal and vertical directions and form 3D architecture. The structure of such interaction differs from similar ones, that paths of horizontal routes, due to complexity of different schemes of convergent-divergent processes, vary (change genetically at defined level). The path of these routes can slightly vary in the process of training. One of the central ideas of this article is realization of such statement. How is real time can the redundancy of multistage structure (for instance, neural network) can be optimized on the level of its inter element bonds? The answer to this question can be the suggested concept of multistage network. Formation of multistage network assumes the process of serial transformation of correlated space areas and creation of decor related in time element of physical environment while its transition from one stable state into another.
Such process of image analysis is performed at many stages, each of which includes the many stages, each of which includes the realization of above-mentioned procedure. The condition of complex image transition into higher level is dynamics of processing in time in parallel channels of lower level. The resulted in space-time area image components.
For better understanding of the suggested neural network, we draw certain semantic analogies. Imagine that a group of researchers jointly solves certain scientific problem. Each of researches has his own knowledge regarding this problem: all of them propose their ideas and reach common conclusion, creating matrix of opinions 1 of the first level of discussion. This judgment in the process of discussion can be revised. Each revision, by virtue, is a new general judgment. Mathematical description of this process will form 2nd level of discussion (network) by means of formation of matrix 2 elements. In this case, matrix 2 rows – in the terminology of our example – is time sequence of general judgment formation. The first intermediate result of this discussion will be décor related in time with all other following judgment and presents, the first impression (initial solution) of the given problem. At each following level of problem solving, further revision of the first intermediate results in the discussion and formation of the matrix of judgments . Such revision is carried out each time, when all the judgments at the given moment of time in certain approximation converge. This occurs in the case, when certain general judgment that satisfies all the participants is formed from numerous non-converged judgments. Intermediate results of the discussion are revised results of the previous level of the discussion. General result of the discussion is serial process of multistage revision of the problem being solved and consists of separate intermediate judgments. That is why parallel hierarchical process can be defined as simultaneous analysis of certain phenomena (object) by means of hierarchies’ allocation of most efficient notions about it.
Let us consider in more details a process of G-transformation [
The example of semantic organization of this process [
Concrete semantic content of the nodes of the formed network, can be, for instance, 11 – small object moves, 12– speed up quickly, 13– object has extended form; 14 – mainly of grey color, 15 – considerable black color on the boundaries of the object, 16 – white color is noticed on the object, 17 – moves dawn with great speed, 18 – slightly changes the direction of the motion, 19 – one edge of the object has curved form, 21 – object is of great color and moves at the speed of the bird, 22– if it is a bird, then the speed is high, 23 – moves swiftly, 24 – I have never seen the bird at such coloration, 25 – unusual coloration, 26 – probably, starts diving, 27 – quickly goes out for diving, 28 – speed does not drop, 29 – by speed looks like wild bird, 210 – there are different colors, 211 – the color resembles the color of wild bird, 212– enters into nose dive, 213 – same route of motion as the wild bird, 214 – by form resembled wild bird, 215 – by color does not resemble ordinary bird, 216 – curved edge looks like a beak of the bird, 31 – if it is a bird, then it is very maneuverable with unusual colouring, 32 – speed increase, 33 – many-hued colouration, 34 – continues diving, 35 – by speed and the form resembles birds of prey, 36 – colour is the same as the colour of bird of prey, 37 – by route of motion and by the form of the beak – it is, probably, a bird of prey; 41 – by the route of motion and speed of motion, form and colour it resembles a bird of prey.
From the considered example, it is obvious that the suggested semantic PH
network (Fig. 2) – is semantic organization of dynamic data structure [
Unlike the known structures of semantic networks [
By analogy with known apparatus of formation and storage of information about the object in the form of complex packages, called frames, in the suggested structure of semantic network, information about the object is stored in hierarchically organized frames. Each frame is described by its functional row. For instance, for the considered example (Fig.2), the frames are formed from such blocks of the network: 1st frame –11 → 14 → 17 → 21; 2nd frame – 12 → 15 → 18 → 22 → 24 → 26 → 28 → 210 → 212 → 31; 3rd frame – 13 → 16 → 19 → 23 → 25 → 27 → 29 → 211 → 213 →→ 214 → 215 → 216 → 31 → 32 → 33 → 34 → 35 → 36 → 37 → 41.
Final information about the object is stored in tail blocks of frames, i.e., for out example – 21, 31, 41.
One of the central ideas of this article is realization of such statement. How is real
time can the redundancy of multistage structure [