JPH0462658A - Learning machine - Google Patents

Abstract

PURPOSE:To end the learning with continuous change of the weight even when the weight or the weight changed variable are shown in the limited accuracy by changing the leaning rate based on the error between the weighting output signal of the signal processing obtained when the learning is carried out by a learning machine and a desirable output signal. CONSTITUTION:A learning machine consists of the multi-input/output circuits 94-96 containing the variable weight multipliers 3-8 and the adders 9-11 having the saturated input/output characteristics connected together in a hierarchical form. The circuits 94-96 adds together the input signals with weighting and then apply the non-linear processing to the input signals in accordance with the characteristic function of each adder to obtain the output signals. A learning circuit 93 changes the weights that are multiplied by the multipliers 3-8 so that the output of an output layer 21 is equal to the output of a teacher signal generating part 13. The part 13 outputs a desirable output signal, i.e., a teacher signal to an error calculation part 14. The part 14 outputs a difference signal between the actual output signal and the teacher signal to a weight changing direction deciding part 15. Thus the part 15 obtains the most suddenly falling direction ' g' from the output and input signals of a hidden layer 22, the output signal of the layer 21, and the weight of the layer 21 and then outputs the direction ' g' to a straight line searching part 67.

Description

[Detailed Description of the Invention] Industrial Application Field The present invention relates to a learning machine used in a data processing device, etc.Prior art As a conventional learning machine, for example, E, Rumm.
'Learning repre by Elhart et al.
sentations by back-propag
Ating errors, Nature Vol.
, 323 No. 9 (1986). Fifth
The figure shows a block diagram showing the general configuration of a conventional learning machine, and the constituent elements are (201), (202),
is an input terminal, (217) is a learning terminal (218), (2
19), (220) are multi-input-output circuits (221) are multi-input-output circuits (218), (219) are outputs! (222) is a hidden layer composed of multiple input-output circuits (220). Next, the relative operations of the above components will be explained. ζ as shown in Figure 5
ζ The learning machine is a multi-input-output circuit (218), (219
) and (220) are connected in a hierarchical manner, the signals received from the input terminals (201) and (202) are processed and output from the output terminal (212). In this way, the multi-input-output circuits (218) and (21) are connected in a hierarchical manner.
9), (220') plate The layer consisting of the multi-input-output circuit (220) that outputs the output signal is called the output layer (221), and the other multi-input-output circuits (218), (21
9) is called the hidden layer (222).
22) Multi-input-output circuit (220
) or a multi-input-output circuit having multiple layers. Figure 6 shows a block diagram showing a more detailed configuration of this conventional learning machine. As shown in Figure 6, to ζ as a component (203
) to (208) are variable weight multipliers (209) to (21
1) is an adder with saturated human output characteristics (213) is the teacher signal generation area (214) is the error calculation i (215) is the steepest descent direction determining plate (216) is the weight change ff1L
(217) is a learning circuit. Next, the related operations of the above-mentioned components will be explained. As shown in FIG. It consists of adders (209) to (211) having saturation input/output characteristics. In other words, the output signal of the j-th multi-input-output circuit is y[j] = fnc(Σ(w[i,j] y[i])
)” (1) where E y[i] is the output signal of the first Takuker output circuit in the previous layer, and w[
i, j] is a weight applied when the output signal of the first multi-input output circuit in the previous layer is applied to the j-th multi-input-output circuit. Equation (1) is a sigmoid function with saturation characteristics, and is generally expressed as fnc(x). Go to Figure 7 Adder (2o9) with saturated input/output characteristics, which should be expressed by the sigmoid function described above, (
2IO) and (211) are shown.

The learning machine C has a configuration in which multiple input and output circuits are connected in a hierarchical manner, and in learning (a desirable output signal (hereinafter referred to as a teacher signal) for the friend signal).
to output? Q variable weight multiplier (203) ~ (
208) to change the weight applied. To change the weights, first calculate the teacher signal, the output signal of the output layer (221), and the convergence error. Here, +Q yp[j] is the output signal of the j-th multi-input-output circuit of the output layer (,221) for the 9th input signal, tp[j] is the teacher signal for yp[j], and Σ is the output signal for all The total weight Σ for the teacher signal is the weight W[i, j
] (hereinafter W is referred to as a weight vector). As shown in equation (2), the error E is expressed as the sum of squares of the difference between the teacher signal and the output signal of the output layer, and is a function of the weight vector W. In learning, the weights are changed to minimize the difference between the teacher signal and the actual output, that is, the error.

The amount of weight change is Δ W −−ε 0 g +
α book △ w' ・ ・ ・ Determined by (3). Here, ε is a positive constant called learning rate, α is a positive constant called momentum, and △W
' is a vector representation of the weight change amount in the previous learning, and g is a vector whose component is the differential of the error E expressed by the weight w[i, j], which is called the direction of steepest descent.

FIG. 8 shows a block diagram showing the configuration of the learning circuit (217) of this conventional learning machine. As shown in FIG. 8, the components are as follows: (223) is an input terminal for the layer output of 221), (224) is an input terminal for the output of the hidden layer (222), and (225) is an input terminal for the input signal. The terminals (226) are the output terminals for the weights of the output layer (221), and (227) are the output terminals for the weights of the hidden layer (222). Next, we will explain the relative operations of the above components. In the learning circuit (217) of the learning machine, the teacher signal generator (213) generates the teacher signal tp[j] for the input signal.The error calculator (214N) generates the teacher signal tp[j] and the output layer (2
21) from the output signal yp[j], the error E expressed by equation (2) is calculated.

The error calculation unit (214) outputs the difference signal to[j] −yJj (5) between the teacher signal and the output signal necessary for changing the weight to the steepest descent direction determination unit (215). do. The steepest descent direction determining unit (215) calculates the difference signal, the output layer output signal, the hidden layer specific force signal, the human input signal, and the weight of the output layer (221) and converts it to an error E in the weight space where the weight is expressed as a vector (4 ) Find the steepest descent direction determined by the formula.Steepest descent direction determination unit (215) l;L Multiply the steepest descent direction by the learning rate and output it to the weight change unit (216).

The weight change unit (216) calculates the amount of weight change using equation (3) and changes the weight applied by each variable type multiplier (203) to (208). As described above, by repeatedly calculating the amount of weight change using the steepest descent method, the error is reduced, and when the error becomes sufficiently small, the output signal is assumed to be sufficiently close to the desired value, and learning is terminated. .

Problems to be Solved by the Invention However, in the above configuration, when the weights are expressed with limited accuracy, the weights may not be changed.

For example, when (L weight is expressed with an accuracy of 256 gradations,
When the amount of change in weight becomes 17256 or less,
The weight is not changed t - Once the weight is no longer changed, the next time the weight is changed, the direction of steepest descent for the same weight is determined.Since the same weight change amount is to be calculated, the weight change amount is again calculated for the weight. becomes 1/256 or less, and in the end, the weights are not changed in subsequent learning. In other words, when the weights are expressed with limited precision, the error is not small enough and the learning is not completed (t or
The learning rate ε is a force determined empirically, or a fixed value determined through trial and error.When the learning rate is large, the weights are changed beyond the minimum part of the error surface, increasing the error and causing a problem with learning. However, the present invention takes into consideration the above problem, and the weights are changed.Continued 1
The purpose is to provide a learning machine that can quickly complete learning.

Means for Solving the Problems To achieve the above object of the present invention, a straight line search unit is provided which inputs the output of the weight change direction determining unit, multiplies the learning rate and outputs the weight change amount, and calculates the weight change amount to a predetermined value. When the value is less than or equal to , the weight changing section does not change the weight, but changes the learning rate. As a second invention, when the error between the output of the output layer and the output of the teacher signal generation section is input to the straight line search section, and the error increases due to weight change (as shown in Table 4), the learning rate is reduced. A hidden layer consisting of a multi-input-output circuit that performs nonlinear processing on the weighted sum of human input signals using a characteristic function that has a saturation characteristic, and outputs the nonlinear processing using a characteristic function that has a saturation characteristic on the weighted sum of the output signals of the hidden layer. an output layer consisting of a multi-input-output circuit that outputs a desired output signal from the output layer, a teacher signal generation section that generates a desired output signal of the output layer, and a teacher signal generation section that minimizes the error between the output of the teacher signal generation section and the output of the output layer. a weight change direction determination unit that determines the weight change direction for the weight change direction, a straight line search unit that dynamically sets a learning rate regarding the weight change direction and outputs the weight change amount, and a weight change direction determined by the straight line search unit. The learning machine is characterized by comprising a weight changing unit that changes the weight based on the amount of change.

Operation The learning machine of the present invention configured as described above weights and adds input signals in the hidden layer and the output layer, and performs nonlinear processing to obtain an output signal.The desired output signal output by the teacher signal generation unit and the output of the output layer To minimize the error with the signal
After the weight change direction determination unit determines the weight change direction, the linear search unit dynamically sets a learning rate regarding the weight change direction to determine the weight change amount.The weight change unit changes each weight.

In the same way, the learning rate is dynamically set in the direction of weight change and the operation of changing the weight is repeated to make the error sufficiently small. When the weights are expressed with limited accuracy and the weights are not changed because the amount of weight changes is smaller than the minimum unit of precision of the weights (Table This causes the weights to continue to change even when the weights are represented with limited precision, and the learning ends.

In addition, the second invention reduces the amount of weight change by decreasing the learning rate in the straight line search section when the error increases. This prevents the weights from being changed beyond the specified learning rate and allows the learning to be completed in a short time.

Embodiment FIG. 1 is a block diagram showing the configuration of a learning machine in a first embodiment of the present invention. As shown in Figure 1, the components (1) and (2) are input terminals;
(3) to (8) are variable weight multipliers (9) to (11) are adders with saturation input/output characteristics (12) are output terminals, (1
3) is the teacher signal generation unit (14), the error calculation unit (15) is the weight change direction determination R, (21) is the output layer, (22) is the hidden seed (65) is the weight change! (67) is the straight line search part (
93) is a learning circuit A. (94) to (96) are multi-input-output circuits.Next, the related operations of the above components will be explained.The learning machine C of this embodiment is variable weight multiplier (3). ) to (8) and adders (9) to (11) with saturation input/output characteristics. Multi-input-output circuit (94) to
(96) are connected in a hierarchical manner. The multi-input/output circuits (94), (95), and (96) weight and add the input signals, and perform nonlinear processing using the characteristic function of each adder to obtain an output signal.

In other words, the hidden layer (22) weights the input signal with the variable weight multipliers (3) to (6) and has saturation characteristics.
The output layer (21) weights the output signal of the hidden layer (22) with variable weight multipliers (7) and (8), and has saturation characteristics. Adder (11) that performs nonlinear processing using the second characteristic function
It consists of In this embodiment, the weighting CL for the input signal is expressed with an accuracy of 256 gradations.

In the learning circuit (93), the weights multiplied by the variable weight multipliers (3) to (8) are changed so that the output of the CL output layer (21) and the output of the teacher signal generator (13) are equal. If a vector having these weights as components is called a weight vector, the amount of change in the weight vector can be represented by a vector.The direction of this weight change vector is called the weight change direction, and G% In this example, CL weight change The direction of steepest descent expressed by equation (4) is used as the direction. The teacher signal generator (13) outputs a desired output signal, that is, the teacher signal, to the error calculator (14).The error calculator (14) outputs the difference signal ((5) between the actual output signal and the teacher signal
) is output to the weight change direction determining unit (15). Weight change direction determination unit (15) iL Performs bundle number straight line search to find the steepest descent direction g using the output signal of the hidden layer (22), the input signal, the output signal of the output layer (21), and the weight of the output layer (21) output to the section (67).

FIG. 2 shows a block diagram showing the configuration of the straight line search unit (67) and weight change unit (65) of the learning machine of this embodiment.

As shown in Figure 2, as a component, (16) is the learning rate setting! (17) is learning rate multiplication! (18) is a weight adder (19) is a weight memory (23) is a momentum multiplication remover (24) is a memory of the previous weight change amount! (25) is the steepest descent direction input terminal, and (26) is the weight output terminal.

The steepest descent direction g determined by the weight change direction determining unit (15) is input from the input terminal (25). The learning rate setting unit (16) outputs the learning rate ε, and the learning rate multiplier (17) outputs the learning rate ε. In this way, the straight line search unit (67) sets the learning rate and outputs the amount of weight change in the steepest descent direction according to the learning rate. Storage unit (19)il Variable weight multiplier (3)
The weight value W' by which the input signal is multiplied in steps (8) to (8) is stored. This weight value is expressed with an accuracy of 256 gradations. Previous weight change amount storage unit (24) c Stores the weight change amount △W'' in the previous weight change. Momentum multiplication unit (23) i Table Previous weight change amount △W'
and the momentum α.4 Weight adder (18
) is 1. First, add the weight change amount in the steepest descent direction output by the straight line search section (67) and the product of the previous weight change amount △W'' output from the momentum multiplier (23) and momentum α. Calculating the weight change amount △W, that is, △W ε 0 g + α book △W ・・(6
) to find the weight change amount ΔW. Next, the weight addition unit (18) adds the weight change amount △W to the weight w'i;Q weight change amount △W stored in the weight storage unit (19).・
- Change the weight according to (7). Since the weights are expressed with an accuracy of 256 gradations, if the component of the weight change amount ΔW is smaller than the minimum unit of accuracy of the weight W', the weights are not actually changed and the error becomes l,% like this. Even though the weight has not become sufficiently small, if the weight is not changed (i), the weight addition section (18) outputs a weight no change detection signal to the learning rate setting section (16).The learning rate setting section (
16) 41 When the weight-unchanged detection signal is input, the learning rate ε is set to double. The product of the learning rate ε output by the learning rate multiplier (17) and the direction of steepest descent g is also twice as much. ε is doubled, ε 0g is doubled, and the weight change amount ΔW is increased. Therefore, the learning rate increases and the weight change amount also increases until the weight is changed.

When the weight is changed, the weight addition unit (18) does not output a no-weight change detection signal to the learning rate setting unit (16), and outputs the changed weight W to the weight storage unit (19). The weight change amount ΔW is output to the previous weight storage unit (24).The weight stored in the weight storage unit (19) is updated and sent from the weight output terminal (26) to the variable weight multiplier (3).
~ (8) is output. As described above, the weights are changed, and by repeating the weight changes, the error expressed by equation (2) is minimized, and the output signal of the learning machine of this embodiment approaches the desired output signal.

As described above, according to this embodiment, the weight addition unit (18) adds the weight change amount ΔW to the weight W', and when the weight W'' is not changed, the learning rate setting unit (16) doubles the learning rate. By increasing the weight change amount ΔW, it is possible to make the weight change amount ΔW larger than the minimum unit of accuracy in which the weight W' is expressed, and to continue changing the weight.

In this embodiment, the weight change direction output by the weight change direction determination unit (15) is set to be the steepest descent direction, but the weight change direction may be set to the conjugate gradient direction. Conjugate gradient direction (
Yod=g + β zero d′ ・ ・ ・
- Given by (8) However, Lg is the direction of steepest descent given by equation (4), β is a constant given by , and d' is the conjugate gradient direction of the previous weight change. This is the norm of the vector in the steepest descent direction g'.In the first weight change, the weight change direction (friend
Decide on the direction of steepest descent. In addition, the weight variation direction may be adaptively switched between the steepest descent direction and the conjugate gradient direction. -The output circuit may be configured by a multi-input-output circuit connected in a hierarchical manner.Also, in this embodiment, one output signal is output for two human input signals. However, the number of these input/output signals can be u% or output layer (21)
and the characteristic function used for the hidden layer (22) as the first. Although the description has been made separately as the second characteristic function, it goes without saying that the effects of the present invention can be obtained using the same characteristic function. As shown in Figure 3, the components (1) and (2) are input terminals, (3
) to (8) are variable weight multipliers (9) to (11) are addition S with saturation input/output characteristics, (12) is an output terminal, and (1
3) generates a teacher signal! (15) determines the weight change direction! (20) is an error calculation! (21) is the output layer (
22) is a hidden favor (68) is a straight line search ff1L (6
9), the weight change unit (70) is the learning area (94) to (96).
) is a multiple input-output circuit. Next, the relative operations of the above components will be explained.

Similar to the learning machine of the first embodiment, the learning machine of this embodiment has multiple inputs consisting of variable weight multipliers (3) to (8) and adders (9) to (11) with saturated input/output characteristics. Output circuit (
Even if 94) to (96) are connected in a hierarchical manner, the learning circuit (70) uses variable weights so that the output of the output layer (21) and the output of the teacher signal generator (13) are equal. The weights multiplied by multipliers (3) to (8) are changed. In this example, (4)
Use the direction of steepest descent expressed by the formula. Teacher signal generator (
13) outputs a desired output signal, that is, a teacher signal, to the error calculation section (20). The error calculation unit (20) outputs the difference signal (expressed by equation (5)) between the actual output signal and the teacher signal to the weight change direction determination unit (15).
Output the error expressed by equation (2) to the straight line search unit (68) a Weight change direction determination unit (15) 4 & hidden layer (2)
Using the output signal of 2), the input signal, the output signal of the output layer (21), and the weight of the output layer (21), the steepest descent direction g is output to the Kitori straight line search unit (68).

FIG. 4 shows a block diagram showing the configuration of the straight line search section (68) and weight change section (69) of the learning machine of this embodiment.

As shown in Fig. 4, the components are as follows: (27) is the error increase detection unit (28), the error initial value storage unit (29) is the learning rate setting 1K, (30) is the learning rate multiplier, and (31) is the momentum Multiplication ff1L (32) is the previous weight change amount storage unit (33) is the weight addition K (34) is the weight storage unit (35) is the error input terminal, (36) is the steepest descent direction input terminal, (37) is the weight It is an output terminal. Error calculation section (
The error obtained in step 20) is input from the error input terminal (35), and the error value before changing the weight (28) is stored in the error initial value storage section (28).
15) The steepest descent direction g (input terminal (36)
) and set in the learning rate setting unit (29) and the steepest descent direction g, the learning rate multiplier (3o
) outputs S4 In this way, the straight line search unit (68) outputs the weight change amount ε*g in the steepest descent direction with respect to the learning rate ε set by the learning rate setting unit (29). The weight storage unit (34) in the weight change unit (69) includes a variable weight multiplier (
3) to (8), set the weight value W multiplied by the input signal to 25
Even if it is stored with an accuracy of 6 gradations, the weight addition unit (33) adds the weight change amount ε*g in the direction of steepest descent to the weight W' before change, and outputs the weight from the weight output terminal (37) to the temporary learning ε. Output the weights. The output signal for that weight is converted into a hidden layer (
22) and the output layer (21), the output signal and the teacher signal output from the teacher signal generator (13) are temporarily calculated.The error calculation unit (20) calculates the error after weight change. ) is output to the straight line search section (68
), the error input from the error input terminal (35) and
The error increase detection unit (27) compares the error before the weight change stored in the error initial value storage unit (28).a If the error after the weight change is larger than the error before the weight change JL The error increase detection section (27) outputs the error increase detection signal to the learning rate setting section (29)a Learning rate setting section (29)ti When the error increase detection signal is input, the learning rate is halved. The learning rate multiplier (30) outputs the product of the learning rate ε set to half and the direction of steepest descent g. Based on this output, the weight change unit (69) changes the weight and outputs the weight. In this way, the straight line search unit (69)
8), the error after changing the weight in the steepest descent direction is
Decrease the learning rate until the error is less than the error before changing the weights and continue 1
The weight change amount ε in the direction of steepest descent for the learning rate ε
* Output g. When the error after the weight change in the steepest descent direction becomes less than or equal to the error before the weight change, the error increase detection section (27) outputs a learning rate determination signal to the weight addition section (33). Addition unit (33) gel When the learning rate determination signal is input, the weight change amount ε in the steepest descent direction
*g and α*△w′ output by the momentum multiplier 31
(△W' is the previous weight change amount α is the momentum) to find the weight change amount △W expressed by equation (6).Furthermore, by adding △W to the weight Wo before the change, (7) The changed weight W expressed by the formula is determined.

At this time, if the weight change amount △W is smaller than the minimum unit of accuracy of the weight Wo, the weight addition unit (
33) outputs an unchanged weight detection signal to the learning rate setting section (29), and the learning rate setting section (29) sets the learning rate to double. The learning rate ε is increased until the weight change amount ΔW becomes larger than the minimum unit of accuracy of the weight Wo. When the weight change amount △W becomes larger than the minimum unit of accuracy of the weight Wo,
The weight addition unit (33) stores △W in the previous weight change amount storage unit (
32), and outputs the changed weight W to the weight storage unit (34). The weights are changed by the above
By repeating weight changes, the error expressed by equation (2) is minimized, and the output signal of the learning machine of this embodiment approaches a desired output signal.

As described above, according to this embodiment, the error increase detection section (27
), compare the error value before changing the weight with the error value after changing the weight in the steepest descent direction (the amount of change is ε*g).
When the error increases, the learning rate is set to half in the learning rate setting section (29) to prevent the set learning rate from being too large and changing the weight beyond the minimum part of the error surface. The weights are changed depending on the appropriate learning rate, and learning can be completed in a short learning time.

In this embodiment, the weight change direction output by the ct weight change direction determination unit (X5) is set to the steepest descent direction, but the weight change direction may also be set to the conjugate gradient direction. It is also possible to adaptively switch between the direction of the conjugate gradient and the direction of the conjugate gradient (t) In this embodiment, the &yo hidden layer (22) consists of a multi-input-output circuit that processes the input signal and outputs it to the output layer. It may also be configured with multiple input-output circuits connected in a hierarchical manner.In addition, in this embodiment, one output signal was output for two input signals, but the number of these human output signals can be as many as 2v or 1/2' (v is a positive integer), which is convenient for bit processing the learning rate change rate. However, it goes without saying that the same effect can be obtained even if it is not done at this ratio (X.

As is clear from the detailed description of the invention, according to the present invention, the weighting of signal processing during learning in a learning machine is performed by changing the learning rate depending on the magnitude of the error between the output signal and the desired output signal. When the amount of change in L can be expressed with limited accuracy, learning can be completed by continuing to change the L weights.

Furthermore, there is no need to determine the learning rate through experience or trial and error, and learning can be completed in a short time.

[Brief explanation of drawings]

FIG. 1 is a block doctor showing the configuration of a learning machine according to a first embodiment of the present invention. FIG. Block diagram showing the configuration of the learning machine in the second embodiment @ Figure 4 is a block diagram showing the configuration of the straight line search unit and weight change unit in the same embodiment Figure 5 is a block diagram showing the general configuration of the conventional learning machine FIG. 6 is a block diagram showing the configuration of a learning circuit of a conventional learning machine. 13... Teacher signal generation plate 15... Weight change direction determination @ 21... Output signal 22... Hidden signal 6
5... Change weight! 67...Name of straight line search accent agent Patent attorney Shigetaka Awano and 1 other person Figure + 1v Figure ■ Piece 7 Figure Figure

Claims (7)

[Claims] (1) A hidden layer consisting of a multi-input-output circuit that performs nonlinear processing using a first characteristic function that has a saturation characteristic on the weighted sum of input signals and outputs the result, and a hidden layer that has a saturation characteristic on the weighted sum of the output signals of the hidden layer. an output layer consisting of a multi-input-output circuit that performs nonlinear processing using a second characteristic function and outputs the output; a teacher signal generation section that generates a desired output signal of the output layer; a weight direction determination unit that determines a weight change direction for the weighted sum to minimize an error with the output of the output layer; and a weight change amount by multiplying the output of the weight change direction determination unit by a learning rate. a straight line search unit that outputs an output, and a weight change unit that changes and outputs a weight based on the weight change amount determined by the straight line search unit, and the weight change unit is configured to adjust the weight change amount to a predetermined value. The learning machine is configured such that the straight line search unit changes the learning rate without changing the weight when the weight is less than a value. (2) The learning machine according to claim 1, wherein the linear section increases the learning rate and outputs the weight change amount when the weight change section does not change the weight. (3) The learning machine according to claim 2, wherein the learning rate of the straight line search unit increases at a rate of 2^v (v is a positive integer). (4) The learning machine according to claim 2 or 3, wherein the learning rate of the straight line search unit is repeatedly increased until the weight change unit changes the weight. (5) The learning according to claim 1, wherein the straight line search section reduces the learning rate when the error between the output of the teacher signal generation section and the output of the output layer increases due to weight change by the weight change section. machine. (6) The rate of reduction in the learning rate of the straight line search unit is 1/2^v(
6. The learning machine according to claim 5, wherein v is a positive integer. (7) The learning machine according to claim 5 or 6, wherein the learning rate of the straight line search section is repeatedly reduced until the error is reduced by changing the weight.