JP2714600B2 - Associative neurocomputer - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a configuration of an interconnected neurocomputer in an array, and in particular, an exclusive-OR based neuron is arranged adjacently in at least a two-dimensional structure. The configuration of the associative neurocomputer.

It has been shown by Hopfield et al. That combinatorial and optimization problems can be solved by interconnecting analog elements consisting of integrators and quantizers, and that such neurocomputers can be formed using VLSI technology. It has become Generally, there is a combination problem called an NP problem, and this NP problem requires exponential time when a general-purpose sequential computer is used. However, if a neurocomputer with extremely high computational parallelism is used, NP
It may be possible to find a solution to the problem in a practical time. For example, in the traveling salesman problem to find the optimal solution for traveling through cities on the shortest route, there are about 181441 possible combinations even when the number of cities is 10. This problem
If a Hopfield type neurocomputer is used, a highly accurate approximate solution can be obtained with very few calculations. In order to solve the NP problem, neurocomputers aim to artificially realize information processing processes similar to those of the brain and nerves of living things. In a neurocomputer, many neurons are connected to each other and perform calculations and storage in cooperation with each other. A Neumann computer in which one central processing unit sequentially processes according to a program is essentially a neurocomputer. The principle is different.

A basic network for realizing a neurocomputer is called a neural network. In a neural network, the internal state transitions so that the energy function converges to a minimum point. If the output pattern at the convergence point is controlled so as to match the expected pattern, the associative processing can be performed on the neural network.

In such a neural network, the interconnection problem of how to arrange two or three dimensions of two or more neurons on an LSI chip or wafer and how to connect them to each other. There are many indispensable problems, such as a communication problem of how to transmit a signal and a learning problem of how to determine a connection state between neurons.

[Conventional technology]

FIG. 13 is a basic conceptual diagram of a Hopfield type neural network. This neural network constitutes a 4-bit A / D converter, in which 1 is an integrator and 2 is a quantizer. The output value of each neuron consisting of the integrator 1 and the quantizer 2 is a digital value. The value obtained by multiplying the output of each neuron by the weight coefficient is fed back to the input of another neuron.
The variable input to the integrator 1 of each neuron is the sum of values obtained by multiplying the output variable by a weighting factor at the grid point 3 at the connection. For example, the output variable voltage V ₁ which is the output of the quantizer 2
(4) is doubled and input to the second neuron, quadrupled and input to the third neuron, multiplied by 8 and input to the fourth neuron. Further, for example, the input of the second neuron, that is, the differential variable is −V × 2, X × 2, V ₁ ×
2, V ₃ × 8, V ₄ × 16. This differential variable is integrated by the integrator 1 to become a state variable. The quantizer 2 compares the value of the state variable with the threshold value h and quantizes the value into binary. In this neural network, 2 corresponding to the analog input variable X
The digital variable of the value is output as 4 bits. Assuming that the output variables are V ₁ , V ₂ , V ₃ and V ₄ , Is controlled to be satisfied. At this time, the energy function is Becomes

The first item of equation (2) is the square of the number obtained by subtracting the right side from the left side of equation (1), and equation (2) indicates that the output voltage is 0 or 1
Is represented as a binary value corresponding to.

In this neural network, the energy function E in equation (2) is controlled to be minimized, and output variables V ₁ , V ₂ , V ₃ , and V ₄ at the value of E = 0 are obtained, and this is called AD. The result of the conversion. Therefore, this neural net solves the combination problem of decomposing the given input variable X into the form on the left side of equation (1). A combination problem that expresses a given variable by the sum of required variables is an NP problem, and it is known that a Neumann computer generally takes exponential time. The neural network can solve such an NP problem by advanced parallel processing, that is, it can be calculated by analog delay time.

FIG. 14 is a conceptual diagram of a conventional neural network with a learning function. It is a hierarchical structure of the network, and has an input layer 5,
There is an intermediate layer 6 between the output layers 7. If the unit of each layer is a neuron and the sum of input values weighted is higher than the threshold value h, a value is generated at the output. At this time, a variable weighting coefficient W is added to each of the coupling sections between the units.
The input signal 8 is transmitted from the input layer 5 to the output layer 7. On the other hand, learning proceeds from the output layer 7 to the input layer 5. The learning means finding a difference between an actual output and a desired output value, that is, the teacher signal 10, and finding a connection state and a weight coefficient of each layer so that the error signal 12 of the difference becomes small. That is,
When an input signal 8 is given to each unit of the input layer 5, the signal is converted in each unit, transmitted to the intermediate layer 6, and finally exits from the output layer 7. Its output signal 9 and the desired teacher signal
Compared to 10, the strength of the bond can be changed to reduce the difference. At this time, the signal goes from the input layer 5 to the output layer 7, but the signal for calculating the coupling coefficient is output from the output layer 7 to the input layer 5.
, The learning proceeds in a direction opposite to the processing of the input data, that is, in the backward direction. Therefore, such a learning method is called a back propagation method.

The back propagation neural network is described by a recurrence formula that changes the strength of the connection so as to reduce the error in the result, and the iterative calculation by this recurrence formula is repeated until convergence, and the number N until the convergence stage is It becomes the number of times of learning. It has already been shown that pattern recognition or associative processing can be performed using this hierarchically structured neural network.

FIG. 15 shows the structure of a conventional associative memory. In the conventional associative memory, when a search input pattern 13 is given, whether or not this pattern and the associative pattern 14 match on a bit-by-bit basis is searched using exclusive OR. When the search input pattern 13 matches the association pattern 14, data 15 corresponding to the position is output. For example, when a code corresponding to a person's name is input to the search input pattern 13, if a code having the same name as the person's name is found on the association pattern 14, the code matches, and for example, the telephone number of the person Is output.

[Problems to be solved by the invention]

In a conventional Hopfield-type or back-propagation type neural network, it is necessary that a connecting portion connecting neurons be completely graphed in advance. That is,
The output of each neuron is wired to the inputs of the other neurons, and which neuron is connected to the experiment is determined by the value of the weight coefficient of the connection. Even if the optimal coupling state is determined by the back propagation method, the wiring on the LSI is already a complete graph. In other words, the presence or absence of a connection state between neurons is determined by changing the weight coefficient of the technique on the complete graph.

Further, in a conventional neural network, neurons are arranged in a one-dimensional array, and output lines from each neuron are routed to and connected to other neurons. Accordingly, there is a disadvantage that many neurons cannot be arranged on a large-scale LSI in terms of structure.

In a Hopfield-type neural network, the energy function is controlled so as to be minimized.If the energy function has many extrema, the converged extrema may not be the required solution. There is a problem that arises. In addition, since the operation is an extremely analog non-linear operation, it may be unstable and cause an oscillation phenomenon depending on a design method, and therefore, there is a problem that an analysis and a design method are extremely difficult. Hopfield type neural net is
A parallel analog computer for solving an optimal problem,
It is considered that the operation is quite different from the neural network of the human brain, which is good at associative processing.

The conventional associative memory shown in FIG. 15 is based on perfect matching between a search input pattern and an associative pattern, and has no ambiguity processing. Although the appropriate bits can be masked in the search input pattern, this does not correct the bits corresponding to the mask, and therefore the concept of a linear code that can be associated even if there are error bits in the search input pattern is Not used. Furthermore, the associative patterns of the associative section are arranged in the horizontal direction, and thus have a one-dimensional structure. For this reason, a large associative unit cannot be formed for the LSI, and the bit width of the associative pattern of the search input pattern is fixed and determined at the stage of production. Further, when the associating portion has a defect, the defect becomes a fatal defect.

An object of the present invention is to provide an associative neurocomputer suitable for large-scale integration in which neurons based on exclusive OR are arranged adjacently in an array in a two-dimensional or three-dimensional structure and perform associative operations in a code graph theory. With the goal.

[Means for solving the problem]

 FIG. 1 is a block diagram of the present invention.

In a neural network (16) formed by mutually interconnecting neurons, in the present invention, for example, a binary sequence expressing a closed path of a graph forming each partial neural network (17) is made to correspond as a current code. Then, since the minimum inter-code distance of the current code corresponds to the length of the minimum cycle of the graph, the error correction capability determined by the minimum inter-code distance corresponds to the capability of ambiguity of association. In the learning process, a complementary tree learning input pattern is given on 21 complementary trees (thin lines) that are a part of the current code, and a current code of a linear graph code is generated so that there is no bit error. Trees in the partial neural network (17) (thick line (2
0)) Store on top. At the time of the associative processing, each neuron (18) inputs the value of the adjacent branch from the stored tree associative pattern and the complementary tree search input pattern input on the complementary tree, and performs addition modulo 2. , Calculate the syndrome, correct the bit error so that the syndrome becomes 0, and decode it into a current code generated at the time of learning. That is, in the present invention, a current code expressing a cycle in a graph of a neural network is formed using the basic concept of a graph that a cut set and a cycle are orthogonal to each other, and an error correction capability of the current code expressing the cycle is used. The learning processing and the associative processing are performed by using an error correction capability determined from the minimum inter-code distance corresponding to the number of branches of the minimum cycle (19) on the neural network equivalently.

Further, in the present invention, the entire neural network (16) is decomposed into a plurality of such partial neural networks (17) by setting the current value of the cut branch (23) to 0 during learning, and each partial neural network (17) is decomposed. ), The learning and the associative processing are performed independently and in parallel.

[Action]

In the present invention, each neuron is basically an arithmetic unit using addition modulo 2, that is, exclusive OR, and the entire neural network is not a complete graph. By using only addition, learning and association processing can be performed. Further, each partial neural network can be formed by setting the value of the branch (23) on the cut closed curve (24) forming the partial neural network to 0, and when there is a crystal defect or the like that inevitably occurs on a wafer or the like. Is to generate a partial neural network so as to include the crystal defect.

〔Example〕

Next, an embodiment of the present invention will be described with reference to the drawings. First, the principle of the error correction code will be described.

In linear code theory, 0 + 0 = 0, 0+
An addition method modulo 2 of 1 = 1, 1 + 0 = 1, 1 + 1 = 0 or an addition method called exclusive OR is used.
Output pattern Y when input pattern X is sent is Y = X +
e, and if the error pattern e is 0, Y = X and there is no error. If the error pattern e is not 0, the output pattern Y is different from the input pattern X, and the e at that time is an error pattern. At this time, the operator + is an addition modulo 2, that is, an exclusive OR. For example, if X is 0110
If 1 and e are 11001, Y = X + e becomes 10100. The number of 1s in the element of the error pattern e is the distance between X and Y. That is, the number of bit differences between inputs X and Y is called distance.
Generally, the minimum processing d _m of code words, take any two codewords X _i and X _j from the set of code words, say what the distance is minimized when the determined distance therebetween. According to the linear coding theory, the minimum processing d _m it is possible to perform the correction of 1 bit if 3 or more, the minimum distance d _m can perform correction of two bits if is 5 or more.

The code word X is obtained by encoding certain information. The codeword X is represented by X = (I, P), I is called an information sequence, P is called a test sequence, each bit of the information sequence is called an information bit, and each bit of the test sequence is called a check bit. Check series P is appended redundant sequence so that the minimum distance d _m of codeword X increases. The bit number n of X is code length, and the number of information bits is k
, This code is referred to as an (n, k) code. Codes based on addition modulo 2 are called linear codes, and the inner product has a value of 1 or 0. Using addition modulo 2, the linear code is a system of simultaneous linear equations Can be defined as all sets of the solution X.

That is, when a matrix is used in Expression (3), HX = 0... (4) Equations (3) and (4) are called a parity check method, and the coefficient matrix H is called a check matrix. When two rows are exchanged for the matrix H, another row is added to one row, or a basic row operation of excluding a row in which all elements are 0 is performed,
In general, the parity check matrix H is given by H = [UF] (5). It is known that the linear code X does not change even if this basic row operation is performed. In equation (5), U is a unit matrix, and F is a submatrix called a main part. If codeword X is a systematic code that can be separated into information sequence I and test sequence P, substituting equation (5) into equation (4) Is obtained. From equation (6), P = I (7) is obtained. That is, the test sequence P is obtained by multiplying the information sequence I by the main part. Conversely, the information sequence I
Forming a linear code X from

Now, when the code word X 'is given by X' = X + e (8), the distance between X 'and X is the number d of 1 in e.
(E). Here, it is assumed that X satisfies Expression (4). If the received signal is X ', if the error pattern e is known, the error pattern e is obtained by addition modulo 2.
Is added to X ', and X is obtained from X = X' + e (9). This means that X 'is "associative" with codeword X.
This means that the association is ambiguous, and the ambiguity of the association is indicated by the distance between X ′ and X, that is, the number d (e) of 1 in the error pattern e.

For example, when the number of 1s in the error pattern e is 2,
X ′ is associated with X with an ambiguity of distance 2. Therefore, in the present invention, the number of 1s in the error pattern e is called associative ambiguity. X 'is called a search input pattern, and codeword X is called an associative pattern. At this time, the search input pattern X 'is said to be associated with the association pattern X with the degree of ambiguity d (e).

The associative pattern X is formed so as to satisfy the expression (4). However, when the search input pattern X 'is given, the expression (4) is satisfied even when the check matrix H is multiplied by the search input pattern X'. Not necessarily. That is, when the search matrix H is multiplied by the search input pattern X ', HX' = H (X + e) = He (10), He = S (11), and the non-zero vector S becomes can get. This vector S
Is called a syndrome. As a result of applying the search input pattern X ′ to the check matrix H, if a syndrome S that is not 0 is obtained, and if an error pattern e is obtained from the syndrome S, the search input pattern X ′ corresponds to the associative pattern X. You can see that there is. That is, the search input pattern X 'is associated with the association pattern X with the degree of ambiguity d (e).

Now, check matrix H And The column vector of the matrix H is composed of all 3-bit patterns except for the pattern of all 0s. The linear code corresponding to the parity check matrix H is a systematic code in which the information sequence 1 has 4 bits and the parity check sequence P has 3 bits. This check matrix H , The syndrome S becomes the pattern in the fourth column of the parity check matrix H. Becomes

Conversely, the syndrome S formed by applying the search input pattern X ′ to the parity check matrix H is (101) ^T (T represents transpose).
, The syndrome S from the matrix H
If the fourth column of the same pattern is matched, the error pattern e
Can be generated as a sequence of Expression (13) in which the fourth bit is 1. This operation detects the error pattern e from the syndrome S, and is the principle of decoding. When the error pattern e is generated, it becomes possible to associate the associative pattern X by adding e to the search input pattern X '. Matrix H of equation (12)
Is a parity check matrix for forming a Hamming code. This linear code can correct a 1-bit error, and when considered as an associative operation, is a linear code that can be associated with an ambiguity d (e) = 1. That is, in the Hamming code, the distance between any two associative patterns X _i and X _j is 3
As described above, even if X 'that is different from X by one bit is input, that X' can be restored to X, and X 'is associated with X with an ambiguity of 1.

To form a parity check matrix H capable of 2-bit correction, the column vector obtained by adding any two column vectors {h _i , h _j } of the parity check matrix H does not match any column vector of the parity check matrix To do. The above is the simple principle of the linear code decoding method.

The present invention further introduces the concept of graph theory in addition to such linear coding theory.

When the inspection equation is expressed in a standard form, it is expressed by the following equation corresponding to the equation (6).

This is expressed as Qi = 0... (16).

Here, the matrix Q is a matrix of t × b, and shall be decomposed into a main portion F and the unit matrix I _t. The vector i is decomposed into t dimensions of the tree current sign i _t and l dimensions of the complement tree current sign i _l. The code word i is called a current code, and the matrix Q corresponds to a parity check matrix in code theory, but is called a basic cutset matrix in graph theory.

By transforming equation (15), it becomes: i _t = F · i _l (17), and if the l-dimensional complementary tree current code i _l is known, the tree current code
i _t will be is seen. It will be described in more detail with reference to the current graph G _i this relationship.

Figure 2 is an example illustrating a process of obtaining a wood current code i _t from Hoki current code i _l. Graph G _i is a general set of nodes and branches, and is a connected graph. Branches of the graph G _i is capable of dividing the Kieda set and Hokieda set. A "tree" is a set of branches that pass through all the nodes and do not include a cycle, and are indicated by thick lines in the graph of FIG. A set of non-tree branches is called a complement tree branch. In the graph of FIG. 2, the branch indicated by a thin line is a complement tree branch. Now, the sequence of the weighting coefficients (current values) of the complementary tree branches {b ₆ , b ₇ , b ₈ } is the current code i
The information bit is 10 bits in order from the left.
At 1, this is written as (b ₆ , b ₇ , b ₈ ) = (101). It is assumed that a sequence (b ₆ , b ₇ , b ₈ ) of the current value of the complement tree branch is given as an information sequence. Curves ₁ , ₂ , ₃ , ₄ , and ₅ are basic cut sets
This is a closed curve for obtaining Q ₁ , Q ₂ , Q ₃ , Q ₄ , and Q ₅ . Closed curve
₁ is defined by Kieda b _1, only one of the branch group which are cut by ₁ is Hokieda b ₆ except it Kieda b _1. From this, the basic cut set Q ₁ = {b ₁ , b ₆ } is defined. Closed curve ₂ is off the Kieda b _2, the other has become a closed curve to cut the b ₆ and b ₇ is a co-tree branch. ₃ except it off the Kieda b ₃ is off to a b ₇ is a co-tree branch. ₄ except it off the Kieda b ₄ is off to a Hokieda b _7, b _8.
5, except it off the Kieda b ₅ in the same way and has a closed curve to cut the Hokieda b _8. Such a basic cut set Q _i (i
= 1, 2,..., 5) is defined as a branch set cut by the closed curve _i , and is uniquely determined if one tree is defined.

Kirchhoff's current law is that the sum of the currents flowing through the branches on the cutset is zero. When 2 is expressed by adding i.e. exclusive modulo, current law, for example, when the cut set Q ₁ in the current value of Hokieda b ₆ (hereinafter sometimes referred to simply as "value") is 1 Means that the value of the tree branch is determined so that the sum of the branch values on Q ₁ becomes 0 modulo 2. Therefore, b ₁ is 1. Since b ₇ is 0 b ₆ Given over basic Cutset Q ₂ is 1, the value of Kieda b ₂ is 1. On Q ₃ are because Hokieda b ₇ is 0, the Kieda b ₃ also 0. On Q ₄ are, because Kieda b ₄ is Hokieda b ₇ is 0, b ₈ is 1, b ₄ is zero. In basic cutset Q _5, because b ₈ is 1, b ₅ is 1. As described above, when the value of the complementary tree branch is given as a binary sequence, the value of the tree branch is uniquely determined. This is expressed by equation (17). That is, the value of the complementary tree branch corresponds to the information sequence i _l of the current code (hereinafter, referred to as the complementary tree current code), and by multiplying the main part F of the basic cutset matrix, the test sequence i _t ( Hereinafter, this is referred to as a tree current code).

Basic cutset matrix Q corresponding to the graph G _i of FIG. 2
Is given by the following equation.

(18) matrix which can be from b ₁ by the column vectors of b ₅ corresponds to I _t In the equation, the column vector from b ₆ to b ₈ is in the main vision portion F. Each row represents a branch set included in each of the basic cut sets {Q ₁ , Q ₂ , Q ₃ , Q ₄ , Q ₅ } as 1. For example, in other in b ₁ and b ₆ is 1 the first row is zero. It expresses the basic cut set Q ₁ That b ₁ and b ₆ is defined by a closed curve _1. The second row represent the basic cutset Q ₂ to which is defined by b _2, Kieda in b ₂ in only one, because Hokieda is b ₆ and b _7, the main unit F b ₆ , column corresponding to b ₇ becomes 1. Third
Row is a fundamental cut set Q ₃ defined by b _3, there is a 1 in the column of b _7. Basically cutset Q ₄ defined by b ₄ is 1 in the column corresponding because it contains Hokieda b _7, b _7. Basically cutset Q ₅ is defined by b ₅ is 1 in the column of b ₈ because there are Hokieda b _8.

Since the complementary tree current sign is (b ₆ , b ₇ , b ₈ ) = (101), b
_6, b _7, the main unit F which is formed from a column vector b ₈ , The tree current code i _t is obtained, and the following equation is obtained.

This pattern corresponds to the tree branch values shown in FIG. _{Then, i = (i t, i} l) T = (11011101) T is representing the closed _{{b 1, b 2, b} 6} and closing _{{b 4, b 5, b} 8}. That is, the current code i represents a closed circuit orthogonal to the cut set. The linear code obtained from the relational expression (17) is called a current code. The graph forming a current code is called a current graph G _i.

In general, it becomes possible to interpret the basic concept of linear code theory in a graph theory, and if the basic cutset matrix Q of the current graph G _i is made to correspond to the parity check matrix H of the code, the code becomes a closed circuit of the graph G _i . Alternatively, an addition modulo 2 corresponds to a current code that satisfies Kirchhoff's current law. That is, each row of the basic cut set matrix Q represents a basic cut set, and a current code i that satisfies Kirchhoff's current law.
Is a closing of the current graph G _i, the set of edges corresponding to 1 provided in the current code i is in the closing of the graph G _i. In other words, the product of the basic cutset matrix Q and the current code i means that the cutset and the cycle are orthogonal, which is one of the basic concepts of graph theory. The present invention is an associative neurocomputer configured using basic concepts in linear coding theory and graph theory.

By the above, the basic cut set matrix Q of the current graph G _i
Is made to correspond to the parity check matrix H of the code, it has been revealed that the current code i represents a closed circuit. Therefore, if there is no parallel branch to the current graph G _i If, because any closed is also formed by three or more branches, the minimum code distance d _m of the current code i 3
That is all. Generally the minimum code distance d _m linear codes are known to be equal to the minimum of the number of 1s included in the code not zero code. Since current sign i represents the closing of the current graph G _i, the minimum code distance d _m is equal to the number of branches of the minimum closed composed lowest branch in the graph G _i. Therefore, if there are no parallel edges in the graph G _i, there are three or more edges included in the minimum cycle in any graph G _i . So the graph
The number d _m branches of the minimum closing of G _i is referred to as the length of the smallest closed.

Now, if the length of the smallest closed is formed as a neural net current graph G _i is d _m, the minimum inter-code distance of the current code i at the neural network becomes d _m. That is, for a neural network that does not include parallel branches, Q _i =
The current code i determined from 0 has a minimum inter-code distance of 3 or more, and if an encoding / decoding method is established, at least one bit error can be corrected. In general, when the minimum cycle length d _m of the neural network N is d _m = 2T + 1 (21), it is possible to correct a T-bit error by using the current code i. N has an associative ability with an ambiguity d (e) = T.

For example, FIG. 3 is an embodiment diagram showing a graph structure of a simple neural network. The positive 12 shown in FIG.
Since the minimum cycle of the icosahedron is a pentagon, the minimum inter-code distance of the current code i for this decahedral neural network is
And the association of the ambiguity d (e) = 2 becomes possible. Third
Since the minimum cycle of the icosahedron shown in FIG. 7B is a triangle, the minimum inter-code distance is 3, and the association of the ambiguity d (e) = 1 is possible. The minimum code distance of the current code i since a complete graph G _c of n nodes will contain minimal closing distance 3 is three.

Note that the number of code words of the current code i is 2 ^l −1, where the number of complementary branches is 1.

Next, a description will be given of a voltage code v in a case where a basic cycle matrix B having a dual relationship with the basic cutset matrix Q is used and B corresponds to a parity check matrix H.

With respect to the voltage graph G _v, voltage law Kirchhoff is expressed by the following equation.

Bv = 0 (22) Here, the matrix B is a basic cycle matrix, and v is a voltage sign. The voltage sign v is a binary vector elements 1 and 0, representing a cut set of a graph G _v orthogonality of closed and cutset. If the matrix B is a parity check matrix H, the voltage code v corresponds to a linear code. At this time, the tree voltage code v _t of the voltage graph G _v becomes the information sequence, and the complementary tree voltage code v _l corresponds to the test sequence. That is, there is a relationship of v _l = F ^T v _t ... (23). Here, if the voltage graph G _v is defined by the same as the current graph G _i and the tree is the same, the main part F ^T of the basic cycle matrix B is the transposition of the main part F of the basic cutset matrix Q. Become. From equation (23), the organization code v = (v _l , v _t )
There defined as a cut set of voltage graph G _v. Note that a graph forming the voltage code _v is referred to as a voltage graph Gv. Number of code words of voltage sign v is the number of cut set of voltage graph G _v, relative to the branch number t, the 2 ^t -1.

FIG. 4 is a simple embodiment diagram of a current graph G _i for forming a current code i and a voltage graph G _v for forming a voltage code v. A description will be given with reference to FIG. 4 while comparing the voltage code v with the current code i.

In the fourth diagram of the current graph G _i and the voltage graph G _v, tree T
Are indicated by bold lines, and in the following, the suffix l is the complement tree, the suffix t
Indicates that it is a tree.

In current graph G _i, complement wood current code, Gives the tree current sign according to the current law for the basic cutset {Q ₁ , Q ₂ , Q ₃ }. Is determined. The current sign _{i = (i t, i l} ) T represents a single closure {2,3,5,6} of a graph G _i.

Further, in the voltage graph G _v in FIG (b), as the value of the voltage, Given by Kirchhoff's voltage law in the basic cycle {B ₄ , B ₅ , B ₆ } (the rule that the sum of the voltage values of the branches on the cycle is 0) Is determined. The voltage sign v = (v _l , v _t ) is represented by the graph G
represents one cutset {1,2,3} of _v .

Since voltage sign v represents the cut set of voltage graph G _v, the minimum code distance d _m is equal to the number of branches of the minimal cut set consisting of the lowest branch in the voltage graph G _v.
If, by forming a regular graph G _v (d _m) of degree d _m that branches d _m present in each node are linked, Kirchhoff's voltage law Bv = 0 at thereon voltage graph G _v (d _m) voltage sign v determined from the minimum intersymbol distance is d _m. If d _m = 2T + 1, it is possible to correct a T-bit error in this encoding / decoding system.

minimum intersymbol distance voltage sign v by a complete graph G _c of n nodes is n-1.

Voltage sign v of a normal graph G _v (d _m ) of degree d _m with node number n
If the code length of the SO in the branch number _{= (1/2) d m × n} , information points is a Kieda number = n-1, test scores are Hokieda number = (1 /
2) Equal to d _m × n- (n-1). The number of codewords is 2 ^n-1 -1.

In summary, if the corresponding basic cutset matrix Q of the current graph G _i (voltage graph G _v) (base closed matrix B) to the parity check matrix H of the code, the code is closed (cutset) Graph or It corresponds to a current code (voltage code) that satisfies Kirchhoff's current law (voltage law) by addition modulo 2.

 Next, the syndrome will be described.

Now, an error occurs in the current code i (voltage code v) and i ′
If it becomes (v '), to decode it to i (v), the following syndrome I (E) is generally calculated.

I = Qi ····· (24-1) E = Bv ····· (24-2) At this time, the current graph G _i (voltage graph G _v), the syndrome I (E), the cutset It is called a syndrome (closed loop syndrome) and corresponds to the value of an equivalent current source (voltage source) inserted in parallel (series) with a tree branch (supplementary branch).

FIG. 5 is an embodiment diagram of the current graph _i and the voltage graph _v in consideration of the syndrome. For example, FIG.
In the current graph G _i , if i ₄ is erroneously set to 1 instead of 0, for the error pattern e ₄ = [000100] ^T , Since it is, the graph G _i is changed to the current graph G _i as FIG. 5 (a). Conversely, if the error position is not known, it is necessary to find the error position from the syndrome I = [011] ^T. I = [011] ^T represents that basic cutset Q ₁ is correct, there is an error in the Q ₂ and Q _3. Now, assuming that there are no two or more bits of error, it can be found that the value of the branch e ₄ included in common in the basic cutset Q ₂ 'and Q ₃ is incorrect. The value of the branch e ₄ can decode be changed from 1 to 0.

Further, in the voltage graph G _v of example FIG. 4 (b),
If v ₁ is erroneous to 0 instead of 1, the error pattern e ₁ =
For [100000] ^T , E = Be ₁ = [011] ^T. Here, the basic cycle matrix B is It is.

Graph G _v is converted to a voltage graph _v as FIG. 5 (b). Conversely, the syndrome E = [011] ^T given as the value of the voltage source, assuming that there is no two or more bits of error, the value of the branch e ₁ included in common in the basic closed B ₅ and B ₆ erroneously Means that The value of the branch e ₁ can decode be changed from 0 to 1.

Thus, it was shown that the syndrome corresponds to the equivalent current source I or the equivalent voltage source E.

Next, the concept of the learning associating operation of the neural network of the present invention will be described using a linear graph code constructed using graph theory.

6 is a simplified schematic diagram of a neural network G _i of the present invention. In the figure, the neuron N _i is present in each node N _i, each branch b _k is assumed to be synaptic bond linking neurons. Further, the neural network G _i is assumed to be the current graph G _i. Thus, as an example, the basic cut set matrix of the current graph G _i in correspondence to the check matrix H of the code,
The sign becomes the current code i satisfying the current law Kirchhoff's in addition modulo closed or 2 of the graph G _i.

Neural Network G _i of the present invention are, for example, two-dimensional position (X, Y) is a set of partial neural network G _i present in (X, Y), the length of the smallest closed and 6 in this example I do. Each partial neural network G _i (X, Y) is a part associated with a distinctive individual. For example, when information corresponding to “large ears”, “large eyes”, and “large teeth” is input,
It is the part that fires in association with "wolf". In FIG. 6, the individual partial neural networks G _i (X, Y) forcibly set all the current values of the branches on the cut set Q (X, Y) cut by the cut set closed curve (X, Y). It is generated by setting it to 0. Partial neural net G _i (X,
Making all 0 the value of the current entering the Y) are shorted all other parts neural network, that portion neural network G _i (X, collectively as a ground node N ₀ for Y), further the ground node N ₀ Means that all the currents flowing out of the circuit are zero. Thus, the partial neural network G _i (X,
By setting all branch values in Y) to 0, the associative processing using the current code i allows each partial neural network G _i (X,
Y), and these processes are executed independently and in parallel.

The current code i using the basic cutset matrix Q for the partial neural network G _i (X, Y) as the check matrix H is configured so that Qi = 0. The current code i is a binary sequence representing the closed circuit of the partial neural network G _i (X, Y). The current sign i includes "1" of 6 or more lengths of at least a minimum closed, a minimum code distance is 6, the neural network G _i can at least ambiguity d (e) = 2 associative and Become.

FIG. 7 is an embodiment of a partial neural network according to the present invention. This portion neural network G _i (X, Y) is connected to the adjacent portion neural network, G _i (X, Y)
The learning associative operation can be executed independently of the others by forcibly making the value of the current entering into all zeros by learning.

Hereinafter, a description will be given as a learning associative operation in the partial neural network G _i (X, Y). Incidentally, considering only one branch b ₂₈ of the branches to be connected to an adjacent portion neural net, the branches b ₂₈ is as Kieda, virtual ground node N
₀ (all of the other partial neural networks are short-circuited).

Partial neural network G _i of FIG. 7 (X, Y) in,
The basic cut set matrix Q is one of the tree {b _7, b _8, ···
When b ₂₈ ｝ is defined, it is defined by a closed curve _{i of a} basic cut set for cutting each tree branch.

Now, instead of the basic cutset matrix Q, each node ｛N ₁ , N
_2, consider the use of cut-set matrix equivalent connection matrix A cutset cut ··· N _22}. By introducing this concept, the basic operation of each neuron N _i is the controls so that the sum of currents entering his becomes zero.

FIG. 8 is a connection matrix of the partial neural network G _i (X, Y) of FIG. The connection matrix A has rows whose neurons N ₁ , N _2.
Corresponding to _{·· N n (n = 22)} , column branch _{b 1, b 2 ··· b m} (m
= 28). Each column vector corresponding to the branch other than the branch b ₂₈ includes one of two connection states of the corresponding branch of neurons is shown in its 1. For example, branch b ₁
Is because it is connected to the neurons N ₁ and N _6, the first column corresponding to b ₁ is the first row and the sixth row is 0 otherwise 1. Also, branch b ₂ is because it is connected to the neuron N ₃ and N _8, the second column is a column vector such that all three row and 8 row 1 other rows 0. Although the connection state of the neurons N ₁ and the ground neuron N ₀ to the connected branch b ₂₈ are shown in the last column of the connection matrix A, the rows corresponding to the ground N ₀ is removed. Therefore, the column vector corresponding to b ₂₈ are included 1 only one.

This connection matrix A is composed of neurons N _i (i = 1, 2,...,
n) is equal to a basic cutset matrix Q defined by a Grange's tree (hereinafter referred to as an L-tree and represented by T _L ) virtually connecting the ground N ₀ to the ground N _0, and at this time, the branches other than the branch b ₂₈ The set {b ₁ , b ₂ ... B _m-1 } is a complement. When this connection matrix A is used as a check matrix and a current code i of Ai = 0 is generated, the current code i is also a binary sequence representing a closed circuit. Moreover, the current code i is determined as the sum of the currents flowing in each neuron N _i is zero. And Qi = 0
If the current code i satisfies
Ai = 0 is satisfied.

For example, to define the tree T of a thick line for the partial neural network G _i of FIG. 7 (X, Y). If the value of the tree branch is as shown in the figure, the value of the tree branch T is determined according to Kirchhoff's current law Qi = 0. That is, if the logic of the complementary tree branch is determined so that Kirchhoff's current law is satisfied by addition modulo 2 in the basic cut set defined by each tree branch, the result is shown in FIG. The value of the tree branch is determined so that For example, since the basic cut set defined by b ₇ is a set of branches cut by the closed curve ₇ , the complement tree branch on ₇ is b ₁ . The value of Kieda b ₇ the value of the on Hokieda b ₁ is 1 is 1 so that the current law Kirchhoff is satisfied. The basic cutset Q ₁₃ defined by Kieda b ₁₃ is a branch group that is cut by the closed curve _13. The state of the prosthetic branch is (b ₁ , b ₂ ,
Since b ₃ ) = (111), the value of the tree branch b ₁₃ is 1 so that Kirchhoff's current law is satisfied.

Thus, the values of all tree branches are determined from the values of the complementary tree branches,
The result is shown in FIG. However, the state of the tree branch b ₂₈ connected to the ground N ₀ is 0. When one tree T is defined in this way, the value of the tree branch T is determined from the value of the complementary tree branch. At this time, in fact, when observed at each node, the sum of the currents entering all the nodes is zero. For example, neurons
Since the number of 1s in N ₂ is 2, the addition modulo 2 is 0. The current into the neuron _{N 3 (b 2, b 8} , b 9) =
Since it is (110), the sum is also 0.

Since the value of all the branches is a current code i, the current code i becomes m (m = 28) dimensional vector from b ₁ to b _m, Becomes

Branch connected to neuron N ₁ is _{b 1, b 7, b 28} , the connection relationship corresponding to the first row of the connection matrix A in Figure 8. First row _first column b is 1, b ₇ column of connection matrix A is 1, b
₂₈ column is 1, otherwise has become 0, representing the information as to this row vector are connected to which branch neurons N _1. When this row vector is multiplied by the current code i determined by the above method, that is, by a binary sequence representing the values of all the branches, the result becomes 0. This means that the sum of currents writing into the neurons N ₁ is 0. Thus, the neurons N ₁ , N ₂ ... N _n (n = 22) at each node on the partial neural network G _i (X, Y) input the value of the adjacent branch and modulo 2 The addition is controlled so that the sum always becomes 0, that is, the number of 1 is counted so that the sum becomes an even number.

Now, it is assumed that an information sequence (111000) is input to the complementary tree branch (b ₁ , b ₂ ,..., B ₆ ) in the partial neural network G _i (X, Y). If the number of branches of the complement tree is l (= 6), this l bit is arbitrarily given. This input pattern given to the complementary tree is called a complementary tree learning input pattern in the learning process, and is called a complementary tree search input pattern in the associative process. A pattern given to a tree branch is called a tree association pattern, which is input in advance during learning. First, the learning operation of the present invention will be described.

In the learning process using the partial neural network G _i (X, Y), when a complementary tree learning input pattern is given, each neuron N _j controls the current of each tree branch in order from the initial state, and constantly controls the current of each input branch. The sum of the currents is always 0 in addition modulo 2.
Control so that For example, the initial value of branch all trees to 0, changing the value of the Kieda so that the sum of currents entering his neuron N _j becomes 0. The control is G _i (X,
Y) Kirchhoff Current Law on all neurons N _j on is continued until satisfied. If the sum of the currents input on all the neurons becomes 0, the input complementary tree learning input pattern has been completely learned. This is said to have been learned in syndrome 0. For example, if the value of the branch shown in FIG. In the figure, a state shown in nodes of each neuron N _j is the value of the syndrome S (N _j) = 0. Complementary tree learning input pattern (b ₁ , b ₂ , b ₃ , b ₄ , b ₅ , b ₆ ) = (1
For example, if the information is (large ears, large eyes, large teeth, unfriendly, not wrinkled, not handsome), the tree association pattern (b ₇ , b) in syndrome 0 obtained by learning is obtained. ₈ ,... B ₂₈ ) = (1,
1, ..., 0) expresses "wolf". Since this tree association pattern is the number of bits is large, usually is not output to the neural net external decoding position (X, Y) or at the time of an associative part neural network G _i to represent "Wolf" (X, Y) The complemented tree pattern and the like are subjected to input and output. Thus, partial neural network G _i (X, Y) position by a complement tree learning input pattern (111000) (X, Y) will be storing the "wolves". Therefore, in the learning process of the present invention, when a complementary tree learning input pattern is input to a complementary tree branch, the sum of the currents that always enter each neuron starting from an initial pattern with a state of the tree branch is fixed while this input pattern is fixed. Is controlled to be 0. Each neuron N _j is the sum of the nodal current source value of the branch adjacent the respective steps of the control (current source located between the N _j and ground N ₀₎
Output the nodal syndrome S (N _j ) corresponding to
If (N _j ) = 1, control is performed so that S (N _j ) = 0 according to a learning algorithm described later. Here, it can be said that the nodal syndrome is a cutset syndrome for the L-tree. That is, in the learning process of the present invention, the complementary tree learning pattern is fixed, and the tree association pattern is obtained. The current value of the tree is determined so that the current rule is satisfied at each node starting from the initial pattern. Processing. At the final value, the sum of the currents flowing through the basic cut set is also zero. Whole partial neural net G
Each neuron may be controlled so that the sum of the branch values on the basic cut set Q _K cut by each closed curve Q _K at _i (X, Y) becomes 0, but in this case, The value of the tree needs to be transmitted to the tree. Therefore, a communication problem occurs. The configuration of each neuron is simpler when inputting only the value of the adjacent branch is controlled.

Since complement tree learning input pattern is information sequence, be any pattern, it is possible to G _i (X, Y) of all 0 nodal syndromes of each node on the learning algorithm converges When all the states of the tree branches are determined, the pattern of the values of all the branches formed is a current code i that satisfies Qi = 0 (and Ai = 0). The complementary tree learning input pattern given to the complementary tree branch differs depending on the individual to be associated, such as "wolf", "kikori", "grandmother", and is given to the partial neural net corresponding to the individual such as the sky. At this time, in each partial neural network, the nodal syndrome is 0
The learning algorithm is executed so that the tree association pattern is stored as it is on the tree branch when it converges.

FIG. 9 is an embodiment diagram for explaining a learning algorithm using a partial neural network according to the present invention. For the sake of simplicity, the graph structure of the partial neural network is simplified, and a current graph composed of six neurons and eight branches will be described. In the figure, the branches b ₁ , b ₂ , b ₃ are complementary branches,
It is assumed that b ₄ , b ₅ , b ₆ , b ₇ , and b ₈ are tree branches. In the learning processing of the present invention, the complementary tree learning pattern (b ₁ , b ₂ , b ₃ ) =
When (110) is given, the operation is to find a tree association pattern such that the node syndrome S (N _j ) becomes 0. Node syndromes S (N ₁ ) to S (N ₅ ) are the result of the sum of currents flowing into each node of each neuron N ₁ to N ₅ . Syndrome S 'inserted in parallel to each tree branch
(N ₁ ) to S ′ (N ₅ ) are cutset syndromes corresponding to the sum of currents flowing on the basic cutset.

Node syndrome S (N ₁₎ from the S (N ₅₎ each cut set up with the N ₁ other than N ₆ Given node N ₆ and now grounded to N ₅ syndrome S '(N ₁₎ from S' (N ₅ ) One-to-one correspondence. That is, in general, S (N _j ) = S ′ (N _j ), and the node syndrome S (N _j ) corresponds to the cut set syndrome S ′ (N _j ). It is always possible to make this correspondence, and it is clear that the number of nodes other than the ground is n-1 and the number of tree branches is only n-1 in the connected graph. More specifically, it is clear from the fact that elementary transformation can be performed on a one-to-one basis to a branch of a tree T defined from a tree branch of a Lagrange tree (L-tree) corresponding to the nodal syndrome. In FIG. 9, the information on the dotted line is the nodal syndrome S (N _j ), and the value becomes the value in the circle, and becomes the cut set syndrome S ′ (N _j ).

In the learning processing of the present invention, the complementary tree learning input pattern input to the complementary tree is fixed, and when an arbitrary initial pattern is given on the tree branch, the node syndromes are all zero and the cut set syndromes are all zero. Is controlled as follows. For example, as shown in FIG. 9A, the values of the tree branches are all set to 0 as the initial pattern. In this initial state, it is assumed that all of the cut set syndromes S ′ (N _j ) are also 0. The process shifts from such an initial state to FIG. 9B.

In neurons _{N 1, b 1 = 1,} b 4 = 0 a is from node syndrome S (N ₁₎ becomes 1, the corresponding cutset syndrome S '(N ₁₎ also becomes 1. Since in the N ₂ is b _4, b _5, b ₆ all 0, S '(N ₂₎ is zero. In N ₃ , b ₁ = 1, b ₅ = 0 and b ₂ = 1, so that S ′ (N ₃ ) becomes 0 when the sum is calculated. B ₆ = 0 In N _4, b ₇
= 0 and b ₈ = 0, so that S ′ (N ₄ ) becomes 0. S '(N ₅₎ is 1 because it is _{b 2 1, b 7 = 0} , b 3 = 0 in the N _l5. Then, the process proceeds to (c) of FIG.

In FIG. 9 (c), the value of the tree branch whose cut set syndrome S ′ (N _j ) is 1 is inverted. That is, the value of the tree branch existing in parallel with the cut set syndrome S ′ (N _j ) = 1 is corrected by inverting the previous state. Therefore, Kieda b ₄ is changed to 0 or _1, S '(N 1) is 0
Changes to The value of Kieda b ₇ also changes from 0 to 1, corresponding cutset syndrome S '(N ₅₎ is zero. It moves to FIG. 9 (d).

In Figure 9 (d), since the sum of the current writing into the neurons N ₂ becomes 1 1 + 0 + 0, S ' (N 2) is changed to 1. Moreover, consisting of a _{b 6 = 0, b 7 =} 1, b 8 = 0 even in the N _4, node syndrome S (N ₄₎ is 1, cutset syndrome S '(N ₄₎ which also corresponds to 1 and . Ninth
It moves to a figure (e).

Since S ′ (N ₂ ) is 1 in the previous state, the value of the corresponding tree branch b ₆ changes from 0 to 1. Similarly, S '
Since (N ₄ ) is 1, the value of the corresponding tree branch b ₈ changes from 0 to 1. Then, the processing moves to FIG. 9 (f).

In FIG. 9 (f), the sum of the currents flowing into N4 is 1
Since it is + 1 + 1, it becomes 1 and S '(N ₄ ) changes to 1 again. Turning to FIG. 9 (g), in FIG. 9 (f),
Since S ′ (N ₄ ) is 1, the value of the corresponding tree branch b ₈ changes from 1 to 0.

In FIG. 11 (g), the cut set syndrome S '
(N _j ) are all 0. This means that, for a given complementary tree branch pattern, all the tree branch patterns have been determined so that the sum of currents flowing through the basic cutset becomes zero. For example, the basic cut set defined in Kieda b ₄ a b ₄ and b ₁ are both 1 because, the sum is zero. Basic cut set defined by Kieda b ₅ is the sum because a b _5, b _1, b ₂ is also zero.
Since the basic cut sets defined by the tree branch b ₆ are b ₆ and b ₂ , both are 1 and the sum is 0. Basic cut set defined by Kieda b ₇ is set to 0 when summing in _{b 7, b 2, b 3} . Moreover, it is both zero because the basic cut set defined a b ₈ and b ₃ by Kieda b _8. Therefore, this means that learning was performed in syndrome 0.

As described above, in the learning process of the present invention, the sum of the currents at which the tree association pattern enters at the nodes of each neuron with respect to the given complementary tree learning input pattern, that is,
The node syndrome is determined to be zero, and as a result, the sum of the currents on the basic cutset is determined to be zero.

Next, the association process in the partial neural network G _i of the present invention (X, Y). At the time of associating processing, unlike at the time of learning processing, a tree associative pattern on a tree branch is fixed as a pattern determined at the time of learning, and a complementary tree search input pattern is input to a complementary tree branch. At this time, a pattern that does not belong to the code word may be given to the branch, and the pattern for all the branches does not always have the node syndrome set to 0. Now, suppose that a pattern i 'in all branches is given. If this i 'is the current code, the value of the node syndrome S (N _j) in neurons N _j of each node should be zero. However, if they do not belong to a code word, i ′ = i + e, and the error pattern e is not zero. Then, it comes out what node syndrome S (N _j) is not zero in course of each neuron N _j. That is, given a pattern on the branch, if each neuron N _j
The syndrome S that neuron N _j as current law on nodes in satisfies the current law if it is not satisfied
(N _j ) is output as 1. This means that the syndrome S of the product of the check matrix H and the error pattern e is not 0 in the linear code theory, and the value obtained by multiplying the connection matrix A by e corresponds to the node current source in the graph theory. Output as a value of the nodal syndrome. At this time, since Ae = S, in order to output the error pattern e, the associative algorithm is executed so that the node syndrome S is made as small as possible. That is, this associative algorithm is a procedure for finding an error pattern e from the node syndrome S while keeping the tree associative pattern fixed. The process of obtaining the error pattern e from the syndrome S is the same as the coding theory, but in the present invention, this associative algorithm is directly executed on a neural network. As is clear from the coding theory, the nodal syndrome S is obtained by adding the column vector of the parity check matrix A corresponding to one element of the error pattern e, so if e is obtained from the nodal syndrome S, the If the value of the complement tree branch corresponding to the element of 1 is inverted, it becomes an associative decoding operation. If the current code i is a code capable of correcting two bits, the number of 1s in the error pattern e is one or two. If the nodal syndrome becomes 0 by inverting the value of the complement tree branch corresponding to the 1 element of the error pattern e, i 'is the current within the range of the 2-bit correction capability, that is, the ambiguity d (e) = 2. This is associated with the symbol i. The current code i has a lower ratio between the number of information points and the number of check points, that is, the transmission speed, as compared with a code generated by the conventional code theory. Therefore, the use form of the code is different from the conventional one. In the associative processing according to the present invention, it is assumed that there is generally no error in the tree associative pattern, and only the complementary tree search pattern has an error due to ambiguity, and the complementary tree search input pattern is associated.

Next, the operation of the continuous processing of the present invention will be described in more detail. FIG. 10 is a partial neural network G _i (X, Y) of the present invention.
FIG. 6 is an embodiment diagram for explaining the associative operation according to FIG. In the figure, the bold line is a tree and the tree association pattern (b ₇ , b ₈ ,.
.., B ₂₈ ) = (1, 1,..., 0) are the same as the tree association pattern shown in FIG. I do. The associating process is a process in which the value on the tree branch is fixed, contrary to the learning process, and the complementary tree search input pattern given to the complementary tree branch is associated with the tree association pattern with ambiguity 2. The tree association pattern shown in FIG. 10 corresponds to, for example, "wolf". In this state, it is assumed that (b ₁ , b ₂ , b ₃ , b ₄ , b ₅ , b ₆ ) = (111100) is input as a complementary tree search input pattern as shown in the figure. This complementary tree search input pattern corresponds to information such as (large ears, large eyes, large teeth, gentle, no wrinkles, not handsome), and is almost associated with "wolf" except for "friendly". It is to let.

When the above complementary tree search input pattern is given to the complementary tree, each of the neurons N ₁ , N ₂ ,..., N _n (n = 22) at each node on the partial neural network G _i (X, Y) The neuron _Nj inputs the value of the adjacent branch, performs addition modulo 2, and calculates a nodal syndrome S (N _j ) (j = 1, 2,..., N). In figure each neuron N nodes the conditions shown in the nodes of the _j syndrome S (N _j), in the FIG. 10 node N ₉ and N ₁₄
Is 1 in the nodal syndrome. That is, S (N ₉ ) = 1 and S (N ₁₄ ) = 1, and the other node syndromes are 0. At this time, the value of the complement tree branch b4 is _{4 in} the above-described complement tree search input pattern.
It is a bit and corresponds to "easy".
If the correct value of this Hokieda b ₄ from 1 to 0 instead to the information of "unfriendly", this time node syndrome S
(N ₉ ) = 0, S (N ₁₄ ) = 0, and the partial neural network
All node syndromes S (N _j ) on G _i (X, Y) become zero. Thus "Wolf" is that which is associative with ambiguity d (e) = 1 This part neural network G _i (X, Y).

By the way, in this case, the complementary tree branch b ₄ is included in both the node cut set that cuts the node N ₉ and the node cut set that cuts the node N _14, and in the present invention, it is commonly included in these node cut sets. to correct the value of the branch b ₄ to the the first of the process. The reason for this will be described in the code theory.

In order to explain the reason, a relational expression of Ai '= A (i + e) = Ae = S will be used. Nodal syndrome S
Syndrome S (N _j ) (j = 1,2,
..., a column vector of 22), which is the fourth column of the column vectors equivalent corresponding to b ₄ of the connection matrix A in Figure 8. Therefore, only the fourth bit of the error pattern e is 1 (00010... 00). Complement cuttings code i It is formed from the values of the branches a given b ₄ of the value from 1 to correct the 0 '= 0 to 4 bit from the first (111,100,011 ... 0)
Means to correct. That is, the code i ′ is i =
The current code i = 0 for the node syndrome from i ′ + e
(111000011... 0).

As described above, in the present invention, the node syndrome S of the nodes N _i and N _j connected to the complement tree branch b _k for the value of the complement tree branch
When both (N _j ′) and S (N _j ) are 1, control is performed so that the value of the complementary branch b _k is automatically inverted. The same applies to the case of a two-bit error.

FIG. 11 is an embodiment for explaining the associative operation by the partial neural network according to the present invention. In the figure, the tree association pattern is the same as that shown in FIGS. 7 and 10,
It corresponds to "wolf". In this state, it is assumed that (b ₁ , b ₂ , b ₃ , b ₄ , b ₅ , b ₆ ) = (111101) is input as a complementary tree search input pattern as shown in FIG. This input pattern can be "big ears", "big eyes", "big teeth", "friendly",
It corresponds to the information of "no wrinkles" and "handsome", and is almost reminiscent of "wolf" except for the information of "easy" and "handsome". That is, the associative pattern of “wolf” having the degree of ambiguity 2. Also in this case, since the minimum cycle length of the partial neural network shown in FIG. 11 is 6, the 2-bit correction can be performed on this partial neural network.

Each neuron N _j to perform an addition to the 2 inputs the value of the branch adjacent law, to calculate the node syndrome S (N _j). Nodal syndrome S (N ₉ ) of neurons N ₉ and N ₁₄ =
1 and S (N ₁₄ ) = 1 are the same as in FIG.
Figure In, S (N ₁₅₎ against node syndrome in neurons N _l5 and N ₂₀ = 1, the S (N ₂₀₎ = 1. Node syndromes other than the neurons N ₉ , N ₁₄ , N ₁₅ , and N ₂₀ are all zero. Here, if the node syndromes of the nodes connected to the complementary tree branch are both 1, the value of the complementary tree branch is inverted. That is, the complementary branches b ₄ and b ₆ are both inverted to 0. The complementary tree search input pattern input by this error correction is corrected to (b ₁ , b ₂ , b ₃ , b ₄ , b ₅ , b ₆ ) = (111000), which is clearly shown in FIG. This is the same as the input pattern given to the tree branch, and is a complementary tree learning input pattern of “wolf” input during learning. Therefore, "wolf" is associated with the 2-bit ambiguity by the partial neural network Gi (X, Y).

In the partial neural network shown in FIG. 11, each complementary tree branch is separated by a tree branch, and two complementary tree branches are not adjacent to each other via a node. Next, a description will be given of a 2-bit correction in the case where a complementary tree branch is continuous via a node on a partial neural network.

FIG. 12 is a graph showing a part of a partial neural network when two complementary tree branches are continuously connected via one neuron. In the figure, N _i , N _k , and N _j are neurons on the partial neural network, and a branch b _ik connecting N _i and N _k
And the branch b _kj connecting N _k and N _j are both complementary tree branches. Now, assume that the value of the complementary tree branch {b _ik , b _kj } is erroneous in both 2 bits. The minimum cycle length of this partial neural network is 5 or more, and 2-bit correction is at least possible. And In such a case, Hokieda b _ik, node syndrome neuron N _i by the error of Hokieda b _ik When b _kj is limited both S (N _i) is 1, and further N _k
Node syndrome S (N _k) is also set to 1, at the same time Hokieda b _kj also a neuron N _j node syndrome S (N _j) is 1 because there is an error, further nodes syndrome S of N _k
(N _k ) is also 1. As a result, as a result of the sum of the nodal syndrome by the error by node syndrome S (N _k) is node syndrome and b _kj by the error of b _ik of N _k, it becomes 0 as shown in FIG.

In this case, the neurons N _i in the present invention is to input both syndrome values and the node N _k node syndrome neuron N _j, N _i, N _k, node syndrome S (N _i) of N _j, S
(N _k), if the value of S (N _j) becomes 101 controls to correct the value of Hokieda b _ik. Also, similarly for the node N _j, neuron N _j inputs a node syndrome neuron N _i and the node N _i, N _i, that node syndrome N _k及to N _j is the pattern that 101 If detected,
Correct the value of the complement tree branch b _kj .

Incidentally, N _i is the S than N _j (N _j) input via the control line b _ij, N _j is input via the control line b _ij and S (N _i) from N _i.

This is extended to the general case, and is a partial neural network having a correction capability of 2 bits or more, and complements the shortest path that is continuous between the neurons N _i and N _j having the node syndrome of 1. A control line is added so that the value of the tree branch, that is, the value of the complementary tree branch commonly included in the node cut set having the node syndrome of 1 is corrected. Then, control is performed to input the information sequence of the node syndrome on the shortest path to one neuron of the node syndrome and invert the value of the complement tree branch on the shortest path.

Although the neural network based on the current code has been described above, the neural network based on the voltage code is similarly described based on the concept of “dual” in the graph. When a linear graph code representing a cut set of a voltage graph forming a neural network is used, the minimum inter-code distance when the minimum inter-code distance of the linear graph code corresponds to the length of the minimum cut set of the voltage graph. The error correction capability determined by the above corresponds to the capability of ambiguity of association. Then, at the time of the learning process, the tree learning input pattern of the voltage code is input to a tree in the neural network, and a complementary tree association pattern is formed on the neural network and stored on the complementary tree so that there is no bit error. . At the time of the associative processing, each neuron inputs only information on the neuron's network (a closed cycle without an internal cycle) from the complementary tree associative pattern and the input tree search input pattern,
The bit error is corrected while calculating the network syndrome by addition modulo, and is decoded into a voltage code generated during the learning process. Here, the network syndrome is the sum of the voltage values of the branches included in the network. In this partial neural network, a basic cycle matrix or a network matrix (each row corresponds to a network, and a column corresponds to a branch, and when the branch is included in the network, 1 is used as a parity check matrix) Corresponding,
The error correction capability of the voltage code representing the cut set in the voltage graph of the partial neural network, that is,
Equivalently, the learning process and the associative process are performed using the error correction capability determined from the minimum inter-code distance corresponding to the number of branches of the minimum cut set (the one having the minimum number of branches of the cut set) on the partial neural network. Become. That is, when the neural network is divided into a plurality of partial neural nets, a branch set is divided into a tree and a complementary tree in each partial neural network. At this time, the learning processing means, when given to the tree branch (tree learning input pattern), sums the values of the branches of the basic cycle defined by the complementary tree, as in Kirchhoff's voltage law. Is a means for generating a complementary tree associative pattern so that it becomes 0 by addition modulo. The associative processing means fixes the complementary tree associative pattern generated at the time of learning, calculates a closed syndrome (sum of values of branches in a closed circuit or a network) for the input tree search input pattern, and obtains An error pattern is generated from the obtained closed syndrome, and the voltage value of the branch corresponding to the error bit in the error pattern is corrected.

In the learning process of each partial neural network, a complementary tree associative pattern is given as an initial pattern for a given tree search input pattern, and neurons existing in each network are modulo 2 by a branch voltage included in the network. This is an operation of obtaining a network syndrome so as to become 0 by the addition, and inverting the value of the complementary tree branch corresponding to the network one-to-one using the value of the network syndrome. Is repeated until all network syndromes become 0, that is, the sum of the voltage values of the branches included in the network becomes 0 by addition modulo 2. Then, a complementary tree association pattern for the given tree learning input pattern is generated on the complementary tree branch. In the associative processing, the complementary tree associative pattern stored at the time of learning is fixed, and a neuron of each network is calculated as a sum of branch values included in the network with respect to a tree search input pattern given to the tree branch. Is calculated by addition modulo 2. Then, by inverting the tree branch value on the shortest path while the value of the network syndrome is 1, the given tree search input pattern is corrected so that the syndrome becomes 0.

In this way, a neural network having a large minimum cut set can be formed on, for example, a spherical surface so that the transmission speed is increased with respect to the voltage-neutral neural network. What is necessary is just to form it.

In a neural network based on a current code (voltage code), one neuron is inserted into a branch in order to increase the length of a minimum closed circuit (minimum cut set), and two branches connected to the branch are connected in series (parallel). May be used.

The application of the neural network of the present invention is extensive,
For example, each bit of a complementary tree search input pattern (tree search input pattern), which is an information sequence on a partial neural network, is set to 2
Image recognition can be performed by executing the learning and association processing of the present invention for each image block on the partial neural network with respect to a given pixel input in correspondence with the pixels of the value image.

In the associative processing based on the current code, the nodal syndrome finds the shortest path of the complement tree branch between one neuron, and replaces each branch with a unit resistance. A unit current is applied to the node where the nodal syndrome is 1, and a voltage is applied. A branch with a large descent may be followed.

〔The invention's effect〕

According to the present invention, each neuron can simply construct an associative neural net simply by using addition modulo 2, that is, exclusive OR, and the neural net is not a complete graph, and thus is constructed as an LSI. The operation of each neuron can be performed only on the information from the neighboring neurons or the information on the neighboring branches, and as a whole, learning and associative processing by extremely high parallelism can be performed. The partial neural network can be formed freely by setting the value of the branch on the closed curve to 0, and the information of the 0 can be given at the time of learning to the manufactured integrated circuit, and the size of the partial neural network can be changed Can be. Furthermore, if a partial neural net is formed so as to include the crystal defect, which is inevitably generated in a wafer or the like, the defective partial neural network is separated from other normal partial neural nets, and the By setting the branch current to 0, it can be made operationally meaningless. Therefore, in the present invention, even if there is a crystal defect, the entire learning and associative operation can be executed as it is. Further, the information inside and transmitted to each neuron is digital information, and a highly reliable neural network can be formed. Further, the learning and the associative processing are all parallel processing for each neuron, so that the speed is extremely high.

[Brief description of the drawings]

Figure 1 is a configuration diagram of the present invention, FIG. 2 embodiment for explaining a process of obtaining a wood current code i _t from Hoki current code i _l view, FIG. 3 (a), (b) Easy FIGS. 4 (a) and 4 (b) show a current graph G _i for forming a current code i and a voltage graph Gv for forming a voltage code v.
Simple embodiment diagram of, FIG. 5 (a), (b) the embodiment diagram of the current graph _i and voltage graphs _v considering syndrome, simple conceptual diagram of a neural network G _i in FIG. 6 is the invention example view of a portion a neural net in Figure 7 is the present invention, FIG. 8 is a diagram showing the connection matrix of the partial neural network G _i of FIG. 7 (X, Y), Figure 9 (a) ~ (g ) the embodiment for explaining a learning algorithm by partial neural network view of the present invention, Fig. 10 embodiment diagram for describing the associative operation by the partial neural network G _i (Y, Y) of the present invention, the FIG. 11 is an embodiment diagram for explaining the associative operation by the partial neural network of the present invention. FIG. 12 is a diagram of the partial neural network when two complementary branches are continuously connected via one neuron. Graph showing a part, Fig. 13 is a Hopfield type neural Tsu basic concept of bets diagram, FIG. 14 is a conceptual diagram of a neural network of conventional with learning function, FIG. 15 is a structural view of a conventional associative memory. 16: Whole neural net, 17: Partial neural net, 18: Neuron, 19: Minimum cycle, 20: Tree, 21: Complementary tree.

Claims (1)

(57) [Claims] In a neural network formed by mutually interconnecting neurons, a closed circuit (or a graph) forming the neural network is provided.
Cutoff set), and is determined by the minimum intersymbol distance when the minimum intersymbol distance of the linear graph code corresponds to the length of the minimum cycle (or minimum cutset) of the graph. In the learning process, a part of the linear graph code is input as a learning input pattern into the neural network using a code whose error correction capability corresponds to the capability of associative ambiguity. Learning processing means for forming the other part of the graph code on the neural network and storing it on the neural network as an associative pattern; and during the associative processing, each neuron generates the associative pattern and the input search input pattern. Input only information in the vicinity of the neuron from inside and correct bit errors while calculating syndrome by addition , Associative neuro-computer, characterized in that having an associative processing means for association by decoding a linear graph code generated at the time of learning processing, utilizing the orthogonality of closed and cut set in the graph.