JP2732603B2 - Learning process monitoring device for network configuration data processing device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Summary] By forming a hierarchical network using a basic unit that converts a product sum of a plurality of inputs and weights by a threshold function as a basic unit, a desired output for an input pattern is obtained. In a network configuration data processing device that processes to obtain a pattern, the purpose of the present invention is to provide a visual display of the learning realization status when the weight value is set by learning. By supplying an input signal to the output unit, a corresponding output signal from the basic unit of the output layer and a teacher signal indicating a value to be taken by the output signal are used.
By calculating an error value representing the magnitude of the mismatch between the two signals, and sequentially updating the weights from the initial value according to the weight update amount calculated based on the sum of the calculated error values, Weight learning means for processing so as to obtain a value of a weight such that the sum of values falls within a predetermined allowable range, and information on the structure of the hierarchical network and information on a learning pattern held in a learning pattern holding unit. And an evaluation function distribution display unit for visually displaying the distribution of evaluation functions representing the progress of learning in response to a change in the weight of a small number of connections selected as appropriate. A weight search path display unit for receiving the weight of the connection that changes with the progress of the learning by the learning means and plotting the weight on the display image obtained by the evaluation function distribution display unit. It is configured for visually observing the quality of the setting of the coefficients that affect the progress of learning (epsilon and / or alpha).

[Industrial applications]

The present invention relates to a learning process monitoring device for a network configuration data processing device.

With a conventional sequential processing computer (Neumann-type computer), it is difficult to adjust the data processing function of the computer according to changes in usage or environment. Processing methods have been proposed. In particular, a processing method called the back propagation method (DERumelhart, GE Hinton, and RJ Williams, “Lear
ning Internal Representations by Error Propagatio
n, "PARALLEL DISTRIBUTED PROCESSING, Vol.1, pp. 318-3
64, The MIT Press, 1986) has attracted attention because of its practicality.

In the back-propagation method, a hierarchical network is composed of a kind of node called a basic unit and an internal connection having a weight. FIG. 8 shows the basic configuration of the basic unit 1. The basic unit 1 is a multi-input / one-output system, and accumulates a plurality of inputs by a weight of an internal connection and sums all multiplication results thereof.
And a threshold processing unit 3 that performs a non-linear threshold process on the accumulated value and outputs one final output. Then, a hierarchical network is formed by connecting a number of basic units 1 having such a configuration in a hierarchical manner as shown in FIG. 9, and converts a pattern of an input signal into a pattern of a corresponding output signal. The data processing function will be demonstrated.

In this back propagation method, the weight of the internal connection in the hierarchical network is determined according to a predetermined learning algorithm so that the output signal for the selected input signal becomes a teacher signal indicating the signal value to be taken. Will be done. Then, when the weight is determined by this processing, even if an unexpected input signal is input, by outputting an appropriate output signal from this hierarchical network, a “soft” parallel distributed The data processing function is realized.

In order to make the network configuration data processing device having such a configuration practical, it is necessary to realize a weight learning process in a shorter time. This is one of the issues that must be solved in the context of the need to increase the scale of the hierarchical network in order to realize complex data processing. .

[Conventional technology]

If the h-th layer is the first layer and the i-th layer is the second layer, the operation performed by the accumulation processing unit 2 of the basic unit 1 is as follows:
The calculation performed by the threshold processing unit 3 is shown in the following equation (2).

Where, h: unit number of the h layer i: unit number of the i layer p: input signal pattern number θ _i : threshold value of the i-th unit of the i layer W _ih : weight of internal coupling between the h−i layers x _pi : With respect to the input signal of the p-th pattern, the product sum of the input from each unit of the h-layer to the i-th unit of the i-th layer y _ph : the output of the h-layer for the input signal of the p-th pattern y _pi : the input signal of the p-th pattern In the output back propagation method of the i-th layer, the weight W _ih and the threshold θ _i are adaptively and automatically adjusted by error feedback. As is apparent from the equations (1) and (2), the adjustment of the weight W _ih and the threshold θ _i needs to be performed at the same time, but this task is a difficult task that interferes with each other.

Next, a conventional technique of weight learning processing will be described.
The present invention is carried out with a hierarchical network having a structure of h layer-i layer-j layer as shown in FIG.

In the learning process of the weights, first, according to the following equation, the error vector E _p is the square sum of the error between the output signal from the teacher signal and the output layer is calculated as the error of the hierarchical network. Here, the teacher signal is a signal to be taken by the output signal.

Where E _p : error vector for p-th pattern input signal E: sum of error vectors for all pattern input signals (corresponding to evaluation function) d _pj : j for p-th pattern input signal Teacher signal to layer j-th unit Here, in order to find the relationship between the error vector and the output signal, the equation (3) is partially differentiated with respect to y _pj . Get. Furthermore, to determine the relationship between the input to the error vector E _p and j layer, the error vector E _p is partially differentiated by x _pj, Get. Furthermore, to determine the relationship between the weight of the error vector E _p and i-j layers, the error vector E _p is partially differentiated with W _ji, To obtain a solution represented by the product sum of.

Then, when determining the change of the error vector E _p for the output y _pi of the i-layer, Get. Furthermore, when the change of the error vector with respect to the change of the sum x _pi to the i-th layer input unit is calculated, To obtain a solution represented by the product sum of. Further, when the relation of the change of the error vector to the change of the weight between the hi and i layers is obtained, To obtain a solution represented by the product sum of.

From these, the relationship between the error vector for all input patterns and the weight between the ij layers is obtained as follows.

Also, the error vector and h−i for all input patterns
When the relationship with the weight between layers is obtained, it is as follows.

Equations (11) and (12) show the rate of change of the error vector with respect to the change of the weight between the layers. Therefore, if the weight is changed so that this value is always negative, the known gradient method can be used. , An error vector E (evaluation function) can be asymptotically set to zero. Therefore, in the conventional back propagation method, the update amount per weight ΔW _ji
And ΔW _ih are set as follows, and the updating of the weights is repeated so that the sum E of the error vectors converges to a minimum value.

Here, ε is a coefficient corresponding to a learning control parameter.

Further, as an extension of the expressions (13) and (14), the following is also used.

Here, α is a coefficient corresponding to the control parameter. T is the number of updates.

FIG. 11 shows a flowchart showing the learning process.

[Problems to be solved by the invention]

The biggest problem with the back propagation method is that the number of learnings required for convergence is long. This problem becomes more serious as the network structure becomes larger.

If the coefficients ε and α corresponding to the control parameters are made sufficiently small, the sum E of the error vectors will almost certainly converge, but the number of times of learning until the convergence will increase. On the other hand, if both parameters are increased in order to reduce the number of times of learning, there is a risk that the sum E of the error vectors may fluctuate. The number of units in the input layer is “13” and the number of units in the middle layer is “8”
Assuming a hierarchical network in which the number of units in the output layer is “7”, the learning result obtained when learning using 62 input pattern signals and the corresponding teacher pattern signal is shown in FIG.
Figure 12 shows. In FIG. 12, the horizontal axis is the number of times of learning.
The vertical axis is the sum of the error vectors at that time. here,
The coefficients corresponding to the control parameters were set to ε = 0.3 and α = 0.2.

As is clear from FIG. 12, although a slight difference can be caused by a difference in parameter setting, learning is repeated a considerable number of times until an optimum weight is determined. Then, how to set the values of the coefficients ε and / or α greatly affects the number of times of learning until an optimum weight is obtained.

From this, depending on how the values of the coefficients ε and / or α are selected for each of the plurality of weights W _ih and W _ji ,
Under what circumstances the above learning will be completed
It is desired to visually display such that the operation training personnel are aware of the quality of the setting of the coefficient ε and / or α, for example.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a network configuration data processing device that can visually display a learning implementation status when a weight value is set by learning.

[Means for solving the problem]

 FIG. 1 is a diagram illustrating the principle of the present invention.

In the figure, reference numeral 1 denotes a basic unit which is a basic unit of the hierarchical network. The unit receives a plurality of inputs and weights to be multiplied with these inputs to obtain a product sum, and obtains the obtained product sum value. Processing is performed so as to obtain a final output by conversion using a threshold function. 1-h is a plurality of basic units forming an input layer, 1-i is a plurality of basic units forming one or more intermediate layers, and 1-j is one or more forming an output layer Is the basic unit. Basic unit 1-h
And the basic unit 1-i, between the basic units 1-i, between the basic units 1-i and the basic units 1-j, and weights set corresponding to the respective connections. Thus, a hierarchical network indicated by 10 is configured.

Reference numeral 20 denotes a learning pattern holding unit for holding a learning pattern necessary for the weight learning process, and an input signal (or input signal holding area) 21 for holding a plurality of predetermined input signals.
And a teacher signal (or teacher signal holding area) 22 for holding a teacher signal to be an output signal with respect to the predetermined input signal.
13 is an output signal deriving means for converting the input signals held in the input signal holding area 21 into the hierarchical network 10
To obtain an output unit of each layer of the result of the supply against, 12 holds the above-mentioned W _ih and W _ji a weight of binding, 30 is a weight learning means, the error value calculation unit 33 An error value indicating the degree of mismatch between the two signals is calculated from the output signal from the output signal deriving means 13 and the held teaching signal 22, and the sum of the error values of all input signals supplied is calculated. It is processing to ask.

The weight learning means 30 includes a control parameter (coefficient ε, α) 32 for calculating the weight update amount ΔW and an update rule 31 for updating the weight, and a weight of the connection in the hierarchical network 10.
12 is sequentially updated each time the number of times of learning progresses from the initial value, and stored as a new connection weight 12. That is, And , The connection weights _Wih and _Wji are updated.

The evaluation function distribution display unit 50 is used to calculate the distribution of the evaluation function.
51, processing 52 for calculating a cutting plane, and processing 53 for displaying the distribution of the evaluation function.

Given the structure of the hierarchical network 10 and the learning pattern, the weights W _ih and W _ji
At which value the sum of the error vectors, ie, what value the evaluation function E takes, can be known. That is, the value of the evaluation function E can be calculated for a large number of connection weights by cut-and-try. In the case of the monitoring device of the present invention, such calculation of the distribution of the evaluation function may be considered to have been executed in an off-line manner. When the state of the distribution of the evaluation function is calculated, which of the many existing connection weights has a large influence on the value of the evaluation function E based on the change in the weight is determined. You can know about. When the monitoring device of the present invention is to selectively extract the weight W _x of a certain binding, the weight
Coefficient of the above the W _x on going learning manner to determine ε and /
Alternatively, when α is selected, each time learning progresses, it is possible to visually display what path the weight approaches the optimal weight which should be approached.

Therefore, in the calculation process 52 of the cutting plane shown, when attention is paid to the weight W _x to perform the monitoring of the desired certain weight W _x, on a visual display on a two-dimensional plane Determines the preferred plane. Then, the display process 53 of the distribution of evaluation function to obtain a figure which indicates whether the value of the evaluation function corresponding to the value of the weight W _x on the determined plan how corresponding to.

The weight search path display unit 60 receives the situation in which the weight learning unit 30 generates a new connection weight each time the number of times of learning advances, and displays the new connection weight on the graphic to be displayed on the evaluation function distribution display unit 50. Is calculated in what position the weight is located. This calculation is performed in a weight search path calculation process 61 shown in the figure. Then, based on the calculated result, the display processing 62 of the weight search path
Plot the positions of the new connection weights on the figure.

These results are displayed on the display device 70. That is, when a certain value is set as the coefficient ε and / or α,
As the number of times of learning by the weight learning means 30 progresses, it is visually displayed under what condition the position of the plot approaches the optimum weight.

Of course, the premise of the present invention is that the optimum weight is known in advance, but how to approach the optimum weight depends on the setting of the value of the coefficient ε and / or α. Inform trainees.

(Operation)

Information about the structure of the hierarchical network 10 and the contents of the learning pattern storage unit 20 are given to the evaluation function distribution display unit 50, and the distribution of the evaluation function when viewed on a desired plane is displayed so as to represent, for example, a contour line of a two-dimensional figure. You. The coefficient ε and / or α for the corresponding weight W _x is set as the control parameter 32, and the initial value is set as the weight 12 of the coupling.

In this state, each time the learning in the weight learning means 30 progresses (or every suitable number of times), the weight search path display unit 60 plots the position of the newly generated weight W _x on the figure. I will do it. The coefficient ε and / or α
It can be visually recognized that an undesired oscillation occurs depending on how the value is given.

〔Example〕

In a state where the characteristics of the distribution of the evaluation function are grasped, in order to display the characteristics well,
A cutting plane calculation process 52 shown in FIG. 1 is performed. The following two methods are considered in obtaining a plane for obtaining a display in which the characteristics appear well as described above.

(A) Cutting plane selection method (part 1) It is now assumed that optimum weights are obtained for three types of weights W ₁ , W ₂ , and W ₃ , and the optimum weights W _c are coordinates ｛W _c1 , W _c2 , _Assuming that the position vector is given by W _c3 }, the position vector for the optimal weight is represented as shown in FIG. 2 (W _c ). Therefore, a plane S including the position vector (W _c ) is considered. The plane containing the position vector (W _c ) exists infinitely, so to speak, the plane containing the vector (W _c ) and the vector (W _x ) should be cut in consideration of an arbitrary vector (W _x ) If it is a plane, any point W on the plane S
_p is represented by W _p = aW _c + bW _x (where a and b are arbitrary real numbers). When such a plane S is selected, it is preferable that the learning is performed so as to be directed to the tip of the position vector (W _c ) corresponding to the optimum weight. It is possible to efficiently monitor what path the learning progresses toward.

(B) the cutting plane selection method (Part 2) Now, as for the optimal weights coordinates _{{W c1, W c2, W} c3} are given, for example contact is fixed to a fixed value W _c2 for weight W ₂ There considered to change the values for the weights W ₁ and W ₃ are, as Figure 3 illustrated, a plane S 'passing through the fixed value W _c2
Is selected as the cut surface. When the plane S 'is selected in this manner, it is preferable that learning is performed so as to be directed to a point on the plane S' (the tip of the position vector (W _c )). Thus, it is possible to efficiently monitor what path the learning proceeds toward the tip.

A general description of this cutting method is as follows. That is, In the above equation (1), x _pi is linear with respect to y _ph . From this, when considering in a space where x _pi and y _ph are coordinate axes, equation (1) is a hyperplane equation (where p and i
Is fixed). Assuming that y _ph is two-dimensional and x _pi is one-dimensional, x _pi = _{Wi 1} y _p1 + _{Wi 2} y _p2 −θ _i , and as shown in FIG. 4, x _pi becomes x _pi = W _i1 y _p1 + W _i2 y comprises _p2 - [theta] _i = 0 becomes linear and the plane of the coordinate axes (x _pi) can theta _i.

The position of the line where x _pi = 0 depends only on the ratio between W _ih and θ _i, and is not affected by changes in the absolute value of x _pi . Dependent on this absolute value is the slope of the hyperplane.

Therefore, instead of FIG. 4, using a step function as a threshold function between x _pi and y _pi is shown in FIG. 5. In FIG. 5, the weights W _ih and Threshold θ
It will only depend on the ratio between _i . As a threshold function, assuming that the step function is an S-shaped function that is blunted, the positional relationship depends on the ratio between W _ih and θ _i, and the absolute value | y _pi | reflects the effect of the blunting .

Therefore, when the purpose of use of the hierarchical network is identification, what contributes to determining the boundary is the ratio between the weights, and the absolute value contributes to the ambiguity of the boundary. Therefore, for example, considering a three-dimensional figure in which the values of the above-described evaluation function E are plotted for each point on the two-dimensional plane using two weights as two-dimensional coordinate axes,
A shape with a canyon or conical distribution spreading radially from the origin of the coordinates appears.

Figure 6 shows an example of a figure of the evaluation function E corresponding to the vector W _c and W _x.

The value of the evaluation function E at the point given by aW _c + bW _x is shown, and has a three-dimensional graphic.

FIG. 7 shows an evaluation function E for the three-dimensional figure shown in FIG. 6 in consideration of a plane corresponding to the cutting plane selection method (part 1).
Is shown in a display figure in which the value of is represented by a contour line. Weights newly generated by learning are plotted on the display figure, and the progress of learning is monitored. In the case of the above cutting plane selection method (Part 1), the vertical cross section of the above-mentioned "shape having a valley or conical distribution spreading radially from the origin of the coordinates" is seen, and the optimum weight search process is almost completed. Rest on a flat surface. In the case shown in FIG. 7, it is preferable that the learning progresses so as to proceed along the valley of the gorge which extends diagonally upward to the right in the figure.

In the case of a graphic displayed with a plane corresponding to the above-described cutting plane selection method (No. 2), the cross section of the gorge or the cone is viewed. On this display figure,
The newly generated weights are plotted as described above.

〔The invention's effect〕

As described above, according to the present invention, the progress of learning can be visually checked, and the operation trainee can observe the quality of the coefficients ε and / or α given by himself / herself. Becomes

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing the principle of the present invention, FIG. 2 and FIG. 3 are explanatory diagrams for explaining a method of selecting a cutting plane, and FIG. 4 and FIG. FIG. 6 is a diagram showing an evaluation function E, FIG. 7 is a display diagram shown by a plane corresponding to a cutting plane selection method, FIG. 8 is a configuration diagram of a basic unit, FIG. 9 is a hierarchical network Fig. 10 is an illustration of the back propagation method.
FIG. 11 is a flowchart showing a learning process, and FIG. 12 is a diagram showing a situation in which weights change due to learning. In the figure, 1 is the basic unit, 2 is the accumulator, 3 is the threshold processor, 1
0 is a hierarchical network, 20 is a learning pattern holding unit, 30 is a weight learning means, 50 is an evaluation function distribution display unit, 60 is a weight search path display unit, and 70 is a display device.

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Nobuo Watanabe 1015 Uedanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture Inside Fujitsu Limited (72) Inventor Takashi Kimoto 1015 Ueodanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture Fujitsu Limited

Claims (1)

(57) [Claims] The present invention obtains a product sum by receiving one or more inputs from a preceding layer and a weight (12) of a connection to be multiplied with the input, and obtains a product sum value by a threshold value. A basic unit (1) that is converted by a function to obtain a final output is a basic unit, a plurality of the basic units (1-h) are an input layer, and a plurality of the basic units (1-i) are an intermediate layer. One or more intermediate layers, and one or more of the basic units (1-j) as an output layer, between the input layer and the frontmost intermediate layer, between the intermediate layers, and In the data processing device forming an internal connection between the intermediate layer and the output layer in the final stage and configuring the hierarchical network (10) by setting the weight corresponding to the internal connection, For a plurality of basic units (1-h) The output signal deriving means (13) for obtaining an output signal corresponding to the input signal from the basic unit (1-j) of the output layer by supplying the input signal (21) of ) Using the output signal of each layer unit and the teacher signal (22), which is stored in the learning pattern storage unit (20) and indicates the value to be taken by the output signal, to determine the mismatch between the two signals. According to an error value calculating means (33) for calculating an error value representing the magnitude and a weight update amount to be calculated based on the sum of the error values calculated by the error value calculating means (33), A weight learning means (30) for updating the weight (12) of the connection sequentially from the initial value so as to obtain the value of the weight such that the sum of the error values falls within a predetermined allowable range. And the weight learning means (30) In both cases, processing is performed to determine the update amount of the weight in the current update cycle in consideration of the data factor related to the update amount of the weight determined in the previous update cycle, and the structure in the hierarchical network (10) is determined. The input signal (21) and the teacher signal generated when the weight of the combination (12) is changed by receiving the information about the learning pattern and the information about the learning pattern held in the learning pattern holding unit (20). Based on the error value from (22), an evaluation function with the error value as a variable is used to obtain the distribution of the evaluation function with the weight of the connection (12) as the coordinate axis. An evaluation of obtaining a display image of the distribution of the evaluation function by specifying the weight of an arbitrary small number of connections that have a large influence and projecting the evaluation function on a cutting plane using the specified weight of the connection as a coordinate axis and displaying the evaluation function. A value function distribution display unit (50) and a weight image learning unit (30) receive a change state of the weight (12) of the connection while learning is progressing, and display the distribution of the evaluation function on a display image corresponding to the display. A weight search path display unit (60) for plotting a change situation of the connection weight (12); a display image of the evaluation function distribution obtained by the evaluation function distribution display unit (50); A display device (70) for visually displaying the plot obtained by the search route display unit (60).
A value is set for a coefficient (ε and / or α) that affects the change state of the weight (12) of the connection by the weight learning means (30). A learning process monitoring device for a network configuration data processing device, characterized in that observation is possible.