JPH02222061A - Learning machine - Google Patents

Abstract

PURPOSE:To minimize an error with high efficiency and to shorten the learning time by obtaining the optimum value of a learning parameter in the minimum point searching direction of the error and at the same time changing the weight of a variable weight multiplier. CONSTITUTION:A learning parameter near the minimum point of an error set in its searching direction is extracted 18 after decision 16 of the searching direction of a point where the error is minimized in a weight space. The paraboloidal approximation is applied to the periphery of the minimum point of the error and an error produced at an apex of the paraboloid is extracted 19. Then the weight of each of variable weight multipliers 3 - 8 is changed 20 by means of a learning parameter obtained with the minimum error. Then the searching direction is obtained for a new minimum error point and the optimum value of the learning parameter obtained in the preceding search of the minimum point is reflected to set 17 the initial value of the learning parameter. The minimum error point between both searching direction is obtained and the weight is changed. An error minimizing circuit 21 of such a constitution searches continuously the minimum error points until the error is reduced down to a satisfactory level.

Description

[Detailed description of the invention] Industrial applications The present invention relates to learning machines.

BACKGROUND OF THE INVENTION Conventional learning machines include, for example, the ``Learning'' error (Learning'' error) by Ruw+Gwelhart et al.
g representations by b
ack-propagating errors)”
, Naichi +- (Nature) Vol, 323 N
o, 9 (1986).

FIG. 9 shows a configuration diagram of this conventional learning machine, where 51.52 is an input terminal, 53 is an input terminal,
8 is a variable weight multiplier, 59 is a mark, 61 is an adder with saturation input/output characteristics, 62 is an output terminal, 63 is a teacher signal generation section, 64 is an error calculation section, 65 is a search direction determination section, 66 is a weight This is the change section. As shown in Figure 9, a conventional learning machine connects adders with saturated input/output characteristics in a hierarchical manner.
It has a configuration in which variable weight multipliers are connected between adders in each layer.

The input/output characteristics of adders 60 and 61 in the conventional learning machine configured as described above are shown in FIG.
As shown in Figure O, the input/output characteristics of adders 59, 60 and 61 have saturation characteristics. That is, the input/output characteristics of the adder are output[jl = func (Σ1nput[
il)” (1). Here, ou
tput[jl is the output signal of the j-th adder, 1np
ut[il is the i-th input signal input to the j-th adder, funcO is a sigmoid number with saturation characteristics furlc(x) = 2 / (1+ exp(
-x) ) -1 etc.

As shown in FIG. 9, the signal input to the adder is
The output signal of the adder in the previous stage is weighted. That is, 1nput[il = enemy[L J]nex[il...
(2) Here, x[:il is the output signal of the i-th adder in the previous stage, and %'[L Jl is the output signal of the i-th adder in the previous stage to the third adder. This is the weight that is multiplied by the variable weight multiplier when it is input.

In the conventional learning machine, a teacher signal generator 63 generates a desired output signal for the input signal as a teacher signal in accordance with signals input from input terminals 51 and 52, and an error calculator 64 outputs a desired output signal from an output terminal 62. An error E is calculated from the difference between the actual output signal and the teacher signal. The error E is E=0.5 zeroii (z[kl −t[kl)”=E
(w)...(3) It is expressed as follows. Here, 2[kl is the output signal of the th adder in the output layer, t[kl is the teacher signal for 2[kl, i is the sum of the number of patterns of the teacher signal, and n is the output signal of the adder in the output layer. W is a vector representation of the weights of the variable weight multiplier. The search direction determination unit 65 determines the minimum point search direction of the error in the weight sky that expresses the weight as a vector. The search direction is the direction of steepest descent, and is determined by . Based on the search direction determined in this way,
The weight change unit 66 includes each variable weight multiplier 53, 54, 55.
, group, 57. Find the amount of change in the weight of 58 and change the weight. The method of finding the amount of change in 0 weight is based on the steepest descent method and the acceleration method. α is a positive constant called the Xi parameter, and α is the acceleration parameter. A positive constant called ΔW" is the ΔW at the previous weight change. By repeating the process of determining the amount of weight change as described above, the error becomes smaller, and when the error becomes sufficiently small, the output signal becomes Learning ends when the value is sufficiently close to the desired value.

Problems to be Solved by the Invention However, in the above configuration, the learning parameter ε
and acceleration parameter α are determined empirically, so
These values are not necessarily optimal values, and there is a problem in that the time required for learning is long.

In view of this, an object of the present invention is to provide a learning machine that requires less time for learning.

Means for Solving the Problems The present invention includes a search direction determination unit that determines the minimum error point search direction in a weight space that expresses the weight of a variable weight multiplier as a vector, and a search direction determination unit that determines the minimum error point search direction in the weight space that expresses the weight of a variable weight multiplier as a vector. A learning parameter changing section that calculates the error by gradually increasing or decreasing the parameter value; a paraboloid approximation section that approximates the error surface near the minimum point of the error with a paraboloid and calculates the error at the vertex; A weight change unit that changes the weight of each variable weight multiplier by using the learning parameter at the point where the error is minimum as the optimum value of the learning parameter, and a weight changing unit that changes the weight of each variable weight multiplier by using the learning parameter at the point where the error is minimum as the optimum value of the learning parameter. a learning parameter initialization unit that reflects the learning parameter in the initial value of the point search; the search direction determination unit; the learning parameter initialization unit; the learning parameter change unit; the paraboloid approximation unit; and the weight change unit. It is a learning machine equipped with an error minimization circuit that can be used repeatedly and minimize the difference sufficiently.

According to the above-described configuration, the present invention determines the search direction of the point with the minimum error in the weight space in the search direction determining section, and then the learning parameter changing section changes the learning parameter near the point with the minimum error in the search direction. Then, in the paraboloid approximation section, approximate the neighborhood of the minimum error point to a paraboloid to obtain the error at the vertex, and set the point where these errors are minimum as the point with the minimum error in the search direction, and perform learning at that point. A weight change unit changes the weight of each variable weight multiplier using the parameter. Next, the search direction determination section calculates a new search direction for the point with the minimum error at the point with the minimum error, and the learning parameter initialization section reflects the optimal value of the learning parameter in the previous minimum point search to adjust the learning parameter. After setting the initial value, similarly to the previous search for the minimum error point, find the minimum error point in the current search direction and change the weight.
The error minimization circuit repeats the search for the minimum error point until the error becomes sufficiently small. As described above, once the minimum error point search direction is determined, the optimal learning parameters are automatically found in that direction, and by reflecting the optimal values of the learning parameters in the previous search in the initial values of the current search, the optimal In order to proceed with learning by reducing the error while efficiently determining the learning parameters, the error becomes sufficiently small and the learning can be completed in a short learning time.

Examples Examples of the present invention will be described below with reference to the drawings.

FIG. 1 shows a configuration diagram of a learning machine in a first embodiment of the present invention. In FIG. 1, ■ and 2 are input terminals, 3.4.5.6.7 and 8 are variable weight multipliers, and 9
．． 10 and 11 are adders with saturation input/output characteristics, 12 is an output terminal, 13 is an output signal calculation circuit, 14 is a teacher signal generation section, 15 is an error calculation section, I6 is a search direction determination section, 17
18 is a learning parameter initialization unit, 18 is a learning parameter change unit, 19 is a paraboloid approximation unit, 20 is a weight change unit, and 21 is an error minimization circuit.

FIG. 2 shows a contour diagram of an error surface in a weight space in which the weights of the variable weight multiplier are represented by vectors.

In Figure 2, WE! s, j+] and w[+pt J
2] are the weights of any two variable weight multipliers among variable weight multipliers 3.4.5.6.7 and 8. In the learning of the learning machine of this embodiment, starting from the initial value of the weight of the variable weight multiplier represented by the starting point of the error surface shown in FIG. The goal is to repeat the search and reach the global minimum point of error. The variable weight multipliers 3.4.5.6.7 and 8 multiply the input signals with weights and output the resultant signals. Adder 9.10
and 11 have saturation input/output characteristics expressed by equation (1),
The output signal calculation circuit 13 calculates an output signal by multiplying and adding human input signals input from input terminals 1 and 2.

The teacher signal generator 14 generates a desired output signal as a teacher signal for the human input signal, and the error calculator 15 outputs a terminal! 2
From the actual output signal output from and the teacher signal (
3) Find the first value of the error according to the formula. The search direction determination unit 16 determines the search direction for the minimum point of error in the weight space that represents the weight of the variable weight multiplier as a vector. The search direction is determined by the steepest descent direction g at the starting point, that is, by equation (4). FIG. 3 is an explanatory diagram of the operation of the error minimization circuit in the initial minimum point search of this embodiment. The starting point and PI shown in FIG. 3 coincide with the starting point and P i of FIG. 2, and FIG.
The error curve of the cross section by the straight line connecting I is shown. The learning parameter initialization unit 17 sets the initial value of the learning parameter to εθ in the first minimum point search, and sets the learning parameter value used for the previous weight change or ε6, whichever is larger, in the second and subsequent minimum point searches. The learning parameter is determined to have a value, and the error with respect to the initial value of the learning parameter is determined. Here, εe is a positive constant. In the first minimum point search shown in FIG. 3, the initial value of the learning parameter is εB. When the error with respect to the initial value of the learning parameter becomes smaller than the initial value of the error, the learning parameter changing unit 18 doubles the value of the learning parameter ε to obtain the error value. Repeat until it starts to increase.

That is, ε k = ε k−1 ne 2 (6), and the error is Eh = E(w + t k *
g)...Calculate as (7). In the first minimum point search shown in Fig. 3, since Es < Eorg, the value of the learning parameter ε is doubled, and Eoro > EII > E
l > E2 (Es), so the learning parameter changing unit 18 calculates up to Es. Note that when the error with respect to the initial value of the learning parameter increases from the initial value of the error, the learning parameter changing unit 18 changes the value of the learning parameter. The operation of calculating the error by multiplying by 1/2 is repeated until the error becomes smaller than the initial value of the error. That is, ε
:εb-+/2...◆(8) and the error is (7
) is calculated using the formula. The paraboloid approximation unit 19 approximates the vicinity of the minimum error point with a paraboloid. In order to find the error at the points where the weight values change at equal intervals in the weight space in FIG. Find the error at ε2.5'' (ε2+ε3)/2. In Figure 3, E2.S < E2 <
Since Es < El, E2 * E2, s,
The error surface near the point with the minimum error is approximated by a paraboloid that passes through the three points of Es, and the error at its vertex is determined. That is, Ev = E(w+εv*g) (9) However, the weight change unit 20 uses the learning parameter for the smallest error among the errors determined as described above to change each variable weight multiplier. change the weight of

In Figure 3, EII E2. E2. S, E3t Ev
The learning parameter ε3 corresponding to Es having the smallest error among them is set as the optimum value of the learning parameter in this search direction, and the weight of each variable weight multiplier is changed using ε3.

Regarding the changed weights, the output signal calculation circuit 13 calculates an output signal, and the error calculation unit 15 calculates the output signal based on the difference between the teacher signal outputted by the teacher signal generation unit 14 and the output signal, which is given by equation (3). Calculate the error. Similar to the first minimum point search, the search direction determining unit 16 determines the minimum point search direction of the error in the weight space to be the steepest descent direction in PI. FIG. 4 is an explanatory diagram of the operation of the error minimization circuit in the second minimum point search of this embodiment. Pl and Pl shown in Fig. 4 correspond to Pl and Pl in Fig. 2, and Fig. 4 shows the error curve of the cross section by the straight line connecting pt and Pl of the error surface in Fig. 2. The initialization unit 17
The initial value of the learning parameter is set to εB in the first minimum point search.
Then, in the second and subsequent minimum point searches, the larger value of the learning parameter value used for the previous weight change or ε8 is determined, and the error with respect to the initial value of the learning parameter is determined. That is, the optimal value of the previous learning parameter is εB
When it is larger than εB, the optimum value of the previous learning parameter becomes the initial value of the learning parameter, and when the optimum value of the previous learning parameter is smaller than εB, ε8 becomes the initial value of the learning parameter. This is because by setting the optimal value of the previous learning parameter as the initial value of the learning parameter for the current search, the optimal learning parameter for the current search can be set efficiently, and the optimal value of the previous learning parameter is small. If this is used as the initial value of the learning parameter for the current minimum point search, it is possible to prevent the local minimum point of the error surface from becoming stuck. In Figure 4,
Since the previous optimal value ε3 of the learning parameter is larger than ε8, ε3 is set as the initial value of the learning parameter.

In FIG. 4, since the error E3 with respect to the initial value ε3 of the learning parameter is smaller than the initial value Es of the error, the learning parameter changing unit 18 doubles the value of the learning parameter ε to obtain the error value. Repeat until the value starts increasing. In Figure 4, Es > E3 < E
Since it becomes a, find up to Ea. The paraboloid approximation unit 19 approximates the vicinity of the minimum error point with a paraboloid.

In FIG. 4, the weight value in the weight space is the learning parameter value 0. ε3. Since it changes at equal intervals with ε4, the error surface is approximated to a paraboloid from the errors at these points, and the error at the vertex is determined by equation (9). However, . The weight change unit 20 uses the error E3. The smallest error Ev among Ea and Ev
The learning parameter ε9 for the second search is set as the optimum value of the learning parameter for the second search, and is used to change the weight of each variable weight multiplier. Hereinafter, the error minimization circuit 21 includes a teacher signal generation section 14, an error calculation section 15, a search direction determination section 16, a learning parameter initialization section 17, and a learning parameter change section 1.
8, the paraboloid approximation section 19, and the weight change section 20 are repeatedly used to reduce the error. This process is repeated until the error becomes sufficiently small, and the learning is completed.

As described above, according to this embodiment, the learning parameter initialization section 17, the learning parameter changing section 18, and the paraboloid approximation section 1
9, the weight of the variable weight multiplier is changed while always efficiently finding the optimal value of the learning parameter in the direction of searching for the minimum point of error, so the error can be minimized efficiently, and the learning It can save time.

In this embodiment, the search direction determining unit 16 determines the direction of the minimum error point search to be the steepest descent direction, but the direction of the minimum point search may be the conjugate gradient direction. The conjugate gradient direction is given by p=g+β*p゛ (12). However, g is the steepest descent direction, p' is the conjugate gradient direction in the previous minimum point search, and g'
is the steepest descent direction in the previous minimum point search. In this case as well, the initial minimum point search direction is determined to be the steepest descent direction. As described above, in the first embodiment, the search direction determining unit 1
6, the same effect can be obtained even if the direction of the search for the minimum point of error is the direction of the steepest descent or the direction of the conjugate gradient.

FIG. 5 is a block diagram of a second embodiment of the present invention. Fifth
In the figure, 22 is a steepest descent direction determining section, 23 is a learning parameter maximum value limiting section, and 24 is an error minimization circuit.

In this embodiment, the steepest descent direction determination unit 22 determines the minimum error point search direction to be the steepest descent direction expressed by equation (4). Similarly to the first embodiment, the learning parameter initialization unit 17 sets the initial value of the learning parameter to 8 days for the first minimum point search, and sets the initial value of the learning parameter to 8 days for the second and subsequent minimum point searches. The optimum value of the learning parameter or the larger value of εθ is determined, and the error with respect to the initial value of the learning parameter is determined. In the learning parameter changing unit 18, when the error with respect to the initial value of the learning parameter is smaller than the initial value of the error, the learning parameter ε
The operation of calculating the error value by doubling the value of is repeated until the error value starts to increase, or when the error with respect to the initial value of the learning parameter increases more than the initial value of the error, the learning parameter ε The operation of multiplying the value by 1/2 to obtain the error value is repeated until the error value becomes smaller than the initial error value. However, in this embodiment, if the error does not increase even if the value of the learning parameter ε exceeds an appropriate positive constant εsaw, the weight of each variable multiplier is changed by the value of the learning parameter at that time. .

When the error starts to increase within a range where the value of the learning parameter ε does not exceed ε, □, the operations of the paraboloid approximation unit 19 and the weight change unit 20 are the same as in the first embodiment. In this embodiment, in the search for the minimum point of error, the search direction is determined to be the direction of steepest descent, and the learning parameter is varied within a range where the value of the learning parameter ε does not exceed a positive constant ε□8. It is different from FIG. 6 is an explanatory diagram of the effect of the second embodiment of the present invention. According to the first embodiment, in FIG. 6, in the initial minimum point search, the point with the minimum error in the search direction was found based on the steepest descent direction of the starting point, so the initial minimum point search was performed. The search ends at Pl', and the second minimum point search ends at P2', resulting in a local minimum point. According to this embodiment, the value of the learning parameter ε is a positive constant ε11. Since the learning parameters are changed within a range that does not exceed Then, the minimum point search direction is determined, and the second minimum point search ends at a point P2 corresponding to the maximum values ε and □ of the learning parameters. Similarly, the third minimum point search ends at P3, the fourth minimum point search ends at P4, and eventually the global minimum point can be reached. As described above, in this embodiment, by limiting the maximum value of the learning parameter, falling into a local minimum point can be prevented.

FIG. 7 is a block diagram of a third embodiment of the present invention.

In FIG. 7, 25 is a search direction determining section, 26 is a steepest descent direction determining section, and 27 is an error minimization circuit. In this embodiment, the search direction determination unit 25 determines the minimum error search direction to be the direction of steepest descent expressed by equation (4) in the first search, and in the second and subsequent searches by equation (l). Determine the expressed conjugate gradient direction. Learning parameter initialization unit 17
Similarly to the first and second embodiments, the initial value of the learning parameter is set to ε day in the first minimum point search, and the optimum value of the learning parameter in the previous minimum point search is set in the second and subsequent minimum point searches. or ε8, whichever is larger, and find the error with respect to the initial value of the learning parameter. When the error with respect to the initial value of the learning parameter is smaller than the initial value of the error, the learning parameter change unit 18 changes the operation of doubling the value of the learning parameter ε to obtain the error value so that the error value increases. The learning parameter ε is repeated until the learning parameter ε
The operation of multiplying the value by 1/2 to obtain the error value is repeated until the error value becomes smaller than the initial error value.

However, in this embodiment, if the value of the error does not become smaller than the initial value of the error even if the value of the learning parameter ε is made smaller than an appropriate positive constant ε1n, the minimum point search direction is changed from the conjugate gradient direction to the maximum value. Switch to steep descent direction. The operations of the paraboloid approximation section 19 and the weight change section 20 are similar to those in the first embodiment.

In this example, in the second and subsequent searches for the minimum point of error, the search direction is determined to be the conjugate gradient direction, and the first point is that the learning parameter is changed within a range where the value of the learning parameter ε does not become smaller than the positive constant ε1n. This is different from the example.

FIG. 8 is an explanatory diagram of the effect of the third embodiment of the present invention.

According to the first embodiment, in FIG. 8, in the initial minimum point search, the point with the minimum error in the search direction is found based on the steepest descent direction of the starting point, and the initial minimum point search is performed at PI. The second minimum point search ended at P2' because the conjugate gradient direction in Pi was used as the search direction to find the point where the error was minimum in that direction. According to this embodiment, the value of the learning parameter ε is a positive constant ε1. , l. Therefore, in the second minimum point search, the value of the learning parameter ε is set to ε□. If the error does not become smaller than the initial value of the error even if it is made smaller, the search in the conjugate gradient direction is discontinued, the search direction is switched to the steepest descent direction, and the second minimum point search ends at P2. As described in 1 above, in this example, the minimum value of the learning parameter in the conjugate gradient direction is limited, and when the value becomes smaller than that, the search direction is switched to the direction of steepest descent, thereby efficiently reaching the global minimum point. be able to.

As described in detail, according to the present invention, the weight of the variable weight multiplier is changed while always efficiently finding the optimal value of the learning parameter in the direction of searching for the minimum point of error, thereby minimizing the error. can be performed efficiently, and the time required for learning of a learning machine can be shortened, which has a great practical effect.

[Brief explanation of the drawing]

Fig. 1 is a block diagram of a learning machine according to a first embodiment of the present invention, Fig. 2 is a contour diagram of an error surface in a weight space, and Fig. 3 is an error minimization circuit in the first minimum point search of the same embodiment. FIG. 4 is an explanatory diagram of the operation of the error minimization circuit in the first minimum point search of the same embodiment. FIG. 5 is a block diagram of the learning machine of the second embodiment of the present invention. is an explanatory diagram of the effect of the same embodiment, FIG. 7 is a block diagram of a learning machine according to the third embodiment of the present invention, FIG. 8 is an explanatory diagram of the effect of the same embodiment, and FIG. 9 is a conventional learning machine. Block diagram, 1st
Figure O is an input/output characteristic diagram of the adder. 3.4.5.6.7.8...Variable weight multiplier, 9.
1O111...Adder, ]4...Teacher signal generation unit, I5...Error calculation unit, 16.25...Search direction determination unit, 17...Learning parameter initialization unit ,1
8... Learning parameter changing unit, 19... Paraboloid approximation unit, 20... Weight changing unit, n, 26... Steepest descent direction determining unit, 23... Learning parameter Maximum limit part. Name of agent Patent attorney Shigetaka Awano 1 person 1 Figure 3 Figure 2 Figure 4 IME L(r J 11 TQ/i″ζV”t Figure

Claims (3)

[Claims] (1) an output signal calculation circuit in which multi-input one-output adders having saturation input/output characteristics are connected in a hierarchical manner, with the adder in each layer connected to the adder in the next layer via a variable weight multiplier; a teacher signal generator that provides a teacher signal as a desired value of the output signal of the adder in the output layer each time an input signal is input; an error calculator that calculates an error between the output signal and the teacher signal; and the variable weight multiplier. a search direction determination unit that determines a search direction for the minimum point of error in a weight space that expresses the weight of as a vector; and learning that determines the error by gradually increasing or decreasing the value of a learning parameter in the direction of searching for the minimum point of error. a parameter changing section, a paraboloid approximation section that approximates the error surface in the vicinity of the minimum error point with a paraboloid and calculates the error at the vertex, and a paraboloid approximation section that calculates the error at the point where the error is minimum. a weight changing unit that changes the weight of each variable weight multiplier as an optimal value;
a learning parameter initialization unit that reflects an optimal value of a learning parameter in the previous search for the minimum point of error to an initial value of the learning parameter in the current search for the minimum point of error; the teacher signal generation unit; and the error calculation unit; an error minimization circuit that repeatedly uses the search direction determining unit, the learning parameter initializing unit, the learning parameter changing unit, the paraboloid approximation unit, and the weight changing unit to sufficiently reduce the error. A learning machine characterized by: (2) A steepest descent direction determining unit that determines the minimum point search direction of the error in a weight space that expresses the weight of the variable weight multiplier as a vector as the steepest descent direction, and a learning parameter maximum value that limits the maximum value of the learning parameter. The learning machine according to claim 1, further comprising a restriction section. (3) A conjugate gradient direction determining unit that determines the minimum point search direction of the error in the weight space that expresses the weight of the variable weight multiplier as a vector in the conjugate gradient direction; 2. The learning machine according to claim 1, further comprising: a search direction changing unit which sets the steepest descent direction as the direction for searching for the minimum point of the error when the error does not decrease.