JPH07152715A - Pattern learning device using hopfield type neural network and pattern recollecting device - Google Patents

Abstract

PURPOSE:To easily and simultaneously learn many patterns by adjusting connection load between respective neuro-elements so that the energy value of a network has a certain specified external value on an energy curve. CONSTITUTION:In a Hopfield type neural network connecting each neuro-element to all neuro-elements other than itself, a connection load omegaif between respective neuro-elements is adjusted and learned so that the energy value E of the network to each learning pattern (p) has a certain specified energy external value Etp on an energy curve. Where the internal state, threshold and output of an i-th neuro-element are expressed respectively by mui, thetai and nui, a connection load between two neuro-elements i, j by omegaij; and when alpha1, alpha2 and alpha3 are defined as respective coefficients, an energy value and an error function at the time of presenting a pattern (p) to a current network are respectively expressed as EP and Ei.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pattern learning device and a pattern recalling device using a Hopfield type neural network in which each neuro element is synapse-connected to all neuro elements other than itself.

It is known in the literature that the interconnected neural network represented by the Hopfield neural network or the Boltzmann machine has excellent ability for combinatorial optimization problems, pattern recognition, associative memory, and the like. It is shown.

However, the learning methods such as the correlation learning for the mutual coupling type neural networks which have been proposed so far have a low learning ability, and the number of patterns that can be learned is a value much lower than the theoretical limit. The current situation is that there is a need for an effective learning device.

[0004]

9 to 11 are diagrams for explaining a Hopfield type neural network, and FIG.
9B shows an example of the configuration of the Hopfield type neural network, and FIG. 9B shows the internal state u _{i, the} threshold value θ _{i, the} output v _{i, and the} neuron of each neuro element i forming the Hopfield type neural network. shows the relationship between the coupling weight w _ij of the element i and neuro device _j, FIG. 9 (c) shows a step function is an example of the function f (u _i), FIG. 10 (a), the state of the neural network 10 (b) shows the learning method of the Hopfield, and FIGS. 11 (a) and 11 (b) show the correlation learning method.

Regarding the above-mentioned Hopfield type neural network, for example, "Neural network information processing (-introduction to connectionism or toward soft symbols-), 1.3 interconnection network, Hop field
Network, P20-P27, Hideki Aso, Sangyo Tosho Co., Ltd., 2nd edition, July 8, 1988 ”, but the Hopfield neural network is as shown in Fig. 9 (a). , Each neuro element (indicated by a circle) synapse-connects to all neuro elements other than itself, and the internal state u _i , which is determined by the states of the other neuro elements, and
The output is asynchronously changed by its own threshold value θ _i .

That is, the n neuroelements shown in FIG.
Hopfield neural network consisting of children
Where u is the internal state of the i-th neuro element_i,Threshold
Θ _i,Output v_iAnd the neuro element i and the neuro element
coupling weight w of j_ijThen, the state of each neuro element is
It is expressed by the equations (1) and (2) shown in FIG. 9 (b). However, f (u
_i) Is an appropriate decision function, usually shown in Fig. 9 (c).
A step function is used.

Further, as an important assumption for determining the properties of the Hopfield type neural network, the coupling weights between the neuro element i and the neuro element j are equal. That is, it is assumed that w _ij = w _ji formula (3).

As an index showing the state of the Hopfield type neural network, the equation (4) in FIG. 10 (a) is used.
The amount given by is called the energy of the network. Here, referring to FIGS. 9 (a), (b), (c), and FIG. 10 (a),
A learning method in the Hopfield neural network will be described with reference to FIG. The learning in the Hopfield neural network is performed by giving a predetermined pattern (for example, a binary pattern) as a teacher signal to each neuro element that constitutes the Hopfield neural network, and This is done by determining the coupling weight w _ij .

That is, in the equation (1) of FIG. 9 (b), by setting the coupling weight w _ij between the neuro elements to an appropriate value, the desired binary pattern in the Hopfield type neural network can be obtained. Can be learned.
Several methods for determining the connection weight w _ij have been proposed so far, but here, first, the method proposed by Hopfield and the correlation learning method, which is the most general learning method, are used. Will be described.

1) Hopfield learning method: First,
In 1982, we present the self-associative associative memory method proposed by Hopfield himself. However, assuming that the P patterns to be learned by the network are represented by the output v _i (0,1) of each neuro element i of the network, the P patterns are expressed by the equation (5) in FIG. 10 (b). Will be represented by.

In this learning method, first, each neuron element is
When the binary values of 0 and 1 are taken, the coupling load w _ij between the neuro elements and the threshold value θ _i are expressed by the equation (6) in FIG. 10 (b),
(7). However, at this time, there must be a relationship between the pattern p and the pattern q shown in the equation (8) of FIG. 10 (b).

Regarding the above equation (6), "Neural network information processing (-Introduction to connectionism or toward soft symbols-), 1.3 Mutual interconnection network, Hop field network, P20-P27, by Hideki Aso" ,
Sangyo Tosho Co., Ltd., July 8, 1988, 2nd edition ”formula 1.7
Is the same as that shown in.

This method has a problem that the learning ability becomes low because the conditional expression shown by the expression (8) in FIG. 10 (b) becomes a constraint condition. 2) Correlation learning method: Next, the correlation learning method, which is the most general learning method of the Hopfield neural network, will be described with reference to FIGS. 11 (a) and 11 (b).

In this correlation learning method, attention is paid to the energy E of the network, and an attempt is made to derive the correlation learning method from the viewpoint of the steepest descent method of the energy E. As shown in the above equation (4) of FIG. 10 (a), the energy E of the Hopfield neural network is
Is given by equation (9) in FIG. 11 (a). Here, when this energy E is partially differentiated by the coupling load w _ij , FIG.
Equation (10) of (a) is obtained.

Therefore, as to learn P patterns, with respect to the connection weight w _ij, for the energy E _P of the network, the steepest descent method, specifically, in the pattern in which the energy E is presented, the connection is performed. in a direction having an extreme value with respect to the load w _ij, based on the partial differential coefficients shown by the formula (1O), to change the connection weights w _ij. This process is shown in FIG. 11 (b).

That is, the energy E of the network is
When the steepest descent method is applied, the coupling load w_ijIs shown in FIG.
(b) dot w_ijEquation (11) shown as
Energy E and coupling load w attached to_ijRelationship with
As shown in the figure shown in FIG. 11 (b),
The steepest descent method is applied to the energy E, and the coupling load w _ij
Value of the energy E in the pattern presented
And the joint load w_ijIs changing to have extreme values for
The energy E of the network is
And the combined load w_ijSince it is a function of
Energy E for the pattern_PMoves in the lower direction
It Further, similarly, the threshold value is also expressed by the equation (12).
Dot θ_iBecomes However, α is a coefficient.

The above equations (11) and (12) are generally called the correlation learning method. Thus, when focusing on the energy E of the network, this method shows that the energy for each pattern is It can be thought of as a "drilling method" in which holes (that is, extreme values) on the curved surface of energy are continuously dug with respect to E _p .

[0018]

As described above, in the learning method of the Hopfield described above, the condition of the relationship shown in the equation (8) of FIG. 10 (b) is caused between the pattern p and the pattern q. Then, there is a problem that the ability to learn a plurality of patterns is low. As will be described later with reference to FIGS. 6 and 7 (a), the applicant of the present application can learn patterns (see FIG. 6) that satisfy the condition, but patterns that do not satisfy the condition {see FIG. Regarding (a) reference}, it is confirmed by a simulation of pattern recall that the learning ability is low.

Further, as shown in FIG. 11 (b), the above correlation learning method is a method for making the energy E _P of the network for the presented pattern as low as possible, and using the network after learning, When recalling a predetermined pattern, the energy value of the pattern to be recalled is expected to have an extreme value (minimum value) on the curved surface of the energy function.

Therefore, in the case of the network learned by the correlation learning method, when the coupling weight is changed so that the energy decreases from the high energy state, the state of the network is an extreme value with an energy curved surface, that is, It will converge to a certain learning pattern, and by this method,
Recall the learned patterns.

However, the above-mentioned correlation learning method has been described above.
Then, based on equation (11), the coupling load w_ijBy changing
Energy of the network for the indicated pattern
-E _PSince it is a method to make the extreme value of
The binding load and the threshold became lower as
The difference in the energy extremes of each pattern is relatively small
Therefore, it is difficult to learn many patterns at the same time.
There was a problem that it was difficult.

Also, using a trained network,
When recalling a given pattern, the recalled pattern is
There is a problem that the learned pattern cannot be recalled selectively because it depends on the initial value of the network. That is, in the case of recalling a pattern by inputting an initial value close to the recalled pattern, even if the predetermined pattern can be recalled, a pattern with a large difference (hamming distance described later) is used as the initial value. When inputting, there is a problem that the pattern cannot be recalled.

The recall of the pattern in the above Hopfield type neural network is the same as the internal state u of the n neuro elements i shown in FIG. 10A for the network having the learned connection weight w _ij . After inputting initial value data to _i , one of the n neuro elements is randomly selected (this random selection operation is called asynchronous operation), and the internal state u _{i of} the neuro element and the output v
By repeating the calculation of _i a plurality of times, the output v _i of each neuron is calculated from the given initial value
The process of converging on the output corresponding to the pattern you want to recall.

In view of the above-mentioned conventional drawbacks, the present invention provides a learning problem using a Hopfield neural network so that the energy value of the network for each learning pattern does not have a too low energy extreme value on the energy curved surface. Providing a Hopfield neural network capable of simultaneously learning more patterns than before by adjusting the connection weight of each neuro element so as to have a specified extreme value E _tp , and It is specified by causing the learned Hopfield neural network learned as described above to perform the above-mentioned starting action so that the energy value of the network becomes equal to the energy value of the pattern to be recalled. Can selectively recall patterns It is an object to provide a-up field type neural network.

[0025]

1 to 3 are diagrams for explaining the principle of the present invention, FIGS. 1 and 2 show the principle of the energy learning method, and FIG. 3 shows the principle of the pattern recall method. Shows. The above problems are solved by the Hopfield type neural network configured as follows.

(1) A pattern learning device using a Hopfield neural network in which each neuro element is synapse-connected to all neuro elements other than itself, and the energy value (E) of the network for each learning pattern is , On the energy surface, adjust the coupling weight (w _ij ) between each neuron so that it has a specified energy extremum (E _tP ), and perform learning.

(2) A pattern recall device using a Hopfield type neural network in which each neuro element is synapse-connected to all neuro elements other than itself, and is learned by the learning device described in the above item (1). Operates the neural network so that the energy value (E) of the neural network matches the energy value (E _rp ) of the pattern you want to recall, and selects the specified pattern above. It is configured so that it can be recalled.

[0028]

1 to 3 are explanatory views of the principle of the present invention. The action and operation of the energy learning method will be described with reference to FIGS.

From the above equation (4), the energy E of the Hopfield type neural network is calculated by the equation (13) in FIG.
Given in. Here, the target extreme value of the energy of the network for a certain pattern p is E _tp, and the energy value when the pattern p is currently presented to the network is E _p .

In the present invention, the error function E _e
Is the sum of squares of the difference between the target extreme value E _tp of the above energy for all learning patterns and the current energy value E _{p ,} and the condition for the energy of the network to have an extreme value in a predetermined pattern p. And the above error function E
Define _e as shown in equation (14).

Here, when the first term E ₁ on the right side of the equation (14) is partially differentiated by the coupling load w _ij , the equation (15) is obtained. Also, the formula (1
The right-handed second term E ₂ of 4) is expressed by the equation (16) based on the above equation (1).
Therefore, when this equation (16) is partially differentiated by the connection weight w _ij , equation (17) is obtained.

Therefore, the coupling load w_ijThe above error relation to
Number E_eThen, the steepest descent method is applied to
And the threshold θ_iEquation (19) is obtained for
It In the above equation (18), the first term on the right side is the network
Energy value E of Ku_pTo the pattern p
Target energy value E_tpIs a condition for
The second term on the right side is the target energy value E of the network.
_tpShows the condition that makes the pattern p extreme
{Energy value E and coupling load w in FIG. 2_ijSee the figure}
Therefore, in the direction that satisfies the above equation (18),
Coupling load w _ijTo the pattern p by changing
Coupling load w_ijTo learn the pattern p
it can.

Similarly, it is easy to learn a plurality of patterns by repeatedly presenting the target extremums of energy E _tq , _-for the other patterns q,-.

Next, the means for recalling a specific pattern in the Hopfield type neural network in which a plurality of patterns are learned as described above will be described with reference to FIG.

First, the energy value of the pattern p to be recalled is E _rp , the current energy value of the network is E, and this energy difference E _er is defined by the equation (20) in FIG.

The expression (20) is partially differentiated by a variable (output value of the neuro element i) v _i that determines the internal state u _j of the neuro element j selected at random, and the expression (21) is obtained. Expression (2
Partial differential value by v _i to the energy E 1) from equation (1) described above, from the equation (22), after all, equation (21), wherein
As shown in (23), when the above-mentioned steepest descent method is applied to the energy error E _{er with} respect to the output v _i of the neuro element i, the formula (24) is obtained.

Therefore, when recalling a specific pattern, the output v _i of the randomly selected neuro element i is
The energy value E _{rp of the} pattern to be recalled is previously obtained by repeating the calculation based on the equation (24) instead of the above equation (2) for the plurality of neuro elements randomly selected. By setting, the pattern having the energy value E _rp can be selectively recalled.

That is, the energy learning method using the Hopfield type neural network according to the present invention is
This is a method for performing learning on the Hopfield neural network so that the energy value of the network for each learning pattern has a specified extreme value on the energy curved surface. Therefore, since the energy extreme value of each pattern can be specified in advance, even if the learning is continued, the coupling weight or the threshold value becomes a very low value like the conventional correlation learning method, Since the difference between the extreme values of energy does not become small, more patterns can be learned as compared with the conventional correlation learning method.

Further, in the pattern recall method according to the present invention, when recalling a specific pattern, as described above, the output v _i of the neuro element i selected at random is expressed by the above equation.
Instead of (2), it is possible to set the energy value E _{rp of the} pattern to be recalled in advance by repeating the calculation based on the equation (24) for the plurality of randomly selected neuro elements. And the energy value E _rp
Patterns with can be selectively recalled.

[0040]

Embodiments of the present invention will be described in detail below with reference to the drawings. 1 to 3 described above are explanatory views of the principle of the present invention.
4 to 8 are views showing an embodiment of the present invention,
FIG. 4A is a diagram schematically showing the Hopfield neural network used in the embodiment.
(b) shows an example of the learning pattern, and FIG. 6 (a) shows
An example of another learning pattern is shown, and FIG. 6 (b) shows a simulation result when the learning pattern shown in FIG. 6 (a) is learned by the Hopfield learning method.
Shows the simulation result of the learning result in each learning method in the learning pattern shown in FIG.

In the present invention, means for performing learning for the Hopfield neural network so that the energy value of the network for each learning pattern has a specified extreme value on the energy curved surface,
Further, in the case of recalling a specific pattern, calculating the output v _i of the randomly selected neuro element i based on the equation (24) instead of the above equation (2) is performed randomly. The means for repeating the plurality of selected neuro elements is the means necessary for carrying out the present invention.
The same reference numerals indicate the same objects throughout the drawings.

Hereinafter, referring to FIGS. 1 to 3, FIGS.
FIG. 8 evaluates the performance of the energy learning method according to the present invention. That is, in the main memory of the computer, 10 × 10 = 100 neuro elements (units 1,1 to un) shown in FIG.
(10, 10) is constructed, a predetermined learning pattern p is input to each neuro element, and the connection weight between the neuro elements constituting the Hop field neural network is constructed. The error function E _{e with} respect to w _ij is subjected to the steepest descent method so that the energy value E _tp targeted by the network becomes an extreme value, the formulas (13) to (1) shown in FIG.
Based on 8), the energy learning method of the present invention is evaluated by simulating a calculation for changing the coupling load w _ij between the neuro elements in a direction satisfying the expression (18). At this time, the output v _i that each neuro element i can take is (-1,1)
6 and the learning pattern is shown in FIG.
It is assumed that the pattern shown in (a) and the five characters A, B, C, D, and E shown in FIG.

First, the simulation results of the conventional Hopfield learning method will be described. In this case, the learning pattern shown in FIG.
By inputting to each neuro element of the Hopfield type neural network shown in (4) and calculating the coupling weight w _ij between each neuro element by the equation (6) of FIG. 10 (b) described above, the learning pattern is , The condition shown by the equation (8) in FIG. 10 (b) is satisfied, and it can be seen that the conventional Hopfield learning method can be used to learn this pattern.

However, when the five patterns shown in FIG. 5 (b) are learned, each learning pattern does not satisfy the above conditional expression (8), so that the conventional Hopfield learning method is used. Then, as shown in the simulation result in FIG. 7 (a), it can be seen that the learning cannot be performed at all. As described above, the learning ability of the conventional Hopfield is considered to be considerably low, but as shown in the equation (7) of FIG. It seems that it is due to not considering.

Then, the simulation results by the above correlation learning method and the energy learning method of the present invention will be described with reference to FIGS. 4, 5, 7, and 8. In the simulation, first, each neuro element of the Hopfield type neural network shown in FIG. 4 (a) is provided with 500 patterns of each of the five patterns shown in FIG. 5 (b).
Present and learn once.

Specifically, the steepest descent method is applied to the coupling weight w _ij between the neuro elements i and j so that the five patterns are learned, and the energy value of the network has the extreme value. Then, changing the value of the coupling load w _ij is repeated.

In the conventional correlation learning method, the calculated value of the coupling weight w _ij is shown by the equation (11) in FIG. 11B, and in the energy learning method of the present invention, the equation (1) in FIG. It becomes the one shown in 18). Similarly, for the threshold value of each neuro element i, the equation (12) in FIG. 11 (b) and the equation (1) in FIG.
Based on the calculation formula shown in 9), the value of the threshold θ _i is changed so that the energy value of the network has an extreme value.

After performing the above learning, one pattern is randomly selected from the learning patterns, and the pattern is separated by 50 hamming distances from the pattern (input to 50 neuro elements out of 100 neuro elements). As a pattern value to be set, a value obtained by inverting the value of the learning pattern is input), and the network is operated 1000 times. Specifically, as described above, when the internal state u _i of the randomly selected neuro element _i is calculated, the output v _i of the network is changed based on the above equation (24).

In this way, the learning ability of the network by the correlation learning method, as shown in the simulation result of FIG. 7 (b), is the method of the Hopfield learning method (see FIG. 7 (a)). Compared to the above, it can be seen that it is greatly improved, but it is not enough to recall all the patterns.

FIG. 5 (c) shows the result of recall by simulation in the case of the energy learning method of the present invention. Figure 8 (c)
In the example shown in, the extreme value (E _tp ) of the target energy set for each character is A = -20000, B = -22000, C = -24000, D
= -26000, E = -28000 is shown, but Fig. 8 (c)
As is clear from the simulation results shown in
It can be seen that all patterns can be recalled almost completely, and that the energy learning method according to the present invention has a large learning ability as compared with the above learning method.

As described above, in the learning device and the recollecting device using the Hopfield type neural network of the present invention, the energy value (E) of the network for each learning pattern is a specified pole on the energy curved surface. Learning is performed by adjusting the coupling weight between each neuron so that it has a value (E _tP ). In addition, for the learned Hopfield neural network described above, operate the neural network so that the energy value (E) of the network matches the energy value (E _rp ) of the pattern you want to recall, and specify the specified pattern. It is characterized by selectively recalling.

[0052]

As described above in detail, according to the present invention, for a Hopfield neural network, the energy value of the network for each learning pattern is a specified extremum on the energy curved surface. (E
It is a method to perform learning so as to have _tP ). Therefore, since the energy extreme value (E _tP ) of each pattern can be specified in advance, even if the learning is continued, the coupling weight and the threshold value become very low as in the conventional correlation learning method. Since the difference between the extreme values of the energies of the respective patterns does not become small, it is possible to learn more patterns as compared with the conventional correlation learning method.

Further, in the pattern recall method according to the present invention, when recalling a specific pattern, as described above, the output v _i of the neuro element i selected at random is expressed by the above equation.
Instead of (2), it is possible to set the energy value E _{rp of the} pattern to be recalled in advance by repeating the calculation based on the equation (24) for the plurality of randomly selected neuro elements. And the energy value E _rp
There is an effect that a pattern having a can be selectively recalled.

[Brief description of drawings]

FIG. 1 is an explanatory diagram (1) of the principle of the present invention.

FIG. 2 is an explanatory diagram of the principle of the present invention (No. 2)

FIG. 3 is an explanatory diagram of the principle of the present invention (No. 3)

FIG. 4 is a diagram showing an embodiment of the present invention (No. 1).

FIG. 5 is a diagram showing an embodiment of the present invention (part 2).

FIG. 6 is a diagram showing an embodiment of the present invention (part 3).

FIG. 7 is a diagram showing an embodiment of the present invention (Part 4).

FIG. 8 is a diagram showing an embodiment of the present invention (No. 5).

FIG. 9 is a diagram (1) explaining a Hopfield neural network.

FIG. 10 is a diagram for explaining the Hopfield neural network (No. 2).

FIG. 11 is a diagram (No. 3) explaining the Hopfield neural network.

[Explanation of symbols]

u _i to learn the energy dot w _ij pattern P connection weights E Hopfield neural network output w _ij neuro device i and neuro device j of the internal state theta _i threshold v _i neuro device of neuro device, network energy Partial differential value when E is subjected to the steepest descent method with respect to the connection weight w _ij A partial differential value is obtained when the steepest descent method with respect to the coupling load θ _{i is} applied to the energy E of the network so as to learn the dot θ _i pattern P.

Claims (2)

[Claims] 1. A pattern learning device using a Hopfield neural network in which each neuro element is synapse-connected to all neuro elements other than itself, and the energy value of the network for each learning pattern.
A hop characterized by adjusting the coupling weights (w _ij ) between each neuron so that (E) has a specified energy extremum (E _tP ) on the energy surface. Pattern learning device using field type neural network. 2. A pattern recalling device using a Hopfield type neural network in which each neuro element is synapse-connected to all neuro elements other than itself, which has already been learned by the learning device according to claim 1. For the Hopfield neural network, operate the neural network so that the energy value (E) of the neural network matches the energy value (E _rp ) of the pattern you want to recall, and select the specified pattern above. A pattern recalling device using a Hopfield neural network characterized by recalling.