# Neuron network for correcting mistakes in modular neuron computers

FIELD: computer science.

SUBSTANCE: network has end ring neuron network, Hopfield neuron network, demultiplexer and multiplexer.

EFFECT: broader functional capabilities, higher efficiency, higher speed of operation.

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The invention relates to computer technology and can be used in modular neurocomputer systems.

A device for monitoring and correcting errors in a redundant modular code (Patent No. 2022472, 5 H 03 M 13/00, RU, BI, No. 20, 1994), containing the input code Converter, myCitadel output Converter, unit groups of elements of comparison, the block groups of elements OR block elements I.

However, this device has the following disadvantages: low speed, large hardware costs, small functionality, because the device uses a single redundant module; error correction is carried out on a large module, equal to machine adjustment range of numbers.

The closest to the essence of the technical solution of the invention is a device for detecting errors in the information presented in the system of residual classes (A.S. 798846, G 06 F 11/081, USSR, BI No. 3, 1981), containing the input register, the circular shift register, the transmitter of the numbers in the system of residual classes (JUICE) in the generalized positional notation (SVR), the block comparison of the projection of numbers with a constant group of elements And / OR.

A disadvantage of the known device is a low speed, which is determined by the computation of all n projections (where n is the number of bases JUICE).

The purpose of the invention is a speed boost error correction redundant modular code.This objective is achieved in that the device containing the neural network of end rings (NJC), connected to the input data, a demultiplexer, a neural network (NS) hopefield, multiplexer, the input of which is the output of the NS error correction.

The proposed device uses a method of detecting and correcting errors based on the use of modular NJC and the national Assembly of hopefield.

Known methods of detection and correction of errors when using the excess JUICE from two reference bases is not always possible to correct a single error, if the error appeared simultaneously with the overflow. This is one example, when the residual arithmetic is not able to completely solve the problem of the absolute correction of erroneous data.

To solve this problem we will use the properties of the JUICE and the national Assembly, namely error detection will conduct on the basis of the properties of the JUICE, and the localization and correction of errors based on the properties of the NA. Architecture NA detection and error correction of the data presented in modular code is a multi-layer network, consisting of the NJC error detection and NA of hopefield for localization and bug fixes.

Modular NJC detects an error in the data presented in the JUICE with the bases of p_{1
p2,... , pnaccording to the value of the coefficients anand an-1generalized positional numeral systems (SVR). If an=an-1=0, then there is no error, otherwise there is an error.}

Signals a_{n}and a_{n-1}served on the control inputs of the demultiplexer and multiplexer. If a_{n-1}=a_{n}=0, then undistorted data via the demultiplexer and the multiplexer receives the output of the correction block of data.

If a_{n}≠_{}0 or a_{n-1}≠_{}0, i.e. the data are erroneous bits, the activation of governors (address) input multiplexer and demultiplexer, and data error through the demultiplexer is fed to the input of the national Assembly of hopefield in binary code, i.e. each residual discharge represented by a binary code. The hopefield network with associative property allows you to recover corrupted data. A common bit of code is determined by the expression

where: n - number of modules JUICE, p_{i}module JUICE. The hopefield network consists of a single layer of neurons that decide asynchronously, the relationship between them is instant and all communication is symmetric, i.e. w_{ij}=w_{ji}then the synaptic weight of the national Assembly have the form

The functioning of the network is determined by the expression

where: w_{ij}- the i-th synaptic weight of the j-th neuron; x_{i}- the i-th element of the input signal network;- the i-th element of the input vector; y_{j}the output of the j-th neuron; N is the dimensionality of the input vector; M is the number of samples (codes allowed). The network operates cyclically. During operation decreases the energy function

In the relaxation process, the network reaches a steady state in which none of its elements does not change its state.

The network selects the pattern with the minimum haminhagim distance from the presented input vector by activating only one of the network output corresponding to this standard. The Hamming distance between two binary sequences X and X’ is defined as the number of coordinates in which the numbers are different. Hemmingway distance is an example of a measure of similarity, or, rather, differences, originally introduced for binary functions image in Cartesian space. It is applicable for comparison of any ordered sets, taking discrete values, and is probably the best known measure of similarity between the digital codes.

For example, in excess JUICE that consists of 4 modules p_{1}=2, p_{2}=3, p_{3}=5, p_{4}=7, input n the Bor will consist of 9 bits.
If you take the modules p_{3}and R_{4}excessive, then the operating range will be equal to R_{1}·_{}p_{2}=6, and areas of legal and illegal values in binary code can be represented in the form

For example, the distorted vector X’=(1, 0, 1, 3)=(1, 00, 001, 011), it is a vector X=(1, 0, 3, 3)=(1, 00, 011, 011), then for binary sequences X and X' Hemmingway distance is defined as

Here the function ƒ is dependent on the number of modules JUICE, having sets the value "1".

It is easy to show that in this example, the logical unit will be modulo p_{3}=5, i.e. the error occurred on this module.

The hopefield network determines the number of standard nearest to the required vector, this is the way(1, 00, 011, 011), as he distorted vector smallest Hemmingway distance. Thus, using the associative property and Hemmingway distance, hopefield network locates and corrects the error. To increase network capacity and improve the quality of pattern recognition you can use the network of higher order.

As input Hopfield net, you can use the binary signals 1 and 0, or enter denote respectively +1 and-1.

Combined input element is defined by the expression

where s_{i}indicates the status of the item number i.

When updating the status changes in accordance with rule

where s_{j}- sign function s_{j}=sign{net_{j}).

The weight values for the Hopfield net are determined directly from the data, and there is no need of training in the more usual sense.

The hopefield network behaves as a memory, and for storing a separate vector represents the calculation of the direct product of the vector with itself. This is determined by the weight matrix for the Hopfield net, in which all diagonal elements must be set to 0. Thus, the weight matrix corresponding to the conservation of the vector X, is given by the expression

where I is the identity matrix.

Consider the method of determining the weights of the Hopfield net.

Example 1. To find the set of weights of the Hopfield net, the corresponding storing one binary image Y=100011011, then

When you subtract the identity matrix nullable diagonal elements, and the matrix will look like the following:

The first column corresponds to the weight values of the first neural element, the second second, etc. hopefield Network can work with Hronom or asynchronous modes.

Asynchronous mode. If the input network file undistorted input vectorall items after the upgrade will be in the same condition, and items will be updated in a random order. Suppose, at time t_{0}=1 will select the first neural element whose state will change. The first element will be updated by multiplying the vector tips on the first column of the matrix of weights, then

We see that the first item remains in the same state. Similarly, you can ensure that updates will remain unchanged and the other elements.

Now consider, how will it change the state of the neural elements, if the input network is fed distorted vector. Items are updated in a random order, but for definiteness we check update elements accept the natural order, i.e. the 1, 2, 3, 4, 5, 6, 7, 8, 9, then

Thus, the element 1 will remain in the same state. The following is item 2.

Item 2 is also located in the same state. Find the s_{3}=-6, sign(-6)=-1, s_{4}=-6, sign(-6)=-1. Now test

This shows that neural element 5 has changed its state from -1 to 1. When Yes is ineichen the functioning of the network ceases to change its state,
i.e. the elements of s_{6}, s_{7}, s_{8}and s_{9}will remain in the same state, which indicates the transition network in a stable state.

The result has been a correction to an error image with the X values’=(1, 0, 1, 3) to X=(1, 0, 3, 3).

Synchronous mode. In this mode, the network can be represented as y(t+1)=sign(s(t))

Let, in the first stage to the input of the network is served distorted vector Y=(100001011), then

In 2,3 and 4 bars s(1)=s(2)=s(3)=-6, a sign(-6)=-1, i.e. the state of the elements have not changed. In the 5th step of s(4)=8, a sign(8)=1, i.e. the 5th element has changed its state from -1 to 1. Now Y=[1 -1 -1 -1 1 1 -1 1 1]. 6, 7, 8 bars s(5)=8, s(6)=-8, s(7)=8 and s(8)=8, sign(s(8))=1, sign(s(-8))=-1. After the 5-th quantum state of the elements is not changed. The result was a hotfix 5-th category.

To save multiple images in a Hopfield net, you must calculate all direct products of each vector, and thus obtained the weight matrix to fold.

Example 2. To determine the weight matrix Hopfield net, corresponding to the conservation of the following two vectors

[-1 1-1-11 -1 -1 1 -1], [1 -1 -1-111-11 1].

The weight matrix of these vectors has the form

fold matrix and zero diagonal elements

Can the conclude, the combination of JUICE and NA provides detection and correction of errors in all cases, when the full range occurs simultaneously with the appearance of errors. The proposed approach allows to build high-performance and reliable computing structure.

The drawing shows the NS network for error correction in modular neural computers.

The national Assembly consists of the input data bus 1, the NJC 2, consisting of n subnets (where n is the number of bases of the system of residual classes), the demultiplexer 3, Hopfield net 4, a multiplexer 5, the output data bus 6, the inner tire 7, 8 and 9, the control bus by the demultiplexer 10, the bus control multiplexer 11.

Input 1 is fed to the input of the NJC 2 and the demultiplexer 3. Address (control) inputs of the demultiplexer is not active. The NJC 2 calculates the coefficients of the round. If the coefficients and_{n}=a_{n-1}=0, then there is no error, the generated address signals 10 and 11, which are received respectively to the input of the demultiplexer 3 and the multiplexer 5. Under the action of the signal demultiplexer 10 3 switches the data input of the multiplexer 5, and under the action of signal 11 to the output of the multiplexer 5, bus 6.

If the input data has an error, then the older coefficients SVR a_{n}and a_{n-1}generated by the NJC 2, not 0. At the address inputs of the demultiplexer 3 bus-10 code comes to the th commutes input data bus 8.
Input data error is fed to the input Hopfield net 4, which are fixed, and the bus 9 corrected is fed to the input of the multiplexer 5 which, under the action code received at the address input bus 11, and transmits them to the input 6. Thus, the detection and error correction is carried out for three cycles synchronization: two cycle synchronization of the NJC and one cycle synchronization Hopfield net which provides high speed correction numbers.

The advantage of this invention over the known is that the correction number is performed without determining the n projections.

Neural network for error correction in a redundant modular code that contains the neural network of hopefield, a demultiplexer, a multiplexer, a neural network end ring that is used to calculate the coefficients of the generalized positional numeral systems, which are address signals of the demultiplexer, in which the input data is fed to the input of the neural network of the end rings and the information inputs of the demultiplexer, the address inputs to receive control signals from the output of the neural network of the end rings, the outputs of the demultiplexer is connected to the input of the multiplexer and the input of the neuron Hopfield net, the outputs of which are the inputs of the multiplexer, the address input of which is connected to control what the output of the neural network finite rings, the outputs of the multiplexer are the outputs of the neural network for error correction in modular neural computers.

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