JP3238178B2 - Learning machine learning method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a learning method of a learning machine applied to a neural network, a non-linear data converter and the like.

[0002]

2. Description of the Related Art In recent years, a learning machine which performs non-linear data conversion represented by a neural network has attracted attention. Neural networks have been proposed as models of neural circuits in the brain.Since they have both a learning function and nonlinearity, they are used as a method for pattern recognition, stock price prediction, diagnosis, and control of robots. It has begun to be applied to optimal motion control.

In the above learning machine, control parameters for determining the operation of the learning machine are adjusted by known input / output data so that the learning machine can operate properly before it is actually used for robot control or the like. I have to put it. In other words, the learning machine must be trained.

[0004] "Supervised learning" is known as one of the neural network learning methods. In the “supervised learning”, as represented by back propagation learning, given learning data composed of a pair of an input vector and a correspondingly obtained output vector with a target teacher signal, is given. The control parameters such as the coupling coefficient between neurons are finely adjusted so that the determined loss function becomes small. The learning method based on “supervised learning” is also applied to a learning machine that performs non-linear data conversion other than a neural network.

In other words, in the conventional learning method, a teacher signal to be output, that is, a model teacher signal (hereinafter referred to as a model teacher) is set, and the difference between the output vector output by the learning machine and the model teacher is small. I was learning the learning machine to become.

On the other hand, in a robot control or the like that actually uses a learning machine, for example, when an operation of a robot arm is designated, it is necessary to provide a condition that the passage of the arm is prohibited in order to avoid an obstacle. There are many. Further, in the diagnosis in the medical field, for example, when a doctor determines a patient's disease name by examining an X-ray or an electrocardiogram, the doctor deletes a disease name that is not possible by an elimination method, and finally the true disease name of the patient. To determine. As described above, in the industrial field using the learning machine, there are many occasions in which a teacher signal that is not desired to be output, that is, a teacher signal to be avoided (hereinafter, referred to as a teacher) is given.

[0007]

However, when a learning machine is given a teacher as a part of the learning data, the learning machine cannot be trained so as not to output this as an output vector. Therefore, when the worker is given a teacher, on the other hand, the model teacher is reset based on the worker's ambiguous knowledge and experience, and the reset model teacher is given to the learning machine as a part of the learning data, and the learning is performed. The learning was performed so that the difference between the output vector output by the machine and the model teacher became small.

Therefore, the learning method of the learning machine using the model teacher is troublesome.

When an example teacher is given to a learning machine as a part of learning data, the output vector must converge on the example teacher regardless of whether the example teacher is complete data or incomplete data. Therefore, sometimes convergence is impossible. Also, when a large number of model teachers are given, the control parameters may be adjusted so that the output vector converges on a specific model teacher. On the other hand, when the teacher is given to the learning machine as compared with the case where the model teacher is given, the range in which the output vector should converge is wider and the convergence is easier. Also, by giving various teachers, it is possible to obtain a well-balanced output vector.

SUMMARY OF THE INVENTION In view of the above-mentioned problems, an object of the present invention is to adjust a control parameter so that convergence is easy when learning a learning machine, and an output vector converges toward a specific model teacher. An object of the present invention is to provide a learning method of a learning machine that can adjust a control parameter to output a well-balanced output vector without being performed.

[0011]

In order to achieve the above object, the present invention provides a learning machine which outputs an output vector using a predetermined control parameter for an input vector, and trains the control parameter using a teacher signal. In the method, a teacher signal is defined as a teacher signal, which means data to be avoided that should not be output as an output vector, and a learning machine is provided with a value of an input vector and a value of a teacher signal corresponding to the input vector. Calculate the output vector value using the initial control parameters for the vector value,
On the other hand the difference x between the teacher and the output vector, and calculates the loss function r to decrease with increasing difference x in the following equation, when the value of r = exp (-x ²⁾ loss function is larger than a predetermined value Until the value of the loss function becomes smaller than the predetermined value, the control parameter is updated so that the value of the loss function is reduced, and the value of the loss function is repeatedly calculated, and the calculated loss function is smaller than the predetermined value. It is characterized in that when the value reaches a small value, the learning machine incorporates the updated latest control parameters.

[0012]

[Action] In the above configuration, the difference x between the output vector and the contrary teacher was assumed to follow the loss function r = exp (-x ^2). This function has been determined based on a number of calculations made by the applicant.

Then, the parameters inside the learning machine are adjusted so that the loss function becomes a minimum value.

By adjusting the parameters in this manner, the parameters inside the learning machine that performs learning using the teacher can be adjusted to optimal values.

[0015]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a conceptual diagram of a learning machine according to a first embodiment of the present invention.

This learning machine has an L-dimensional input vector I
An input terminal _{1 1} ~I _L is input, the parameter θ
and _{j (j} = 1~M) converter 2 which is defined, and the output terminal 3 of output vector O ₁ ~ O _N N-dimensional is outputted, the parameter adjusting means 7, losses due to model teaching function calculating means 9 And a loss function calculating means 8 comprising a loss function calculating means 10 by a teacher.

When learning, the loss function calculating means 8 is used.
Loss function and calculated by, the loss function, by using the value of the differential coefficient for the parameter theta _j, parameter adjusting means 7 to adjust the parameters theta _j of the transformation unit 2, so that the value of the loss function is reduced Train the learning machine. When the model teacher is given, the loss function calculating means 9 by the model teacher calculates the loss function and the differential coefficient by the conventional method, and when the model teacher is given, the loss function calculating means 10 by the reverse teacher gives the loss. Calculation of functions and derivatives is performed.

Next, a case will be described in which this embodiment is applied to back propagation learning of a three-layer feedforward neural network.

FIG. 2 is a diagram showing this concept. This learning machine comprises a neuron element 11 and input vectors I _{1 to} I _1.
An input layer 12 _{which L} is input, a hidden layer 13, and the output layer 14 output vector O ₁ ~ O _N is output, the input layer 12
The coupling unit 15 in which the coupling coefficient w ^HI _ji is defined between the hidden layer 13 and the hidden layer 13, and the coupling coefficient w between the hidden layer 13 and the output layer 14
^A three-layer feedforward neural network comprising a coupling unit 16 in which ^OH _kj is defined; a parameter adjusting means 17; a loss function calculating means 19 by a model teacher; and a loss function calculating means 18 comprising a loss function calculating means 20 by a teacher. It is composed of The threshold theta ^H _j is defined in the neuron element 11 of the hidden layer 13, the threshold theta ^O _k is defined on the neuron element 11 of the output layer 14.

At the time of learning, the loss function calculating means 18 calculates a loss function, a differential coefficient for a coupling coefficient of the loss function, and a differential coefficient for a threshold value of the loss function, and uses these results. Then, the parameter adjusting means 17 adjusts the coupling coefficients w ^HI _ji and w ^OH _{kj of} the coupling units 15 and 16 and the threshold values θ ^H _j and θ ^O _i of the neuron element 11,
Learning is performed so that the value of the loss function becomes small.

Hereinafter, this learning method will be specifically described.

Now, the input data to the i-th neuron element 11 of the input layer 12 is I _i , the input to the j-th neuron element 11 of the hidden layer 13 is I ^H _j , and the output is O ^H _j ,
The input to the k-th neuron element 11 of the output layer 14 is
^O _k, and the output data to O ^O _k, O is represented by the following (1) to (4) below.

[0023]

(Equation 1) However, the function f (x) in the equations (2) and (4) is

(Equation 2) This derivative is expressed by the following equation (6).

[0024] _{^{f '(I H j) =}} O H j (1-O H j) ... (6) Further, M shown in (3)' is the number of neuron elements 11 of the hidden layer 13, the learning Let the number of data be P. And in particular when it is desired to express the output corresponding to the p-th training data, ^{_{respectively, I i p, I H j}} p, O H j p, expressed in O _k ^p, the p-th teacher signal y ^p _k ( k = 1, ...,
N). Also, the type of the teacher signal is represented by T _p ,
If the p-th teacher signal is a model teacher, it is represented by T _p = +, and if it is a teacher, it is represented by T _p = −.

Now, if the loss function r is expressed in the form of the sum of the model teacher term r ₊ and the inverse teacher term r ₋ , the following equation (7) is obtained.

R = r ₊ + r ₋ (7) Then, the model teacher term r ₊ and the opposite teacher term r ₋ are represented by the following equations (8) to (10).

[0027]

(Equation 3) However, it is as follows.

[0028] r ₊ ^p: the contribution of the p-th teacher signal in r ₊ r _- ^p: r _- contribution of p-th teacher signal in R _p: difference between p-th teacher signal and the output data sigma _{p: D:} sum sigma _p for all of the model _{teacher: U:} sum of all the other hand teacher gamma _-: parameter to adjust the ratio of contributing to the loss function model teacher and although teacher beta: contrary teacher affects the output data parameter to adjust the distance and the parameter gamma _- by adjusting, can be selected which come mainly worked on learning of a model teacher and although the teacher. That is, in equation (9), the parameter gamma _- significantly although teacher section loss function if r _-
And the influence of the teacher can be increased. Further, by adjusting the parameter β, it is possible to adjust how much the output vector obtained as a result of the learning must be apart from the teacher.

[0029] Then, it is a function of (9), (10) from the equation, a function-based although teacher term loss function r, for each training data ^{_{y p k, exp (-R p}} 2) Understand. This results in a curve having the characteristics shown in FIG. That is, the derivative of the loss function for the teacher with respect to R _p (hereinafter simply referred to as the “differential coefficient”) is set so as to gradually approach 0 as R _p becomes sufficiently large. Is small, and learning stability is guaranteed. Further, when R _p = 0, the derivative is 0
Therefore, general-purpose and stable teacher learning can be realized. This is because when the output data and the teacher are almost the same (R _p = 0), it does not matter in which direction the learning proceeds if R _p increases anyway. This is because the possibility of proceeding in the direction is preserved. When the differential coefficient of a certain training data is small, it is expected that advances learning primarily by the influence of the other learning data such as R _p is a value of about beta. Further, since the loss function is rapidly attenuated than exponential with respect to R _p, contrary effect of teachers only extends a short distance.

When the teacher signal is considered as an N-dimensional vector, each component of the vector is a model teacher,
On the other hand, he may be a teacher. That is, a model teacher component and a reverse teacher component may be mixed in one teacher signal. However, even in such a case, (7) ~
The loss function can be calculated by slightly changing the expression (10). In this embodiment, the formulation is performed in consideration of a teacher signal composed of only the model teacher component or only the teacher signal.

Then, in learning, the coupling coefficient is calculated by the following (11),
This is performed by changing as shown in equation (12).

[0032]

(Equation 4) However, theta represents the parameters used as the general term for data such as the coupling coefficient w ^HI _ji, w ^OH _kj or a threshold θ ^H _j, θ ^O _k in (1) to (4) below. Δθ (t) is an update amount of the parameter θ when the parameter is finely adjusted t times in learning by iterative calculation. Further, η is a learning coefficient, and α is an inertia term.

In such learning, there is a method of updating the coupling coefficient and the threshold value each time each learning data is presented. In this embodiment, however, a loss function for all learning data and a parameter of the loss function are used. Learning is performed using an algorithm that calculates the derivative of Θ and updates the value of the parameter. Therefore, for example, the loss function when using P pieces of learning data and the loss function when using 2P pieces of learning data obtained by doubling the same learning data as it is, have the same value. In the equation (12), 1 / P is multiplied as a whole.

The learning end condition is set as follows: r <E _L (13) Here, E _L is a parameter indicating a learning end condition.

Further, learning may not be possible due to the non-linearity of the neural network or lack of model capability, or r may not become sufficiently small within a practically long time. Therefore, usually, the maximum number of repetitions is determined in advance, and when the maximum number of times is reached, the learning is terminated, and the learning is repeated several times by changing the initial value of the coupling coefficient and other parameters. In some cases, review the model.

Next, the above-mentioned learning method will be systematically described with reference to the flowchart shown in FIG.

[0037] In the loss function calculating unit 18 shown in FIG. 2, first, the parameter p indicating the number of learning data is set to p = 1 (step ST1), the training data {I _i ^p _(i =
1 to L), y _k ^p (k = 1 to N), T _p } are read (step ST2). Then, (1) to (6), to output the output vector O _k ^p of the neural network (step ST3).

At the same time, it is determined whether the input teacher signal is a model teacher or a teacher (step ST4).
If it is a model teacher (“T _p = +” in step ST4),
Using equations (1) to (6), (8), and (10),

(Equation 5) Is calculated and stored in the memory (step ST5). On the other hand, if it is a teacher (“T _p = −” in step ST4), (1) to
Using equations (6), (9), and (10),

(Equation 6) Is calculated and stored in the memory (step ST6).

Thereafter, it is determined whether or not the learning data number p is equal to the data number P (step ST7).
If ≠ P (NO in step ST7), 1 is added to p (step ST8), and the operation from step ST2 is repeated. On the other hand, when p = P (YE in step ST7)
S), based on the results calculated and stored in steps ST5 and ST6, the coupling coefficient and the threshold are updated by equations (11) and (12) (step ST9).

If the learning end condition is satisfied, the learning ends (YES in step ST10). If the learning end condition is not satisfied (NO in step ST10), the operation from step ST1 is repeated. Thus, learning is performed.

FIG. 5 is a graph showing the results of actual learning performed by the inventor according to the present embodiment.

The values of the set parameters are as follows.

[0043] L = 1, M '= 5 , N = 1, γ - = 1 β = 0.05, η = 10 α = 0.5, E L = 10 -5 , the initial coupling coefficient and the threshold The values are as follows:

Θ ^H ₁ (0) = 0 w ^HI ₁₁ (0) = 10 θ ^H ₂ (0) = + 2.5 w ^HI ₂₁ (0) = 10 θ ^H ₃ (0) = + 5 w ^HI ₃₁ (0 ) = 10 θ ^H ₄ (0) = + 7.5 w ^HI ₄₁ (0) = 10 θ ^H ₅ (0) = + 10 w ^HI ₅₁ (0) = 10 θ ^O ₁ (0) = 0 w ^OH ₁₁ (0) ) = 0 w ^OH ₁₂ (0) = 0 w ^OH ₁₃ (0) = 0 w ^OH ₁₄ (0) = 0 w ^OH ₁₅ (0) = 0 And, in FIG. The result trained by the teacher is a dotted curve, and the result of learning using a total of seven teacher signals of five exemplary teachers indicated by ○ and two opposite teachers indicated by × is a solid line. It is a curve.

As is clear from the figure, the curve shown by the dotted line passes through the model teacher but does not attempt to move away from the teacher, whereas the curve shown by the solid line passes through the model teacher, and It is moving away.

As described above, in the present embodiment, when the teacher signal is the model teacher, learning is performed so as to reduce the difference between the teacher signal and the output vector. On the other hand, when the teacher signal is the teacher, Learning is performed such that the difference between the teacher signal and the output vector increases.

Therefore, learning flexibility and workability are improved,
Learning according to learning conditions and reasonable learning suited to the characteristics of the learning machine can be performed.

Next, a modification of this embodiment will be described with reference to FIGS.

[0049] Figure 6 is contrary teacher term r shown in the aforementioned equation (9) _- a, an example was replaced with the following equation (16).

[0050]

(Equation 7) In this example, the learning speed is high in the initial stage of learning, but the feature is that the direction of learning is limited.

FIG. 7 shows the teaching term r _{− in the} equation (9).
Is replaced by the following equation (17).

[0052]

(Equation 8) In this example, since the derivative diverges at R = 0, the repulsion between the output vector and the other side teacher is strong, and data conversion is realized such that the output vector is sufficiently isolated from all the other side teachers by learning. it can. However, the stability is not very good. The rebound strength can be adjusted by changing the value of n. Further, since the loss function attenuates algebraically with respect to R, the influence of the teacher extends over a long distance.

FIG. 8 shows the teaching term r _{− in the} equation (9).
Is replaced by the following equation (18).

[0054]

(Equation 9) In this example, as in the case of equation (17), learning is performed so as to be away from all the teachers, but the stability is poor.

[0055] In addition, in this example, r _- because ^p is not asymptotically approaches 0 with an increase of R _p, it is necessary to devise the learning end conditions. For example, r ₊ and r _- and to determine the end of the independent of the learning with respect to r ₊ performs the same judgment as the first embodiment, r _- is smaller than the value determined with it with respect to And that both of these two conditions are satisfied is set as the learning end condition.

FIG. 9 is a block diagram showing the configuration of the second embodiment of the present invention. In this example, the loss function calculating means 18 is constituted only by the loss function calculating means 20 by the teacher. That is, only the teacher signal of the teacher is fetched, and learning is performed so that the difference between the teacher signal and the output vector increases.

FIG. 4 shows a learning method according to this embodiment.
In the flowchart shown in FIG.
5 is omitted. On the other hand, since only the teacher is accepted as learning data, T _p is unnecessary. The other points are the same as in the first embodiment.

FIG. 10 is a graph showing a learning result when learning is performed using this embodiment, and the number of learning steps t is t = 1, 10, 100, 1000, 114.
The input / output function at 87 is drawn with a solid line. t = 11
Reference numeral 487 indicates a point in time when learning is completed.

This learning result is an example in which there are a plurality of teachers corresponding to the same input value I ₁ , and it can be seen that a learning result that is apart from all the teachers is obtained. In the case of the model teacher, all the teacher signals have a strong influence on the learning. On the other hand, in the case of the teacher, the difference between the teacher signal having a strong influence on the learning and the teacher signal having little influence is remarkable.

Next, a third embodiment according to the present invention will be described.

Sakamoto, et al .: "Information Statistics" (Kyoritsu, 19
83) According to Chapter 3,

(Equation 10) Is called entropy and is closely related to the criterion of goodness of model approximation. Here, in the above equation, p _i is a probability that an event ω _i (i = 1,..., M) will occur, and p _i ≧ 0, p _i
+ ... + p _m = 1. In other words, p _i is the true probability distribution. Q _i is a probability distribution model. The entropy is 1 / n of the logarithm of the probability that the distribution of n realizations obtained from the model q _i we assumed matches the true distribution.
Is approximately equal to In short, it can be said that the model that maximizes equation (19) is a good model. A good model is a model that has excellent "ability to output an appropriate output vector even for an unlearned input vector", that is, "generalization ability". When learning is required using a limited number of learning data, it is necessary to select a good model as well as possible. The “model” referred to here is a combination of a function system and a value of a control parameter when learning a relationship between input and output in a learning machine. However, here, p _i is considered to be the true distribution of the difference between the teacher signal and the output vector.

Equation (19) is

[Equation 11] However, since the second term depends only on the true distribution, it does not need to be considered when comparing models.
Log likelihood

(Equation 12) If this is defined as n → ∞ by the law of large numbers,
It converges to a value that is n times the first term in equation (20). Where n
_i is the number of times the event ω _i has occurred, and n _i +... + n _m = n holds. In short, a model with a larger log likelihood l (q) in equation (21) has a larger corresponding entropy value, and is a better model. A model that maximizes l (q) is called a maximum likelihood model. The maximum likelihood model is common in the fields of statistics and engineering, and a commonly used least squares method is also derived from the concept of the maximum likelihood model. So far, it is a known technique.

Next, equation (21) is extended to teacher learning. This has been clarified by the study of the present inventors. Equation (21) uses only the number of occurrences of the event ω _i , which corresponds to learning using only the model teacher ω _i . Even if the fact that "any of the other events ω _i happened" is discovered, in the prior art can not be learned using that fact. Therefore,
The above-mentioned “something other than the event ω _i has occurred” is regarded as an event of probability l−p _i , the probability distribution model is l−q _i, and equation (21) is expressed as

(Equation 13) Rewrite. However, N _o the total number of observations, N _i the event ω
a number of times with a focus on _{i, N i + ... + N} n = N o is established. N _i −n _i is the number of times “an event ω _i has been noticed, but other events have occurred”. In short, the policy is to focus on any one event each time and determine a model based on information on whether that event has occurred or whether other events have occurred.

In equation (22), N _i / N _o in l _n (...) is a model-independent term, and is dropped for simplicity.

[Equation 14] Is defined. l _E (q) is equal to the log likelihood except for a model independent constant term.

Next, equation (23) is extended to the case of a continuous variable model to derive a loss function in learning. The q _i density distribution function g | replaced by (x theta), and the region near the x _i containing x _i themselves inside and S, g the integration variable as x in S | obtained by integrating the (x theta) The value is G (x _i | Θ)
Then

(Equation 15) Becomes However, when deriving the equation (24), it is assumed that “event x occurs when an event included in the region S near x occurs, and that events other than event x occur when the event x occurs outside the region S. Event occurs. " By defining in this way, it is possible to add the probability of “event x occurs” and the probability of “other than event x” to be 1 for the first time, and to derive equation (24) which is an extension of equation (23) Will be able to Area S
The shape and size of can not be determined theoretically, and appropriate values need to be determined depending on the situation. However, for example, the validity is not lost even if the region S is considered as a hypersphere or a hypercube centered on x. That is, it suffices if it is appropriate that x represents all points in the area S. Further, the region S does not need to be a closed region.

Θ represents a set of parameters for determining the density distribution function, and is a combination of the control parameters of the learning machine and the parameters for determining the distribution of the difference between the model teacher and the output vector.

Now, in equation (24), the number of times n _i and N _i
If instead of multiplying by −n _{i the} sum is calculated that many times,

(Equation 16) Can be rewritten. Here, p is an index for identifying a teacher signal, Σ _{p: D} is a sum relating to the model teacher, and Σ _{p: U} is a sum relating to the teacher. In short, l in equation (25)
_It is a model that maximizes _E (Θ) or a maximum likelihood model, and it is sufficient that the parameter 与 え る that gives the maximum likelihood model can be obtained by learning.

[0068]

However, according to the learning of the present invention, since the learning is performed with the loss function in the learning as r = -lE (Θ) (26), the area S It is possible to automatically and optimally set all parameters other than the shape and the size of. That is, a maximum likelihood model can be constructed by learning, and a learning machine with the best generalization ability can be obtained.

[0069] The p-th teacher signal _{^{y p k (k = 1,}} ...,
N). In addition, the type of the teacher signal is represented by T _p , and if the p-th teacher signal is a model teacher, T _p = +, and if the _p -th teacher signal is a teacher, T _p = − (where + and − indicate the type of the teacher signal. Is just a sign). Conventional training data had been configured by a pair of the input vector and the teacher signal, the T _p was added to two of the present embodiment, it is assumed that constitute the learning data in a total of three.

For simplicity, it is assumed that N = 1. Extension to N> 1 is easy. Further, the area S is defined as x _p −S / 2 ≦ x ≦ x _p
+ S / 2. The value of s is sufficiently smaller than the variation of g (x | Θ) in the region S, and G (x _p | Θ) = sg (x _p
| Θ) holds, and sg (x _p | Θ)
Ln the case is small _{(1-sg (x p |} Θ)) = - sg
Using the approximate expression (x _p | Θ), expression (25) becomes

[Equation 17] By substituting equation (27) into equation (26), the loss function becomes

(Equation 18) Becomes However, in Equations (27) and (28), a constant term independent of the model parameter Θ was ignored. Here, the parameter theta, coupling coefficient w ^HI _ji in equation (1) to (4), w ^OR _kj, threshold θ ^H _j, θ ^O _k and described below equation (30), such as σ in to Formula (33) May be considered as a vector having all of the parameters as elements.

The method of determining the density distribution function g (x | Θ) of the difference between the teacher signal and the output vector is as follows.
Learning is performed assuming that Θ) is represented by a normal distribution with mean 0 and variance σ ² . At a stage where learning has progressed to some extent, the distribution of the difference between the teacher signal and the output data can be known. With reference to this, the function form of g (x | Θ) is set again and learning is continued. You can also.

G (x | Θ) is expressed as g (x | Θ) = (1 / (2π) ^1/2 σ) exp [−x ² / (2σ ² )] (29) When expressed in ² of the normal distribution, by substituting _{^{x p = O p l -y p}} l, loss function r is
From equations (28) and (29), r = r ₊ + r ₋ , (30)

[Equation 19] It is led. r ₊ is an exemplary teacher term in the loss function r, and r ₋ is a reverse teacher term. r ₊ ^p is a contribution of the p-th teacher signal in r _+, r _- ^p is r _- is the contribution of the p-th teacher signal in. R _p represents the distance between the p-th teacher signal and the output vector. It is assumed that the teacher signal is marked in advance with a mark (T _p ) indicating whether it is a model teacher or a teacher. As can be seen from Expressions (30) to (33), s is a parameter that adjusts the ratio of the model teacher and the teacher on the other hand that contribute to the loss function.

Equations corresponding to equations (27) to (33) in the case of N> 1 can be obtained by substituting an N-dimensional normal distribution for g (x | Θ).

In the present embodiment, the formulation is performed in consideration of only the teacher signal composed of only the model teacher component or only the teacher signal. However, if the teacher signal is N
When considered as a dimensional vector, the case of being a model teacher or a teacher on the basis of each vector component can also be realized by simply extending the above discussion. That is, the model teacher component and the reverse teacher component may be mixed in one teacher. First, consider when an N-dimensional output vector can be divided into two independent vectors in two spaces. And it is divided into a N _B dimensional vectors in N _A dimensional vector and the space B in the space A. In other words, the case where one teacher signal is a model teacher in the space A and a teacher in the space B is considered. Hereinafter, how to create a loss function will be specifically described.

N _A + N _B = N. Then, the difference between the teacher signal in the space A and the output vector is represented by a vector x.
As _A, the density distribution function of x _A is g _A | is assumed to be (x _A Θ _A), the difference between the teacher signal and the output vector in space B as a vector x _B, the density distribution function of x _B g _B (x _B | Θ _B ),
_{p: DD} is the sum of teacher signals that are model teachers in both space A and space B, Σ _{p: DU} is the model teacher in space A and space B
で は_{p: UD} is the sum of the teacher signal in space A and the teacher signal in space B. Σ _{p: UU} is the sum of the teacher signal in space A and Ａ _{p: UU} is the sum of the teacher signal in space A and space B. sum for a certain teaching ^{_{signal, G a (x a p |}} Θ a) a x _a ^p g to the integration variable in the region S _a in the vicinity of x _a ^p containing therein as x _{a a} | a (x _a Θ _a) Integrated value,
^{_{G B (x B p | Θ}} B) g the integration variable as x _B in the region S _B in the vicinity of x _B ^p containing x _B ^p within _B (x _B
^p | Θ _B ), the loss function r

(Equation 20) What is necessary is just to comprise. The same applies to a case where there are three or more parts where the model teacher and the teacher are independently replaced.

In the learning, the parameters are

(Equation 21) This is performed for each learning data by changing according to the equation. This method is called “stochastic descent method”. By updating the value of θ according to the equation (35), the loss function r can be reduced. The fact that θ obtained by equation (35) minimizes the loss function r of equations (30) to (33) on average is based on the theory of the stochastic descent method (Amari, S .: IEEE Trans. EC-16,279). (1967)). Here, θ is a coupling coefficient w ^HI _ji , w ^OH _kj or a threshold value θ ^H _j , θ ^{O in} equations (1) to (4).
_k and parameters such as σ in equations (30) to (33). Δθ (t) is an update amount of θ when the parameter is finely adjusted t times in learning by iterative calculation. η is a learning coefficient, and α is an inertia term.

The learning is continued until r becomes smaller than a predetermined small amount, but sometimes learning is impossible due to the nonlinearity of the neural network and the lack of model capability, or the time is of a practical length. In some cases, r may not be sufficiently small. Therefore, usually, the maximum number of repetitions is determined in advance, and when the maximum number is reached, the learning is terminated, and the learning is repeated several times by changing the initial value of the coupling coefficient and other parameters. In some cases, the model may be reviewed.

That is, the learning method of the learning machine in this embodiment will be described with reference to the flowchart of FIG. 11 when N = 1. First, a parameter indicating the serial number of learning data is set to p = 1 (step S21). ), training data ^{_{{I i p (i = 1}} , ..., L), y p l, T p} reads (step S22), and subsequently, of the neural network by the formula (1) to (5) the output vector After outputting O _l ^p (step S23), it is determined whether the teacher signal is a model teacher or a converse teacher (step S24). If the teacher signal is a model teacher, equations (1) to (5), (31), (33), (3
The parameter value is updated by calculating Δθ (t) in step 5) (step S25). On the other hand, if the teacher is a teacher, Δθ (t) is calculated using equations (1) to (5), (32), (33), and (35). t) is calculated and the value of the parameter is updated (step S2)
6). Next, it is determined whether or not p = P (step S27). If p ≠ P, 1 is added to p (step S2).
8) Return to step S22, but if p = P, proceed to step S29. If the learning end condition is satisfied, the learning ends, and if not, the process returns to step S21 (step 29). In step 24, the case where T _p = + (when all are model teachers) corresponds to the conventional technique.

As described above, according to the present invention, on the other hand, an optimal loss function in learning using a teacher can be selected based on theoretical grounds, and learning with the best generalization ability can be performed.

Next, a fourth embodiment of the present invention will be described. Embodiments will be described with reference to the drawings. This embodiment is different from the third embodiment in that the probability density function g (x | Θ) is replaced with a generalized Gaussian distribution function, and learning is performed in two stages. The description of the same parts as in the third embodiment is omitted.

G (x | Θ) is

(Equation 22) Is a generalized Gaussian distribution function. However, Γ
(X) is a gamma function, and | ... | are absolute values. The parameter b is newly added compared to the normal distribution, and the number of control parameters is increased by one. If b = 2, mean 0, variance σ
It corresponds to a normal distribution of ² . As described above, by increasing the number of control parameters by one, it is possible to cope with a distribution slightly distorted from the normal distribution. b = 1, b = 2, b = 10, b =
FIG. 12 shows the shape of the graph of g (x | Θ) in each case of ∞. However, each graph is drawn so that the maximum values are equal.

In this embodiment, by using the equation (36), learning with higher generalization ability than in the third embodiment can be performed. However, the number of control parameters is large, the processing becomes complicated, and a larger number of learning data is required. Therefore, g (x |
Select ii) as appropriate.

The loss function is

(Equation 23) Since given by the loss function r ^{_{is, x p = O 1 p -y}} p
₁ is substituted into Expression (36), and Expression (36) is further substituted into Expression (3).
By substituting into 7), it can be obtained as in the following equation.

R = r ₊ + r ₋ , (38)

(Equation 24) It is led.

Equations corresponding to equations (36) to (41) when N> 1 can be obtained by substituting an N-dimensional generalized Gaussian distribution for g (x | Θ).

In the learning, the control parameters are

(Equation 25) This is performed for each learning data by changing according to the equation. Here, θ is a coupling coefficient w ^HI _ji , w ^OH _kj or a threshold θ ^H _j , θ ^{O in} equations (1) to (4).
_k and control parameters such as σ and b in equations (38) to (41). In the learning of the first stage, b is fixed to b = 2.

The learning at the first stage is continued until r becomes smaller than a predetermined minute amount E _L1 . When r <E _L1 , the second stage learning is started. In the second stage, the first
The b fixed in the stage is also learned according to the equation (42), like other control parameters. And learning ,, the second stage will continue until the r <E _L2.

It is empirically known that learning by the steepest descent method is faster when b = 2. However, as described in the section of the operation, in order to perform learning with high generalization ability, it is necessary to determine a control parameter using a distribution close to a true distribution. Also, unlike the coupling coefficient and the threshold value, the calculation for learning σ and b is complicated and time-consuming. Therefore, by learning in two stages in this way, it is possible to expect an effect of increasing the speed and the generalization ability. In some situations, only a few adjustments of b in the second stage, and again b
It is also conceivable to learn by fixing.

That is, the learning method of the learning machine in the present embodiment will be described with reference to the flow chart of FIG. 13 in the case of N = 1.
1, the parameter b is set to b = 2 (step S3).
1), and proceed to step S32. Then, set the parameters representing the serial number of the learning data to p = 1 (step S32), the training data ^{_{{I i p (i = 1}} , ..., L), y
^p _l , T _p } are read (step S33).
Equation (1) - (4) after been output an output vector O ^p of the neural network (step S34), a teacher signal or model teacher, or to determine other hand teacher (step S3
5) For model teachers, equations (1)-(4), (39),
(41) and (42) calculate Δθ (t) to update the value of the control parameter. If phase = 2, b is updated in the same manner as the other control parameters (step S36).
Then, the process proceeds to step S38. In step S35, if the teacher signal is a teacher, equations (1)-(4), (40)
In step (42), Δθ (t) is calculated to update the value of the control parameter. If phase = 2, b is updated in the same manner as the other control parameters (step S37). Then, the process proceeds to step S38. In step S38, it is determined whether or not p = P.
(Step S39), the process returns to step S33, but if p = P, the process proceeds to step S40. And r
If <E _L1 , the process proceeds to step S41; otherwise, the process returns to step S32 (step S40). Step S
At 41, the phase is set to phase = 2, and step S
Proceed to 42. If r <E _L2 is satisfied, the learning ends, and if not, the process returns to step S32 (step S42).

Next, a fifth embodiment of the present invention will be described with reference to the drawings. This embodiment is different from the first embodiment in that
Learning is performed by using a boundary teacher, which is a teacher signal that specifies a boundary between a region where output vectors are to be collected and a region to be avoided as a teacher signal (the boundary is a plane in a three-dimensional space). It is an extension. The description of the same parts as in the first embodiment is omitted.

FIG. 14 is a conceptual diagram of a learning machine according to the fifth embodiment. This conceptual diagram is obtained by adding the loss function calculating means 21 by the boundary teacher in FIG. That is, the loss function calculating means 8 comprises a loss function calculating means 9 by the model teacher, a loss function calculating means 10 by the teacher, and a loss function calculating means 21 by the boundary teacher. When a boundary teacher is given, the loss function and differential coefficients are calculated by the loss function calculator 21 by the boundary teacher.

Next, a case where the present embodiment is applied to back propagation learning of a three-layer field forward neural network will be described.

FIG. 15 is a conceptual diagram thereof. This learning machine is shown in FIG.
Is added. That is, the loss function calculating means 18
Is composed of loss function calculating means 19 by the model teacher, loss function calculating means 20 by the teacher, and loss function calculating means 31 by the boundary teacher.

[0094] The p-th teacher signal ^{_{y p k, a p k (}} k =
1,..., N). Also, the type of the teacher signal is represented by T _p, where T _p = + if the p-th teacher signal is a model teacher, T _p = − if it is a teacher, and T _p => if it is a boundary teacher (where, “+”, “−”, And “>” are simply symbols for distinguishing the type of the teacher signal). a ^p _k has a meaning at the time of T _p =>, it becomes a dummy signal that does not have a meaning in a T _p ≠>. Further, conventional teacher signal had been represented by a single vector with the same dimensions as the output data. In this embodiment, the teacher signal with the crude two vectors y _p and a _p.

Using the equations (8)-(10) and the following equation, the loss function r is calculated as follows: r = r ₊ + r ₋ + r _> , (43)

(Equation 26) ^{_{d p = a p · (O}} p -y p), put a ... (45), _r> is a boundary teacher section. r _> ^P is the contribution of the p-th teacher signal in r _> . d _p represents the difference between the p-th teacher signal (boundary teacher) and the output data. Σ _{p: B}
Represents the sum of all boundary teachers. It is assumed that the teacher signal has a mark (T _p ) indicating in advance which of the model teacher, the other side teacher, and the boundary teacher it is. γ
_> Is a parameter for adjusting the contribution of the boundary teacher contributing to the loss function, and a is a parameter for adjusting the distance at which the boundary teacher affects the output data. γ _- and γ _>
By adjusting, it is possible to select one of the three kinds of teachers that mainly works for learning. By adjusting β and a, it is possible to adjust how much the output data must be apart from the teacher and the boundary teacher during learning.

From equations (44) and (45), the function system of the boundary teacher term in the loss function is obtained for each learning data.

[Outside 1] It turns out that it becomes. FIG. 16 is a graph showing the features of this function system.

When the teacher signal is considered as an N-dimensional vector, it is also possible for each component of the vector to be a model teacher, a reverse teacher, or a boundary teacher (8)-
(10), (43)-(45) can be realized by slightly changing the expressions. That is, the model teacher component, the reverse teacher component, and the boundary teacher component may be mixed in one teacher. However, in the present embodiment, the formulation is performed in consideration of only the teacher signal composed only of the model teacher component, only the teacher component, or only the boundary teacher component.

In the learning, the coupling coefficient is calculated by the equation (11) and the following equation.

[Equation 27] This is performed by changing as follows.

Next, the above-described learning method will be systematically described with reference to the flowchart shown in FIG.

The loss function calculating means 18 shown in FIG.
First, the parameter representing the serial number of the learning data is p = 1.
(Step ST51), and the learning data ｛I _i ^p
(I = 1, ..., L ), y p k, a p k, (k = 1, ...,
N), T _p } are read (step ST52), and the output vector Ok p (k = 1,..., N) of the neural network is output by the equations (1) to (6) (step ST53). , Determine the type of the teacher signal (step S
T54), if you are a model teacher, (1) to (6), (8),
In equation (10)

[Outside 2] Is calculated and stored in the memory (step ST55). On the other hand, if the teacher is a teacher, the equations (1) to (6), (8) and (10) are used.

[Outside 3] Is calculated and stored in the memory (step ST56), and if it is a boundary teacher, the equations (1) to (6), (44) and (45) are used.

[Outside 4] Is calculated and stored in the memory (step ST57).

Next, it is determined whether or not p = P (step ST58). If p ≠ P, 1 is added to p (step ST59) and the process returns to step ST52. If p = P, step ST55 is performed. , ST56, and ST57, based on the results calculated and stored, update the coupling coefficient and the threshold value by the equations (11) and (46) (step ST60). If the learning end condition is satisfied, the learning ends, and if not, the process returns to step ST51 (step ST6).
1). Thus, learning is performed.

[0102]

As described above, according to the present invention, when a teacher signal to be avoided is given, learning is performed so as to increase the difference between the teacher signal and the output data, and a model teacher signal is given. Then, learning is performed such that the difference between the teacher signal and the output data is reduced.

Accordingly, learning flexibility and workability are improved, and learning suitable for learning conditions and reasonable learning suitable for the characteristics of the learning machine can be performed.

Further, when learning using a teacher,
It is possible to select an appropriate loss function according to the learning, thereby obtaining an effect that stable and high-speed learning can be realized.

[Brief description of the drawings]

FIG. 1 is a functional block diagram of a learning machine according to the present invention.

FIG. 2 is a functional block diagram of a learning machine using a three-layer feedforward neural network in the first embodiment of the invention shown in FIG. 1;

It illustrates and ^p, the relation between the difference Rp between the teacher signal and the output vector _- Figure 3 loss function r of contrary teacher used in the indicated learning machine in FIG.

FIG. 4 is a flowchart showing a flow of a learning method performed on the learning machine shown in FIG. 2;

FIG. 5 is a characteristic diagram showing a relationship between an input and an output obtained by actually applying the learning method of the learning machine shown in FIG. 3;

It is a characteristic diagram showing the relationship between ^p and R _{p -} [6] loss function r of contrary teacher in the modification of the first embodiment of the invention shown in Figure 1.

It is a characteristic diagram showing the relationship between ^p and R _{p -} [7] loss function r of contrary teacher in the modification of the first embodiment of the invention shown in Figure 1.

It is a characteristic diagram showing the relationship between ^p and R _{p -} [8] loss function r of contrary teacher in the modification of the first embodiment of the invention shown in Figure 1.

FIG. 9 is a functional block diagram of a learning machine according to a second embodiment of the invention shown in FIG. 1;

FIG. 10 is a characteristic diagram showing a relationship between an input and an output obtained by actually applying the learning machine shown in FIG. 9;

FIG. 11 is a flowchart illustrating a flow of a learning method according to a third embodiment performed on the learning machine illustrated in FIG. 2;

FIG. 12 is a characteristic diagram showing a probability density function in a learning method according to a fourth embodiment of the present invention.

FIG. 13 is a flowchart showing a flow of a learning method according to a fourth embodiment performed on the learning machine shown in FIG. 2;

FIG. 14 is a functional block diagram when a learning machine according to the present invention is expanded in the fifth embodiment.

FIG. 15 is a functional block diagram of a learning machine using a three-layer feedforward neural network in a fifth embodiment.

FIG. 16 shows the contribution r _> to the boundary teaching term in the fifth embodiment.
FIG. 4 is a characteristic diagram showing a relationship between ^P and d _p .

FIG. 17 is a flowchart showing a flow of a learning method performed on the learning machine shown in FIG. 15;

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Input terminal 2 Transformation part 3 Output terminal 7, 17 Parameter adjustment means 8, 18 Loss function calculation means 9, 19 Loss function calculation means by model teacher 10, 20 Loss function calculation means by model teacher 11 Neuron element 12 Input layer 13 Hidden Layer 14 Output layer 15, 16 Coupling part 21, 31 Loss function calculating means by boundary teacher

Continuation of the front page (56) References JP-A-2-170265 (JP, A) JP-A-5-20291 (JP, A) JP-A-5-165801 (JP, A) Akiyama, Furuya, Backpropagation Learning Rule with Entropy Term ", IEICE Technical Report, Vol. 91, No. 25 (NC91-1-18), published by The Institute of Electronics, Information and Communication Engineers (May 8, 1991), pp. 39-46 (Patent Office CSDB Literature Number: CCNT 199900623006) Yamada, Tanaka, "Learning Method with Increased Output Difference from Teacher Signal", Proc. Of the 1991 IEICE Autumn Conference, Volume 6, The Institute of Electronics, Information and Communication Engineers (Issue: August 15, 1991; Acceptance date: Japan Patent Office Information Center: November 13, 1991) (58) Field surveyed (Int. Cl. ⁷ , DB name) G06N 1 / 00-7/00 G06G 7/60 JICST file (JOIS) INSPEC (DIALOG) CSDB (Japan Patent Office) IEEEExplore (http://ieeeexplore.ieee.org/)

Claims (5)

(57) [Claims] In a method of learning a control parameter using a teacher signal in a learning machine that outputs an output vector using a predetermined control parameter with respect to an input vector, a learning signal should not be output as an output vector as a teacher signal. On the other hand, define the teacher that means the data to be avoided, give the value of the input vector and the value of the teacher signal corresponding to the input vector to the learning machine, and use the initial control parameters for the value of the input vector and the value of the output vector. Is calculated,
On the other hand, according to the difference x between the teacher and the output vector, a loss function r that decreases with an increase in the difference x is calculated by the following equation. R = exp (−x ² ) When the value of the loss function is larger than a predetermined value, Until the value of the loss function becomes smaller than the predetermined value, the control parameter is updated so that the value of the loss function is reduced, and the value of the loss function is repeatedly calculated, and the calculated loss function is smaller than the predetermined value. A learning method for a learning machine, comprising, when a small value is reached, incorporating the updated latest control parameters into the learning machine. 2. A method for learning a control parameter using a teacher signal in a learning machine that outputs an output vector using a predetermined control parameter with respect to an input vector, wherein data to be output as an output vector is used as a teacher signal. And an instructor that means data to be avoided which should not be output as an output vector, and defines a value of an input vector and a value of a teacher signal corresponding to the input vector to a learning machine. teacher and determined by the difference x ₊ formulas below are as a model teacher term r ₊ calculated by the output vector, r ₊ = x ₊ ² whereas the teacher and the contribution of the difference x _over and although teacher and model teacher output vector It defines the other hand teacher term r _over which is calculated by the parameter gamma _over> 0 to determine the ratio by the following equation, r _over = gamma _{chromatography} exp a ^_(-x-2) model teacher learning machine When given calculates the model teacher term r ₊ to decrease with decreasing difference x _+, contrary to the case of giving the teacher in the learning machine, calculates the contrary teacher term r _over which decreases with increasing difference x _over and, exemplary teacher term r ₊ and loss function r obtained by adding the other hand teacher term r _over
If the value of the loss function is larger than a predetermined value, the control parameters are updated so that the value of the loss function decreases until the value of the loss function becomes smaller than the predetermined value, and the loss function is updated. Learning the learning machine, comprising repeatedly calculating the value, and incorporating the updated latest control parameter into the learning machine when the calculated loss function reaches a value smaller than a predetermined value. Law. 3. A neural network in which a plurality of neuron elements are connected to each other, multiplying an input vector given to a group of neuron elements of an input unit by a predetermined connection weight,
The weighted data is transmitted to the neuron element group connected to the input neuron element group, the threshold value is further subtracted, the value converted by a predetermined monotonically increasing function is multiplied by a predetermined connection weight, and the output neuron element is output. In the learning machine that transmits to the group, subtracts the threshold value again, converts it with a predetermined monotone increasing function, and outputs the output vector from the neuron element group of the output unit, sets the connection weight and threshold value using the teacher signal In the method of learning a learning machine, as a teacher signal, a model teacher that means data to be output as an output vector, and a teacher that means data to be avoided that should not be output as an output vector, The input vector value is given to the neuron element group of the input part of the learning machine, and the model teacher or the other side teacher corresponding to the input vector is given to the learning machine. Using coupling weights and thresholds to convert the input vector, and calculates the value of the output vector from the neuron element group output unit, a model teacher term r ₊ calculated by ₊ the difference between the model teacher and output vector x determined, contrary defines contrary teacher term r _over which is calculated by the difference x _over the teacher and the output vector, when given a model teacher in the learning machine, a model teacher term r ₊ to decrease with decreasing difference x ₊ calculated, on the other hand when given a teacher in the learning machine, the difference x _over
Of the other hand teacher term r _over which decreases computed with increasing calculates the loss function r obtained by adding a model teacher term r ₊ and although teachers term r _over, if the value of the loss function is larger than a predetermined value Until the value of the loss function becomes smaller than a predetermined value, the connection weight and the threshold are updated so that the value of the loss function decreases, and the value of the loss function is repeatedly calculated. A learning method for a learning machine, comprising: incorporating the updated latest connection weight and threshold value into the learning machine when a value smaller than a predetermined value is reached. 4. A method for learning a control parameter て using a teacher signal in a learning machine that outputs an output vector using a predetermined control parameter に 対 し with respect to an input vector, wherein the control parameter と し て is output as an output vector as a teacher signal. A model teacher that means data to be output and a teacher that means data to be avoided that should not be output as an output vector are defined, and the density distribution function g (x ₊ ) of the difference x ₊ between the model teacher and the output vector is defined as using the area s occupied by exemplary teachers, determine the probability distribution _{G (x +) = ∫ s} g (x) dx associated with model teachers, contrary difference x _over the teacher and the output vector, the density distribution function g (x) and using the area s occupied by exemplary teachers, contrary defines a probability distribution G (x _{over) = 1-∫ s g (} x) dx associated with teachers, the learning machine The value of the force vector and the value of the teacher signal corresponding to the input vector are given, the value of the output vector is calculated using the initial control parameter に for the value of the input vector, and the log likelihood lg ( determined as follows exemplary teacher term r ₊ and although teachers term r _over from Θ, -lE (Θ) = - lnG (x +) -ln [1-G (x _over)], r ₊ = -lnG ( x _+), r _over = -ln [1-G (x _over), when the model teacher gave learning machine calculates the model teacher term r ₊ to decrease with decreasing difference x _+, contrary teachers when given to learning machine of the difference to calculate the contrary teacher term r _over which decreases with increasing x _over, exemplary teacher term r ₊ and although teachers term r _over loss is determined by adding the function r
When the value of the loss function is larger than the predetermined value, the control parameter Θ is updated so that the value of the loss function decreases until the value of the loss function becomes smaller than the predetermined value, and the loss function is updated. Is repeatedly calculated, and when the calculated loss function reaches a value smaller than a predetermined value, the learning machine incorporates the updated latest control parameter た. Learning method. 5. A learning machine for multiplying an input vector by a predetermined control parameter to output an output vector, wherein the control parameter is preliminarily learned using a teacher signal. A model teacher that means data and a teacher that means data to be avoided that should not be output as an output vector are defined, and the area s occupied by the model teacher, the difference x ₊ between the model teacher and the output vector, and the variance σ ^Two
Distribution function s * g (x ₊ ) = s (1 / (2π) ^1/2 σ) exp [−] using the normal distribution g (x ₊ ) defined by
defines _{^{x + 2 / (2σ 2)}} ], the area occupied by the exemplary teacher s, contrary to the teaching contrary with normal distribution g (x _over) defined by the difference x _over and variance sigma ² between the teacher and the output vector related to the distribution function 1-s * g (x _over)
= 1-s (1 / (2π) ^1/2 σ) exp [−x ₋ ² /
(2σ ² )], the input value of the input vector and the value of the teacher signal corresponding to the input vector are given to the learning machine, the value of the output vector is calculated using the initial control parameters as the input vector value, and the statistical value is calculated. calculated from log-likelihood l E (x) based on the entropy of the above like the exemplary teacher term r ₊ and although teachers term r _over, -lE (x) = - lng (x +) + s * g (x _{over ) r + = -lng (x +} ) = ln (σ) + x + 2 / (2σ 2) r _over = s * g (x _over ^{2) = s / (1 /} (2π) 1/2 σ) exp when given the [-x _{chromatography} ² / ^{(2σ 2)]} model teacher learning machine calculates the model teacher term r ₊ to decrease with decreasing difference x _+, contrary to the case of giving the teacher learning machine is determined by calculate the contrary teacher term r _over which decreases with increasing difference x _over, adding model teacher term r ₊ and although teachers term r _over The loss function r calculated that, if the value of the loss function is larger than a predetermined value, until the value of the loss function is smaller than a predetermined value, the control parameter so that the value of the loss function is reduced and variance σ ² to repeatedly calculate the value of the loss function, and when the calculated loss function reaches a value smaller than a predetermined value, from incorporating the updated control parameter and variance σ ² into the learning machine. A learning method for a learning machine, comprising: