JP2022161099A - Arithmetic apparatus, integrated circuit, machine learning apparatus, and discrimination apparatus - Google Patents

Abstract

To provide an arithmetic apparatus that enables a treatment of phenomenon expressed by power exponents and enables an accurate derivation of a correlation between an input and an output in the phenomenon.SOLUTION: An arithmetic apparatus outputs an output value from an output layer for a plurality of input data (D0, D1,..., DN) input to an input layer, using a neural network structure including at least the input layer and the output layer. The input layer includes a plurality of power exponents (p0, p1,..., pN) respectively associated with the plurality of input data and powered to the plurality of input data, as a learning parameter. The output layer outputs an output value (y=f(YY0)) based on products (YY0=D0p0*D1p1*...*DNpN) obtained by powering the plurality of input data input to the input layer by the plurality of power exponents (D0p0*D1p1*...*DNpN) respectively.SELECTED DRAWING: Figure 1

Description

The present invention relates to arithmetic devices, integrated circuits, machine learning devices, and discrimination devices.

In recent years, machine learning has been applied to various fields, and in particular, neural network structures have been widely applied to both regression problems and classification problems. In such a neural network structure, multiple pieces of input data input to the input layer are multiplied by respective weighting factors, and an output value based on the sum of the calculated results is output from the output layer (for example, patent See Document 1, Patent Document 2, etc.).

JP-A-7-129535 JP-A-7-141315

Conventional neural network structures such as those described in Patent Document 1, Patent Document 2, etc. perform machine learning by adjusting weighting coefficients, but the "exponent" for a plurality of input data is, for example, It is fixed like "1". Therefore, as a phenomenon to which the neural network structure is applied, if the power exponent for the input data is known in advance and fixed at that value, the weighting factor will converge to appropriately define the phenomenon during machine learning. It is thought that

However, in various phenomena such as natural phenomena, economic phenomena, social phenomena, etc., when the power index for multiple input data is not known in advance, or when multiple input data are multiplied by the power exponent, It is naturally assumed that the output value is calculated accordingly. In such a case, in a conventional neural network structure, even if it is possible to approximate the weighting coefficients that define the phenomenon for a specific combination of input data, the error in the output data for another combination of input data is becomes large, there is a structural problem that it is difficult to converge to an appropriate weighting factor by machine learning. In other words, in the conventional neural network structure, when the phenomenon to be modeled includes the product of power values for the input data, the correlation between the input (input data) and the output (output value) is defined as accuracy. There was a problem that it could not be derived well.

SUMMARY OF THE INVENTION In view of the above-mentioned problems, the present invention is an arithmetic device that enables handling of phenomena represented by power exponents and enables accurate derivation of correlations between inputs and outputs in the phenomena. , an integrated circuit, a machine learning device, and a discrimination device.

In order to achieve the above object, an arithmetic device according to one aspect of the present invention includes:
A computing device that outputs output values from the output layer for a plurality of input data (D0, D1, . . . , DN) input to the input layer using a neural network structure including at least an input layer and an output layer There is
The input layer is
having a plurality of power exponents (p0, p1, .
The output layer is
A product ( ^YY0 =D0 ^p0 *D1 ^p1 *) of a plurality of power values (D0 ^p0 , D1 ^p1 , . . . , output the output value (y=f( ^YY0 )) based on *DN pN ).

According to the neural network structure used by the arithmetic device according to one aspect of the present invention, the input layer has, as learning parameters of the neural network structure, a plurality of power exponents that respectively raise a plurality of input data, and the output layer: An output value is output based on a product of a plurality of power values obtained by powering a plurality of input data input to the input layer by a plurality of exponents. Therefore, the arithmetic unit can handle the phenomenon represented by the exponent and can accurately derive the correlation between the input and the output in the phenomenon.

Problems, configurations, and effects other than the above will be clarified in the mode for carrying out the invention, which will be described later.

It is a figure explaining 100 A of neural-network structures used by the arithmetic device which concerns on the 1st basic form of this invention, and its basic principle. 1 is a diagram illustrating a neural network structure 100B used by an arithmetic device according to the first basic form of the present invention and its basic principle; FIG. It is a figure explaining 100 C of neural-network structures used by the arithmetic device based on the 3rd basic form of this invention, and its basic principle. 1 is a block diagram showing a configuration of an arithmetic device 1 using a neural network structure according to first to third basic forms of the present invention; FIG. It is a figure which shows the structure of the neural network based on the 1st Embodiment of this invention. 1 is a diagram showing the structure of an exponential addition addition neural network according to the first embodiment of the present invention; FIG. 4 is a flow chart showing a method of searching for an optimal exponent solution by the neural network device according to the first embodiment of the present invention; 1 is a diagram showing the structure of a multilayer neural network according to a first embodiment of the present invention; FIG. FIG. 10 is a diagram showing the configurations of a difference matrix and a product input matrix according to the second embodiment of the present invention; 8 is a flow chart showing a method of searching for an optimum solution using a difference search method according to the second embodiment of the present invention; It is the table|surface which listed nine planet names and two measurement data (average distance from the sun, revolution period) which concerns on Example 1 of this invention. FIG. 4 is an output diagram in which the coefficient of variation according to Example 1 of the present invention is the output value, the horizontal axis is the exponent p0 of D0, and the vertical axis is the exponent p1 of D1, and the coordinates are (p0, p1). FIG. 4 is a three-dimensional wireframe plot diagram obtained by transforming the output value of the coefficient of variation into a log value (common logarithm) according to Example 1 of the present invention. It is the table|surface which listed nine planets and the value of YY/W based on Example 1 of this invention. Convert the output value of the coefficient of variation when the formula YY/W=D0^(-5)*D1^(3) according to Example 1 of the present invention is changed to the answer data to a log value (common logarithm) 3 is a three-dimensional wireframe plot diagram; FIG. FIG. 10 is a pictorial view of 10 triangles applied to the discovery of Heron's formula according to Example 2 of the present invention; It is the table|surface which listed the dimension and area of three sides of ten triangles based on Example 2 of this invention. FIG. 10 is a table listing three-side calculation formulas that are product input elements according to Example 2 of the present invention; FIG. It is the table|surface which listed the five-dimensional input data table input into the power search method which concerns on Example 2 of this invention. FIG. 10 is a table listing 10 triangles (SN rows) and YY/W values according to Example 2 of the present invention; FIG. The even-numbered areas S of the 10 triangles according to Example 2 of the present invention are multiplied by 1.0 and the odd-numbered areas are multiplied by 0.9. is. FIG. 10 is a diagram showing a graph of output values Z-Act of the neural network according to Example 2 of the present invention in the order of triangle numbers; It is a figure showing the graph of YY/W triangular number order based on Example 2 of this invention. FIG. 4 is a diagram of a CartPole inverted pendulum according to Example 4 of the present invention; FIG. 11 is a table listing outputs of the CartPole inverted pendulum according to Example 4 of the present invention; FIG. FIG. 11 is a table listing actions that can be taken from state variables of the CartPole inverted pendulum according to Example 4 of the present invention; FIG. FIG. 4 is a diagram showing the structure of a conventional neural network according to Example 4 of the present invention; FIG. 13 is a table listing rewards given at the end of the t-th episode according to Example 4 of the present invention; FIG. FIG. 4 is a flow chart using a conventional policy gradient method according to Embodiment 4 of the present invention; FIG. It is a figure showing the step number transition graph of the result of implementing the conventional policy gradient method based on Example 4 of this invention to a CartPole inverted pendulum simulation. FIG. 10 is a table listing 5 examples of weighting parameters that implemented the conventional policy gradient method according to Example 4 of the present invention to a CartPole inverted pendulum simulation and that the rod could withstand without tipping over. FIG. FIG. 10 is a flow chart of a reinforcement learning algorithm controlled using a power search method according to Example 4 of the present invention; FIG. FIG. 11 is a table in which update amounts Δpn for updating exponents are set in an array of deviations N according to Example 4 of the present invention; FIG. FIG. 12 is a diagram showing a step number transition graph of the result of implementing the power search method to the CartPole inverted pendulum simulation according to Example 4 of the present invention. FIG. 11 is a table listing five examples of power exponent values that the rod could withstand without tipping over when the power search method was implemented in the CartPole inverted pendulum simulation according to Example 4 of the present invention; FIG. YY/W step No. according to the fourth embodiment of the present invention. It is a figure showing the graph of order (time-series order in which the truck was pushed). It is the table|surface which put together the operation|movement of a trolley|bogie when changing the value of the threshold value A based on Example 4 of this invention. According to Example 4 of the present invention, the input data was narrowed down to the angle and angular velocity of the pole (Pole), the power search method was implemented in the CartPole inverted pendulum simulation, and the power exponent value that the pole could withstand without falling It is the table|surface which made the list three examples. It is a picture which implemented the control type|formula which moves a cart (Cart) right and left to the CartPole inverted pendulum simulation, and applied-operated according to Example 4 of this invention. FIG. 10 is a truth table of a two-input exclusive OR (EXOR) according to Example 5 of the present invention; FIG. FIG. 12 is a truth table of a 3-input exclusive OR (EXOR) according to Example 5 of the present invention; FIG. FIG. 11 is a table of discriminant learning results using a 3-input exclusive-OR (EXOR) exponential addition addition neural network according to Example 5 of the present invention; FIG. FIG. 10 is a table showing the relationship between binary numbers and decimal numbers according to Example 5 of the present invention; FIG. FIG. 11 is a table showing the results of a mathematical search using a power-exponent addition addition neural network for a relational expression between binary numbers and decimal numbers according to Example 5 of the present invention; FIG.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a description will be given of a "basic form" showing the basic principle of the present invention and an "embodiment" for carrying out the present invention by applying the basic principle, with reference to the drawings. In the following, the range necessary for the description to achieve the object of the present invention is schematically shown, and the range necessary for the description of the relevant part of the present invention is mainly described. It shall be by technology.

(First basic form)
FIG. 1 is a diagram illustrating a neural network structure 100A used by an arithmetic device according to the first basic form of the present invention and its basic principle.

The arithmetic device uses a neural network structure 100A including at least an input layer 110A and an output layer 120A to generate a plurality of input data Dn=(D0, D1, . . . , DN) input to the input layer 110A. is a device for outputting an output value y from .

The neural network structure 100A shown in FIG. 1 is composed of an input layer 110A having N+1-dimensional (N is a natural number of 1 or more) neurons (nodes) and an output layer 120A having one neuron (node). N neurons in the input layer 110A and one neuron in the output layer 120A are connected by N+1-dimensional synapses (edges). Note that each synapse may be associated with an N+1-dimensional weighting parameter wn=(w0, w1, w2, . . . , wN). will be explained.

The N neurons of the input layer 110A are associated with the N+1-dimensional input data Dn, respectively, and receive the N+1-dimensional input data Dn. The input layer 110A also has N+1-dimensional exponents pn=(p0, p1, . At least one of the N+1-dimensional input data Dn may be data represented by a complex number.

The output layer 120A ^generates N+1-dimensional power values Dn ^pn =(D0 ^p0 , D1 ^p1 , . output value y (=f(YY0)) based on the product YY0 (=D0 ^p0 *D1 ^p1 * . . . *DN ^pN ). Therefore, the output layer 120A outputs an output value y as indicated by (Equation 1-1) and (Equation 1-2) below. Note that "*" represents a product symbol.

(Number 1-1)
YY0=D0 ^p0 *D1 ^p1 *...*DN ^pN
(Number 1-2)
y=f(YY0)
However, each parameter in the above formula is as follows.
Dn (n = 0, 1, ..., N): input data pn (n = 0, 1, ..., N): exponent (learning parameter)
Dn ^pn (n = 0, 1, ..., N): power value YY0: product of power values y: output value

The N+1-dimensional power exponent pn as a learning parameter is a parameter learned by using a plurality of sets of learning data including N+1-dimensional input data Dn and teacher data T associated with the N+1-dimensional input data Dn. is.

The N+1-dimensional exponent pn is the difference between the output value y output from the output layer 120A when the N+1-dimensional input data Dn included in the learning data is input to the input layer 110A, and the teacher data T included in the learning data. Adjustments are made so that the difference (error) between

As described above, when the series of steps for adjusting (searching) the learning parameter using the learning data is repeated a predetermined number of times, or when the difference becomes smaller than a predetermined allowable value, the arithmetic device It is determined that the learning termination condition is satisfied, and the learning for the learning parameters is terminated. This realizes a trained neural network structure 100A having N+1-dimensional exponents pn as learning parameters. By inputting N+1-dimensional input data Dn whose output value is unknown to the input layer 110A of the trained neural network structure 100A, the arithmetic device outputs the output value y for the N+1-dimensional input data Dn from the output layer 120A. do.

Note that the arithmetic unit may perform predetermined preprocessing (normalization, standardization, one-hot encoding, etc.) on the input data before being input to the input layer 110A, or Predetermined post-processing may be performed on the output data.

According to the neural network structure 100A used by the arithmetic device according to the present basic mode, the input layer 110A has a plurality of exponents for exponentiating a plurality of input data as learning parameters of the neural network structure 100A, and the output layer 120A outputs an output value based on the product of a plurality of power values obtained by powering a plurality of input data input to the input layer 110A by a plurality of exponents. Therefore, the arithmetic unit can handle the phenomenon represented by the exponent and can accurately derive the correlation between the input and the output in the phenomenon.

(Second basic form)
FIG. 2 is a diagram for explaining the neural network structure 100B used by the arithmetic device according to the first basic form of the present invention and its basic principle.

A neural network structure 100B (FIG. 2) according to the second basic form includes at least an input layer 110B and an output layer 120B, as in the first basic form (FIG. 1). and perform antilogarithm (antilogarithm) calculation in the output layer 120B. The characteristic portions of the neural network structure 100B according to the second basic form will be mainly described below.

The N neurons of the input layer 110B are associated with N+1-dimensional input data Dn=(D0, D1, . is entered. The input layer 110B also has N+1-dimensional exponents pn=(p0, p1, . Then, the input layer 110B converts the N+1-dimensional input data Dn into logarithms dn=(d0, d1, . Then, the N+1-dimensional multiplication value dn*pn=(d0*p0, d1*p1, . . . , dN*pN) is output to the output layer 120B. At least one of the N+1-dimensional input data Dn may be data represented by a complex number.

The output layer 120B converts the sum (d0*p0+d1*p1+...+dN*pN) of the N+1-dimensional multiplication value dn*pn into an antilogarithm (base ^{d0*p0+d1*p1+...+dN*pN} ), and converts the antilogarithm into Output the output value y (=f(YY0)) as the product of the N+1-dimensional exponentiation values. Therefore, the output layer 120B outputs an output value y as shown in (Equation 2-1) and (Equation 2-2) below.

(Number 2-1)
YY0=base ^{d0*p0+d1*p1+...+dN*pN}
(= D0 ^p0 * D1 ^p1 *... * DN ^pN )
(Number 2-2)
y=f(YY0)
However, each parameter in the above formula is as follows.
base is a positive number excluding 1 Dn = base ^dn (n = 0, 1, ..., N): input data pn (n = 0, 1, ..., N): exponent (learning parameter)
Dn ^pn (n = 0, 1, ..., N): power value YY0: product of power values y: output value

The N+1-dimensional power exponent pn as a learning parameter is, similarly to the first basic form, learning data including N+1-dimensional input data Dn and teacher data T associated with the N+1-dimensional input data Dn. This parameter is learned by using multiple sets.

The N+1-dimensional exponent pn is the difference between the output value y output from the output layer 120B when the N+1-dimensional input data Dn included in the learning data is input to the input layer 110B, and the teacher data T included in the learning data. Adjustments are made so that the difference (error) between

As described above, when the series of steps for adjusting (searching) the learning parameter using the learning data is repeated a predetermined number of times, or when the difference becomes smaller than a predetermined allowable value, the arithmetic device It is determined that the learning termination condition is satisfied, and the learning for the learning parameters is terminated. This realizes a trained neural network structure 100B having N+1-dimensional exponents pn as learning parameters. The arithmetic device inputs N+1-dimensional input data Dn whose output value is unknown to the input layer 110B of the learned neural network structure 100B, and outputs the output value y for the N+1-dimensional input data Dn from the output layer 120B. do.

According to the neural network structure 100B used by the arithmetic device according to the present basic mode, the input layer 110B converts a plurality of input data into logarithms, and multiplies the converted logarithms by a plurality of power exponents. A plurality of multiplied values are output to the output layer 120B, and the output layer 120B converts the sum of the multiplied values into an antilogarithm and outputs an output value based on the antilogarithm after the conversion. Therefore, the arithmetic unit can handle the phenomenon represented by the exponent and can accurately derive the correlation between the input and the output in the phenomenon.

(Third basic form)
FIG. 3 is a diagram illustrating a neural network structure 100C used by an arithmetic device according to the third basic form of the present invention and its basic principle.

A neural network structure 100C (FIG. 3) according to the third basic form includes an input layer 110C and an output layer 120C as in the first basic form (FIG. 1). This embodiment differs from the first basic embodiment in that a hidden layer 130 is further included between . Hereinafter, the characteristic portion of the neural network structure 100C according to the third basic form will be mainly described.

The N neurons of the input layer 110C are associated with N+1-dimensional input data Dn=(D0, D1, . is entered. The input layer 110C also has N+1-dimensional exponents pn=(p0, p1, . At least one of the N+1-dimensional input data Dn may be data represented by a complex number.

The hidden layer 130 receives N+1-dimensional input data Dn via N+1-dimensional weighting parameters wn=(w0, w1, . . . , wN) as learning parameters. A first hidden node 131 that outputs a defined target value YY1 to the output layer 120A, and N+1-dimensional input data Dn are input via N+1-dimensional weighting parameters wn, respectively, and a bias parameter b , and a second hidden node 132 that outputs to the output layer 120A an additive operation output BYA defined by the following equation (Equation 3-2).

The output layer 120C outputs an output value y (=f(YY1, BYA)) based on the target value YY1 and the addition type operation output BYA.

(Number 3-1)
YY1=D0 ^p0 *D1 ^p1 *...*DN ^pN *W0*W1*...*WN
(Number 3-2)
BYA=B*(base) ^{(Σ[n=0→N](wn*pn*dn))}
However, each parameter in the above formula is as follows.
base is a positive number excluding 1 Dn = base ^dn (n = 0, 1, ..., N): input data pn (p0, p1, ..., pN): power exponent Dn ^pn : power value wn = log _base Wn (n=0, 1, . . . , N): weighting parameter (Wn=base ^wn )
b=log _base B : bias parameter (B=base ^b )
YY1: Target value BYA: Addition type calculation output y: Output value

The N+1-dimensional exponent pn, the N+1-dimensional weighting parameter wn, and the bias parameter b as learning parameters are parameters learned by using a plurality of pieces of input data Dn as learning data.

The N+1-dimensional exponent pn, the N+1-dimensional weighting parameter wn, and the bias parameter b are output from the first hidden node 131 when the N+1-dimensional input data Dn as learning data is input to the input layer 110C. The difference (|YY1−BYA|) between the target value YY1 and the additive operation output BYA output from the second hidden node 132 is adjusted so as to be small.

As described above, when the series of steps for adjusting (searching) the learning parameter using the learning data is repeated a predetermined number of times, or when the difference becomes smaller than a predetermined allowable value, the arithmetic device It is determined that the learning termination condition is satisfied, and the learning for the learning parameters is terminated. This implements a trained neural network structure 100C having an N+1-dimensional power exponent pn, an N+1-dimensional weighting parameter wn, and a bias parameter b as learning parameters. The arithmetic device inputs N+1-dimensional input data Dn whose output value is unknown to the input layer 110C of the learned neural network structure 100C, and outputs the output value y for the N+1-dimensional input data Dn from the output layer 120C. do.

According to the neural network structure 100C used by the arithmetic device according to the present basic mode, the hidden layer 130 receives a plurality of input data via a plurality of weighting parameters, and is defined by the above formula (Equation 3-1). A first hidden node that outputs to the output layer the target value to be calculated, a plurality of input data are input via a plurality of weighting parameters, and a bias parameter is input, and the above equation (Equation 3-2 ) to the output layer, and the output layer 120C outputs the output value based on the target value and the addition type operation output. Therefore, the arithmetic unit can handle the phenomenon represented by the exponent and can accurately derive the correlation between the input and the output in the phenomenon.

(Equipment configuration of basic configuration)
FIG. 4 is a block diagram showing the configuration of an arithmetic device 1 using a neural network structure according to the first to third basic forms of the present invention.

The computing device 1 uses a machine learning device 1A that generates a learning model having neural network structures 100A to 100C corresponding to any of the first to third basic forms, and a learning model generated by the machine learning device 1A. function as a discrimination device 1B that outputs a discrimination result AA for discrimination data BB to be discriminated. The machine learning device 1A is used in the learning phase, and the discrimination device 1B is used in the discrimination phase (inference phase).

Arithmetic device 1 includes classifier learning unit 2, learning parameter storage unit 3, learning data storage unit 4, learning data processing unit 5, discrimination result processing unit 6, and discrimination data acquisition unit 7 as its components. Configured.

The discriminator learning unit 2 includes a learning unit 20 that performs learning parameter learning using a learning model having a neural network structure 100A to 100C, and a learning model that reflects the learning parameter being learned or already learned. and a discrimination processing unit 21 that outputs a discrimination result for. The learning parameter according to the first and second basic forms is the N+1-dimensional exponent pn. The learning parameters according to the third basic form are the N+1-dimensional exponent pn, the N+1-dimensional weighting parameter wn, and the bias parameter b.

The learning parameter storage unit 3 stores learning parameters as learning results of the learning performed by the learning unit 20 in the learning phase. Initial values of the learning parameters are stored in the learning parameter storage unit 3 by initialization processing of the learning parameters, and the learning parameters are successively updated as the learning is repeatedly performed in the learning unit 20 . The learning parameter storage unit 3 stores the learning parameters when the learning by the learning unit 20 is completed, and is read by the determination processing unit 21 in the determination phase (inference phase).

The learning data storage unit 4 stores a plurality of sets of learning data including at least a plurality of input data. The learning data according to the first and second basic forms include input data and teacher data associated with the input data. Learning data according to the third basic form includes only input data. The teacher data is, for example, data corresponding to the discrimination result, and if the discrimination result is represented by "0" for normal and "1" for abnormal, for example, "0" or "1" is set.

The learning unit 20 inputs the learning data stored in the learning data storage unit 4 to the learning model via the learning data processing unit 5, and learns the learning parameters so as to minimize the loss function, for example. That is, the learning unit 20 receives the determination result output from the determination processing unit 21 and the learning data read from the learning data processing unit 5, and performs learning using these data. store the learning parameters in

In the learning phase, the discrimination processing unit 21 inputs the learning data acquired by the learning data processing unit 5 to a learning model that reflects the initial values or the learning parameters during learning, so that the output from the learning model A determination result is output to the learning unit 20 and the determination result processing unit 6 based on the value.

Further, in the discrimination phase (inference phase), the discrimination processing unit 21 inputs the discrimination data acquired by the discrimination data acquisition unit 7 to the learning model reflecting the learned learning parameters, thereby output value (for example, feature amount, etc.) from is output to the discrimination result processing unit 6 .

In the learning phase, the learning data processing unit 5 reads the learning data from the learning data storage unit 4 and performs predetermined preprocessing, and then sends the learning data to the learning unit 20 and the discrimination processing unit 21 . At that time, the learning data processing unit 5 sends learning data to the learning unit 20 and the discrimination processing unit 21 in response to a request from the discrimination result processing unit 6 .

The determination result processing unit 6 receives the output value output from the determination processing unit 21, and outputs it as a determination result AA to a predetermined output device such as a display, for example. Further, in the learning phase, the discrimination result processing unit 6 calculates a coefficient of variation, a discrimination rate, etc. based on the discrimination result, and further sends learning data to the learning unit 20 and the discrimination processing unit 21 according to the calculation result. is requested to the learning data processing unit 5 as follows.

In the discrimination phase (inference phase), the discrimination data acquisition unit 7 receives the discrimination data BB from a predetermined input device, performs predetermined preprocessing, and then sends the discrimination data BB to the discrimination processing unit 21 .

The computing device 1 having the above configuration is configured by a general-purpose or dedicated computer. Note that the machine learning device 1A and the discrimination device 1B may be configured by separate computers. In that case, the machine learning device 1A may include at least the learning data storage unit 4, the learning unit 20, and the learning parameter storage unit 3. Moreover, the discrimination device 1B only needs to include at least the discrimination data acquisition unit 7 and the discrimination processing unit 21 .

Among the components of the arithmetic unit 1, the learning parameter storage unit 3 and the learning data storage unit 4 are hard disk drives (HDD), solid state drives (SSD), and other storage devices (built-in type, external type, network connection). type, etc.), or a USB memory, a storage medium (CD, DVD, BD) that can be played back by a storage media playback device, or the like. Among the constituent elements of the arithmetic unit 1, the discriminator learning unit 2, the learning data processing unit 5, the discrimination result processing unit 6, and the discrimination data acquisition unit 7 are, for example, one or a plurality of processors (CPU, MPU, GPU, etc.). ).

(program)
The computing device 1 executes a program stored in various storage devices and storage media, or a program downloaded from the outside via a network, thereby obtaining a discriminator learning unit 2, a learning data processing unit 5, and a discrimination result. It may function as the processing unit 6 and the discrimination data acquisition unit 7 .

(integrated circuit)
Any of the first through third corresponding neural network structures 100A-100C may be implemented by integrated circuits. In that case, the integrated circuit includes an input/output unit constituting an input layer and an output layer, a storage unit storing learning parameters, and a plurality of input data input to the input layer and learning parameters stored in the storage unit. and a calculation unit for performing calculation for outputting the output value from the output layer. The integrated circuit is configured by FPGA, ASIC, etc., for example, and hardware other than these may be used.

(First embodiment)
First, the basic structure of a neural network used in the present invention (hereinafter referred to as an additive neural network) will be described with reference to the drawings. FIG. 5 is a diagram showing the basic structure of an additive neural network. An additive neural network consists of an input layer, a hidden layer and an output layer, each layer having a plurality of nodes. Additive neural networks can solve various problems ( It functions as a discriminator that can solve classification problems or regression problems).

Here, the calculation formula YY (target value) and BYA (additive calculation output) of the hidden layer in FIG. 5 will be described. However, although FIG. 5 shows four-dimensional input for the sake of convenience, the description will be made assuming N-dimensional input. YY and BYA of the hidden layer can be expressed by the following formulas (Formula 1), (Formula 2), and (Formula 3). However, the powers of the bases of the first feature amount wn and the second feature amount b are Wn and B, respectively, and N-dimensional input data elements Dn=(D0, D1, . . . , Dn, . D(N−1)) is assumed to be dn=(d0, d1, . . . , dn, . . . , d(N−1)). Assuming that the loss function L is a differential expression |YY−BYA| It is possible to provide an additive neural network operation method characterized by extracting a value. Here, ^ is used as a symbol for exponentiation, and * is used as a symbol for product.
(Number 1)
YY=D0*D1*...*D(N-1)*W0*W1*...*W(N-1)
(Number 2)
BYA=(base)^(Σ[n=0→N−1](wn*dn+b))
(Number 3)
BYA=B*(base)^(Σ[n=0→N−1](wn*dn))

Next, a first embodiment, which is an invention of a method for searching and finding a relational expression, will be described. FIG. 6 is a diagram showing the basic structure of the exponent addition addition neural network used in the present invention. The difference from the above-described FIG. 1), pN) are newly provided and connected to the input data elements.

N+1 dimensional data is expressed as Dn=(D0, D1, . . . , Dn, . p(N-1), pN) to obtain Dn^Pn = (D0^po, D1^p1, ..., Dn^pn, ..., D(N-1)^p(N-1), DN ^pN). Further, when W=W0*W1*...*WN, equations (4), (5) and (6) are derived from equations (1) and (3). (Formula 5) YY/W is represented by the product of the input data elements Dn to the power of the exponent Pn, so it is expressed as "product of power values". Further, when the group to which the data belongs has a common feature value wn, the value of W, which is the power product of them, is also common. target value) is also approximated to a constant. Therefore, searching for a value that allows YY (target value) to approximate a constant is equivalent to searching for the feature quantities wn, b and power exponent Pn that minimize the loss |YY-BYA|. Optimal relations can be obtained from power exponents.
(Number 4)
YY=D0*D1*...*D(N)*W0*W1*...*WN
(Number 5)
YY/W=D0^p0*D1^p1*...*DN^pN
(Number 6)
BYA=B*(base)^(Σ[n=0→N](wn*pn*dn))

Here, how close the output value is to the predetermined target when searching with the exponent Pn = (p0, p1, ..., pn, ..., p(N-1), pN) as parameters is compared using the loss amount |YY-BYA| for each power exponent, the magnitude of the loss varies greatly depending on the value of the power exponent. As a countermeasure, the evaluation function can be prevented by using a coefficient of variation obtained by normalizing the standard deviation by the average value and evaluating the magnitude of the relative variation with respect to each average value with the exponent as a parameter.

In addition, it is possible to solve a classification problem divided into two or more groups by using a discrimination rate as an evaluation function.

Next, a method of deriving an optimum solution for exponents (hereinafter referred to as exponent search method) using the aforementioned exponent addition addition neural network will be described with reference to FIG.

The discriminator learning unit 2 learns a neural network and performs discrimination using the learned neural network. As its configuration, the discrimination learning unit 2 includes a learning unit 20 and a discrimination processing unit 21 .

The learning unit 20 learns the neural network so as to minimize the loss function. That is, when the learning unit 20 receives the determination result output from the determination processing unit 21 and the learning data read from the learning data processing unit 5, learning is performed using these data, and the learning parameter is stored in the learning data storage unit 3. Remember.

When the weight, bias, and learning data are input from the learning parameter storage unit 3 , the discrimination processing unit 21 sends discrimination results using these to the discrimination result processing unit 6 .

Upon receiving the discrimination result output from the discrimination processing section 21, the discrimination result processing section 6 requests the learning data processing section 5 to input learning data with the exponent as a parameter. The received determination results are output to a predetermined output device such as a display outside the apparatus, such as sorting in order of minimum variation coefficient or maximum determination rate.

The learning data storage unit 3 is a storage unit that stores weights and biases between nodes in the neural network and learning data of the learning data processing unit 5 . The learning data storage unit 3 stores initial values of weights and biases between all nodes of the neural network at the time of weight initialization processing. store the weights and biases between the nodes trained by the neural network in , and the learning data.

The learning data storage unit 4 is a storage unit that stores learning data. The learning data is data for testing indicating the state information and the feature amount in which normality and abnormality are determined in advance. The discrimination data BB, which is data to be discriminated, is sent to the discrimination data acquiring section 7 and sent to the discrimination processing section 21 after being subjected to predetermined preprocessing.

The learning data processing unit 5 inputs the learning data storage unit 4 and converts it into a predetermined learning data type using the exponent as a parameter. The converted learning data is sent to the weight learning section 20 in response to a request from the discrimination result processing section 6 .

Note that the discriminator learning unit 2, the learning data processing unit 5, the discrimination result processing unit 6, and the discrimination data acquisition unit 7 can be obtained, for example, by a microcomputer executing a program in which processing specific to this embodiment is described. , can be realized as concrete means in which hardware and software cooperate.

Further, the discriminator learning unit 2, the learning parameter storage unit 3, the learning data storage unit 4, the learning data processing unit 5, and the discrimination result processing, which are the configuration of the exponent addition addition type neural network device that should have the learning function shown in FIG. An integrated circuit combining the unit 6 and the determination data acquisition unit 7 can be provided at a reduced size, higher speed, lower power consumption, and at a lower cost.

Next, with the configuration of the neural network device shown in FIG. 4, the method of performing weight learning processing using the exponent as a parameter, calculating the coefficient of variation or the discrimination rate, and searching for the optimum solution of the exponent is shown in the flow chart of FIG. I will explain along.

First, the learning data processing unit 5 converts the learning data in the learning data storage unit 4 into an input format for the learning unit 20 in the discriminator learning unit 2 that performs neural network calculations. The learning data in the learning data storage unit 4 is composed of N-dimensional input data and one-dimensional output data. The learning data processing unit 5 converts N+1-dimensional data obtained by connecting N-dimensional input data and 1-dimensional output data into Dn=(D0, D1, . . . , Dn, . . . , D(N-1), DN) (Step SP1).

Next, a search method for exponent Pn is set (step SP2). For example, a round-robin search with integers |pn|≦5 is used. In addition, pn handles real numbers, and it is possible to set an arbitrary increment range. However, it must be within the limits of the memory and computing power of the computer.

Next, the initial value of the exponent search value Pn=(p0, p1, . . . pn, . . . , p(N-1), pN) is set (step SP3). For example, in a round-robin search (also called an exhaustive search) when |pn|≦5 is an integer, the search initial value is the search label No. 0 and exponent P0=(-5, -5, . . . -5).

Next, a search end condition for the exponent search value Pn=(p0, p1, . . . , pn, . . . , p(N-1), pN) is set (step SP4). For example, search label No. 0, exponent P0=(-5, -5, . . . -5), and the next search label is No. The search end condition can be set to a search end value (5, 5, 5) by assigning serial numbers such as 1 to P1=(-5, -5, . . . , -4). Further, the search end condition may be set in advance as a predetermined number of searches, a search label, or a threshold value.

Next, a search table for the data Dn and exponent Pn is created (step SP5). For example, search label No. 0, exponent P0=(-5, -5, . . . -5), and the next search label is No. It is possible to create a search table with sequential numbers such as P1=(-5, -5, .

Next, the data Dn and exponent Pn are extracted from the search table in the order of the search labels (step SP6).

Next, Dn̂Pn is redefined as the input of the neural network (step SP7). Here, the learning data processing unit 5 uses the data Dn received in step SP6 and Dn̂Pn=(D0̂po, D1̂p1, . . . , Dn̂pn, . From the equation (N−1)̂p(N−1), DN̂pN), Dn̂Pn is redefined as Dn and set as the input of the additive neural network.

The above is the procedure for creating the input data Dn of the neural network, and steps SP1 to SP7 in FIG. 5 have been described.

Next, the N+1-dimensional input data Dn=(D0^po, D1^p1,..., Dn^pn,..., D(N-1)^p(N-1), DN ̂pN) is sent to the learning section 20 of the discriminator learning section 2 and subjected to weight learning processing through steps ST1 to ST8. Details of the learning unit 20 will be described below.

First, the learning unit 20 initializes weights and biases, which are feature quantities of the neural network (step ST1). Specifically, 0 is given to the initial value.

Here, the calculation formulas YY (target value) and BYA (additive calculation output) of the hidden layer can be represented by (Equation 1), (Equation 2), and (Equation 3) as described above, and the learning unit 20 calculates the initial value of the loss amount |YY-BYA| represented by the loss function L (step ST3).

Next, the learning unit 20 updates the bias (parameter b) slightly in the positive direction by a set amount (step ST4).

Subsequently, the learning unit 20 calculates the weight (weighting parameter wn) correction amount (appropriate shift amount Δwn) so that the value of the loss amount becomes small (step ST5).

After that, the learning unit 20 updates the weight value from the previous value with the correction amount obtained in ST5 (step ST6).

Further, the learning section 20 repeats steps ST5 to ST6 a set number of times to update the weight amount (step ST7).

After that, the learning section 20 confirms whether or not the end condition of weight learning is satisfied (step ST8). Here, the termination condition is preferably the minimum value immediately before the loss amount turns from decrease to increase. Alternatively, the number of times of learning may be equal to or greater than the set number of times.

When the termination condition is satisfied, the learning unit 20 stores the extracted feature amount that minimizes the loss amount |YY−BYA| in the learning parameter storage unit 3 and sends it to the discrimination processing unit 21 .

Next, the discrimination processing section 21 sends the obtained feature amount to the discrimination result processing section 6 .

Next, the discrimination result processing unit 6 calculates the coefficient of variation and the discrimination rate from the feature amount, and stores the result (step SP8).

Next, the determination result processing unit 6 updates the search label of the search table from the previous value (step SP9). For example, if a round-robin search is set, the search label is advanced by one. Here, using a breadth-first search method or a more heuristic search method, the coefficient of variation or discrimination rate calculated in the current step is replaced with a smaller coefficient of variation or a higher discrimination rate in the previous search order. An algorithm that can predict the possibility of faster arrival may be incorporated to update the search order label to an efficient one.

Next, after updating the search label through step SP9, it is checked whether or not the search end condition is satisfied (step SP10). If the end condition is not satisfied, the process returns to step SP6 and repeats.

The power exponent Pn=(p0, p1, . . . pn, . Detailed descriptions of specific N+1-dimensional data, types of relational expressions, and coefficients of variation and discrimination rates used as evaluation functions will be given later through (Example 1) and (Example 2).

In the above-described first embodiment, an example in which the number of hidden layers is one has been described, but the present invention can also be applied to a plurality of hidden layers. FIG. 8 is a diagram showing the basic structure of a multi-layer exponential addition addition neural network. Here, as the second-level hidden layer that receives the outputs of the first-level hidden layer nodes n1 and n2, the node n3 of the second-level target value ZZ linked to the two weights h0 and h1, the additive output BZA 2 nodes are inserted and extended with n4 as the first node to obtain the one-dimensional output Z-Act. By using such a neural network with two hidden layers, accuracy can be improved for more complicated problems.

(Second embodiment)
Next, a second embodiment of the invention will be described. The second embodiment of the present invention preprocesses the input data elements to the power search method of the first embodiment, including sums and differences between the input data elements, and converts the input data elements to This is a learning method in which a relational expression consisting of addition, subtraction, multiplication, and division is found by inputting to the exponentiation search method and performing calculations.

The first embodiment provides an optimum relational expression when the units of N-dimensional input data to the power search method are different, or when sums and differences between input data are not required. On the other hand, there are relational expressions using sums and differences between input data. For example, Heron's formula (Equation 7), which obtains the area S as the answer using the lengths (a, b, c) of the three sides of a triangle as the original data, is an equation using the product of the differences of the sides. In order to blindly solve this type of equation, preprocessing is performed by adding the sum or difference of the three sides, which are the original data, to the input data for the power search method, creating an input table for the power search method, A power search is performed in order.
(Number 7)
16=(a+b+c)*(-a+b+c)*(a-b+c)*(a+b-c)/(S^2)
(Number 8)
16=D0^p0*D1^p1*D2^p2*D3^p3*D4^p4

According to Heron's formula (Formula 7), the input data using the sum and difference of the lengths (a, b, c) of the three sides, which are the original data of the triangle, are D0=(a+b+c), D1=(- a+b+c), D2=(a+b−c), and the answer data D3 having a predetermined relationship formed by combining the three-dimensional input data elements (D0, D1, D2) is the area S. When a four-dimensional input data element Dn=(D0, D1, D2, D3) is created and a power search is performed using the four-dimensional exponent Pn=(p0, p1, p2, p3), the solution of the exponent Pn is gives (p0, p1, p2, p3)=(1, 1, 1, -2).

Next, a description will be given of a method of performing preprocessing such as adding or subtracting the original data of the object to be measured and creating an input table for the power search method.

Let am=(a0, a1, . Also, a difference element matrix Cm and a coefficient k by which the elements of the original data am are multiplied are defined. The difference element matrix Cm is defined as a matrix of all combinations obtained by multiplying each element of the original data am by a factor k, and is illustrated in FIG. FIG. 9 shows an example of the difference element matrix Cm when the coefficient k is an integer of −1, 0, or 1 and M is three dimensions, which can be represented by a matrix of 27 rows and 3 columns.

Here, the value of the coefficient k can be expressed as k=−1 for the difference between data, k=1 for the sum, and k=0 for unnecessary coefficients. Furthermore, integers can be set in order such as coefficient k=-2, -1, 0, 1, 2 to support various integer multiples. Real numbers such as coefficient k=-1, -0.5, 0, 0.5, 1 can also be set.

Furthermore, the coefficient k can use the imaginary unit i. For example, the circle equation, 1=x^2+y^2, uses factorization with the imaginary unit i, equal to 1=(x+i*y)*(x−i*y), from the original data x,y We can derive the equation of the circle.

Next, a product input element matrix LnS, which is each element of the input data Dn of the power search method, is defined. The product input element matrix LnS is represented by the inner product of Cm and am as shown in (Equation 9). FIG. 9 illustrates the product input element matrix LnS. FIG. 9 shows an example of the product input element matrix LnS when the coefficient k is an integer of -1, 0, or 1 and M is three dimensions, which can be represented by a matrix table of 27 rows and SN columns. Also, the element of the n-th row and SN column of the product input element matrix LnS is defined as the product input element Ln.
(Number 9)
LnS = Cm·am

Next, in order to search for all the elements included in the product input element matrix LnS, if unnecessary product input elements Ln are included, a constraint condition is set so that the unnecessary product input elements Ln are Make it the omitted LnS table. If there are no constraints, the product input element matrix LnS as it is is used as the LnS table.

Next, the number NY of input data elements to be input to the power search method is set from among the product input elements Ln of the LnS table. For example, in the case of (Formula 8), the input data is the product of five-dimensional elements of (D0, D1, D2, D3, D4) and NY=5.

Next, a DnL table with (NY-1) rows (dimensions) is created by extracting and combining (NY-1) rows from the rows of the LnS table.

Further, the end of the DnL table is linked with the one-dimensional answer data to form a DnL table of NY rows (dimensions) to be input to the power search method.

A method of inputting the data of NY rows (dimensions) to the power search method to derive the optimum solution according to the order of the DnL table is called the difference search method. A method of searching for the optimum solution using the difference search method will be described below with reference to the flowchart of FIG.

First, it is checked whether or not the original data am of the object to be measured has an element that can be added or subtracted (step SS1). If there is an element that can be added or subtracted, set the element to be added or subtracted. (Step SS2).

Next, the coefficient k and the number of learning samples SN are set to generate the difference element matrix Cm (step SS3).

Next, if there are constraints on the sum and difference between the elements of the input data am, the constraints are set (step SS4). For example, in the above Heron's formula, when using only the condition that the difference between the sides is a positive value, that is, (±a±b±c)>0, set that condition and omit values other than positive values. .

Next, the product input element matrix LnS is calculated from the equation (9) to create an LnS table that satisfies the constraint conditions set in step SS4 (step SS5).

Next, the number NY of input data elements to be input to the power search method is set. (Step SS6)

Next, a DnL table of (NY-1) rows (dimensions) is created by extracting and combining (NY-1) rows from the rows of the LnS table (step SS7).

Next, one-dimensional answer data is linked to the last row of the DnL table. (Step SS8).

Next, the top data Dn row is obtained from the DnL table (step SP1). The subsequent steps SP2 to SP10 and ST1 to ST8 are the same as in the exponential search method, and descriptions thereof are omitted.

In the next step SS9, the data Dn row is updated to the next data according to the order of the DnL table. In the next step SS10, if the data Dn row is not the final data, the process returns to step SP2 and repeats. It ends when the final order of the DnL table is completed. Alternatively, a threshold value may be set for the coefficient of variation or discrimination rate, and the process may be terminated halfway.

(Example 1)
As a first example, the first embodiment is applied to the discovery of Kepler's third law. Kepler's third law is "The square of the orbital period T of each planet is proportional to the cube of the average distance r from the sun." Nine planet names and two measurement data (average distance r [km] from the sun and revolution period T [day]) are specified in FIG. Here, a method of finding a law by the power search method of the present invention will be described using two-dimensional input data elements D0=r/1E8 and D1=T/1E2. The functional form of the law can be first presumed to be composed of division and multiplication, excluding addition and subtraction, since the units are different.

A function configured by combining the two-dimensional input data elements (D0, D1) can be expressed as f(D0, D1)=1. When some function of the left term to be found is f(D0, D1), the right term is 1 when D2 is answer data having a predetermined relationship. Therefore, the three-dimensional input data elements to the power search method are (D0, D1, 1) and YY/W (the product of power values) is given by the functions (5) to (10).
(Number 10)
YY/W=D0^p0*D1^p1

Next, a method of deriving the optimum relational expression using the power search method will be described according to the flow chart of FIG.

First, a three-dimensional input table (D0, D1, 1) is created from FIG. 8 (step SP1). A method of searching for exponents is a brute-force search in which the exponent is an integer of |pn|≦7, and the search initial value is No. 0, exponent P0=(-7, -7), No. 1, P1 = (-7, -6), and a search table is created in which the search end value is set to (7, 7). A coefficient of variation is used as the evaluation function (steps SP2 to SP5). After setting the search initial value, neural network operations are performed according to the order of the search table until the end of the search (steps SP6 to SP10). In step SP7, a row calculated with initial values Dn^Pn=(D0^p0, D1^p1, 1) is set as an input term. Next, the weights and biases for neural network operations are initialized (step ST1).

Initial settings for feature quantity extraction will now be described. In proceeding with the weight learning shown in the flowchart of FIG. 7, the number of times of bias update, the number of times of weight update, the amount of weight correction (Δwn) and the amount of bias update to be looped are initially set to appropriate values. In this example, the number of bias updates for hidden layer 1 is set to 50, and the number of weight updates is set to 10. When the weight Wn=1 (wn=0), the update amount of the bias can be simplified to only the term of the data product from YY (Equation 1). A division amount is set in increments of 50 times, and 10% of the division amount is set as the set value of the bias update amount. The amount of weight correction (Δwn) was set to 0.1% of the amount of loss. Depending on the purpose, the initial set values may be finely set or may be changed roughly. The set value of base (low) was set to 0.9. The value of the input data d1 in this example deals with a maximum value of 915, and if, for example, 10 is set as the base set value, the upper calculation limit of the computer is easily reached. The patent allows a decimal to be set to base, thus avoiding computational limits.

Next, the initial values of the hidden layer calculation formulas YY (Equation 1) and BYA (Equation 3), and the amount of loss |YY−BY
An initial value of A| is calculated (steps ST2 and ST3).

Next, through the parameter learning loop of steps ST4 to ST8, the minimum value of the loss amount |YY-BYA| is calculated, the parameter learning result is sent to step SP8 to calculate the coefficient of variation, and the result is stored.

Here, the coefficient of variation, which is the evaluation function used in this example, will be described. The coefficient of variation is a value obtained by dividing the standard deviation σ of YY/W (product of power values) in Equation 7 by the average value of YY/W (product of power values).

The next step SP9 is set when a heuristic search method is introduced using the obtained coefficient of variation and the search order is to be changed from the search label of the initial value. be.

The next step SP10 outputs the exponent Pn with the smallest coefficient of variation after the search end value (7, 7) of the search table is completed, and the correspondence list, graph, etc. between the exponent Pn and the coefficient of variation. do. Graph examples are shown in FIGS. If the search end value (7, 7) is not reached, the process returns to step SP6 and repeats.

FIG. 12 is an output diagram of this example in which the coefficient of variation is the output value, the horizontal axis is the exponent p0 of D0, and the vertical axis is the exponent p1 of D1, and (p0, p1) is used as coordinates. The coefficient of variation is the coordinate position of the power index (p0, p1), (-6, 4), (-3, 2), (0, 0), (3, -2), (6, -4) points It can be seen that it is small from 0 to 0.0005. However, for the sake of convenience, values smaller than 0.0001 are indicated as 0. FIG. 13 is a three-dimensional wireframe plot of the log values (common logarithms) of FIG. In FIG. 13, a sphere (●) is displayed to simulate the flow to the minimum point along the slope of the wire frame. Substituting (p0, p1)=(-3, 2) into the formula (10) yields YY/W=D0^(-3)*D1^(2) ≈ 4 (constant). It was shown to. From this result, the optimal function of f(D0,D1), initially expressed as f(D0,D1)=1, is f(D0,D1)=D0^(-3)*D1^(2)/4 I was able to get it. That is, the following law is derived from nine planet names and two measurement data (D0 is the average distance r from the sun, and D1 is the orbital period T). "The square of the orbital period T of each planet is proportional to the cube of the average distance r from the sun."

The method for deriving Kepler's third law by performing a round-robin search using the coefficient of variation as the evaluation function has been described above. When the coefficient of variation is displayed graphically in FIGS. 12 and 13, it can be seen that there are a plurality of minimum values that are the minimum values, and that they are given regularly. A moving neighborhood search method can be used to quickly search to a local minimum that is the minimum value. However, there are many functions that have multiple local minimum values that do not have the minimum loss amount, which is one of the problems that causes gradient vanishing in neural networks. A conventional neural network solution is to avoid local minima by intentionally reducing the accuracy of gradient calculations using coarse data (called mini-batch size) that is sampled without using all the data. However, with this method, it is not possible to know where the minimum value is, and there remains a problem that trial and error is required, such as changing the size of the mini-batch and incorporating random numbers. In this patent, an efficient neighborhood value search method can be considered using a graph whose axis is exponential coordinates.

For example, as an example of a function in which there are a plurality of minimum values where the amount of loss is not the minimum value, Kepler's third law states that "the third power of the orbital period T of each planet is proportional to the fifth power of the average distance r from the sun. ” and performing a brute force search for the relational expression, the power values of the minimum value are given as (−5, 3) and (5, −3), and YY/W=D0^(−5 )*D1^(3), the wireframe plot of which is shown in FIG. From this figure, the power of the minimum value is (-3, 2), (-2, 1), (3, -2), (2, -) between (-5, 3) and (5, -3). It can be seen that the minimum values of 1) exist regularly. Therefore, when using the neighborhood value search method in which the evaluation function decreases or increases as the search method, depending on how the search initial value is selected, it may flow to a singular point (0, 0), or to a local minimum value or maximum value. Inconvenience arises that the correct answer cannot be obtained. In order to avoid this, it is necessary to set the coordinate positions of the search initial values in multiple quadrants, and the search time can be shortened by setting the initial values to positions close to multiple extreme values in consideration of regularity. And it can be understood from the graphs of FIGS. 13 and 15. FIG.

In this manner, a heuristic search method for reaching the correct answer more quickly can be constructed by using a graph expressing the evaluation function by the coefficient of variation with the exponent as the coordinate axis.

Also, the solution of the equation (10) can be obtained quickly by fixing the feature parameter. The bias B in (Formula 3) is fixed at B = 0 (b = 0), and the weight learning loop is not run, that is, the loss amount |YY- A simplification to BYA|=|YY-1| can speed up the computation. This method is effective for a search where it can be judged that the data has little noise (disturbance), especially when it is desired to evaluate a relational expression with only power exponents.

(Example 2)
As a second example, we apply the second embodiment to the discovery of Heron's formula. FIG. 16 is a picture of various triangles with ten numbers (1) to (10), and FIG. It is a table with digits. Since the length of the three sides has a common unit of cm, there is a concern that even if the lengths a, b, and c of the three sides and the area S are directly used for the input of the power search method, the answer cannot be reached. be. As a solution to this problem, a method of inputting the power search method including the addition and subtraction values of the lengths of the three sides will be specifically described with reference to the flow chart of FIG.

First, the original data am of the object to be measured is set to the lengths of three sides (a0, a1, a2), and this is set as three-dimensional data am=(a0, a1, a2) that can be added and subtracted (steps SS1 to SS2). ).

Next, the number of samples (SN) of the original data am is 10 triangles, and SN=10 is set (step SS3).

Next, a coefficient m is set by which the element of the original data am is multiplied. The coefficient m is -1, 0, 1 when using the sum and difference between the three sides (a0, a1, a2). When the difference element matrix Cm is generated using these, the difference element matrix Cm of 27 rows and 3 columns is automatically generated as shown in FIG. 9 (step SS3).

Next, if there are constraints on the sum and difference between the elements of the input data am, the constraints are set. Since it can be easily assumed that a product input element composed of addition and subtraction of three side lengths, such as a triangle, does not have a negative value or zero, the condition that the side difference is a positive value is (±a±b± c) Set >0 (step SS4).

Next, the product input element matrix LnS is calculated from the equation (9) to create an LnS table that satisfies the constraint conditions set in step SS4 (step SS5). FIG. 18 shows an LnS table of 10 rows and 10 columns generated by satisfying the constraint conditions. 10 rows L0 to L9 of the product input elements, 10 rows L0 to L9 given by the equations of the differences and sums of the three sides, and triangles (1) to (10), the differences and sums of the three sides of those equations It consists of 10 columns of elements that are the values of

Next, the number NY of input data elements to be input to the power search method is set. The original data for determining the area of the triangle is the three sides (a0, a1, a2), and the YY/W (product of power values) equation represented by (Formula 5) includes the area S, which is the answer. Since it consists of products of four or more elements, NY is increased to NY=4, then NY=5, and then NY=6 until the optimum solution is obtained, and the loop is run. However, since the number of exponentiation searches increases, an upper limit is set within the limits of computer performance and computation time constraints. Here, for the sake of convenience, an example in which NY is fixed to 5 will be described (step SS6).

Next, a DnL table of 4 rows and 10 columns is created by extracting and combining 4 rows of (NY-1) from the rows of the LnS table (step SS7).

Next, the area S of 1 row and 10 columns, which is the triangle (1) to (10) answer data, is connected to the end of the DnL table. (Step SS8). FIG. 19 shows the generated DnL table. Thus, the five-dimensional data (D0, D1, D2, D3, D4) input to the power search are converted to (D0, D1, D2, D3) extracted from the product input elements L0-L9 of the LnS table. It consists of a table in which a combination of four elements is arranged, an area S is arranged in D4, and 210 (No. 0 to 209) indexes are attached.

Next, the first five-dimensional input data Dn row is obtained from the DnL table (step SP1). Referring to FIG. 19, the top index Dn row No. of the DnL table. (D0, D1, D2, D3, D4) of 0 = (L0, L1, L2, L3, S).

Next, a search method for exponent Pn is set (step SP2). A brute-force search is performed in which the exponent is an integer of |pn|≤4.

Next, the initial value of exponent Pn is set (step SP3). In a round-robin search where the exponent is an integer of |pn| 0 is exponent (-4, -4, -4, -4, -4).

Next, a search end condition for exponent Pn is set (step SP4). The search end value is set to (-1, 4, 4, 4, 4) because the positive power number at the beginning of the input data element D0 is the solution of the reciprocal of the negative power number and is unnecessary because it overlaps. .

Next, a search table for data Dn rows and exponents Pn is created (step SP5). For example, search label No. 0, the power index P0=(-4, -4, -4, -4, -4), and the next search label is No. P1=(-4,-4,-4,-4,-3) is assigned to 1, and a search table is created with search end values (-1, 4, 4, 4, 4).

Next, data Dn rows and exponents Pn are taken out from the search table in search label order (step SP6).

Next, Dn̂Pn is redefined as the input of the neural network (step SP7). From the formula Dn^Pn=(D0^po, D1^p1, D2^p2, D3^p3, D4^p4) using the data Dn row and exponent Pn received in step SP6, Dn^Pn is Dn is redefined and set as the input of the additive neural network.

The subsequent steps ST1 to ST8 are the same addition-type neural network calculation procedure as in the first embodiment, and the description thereof is omitted. However, the set value of base (low) was 0.99.

Next, through the parameter learning loop of steps ST4 to ST8, the minimum value of the loss amount |YY-BYA| is calculated, the parameter learning result is sent to step SP8 to calculate the coefficient of variation, and the result is stored.

In the next step SP9, for a round-robin search, forward feed is performed according to the search label of the data Dn and exponent Pn.

At the next step SP10, when the search end value of the search table is (-1, -4, -4, -4, -4), the process proceeds to step SS9. If the search end value is not (-1, -4, -4, -4, -4), the process returns to step SP6 and repeats.

In the next step SS9, the data Dn is updated to the next data according to the index order of the DnL table.

In the next step SS10, if the data Dn (L6, L7, L8, L9, S) of the final index of the DnL table, the process ends. If it is not the final index, return to step SP2 and repeat.

After the end of the final index of the five-dimensional DnL table, the combination of the product input elements Lm (L0 to L9) that minimizes the coefficient of variation is when the five-dimensional input data Dn = (L0, L4, L7, L9, S) , the exponents Pn=(-1-1,-1,-1,2) are obtained. FIG. 20 shows a table of calculated values of YY/W (product of power values) for power exponents Pn=(-1-1, -1, -1, 2). YY/W (product of power values) converges to a substantially constant value (1/16=0.0625). From this output result, it can be seen that Heron's formula is derived.

The above example is an example in which the coefficient of variation is used as the evaluation function of the power search method. The present invention can apply the discrimination rate to the evaluation function. Hereinafter, a method of deriving Heron's formula using the discrimination rate as an evaluation function will be described using Heron's formula as an example.

The area S of the triangle is halved and used for discrimination. For example, 10 sample nos. The even-numbered areas S of the SN series are multiplied by 1.0 and the odd-numbered areas S are multiplied by 0.9, and are divided into groups A and B, respectively. Therefore, the answer is not the area S of the triangle, but the group A or group B, which is the discrimination result. FIG. 21 shows a list of discrimination results.

For example, by measuring the length of three sides of a triangular product with a measuring instrument and measuring the area from an image, we assume an inspection process in which we want to exclude objects with an abnormal appearance, such as a small area due to missing corners. do. A normal object is determined to be non-defective according to a predetermined threshold according to logical rules, and other objects are determined to be defective.

The answer to this determination is the labels of group A and group B, and there arises a problem that computation cannot be performed unless these are quantified. The present invention can treat the numeric value of the answer as a constant when the answer is a label. Specifically, the area S of the triangle can be added to the input, and the answer can be set to a constant 1 to proceed with the calculation.

The difference between the flowchart of FIG. 10 and the example using the discrimination rate and the coefficient of variation in the evaluation function is that the discrimination rate is set in the search method (step SP2), and the discrimination rate is calculated according to it (step SP8). , and others are the same, and the description is omitted.

Here, a calculation method using the discrimination rate as the evaluation function and a search method for the exponent Pn will be described.

The expression (5) YY/W (product of power values) is given by the function (11) in the case of five-dimensional input, and D4 at the end represents the area S.
(number 11)
YY/W=D0^p0*D1^p1*D0^p2*D3*^p3*D4^p4

When YY/W (product of exponentiation values) of (Equation 11) can be approximated to a constant, the value of the right term is sample number D4 at the end. Since the value of the area S, which is 1.0 times the even number of the SN string and 0.9 times the odd number, is used, the A group constant of 1.0 times and the B There are two distributions of group constants. Using this, five-dimensional inputs are made to the additive neural network, and the one-dimensional output value of the additive neural network is used to automatically calculate a threshold value that maximizes discrimination between the A group and the B group, thereby calculating the discrimination rate. Here, a power exponent Pn of the five-dimensional input data Dn that maximizes the discrimination rate is searched using the one-dimensional output value Z-Act of the two-stage hidden layer power exponent addition addition neural network shown in FIG.

When the final index of the five-dimensional list DnL ends (step SS10), the combination of the product input elements Ln (L0 to L9) that maximizes the discrimination rate is the five-dimensional input data Dn=(L0, L4, L7, L9, S) results in a discrimination rate of 100% and exponent Pn=(-1, -1, -1, -1, 2).

Next, the characteristics of the output graph obtained using the discrimination rate as the evaluation function will be described. The output value obtained by using the discrimination rate as the evaluation function can be easily understood and visualized. FIG. 22 is a graph of the output value Z-Act of the additive neural network in triangular number order, and FIG. 23 is a graph of YY/W (product of power values) in triangular number order. From this graph, it can be visually understood that the output value Z-Act is divided into groups A and B, and that YY/W (product of exponentiation values) is two constant lines without slope.

The Heron's formula used in the example has no noise elements other than the error of rounding the area S to the second decimal place (the grain of the data is good). However, many of the relational expressions based on the data obtained from the object to be measured contain unknown parameters to find solutions, or the optimal relational expressions are estimated from data with complex functional forms or noise. In such a case, a method using a discrimination rate as an evaluation function is effective and can be applied to all fields.

For example, from a large number of medical checkup data, healthy people and a small number of people with a certain disease are divided into groups A and B, and whether there is any optimal relational expression in the items of the checkup data. , can be used for investigation (search). By using the neural network of the present invention, it is possible to find a highly accurate relational expression and contribute to the development of medical treatment to deal with it.

Furthermore, the even-numbered area S of the SN string is intentionally multiplied by 1.0 and the odd-numbered area is 0.9 times, and YY/W (exponential power) is purposely divided into groups A and B, respectively. 23, which shows a graph of the product of values) in order of triangle number, the following can be understood. Between the area of group A and the area of group B, a gray zone blank area (called band C) that cannot be called either group A (called band A) or group B (called band B) is widely formed. . Active use of this gray zone blank area (band C) can be applied to system control.

(Example 3)
As a third example, we apply the second embodiment to the equation of a circle representing a Fermat curve of degree 2, 1=x^2+y^2. 1=x^2+y^2 can be factored into 1=(x+i*y)*(x−i*y). Therefore, by preparing a plurality of values of x and y on the right side of the original data, setting the answer data to a constant 1, and presetting coefficients k = -i, -1, 0, 1, i, ±1 and An LnS table composed of combinations including differences and sums obtained by multiplying coefficients of imaginary unit i is automatically created. A DnL table is automatically created by extracting and combining two-dimensional input data elements from the LnS table, and preprocessing is performed to create a three-dimensional DnL table by concatenating 1, which is one-dimensional answer data. , the equation of the circle, which is the optimal relational expression, is derived.

As described above, the neural network of the present invention can recognize curves of circles or ellipses by equations, and can be used to discriminate curved objects that are more difficult than recognition of straight lines. For example, it is possible to learn the appearance of shafts and bearings in rotating machines and the characteristics of non-destructive inspection data, find relational expressions and thresholds, and determine differences from design values, deformations, scratches, cracks, wear and other defects. .

(Example 4)
As a fourth example, a two-dimensional simulation of the CartPole inverted pendulum device is used to derive a control formula that enables stable control so that the rod does not fall. In this example, 4-dimensional input data is received in real time, and the control formula that returns the output of whether to push the Cart to the right or the left and does not knock the Pole on the Cart is performed reinforcement learning using the power search method. , to search for the control formula as quickly as possible and stabilize the pole without knocking it down.

A platform for evaluating the performance of the CartPole inverted pendulum algorithm is provided by Open Gym, on which a reinforcement learning algorithm using a power search method is implemented to search for a control formula that stabilizes in the shortest time. It is also compared with the policy gradient method, which is one of the conventional reinforcement learning methods using neural networks.

In the CartPole inverted pendulum, as shown in FIG. 24, when a pole (Pole) connected to a pedestal (Cart) is first set vertically to the horizontal axis x=0, a force simulating gravity and fluctuation acts and moves left and right. This is a simulation in which the pedestal (cart) is pushed with equal force to the left and right so as not to fall down in either direction, and the cart is not pushed down for a predetermined time. ) falls down, the game ends.

First, a method for preventing a pole from falling for a predetermined time using a conventional policy gradient method, which is one of the algorithms for preventing the pole from falling, will be described. The information obtained as the output of the CartPole inverted pendulum is shown in FIG. 24 and shown in the table of FIG. One is returned when the pedestal (Cart) is pressed as state variables (d0, d1, d2, d3). Also, as shown in FIG. 26, there are two actions that can be taken from the state variables of a certain state: pushing the pedestal (Cart) to the right or pushing it to the left with the same force.

A conventional neural network uses a simple single-layer structure with four inputs as shown in FIG. 27 to learn and update the weighting parameters wn=(w0, w1, w2, w3) and the bias b. When the bias b is not used and b=0, the output value x is expressed by the following (Equation 12). Also, in the policy gradient method, a method of setting a reward function (Rt) and learning to maximize the value of the reward function is used. The method of updating the weighting parameters is represented by the following (Equation 13) using the learning rate η and partial differentiation of the conventional network.
(number 12)
x=d0*w0+d1*w1+d2*w2+d3*w3
(number 13)
wn←wn+η(∂Rt)/(∂wn)

The policy gradient method is a method in which several episodes are set as one evaluation range and the parameters are updated. In this simulation, one episode is defined as the work of pushing the cart once as one step, and the number of steps until the pole falls down (end) represents the number of actions, and is defined as one episode. Also, the maximum number of steps when the character does not fall down for a predetermined time is set to 200, and the episode is terminated. Therefore, the maximum number of steps per episode was set to 200, and the average number of steps over several episodes is the average number of steps the Pole was able to withstand without falling over. Here, the evaluation range is set every 100 episodes in the past, the average number of steps is recorded, and the progress of learning is monitored, and used as an update parameter of the reward function.

As shown in FIG. 28, if the reward for the t-th episode is Rt, the value of the reward function is (-1) when the reward is completed without falling over 200 steps, and the value is (number of steps -200) when falling within 200 steps. give.

When learning the weighting parameter wn, the initial value is set to 0 or some value is set and started, but depending on the initial value and update status of the weighting parameter wn, the target number of steps 200 is not reached no matter how long the learning is performed. a problem arises. As a solution to the conventional policy gradient method, a random value is provided as the initial value of the weighting parameter w, and an appropriate random value N is added in the middle to cause random behavior to some extent, and the parameter w is updated. A method for maximizing the reward has been proposed and is known as the ε-greedy algorithm. Specifically, based on the equation (13), 10 random numbers N[i] having a standard deviation σ of the parameter wn are reconfigured every 10 episodes (every batch number), and the progress of the episode A random number N[i] is added in the order of i=0 to 9, and the partial differential ∂Rt/∂wn of the reward is added to update and randomly select the next action (Formula 14). A flowchart of the conventional policy gradient method described above is shown in FIG. Here, as initial parameters, the learning rate η for varying the weighting wn and the standard deviation σ of the amplitude are set to η=0.2 and σ=0.05.
(number 14)
wn←wn+N[i]+η(∂Rt)/(∂wn)

An example result of implementing the conventional policy gradient method described above to a CartPole inverted pendulum simulation is shown in FIG. FIG. 30 is a graph showing the number of episodes on the horizontal axis and the average number of steps per past 100 episodes that the pole can endure without falling down on the vertical axis. From this graph, the average number of steps reaches 195 in 1500 episodes and ends. Also, the weighting parameters when the average step number of 195 was achieved were (w0, w1, w2, w3)=(-0.532, 0.610, 1.254, 1.421).

The table in FIG. 31 is an example of weighting parameters that satisfy the average number of steps in the past 100 episodes that the Pole could endure without collapsing≧195, and (w0, w1, w2, w3)= Not only (−0.532, 0.610, 1.254, 1.421) but also many repeated CartPole inverted pendulum simulations exist, and five examples are shown. When the program using the weighting parameters of the five examples shown in FIG. 31 is implemented in the CartPole inverted pendulum simulation, the pole can be kept upright for 200 steps or more from the beginning. However, even looking at the five example weighting parameters obtained from the conventional policy gradient method, it is extremely difficult to comprehend the concept of keeping the Pole standing rather than knocking it down.

As described above, a method of deriving a control formula that does not tilt the pole for a certain period of time using the conventional policy gradient method for the stabilization control of the CartPole inverted pendulum has been described. However, it is difficult to analyze and understand the obtained control equations and develop them into applications. For example, it is not possible to find a control method for controlling and moving a pole to the right or left from a state in which it stands vertically. The reinforcement learning algorithm using the power search method of the present invention can analyze and visualize the obtained relational expression so that people can understand it. Or you can intuitively control how to control and move to the left. Furthermore, it is possible to extract only the state parameters (input data) necessary for the target control and delete unnecessary (surplus) state parameters (input data).

Reinforcement learning using the power search method of the present invention will be described. The movements of the pole and cart of the CartPole inverted pendulum are the same as described above, and the reinforcement learning algorithm for controlling the pole so as not to fall will be described in detail with reference to the flow chart of FIG.

In applying the power search method to the CartPole inverted pendulum, the (base) power value of the four-dimensional state variables (d0, d1, d2, d3) is set to (D0, D1, D2, D3), and the power exponent is set to Pn = ( p0, p1, p2, p3). Here, let D4 be answer data having a predetermined relationship formed by combining four-dimensional state variables. The expected value of D4 can be 1, which is a constant. Therefore, a five-dimensional input element can be put as (D0, D1, D2, D3, 1). YY/W (product of exponentiation values) is given by the functions of (Equation 5) to (Equation 15). Here, simplifying to W=1, the target value YY can be represented by (Equation 16). Next, if both sides of (Equation 16) are expressed as log values, (Equation 17) is obtained. The right side of the equation (17) is equivalent to the equation in which the weighting wn in the equation (11) is replaced by the exponent number Pn, and the left side log(YY) is log(YY)=0 when the target value YY=1. be. Here, setting log(YY)=x is equivalent to equation (12) in which the weighting wn used in the conventional policy gradient method is replaced by the exponent Pn, which is convenient for comparing algorithms.
(number 15)
YY/W=D0^p0*D1^p1*D0^p2*D3^p3
(number 16)
YY=D0^p0*D1^p1*D0^p2*D3^p3
(number 17)
log(YY)=d0*p0+d1*p1+d2*p2+d3^p3

First, initial setting is performed (step SS1). For convenience of explanation, following the conventional policy gradient method, the maximum number of steps in one episode is set to 200, the number of episodes used for mean value evaluation is set to 100, and the number of batches of the deviation N array for updating the exponent Pn is set to 10. . Here, the set value of the four-dimensional deviation N is set to the initial value 0 of the random value in the conventional policy gradient method, but the deviation used in the power search method sets the update amount Δpn for updating the power number. . In this example, the update amount Δpn is shown in the table of FIG. 33 as ±1. Ten deviations N[i] (i=0 to 9) corresponding to the number of batches of 10 are sequentially set to integer values of 1 and -1 in each term of a four-dimensional array (Δp0, Δp1, Δp2, Δp3). However, 0 is set for i=8 and 9. In the case of four dimensions, eight update amounts Δpn are sufficient, so setting i=8 and 9 is redundant. was left as an unupdated redundant part. Next, the initial values of the reward Rt and the normalized variable Rta of the reward Rt are set to zero.

Next, after setting the loop initial value i=0 for 10 batches (step SS2), the exponent Pn is updated. The method for updating the power exponent Pn is represented by the equation (18), and is updated by adding the deviation N[i] and the partial differential ∂Rt/∂Pn of the reward (step SS3).
(Number 18)
Pn←Pn+N[i]+η(∂Rt)/(∂Pn)

Next, after setting the number of steps representing the number of CartPole operations to an initial value step=0, the state variables (d0, d1, d2, d3) are reset to 0 and initialized (step SS4).

Next, the CartPole is released from the initial state (the state in which the pole stands vertically) (step SS5).

First, the truck is pushed once to the left (step SS6).

By pushing the cart, the state variables (d0, d1, d2, d3) are output from the CartPole and stored (step SS7).

The output value x of the neural network is calculated from the equation (11) (step SS8).

Then, based on the output value x, when x>0, push the truck to the right. When x≦0, the truck is pushed to the left (step SS9).

By pushing the carriage, CartPole outputs and stores state variables (d0, d1, d2, d3) and a signal indicating whether or not the pole has fallen (step SS10).

When the stick falls down and ends, a reward Rt=step-200 is obtained, and the number of loops corresponding to 10 batches is increased by 1 (steps SS11→SK1→SS12). If one episode step=200 is achieved without the stick falling down, a reward Rt=-1 is obtained, and the number of loops corresponding to 10 batches is increased by 1 (steps SS11→SK2→SK3→SS12). If the stick does not fall and one episode step<200, the number of steps is increased by 1 and the loop is returned to the beginning of step SS11 (steps SS11→SK2→SK4→SS8).

Next, the batch number loop i is incremented by 1, and the reward Rt for the past 10 times is stored. Next, step, which is a value representing the number of steps in which the player did not collapse in one episode, is stored for the past 100 times, and the average value stepmean is calculated and stored (steps SS12 and SS13).

Next, it is checked whether or not the batch number loop i reaches 10 batch numbers (step SS14). If the number of batches has not reached 10, the process returns to step SS4. When the number of batches reaches 10, the value of stepmean is checked, and if stepmean≧195 is satisfied, the process ends (step SS15). When stepmean<195, Rta, which is obtained by normalizing the past ten rewards Rt, is calculated and stored (step SS16). The inner product of the deviation N for updating the Rta and exponent Pn is calculated and stored as a partial differential value ∂Rt/∂Pn, and then the process returns to step SS2 (step SS17).

FIG. 34 shows an example of the result of implementing the algorithm using the power search method described above to the CartPole inverted pendulum simulation. From this graph, the average number of steps reaches 195 in 110 episodes and ends. Also, when the average step number of 195 was achieved, the exponent was (p0, p1, p2, p3)=(-1, 2, 3, 3). The number of episodes is 1/10 or less compared to the graph of the conventional policy gradient method, that is, the search for a function in which the bar does not fall down in a short period of time has been completed. The table in FIG. 35 is an example of numerical values that should satisfy the average number of steps for each past 100 episodes≧195 that the pole could withstand without collapsing. =(−1, 2, 3, 3), and there are many repeated CartPole inverted pendulum simulations, and five examples are shown.

The neural network of this patent can be used to analyze and visualize the reason why the stick does not fall down and is stable so that people can understand it. The power values (p0, p1, p2, p3)=(-1, 2, 3, 3) will be described as an example.

The exponent values (p0, p1, p2, p3) = (-1, 2, 3, 3) are implemented in the CartPole inverted pendulum and simulated. Input values of four-dimensional state variables (d0, d1, d2, d3) in 200 steps from the beginning in one episode, and two classifications: group A for steps that push the cart to the right and group B for steps that push the cart to the left. As data for the answer to , input to the neural network of the present invention in the same manner as in the method of using the discrimination rate for the evaluation function described in the second embodiment (Heron's formula), the vertical axis YY/W ( A graph of the product of power values) was obtained and shown in FIG. In FIG. 36, the horizontal axis indicates the chronological order of pushing the carriage, that is, the step number. YY/W (product of exponentiated values) is plotted on the vertical axis, and step group A that pushes the truck to the right is indicated by ●, and step group B that pushes the truck to the left is indicated by diamonds. . Note that the value of YY/W (product of power values) is the base for converting to the power values (D0, D1, D2, D3) of the four-dimensional state variables (d0, d1, d2, d3). Using 10, the five-dimensional input elements to be input to the neural network are (D0, D1, D2, D3, 1), and the output value based on the equations (Equation 5) and (Equation 15) that maximizes the discrimination rate is obtained as

From the above description of operation, when YY/W=D0^p0*D1^p1*D2^p2*D3^p3>1, the carriage is pushed to the right, YY/W=D0^p0*D1^p1*D2^p2 *When D3^p3≤1, the rule is to push the truck to the left, and the following can be explained using the graph of FIG.

In the graph of FIG. 36, the value of the vertical axis YY/W (product of exponentiation values) shows a group A that surely pushes the carriage to the right, a group B that surely pushes the carriage to the left, and a group B that pushes the carriage to the right and to the left. It is possible to distinguish between regions of group C in which the pressing time is mixed. Its central value is YY/W=1. Here, if a threshold for judging the value of YY/W (product of power values) is introduced as a variable A, the pole moves left and right using the threshold A of YY/W (product of power values). You can control it. Specifically, when the threshold value A of YY/W is 1, the trolley maintains a state in which the stay pole (Pole) stands vertically in the center. When the threshold value A of YY/W (the product of exponentiation values) is greater than 1, there are many opportunities to push the carriage to the right in the initial state, and the pole leans to the right. The next action is to push the carriage to the left so as not to knock over the Pole, and the carriage moves to the left. Conversely, when the threshold value A of YY/W (product of exponentiation values) is smaller than 1, there are many opportunities to push the carriage to the left in the initial state, and the pole leans to the left. The next action is to push the trolley to the right so as not to knock over the Pole, and the trolley moves to the right. Furthermore, it can be intuitively understood that the moving speed of the truck can be controlled by the threshold depth centered on YY/W=1. As a specific example, the value of the power exponent is (p0, p1, p2, p3) = (-1, 2, 3, 3), and the formula of YY/W (product of power values) and the value of the threshold value A are changed. Fig. 37 summarizes the motion of the truck when it is moved.

Moreover, No. in FIG. 4 and no. Focusing on the value of 0 for each of the power exponents p0 and p1 of 5, it indicates that D0 and D1, which are status variables for the position and speed of the pedestal (Cart), are unnecessary for stable control in which the rod does not fall down in the center. ing. When the bar is stable in the center, the position of the pedestal (Cart) is almost 0, the speed is almost 0, and it is positioned at the center. For this reason, D0 and D1 are removed, and using the two state variables of D2 and D3, the angle and angular velocity of the pole (pole), reinforcement learning is performed using the power search method described above, and the pole does not fall down. FIG. 38 shows three examples of numerical values that should satisfy the average number of steps for each past 100 episodes≧195. Furthermore, in FIG. 39, using the state parameters (D2, D3) and exponents (p2, p3)=(5, 3), the pedestal (Cart) is moved from the center position to the left without tilting the pole (Porl). An application example of a control formula that moves to, then moves to the right, and then controls to move to the left end is shown.

Thus, this patent can narrow down the input data needed to get an answer. In other words, by removing unnecessary (surplus) input data, it is possible to eliminate the calculation time and reduce the number of sensors required as means for obtaining input data.

As an application example of this example, an educational version assembly kit equipped with various sensors, motors, communication and control microcomputers, and building blocks (blocks) are used to assemble an inverted pendulum device. You can learn AI (Artificial Intelligence) through the experience of controlling left and right. Depending on the teaching material, there are cases where the relational expressions lead to formulas and laws, and they are provided in a form similar to that, giving the students a sense of excitement as if they were discovering something, which motivates the learners.

A control formula is provided that learns the control method and contains the product of power values. A simple control formula is obtained, and the origin of the formula and the control method are easy to understand. In some cases, this may lead to the reduction of unnecessary input data components (sensors, etc.) that contribute little to control, or to the discovery of new control methods.

By applying the obtained control formula to the controller, the stability of the control formula can be evaluated and optimized in real time. For example, learning the control state of the same device in different environments, updating the control formula to maintain a good control state when the operation is deteriorating, so-called deviation correction in real time, pursuing higher stability Feedback control can be automated.

Industrial robots are transported to various sites, assembled, and adjusted so that they operate under the desired conditions. When the control parameters need to be reconfigured or the control formula needs to be corrected, re-learning using reinforcement learning using the power search method according to this patent will lead to a faster and more stable optimal control formula, It is easy to reimplement control parameters or control equations. Similarly, it can be applied to the automatic control of automobiles and flying objects.

(Example 5)
In the first to fourth embodiments described above, it has been explained that appropriate laws, equations, and relational expressions (control expressions) can be derived using exponential addition addition neural networks. In this way, the present invention is excellent in generalization ability with the ability to give appropriate outputs to unlearned inputs other than learned inputs. It is quite logical to make good predictions about similar processes. Behind this is the ability to easily learn logical operators (AND.OR, NAND, NOR, EXOR), and to easily convert numerical data of logical operations such as converting n-ary to decimal. It has an excellent arithmetic function that can learn and present general-purpose formulas.

Since the exclusive OR (EXOR) of logical operators has non-linearity, it is not possible to divide the true/false output by a single straight line (threshold) using a conventional simple perceptron. Therefore, as shown in FIG. 40, the two-input truth table involves a significant design change to a multi-layered neural network structure in which NAND, OR, and AND logic operators configured by simple perceptrons are connected. The learned discriminant output formula becomes a complicated parameter formula, and the formula is not easy to understand. On the other hand, the exponent addition addition neural network can handle non-linearity, and the basic structure of the exponent addition addition neural network in either one of FIGS. A simple discriminant output formula can be derived that divides the output of by a straight line.

For example, the output data d3 of the exclusive OR (EXOR) shown in the three-input (d0, d1, d2) truth table shown in FIG. D2, D3), and performing discriminant learning for output classification using a power exponent addition addition neural network, as shown in FIG. is derived and split correctly using a single straight line (threshold) 5 . Note that the exclusive OR (EXOR) of two inputs is too easy to solve, so the explanation is omitted.

Next, FIG. 43 shows a table representing the relationship between binary numbers and decimal numbers. FIG. 43 is a table of four-dimensional binary input data (d0, d1, d2, d3) and its decimal output value d4 of 0-9. Using this as the five-dimensional input values (D0, D1, D2, D3, D4) with a base of 10, the basic structure of the exponential additive addition neural network shown in either one of FIGS. Applying it as it is and performing a formula search between exponents -10 to 10, as shown in FIG. is guided. From this, the relational expression of the decimal output d4 is expressed as d4=log10(D0^8*D1^4*D2^2*D3)=2^3*d0+2^2*d1+2^1*d3+2^0*d0 , is a formula (general-purpose formula) itself for converting a binary number to a decimal number. From this, it can be seen that the values of unlearned decimal values 10 to 15 that can be represented by four-dimensional binary data are also correctly predicted.

In this way, the exponent addition addition type neural network is a calculation method with a wide range of applications that can derive relational expressions and discriminants without modifying its structure, and ICs and microcomputers made into integrated circuits are provided. However, when it is installed in the discriminating device and the control device, it is possible to increase the speed, reduce the size, and reduce the power consumption of the device.

(Other embodiments)
The present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the gist of the present invention. All of them are included in the technical idea of the present invention.

DESCRIPTION OF SYMBOLS 1... Arithmetic device, 1A... Machine learning device, 1B... Discrimination device,
2... classifier learning unit, 3... learning parameter storage unit, 4... learning data storage unit,
5... Learning data processing unit, 6... Discrimination result processing unit, 7... Discrimination data acquisition unit,
20... Learning unit, 21... Discrimination processing unit,
100A to 100C ... neural network structure,
110A to 110C input layer 120A to 120C output layer 130 hidden layer 131 first hidden node 132 second hidden node

Claims (9)

A computing device that outputs output values from the output layer for a plurality of input data (D0, D1, . . . , DN) input to the input layer using a neural network structure including at least an input layer and an output layer There is
The input layer is
having a plurality of power exponents (p0, p1, .
The output layer is
A product ( ^YY0 =D0 ^p0 *D1 ^p1 *) of a plurality of power values (D0 ^p0 , D1 ^p1 , . ... outputting the output value (y=f( ^YY0 )) based on *DN pN );
Arithmetic unit. The neural network structure is
further comprising a hidden layer between the input layer and the output layer;
The hidden layer is
A plurality of the input data are input via a plurality of weighting parameters (w0, w1, . a first hidden node that outputs to the output layer;
A plurality of input data are respectively input via the plurality of weighting parameters, and a bias parameter (b) as the learning parameter is input, and an addition type operation output defined by the following formula [Equation 2] a second hidden node that outputs (BYA) to the output layer;
The output layer is
outputting the output value (y=f(YY1, BYA)) based on the target value (YY1) and the addition type operation output (BYA);
A computing device according to claim 1 .
[Number 1]
YY1=D0 ^p0 *D1 ^p1 *...*DN ^pN *W0*W1*...*WN
[Number 2]
BYA=B*(base) ^{(Σ[n=0→N](wn*pn*dn))}
however,
base is a positive number excluding 1 Dn=base ^dn (n=0,1,...,N)
Wn = base ^wn (n = 0, 1, ..., N)
B = base ^b
is. The plurality of power exponents, the plurality of weighting parameters, and the bias parameters as the learning parameters are
A parameter learned by using a plurality of sets of the input data as the learning data,
The target value (YY1) output from the first hidden node and the additive operation output from the second hidden node when a plurality of the input data as the learning data are input to the input layer. Adjusted so that the difference (|YY1-BYA|) between the output (BYA) is small,
3. The computing device according to claim 2. The input layer is
A plurality of logarithms (d0, d1, ..., dN) obtained by multiplying the plurality of input data (D0, D1, ..., DN) by the logarithms (d0, d1, ..., dN) and multiplying the plurality of logarithms of the plurality of input data by the plurality of exponents output the multiplied value (d0*p0, d1*p1, ..., dN*pN) to the output layer,
The output layer is
The sum (d0*p0+d1*p1+...+dN*pN) of the multiple multiplied values is converted into an antilog (base ^{d0*p0+d1*p1+...+dN*pN), and the antilog} is the product, and the output value (y =f(YY0)),
A computing device according to claim 1 . The plurality of power exponents as the learning parameters are
A parameter learned by using a plurality of sets of learning data including a plurality of the input data and teacher data associated with the plurality of the input data,
so that the difference between the output value output from the output layer when the plurality of input data included in the learning data is input to the input layer and the teacher data included in the learning data is reduced. adjusted,
The computing device according to claim 1 or 4. at least one of the plurality of input data,
data represented by complex numbers,
The computing device according to any one of claims 1 to 5. An integrated circuit constituting the neural network structure used by the arithmetic device according to any one of claims 1 to 6,
an input/output unit that configures the input layer and the output layer;
a storage unit that stores the learning parameters;
a computation unit that performs computation for outputting the output value from the output layer based on the plurality of input data input to the input layer and the learning parameters stored in the storage unit;
integrated circuit. A machine learning device that generates a learning model having the neural network structure used by the arithmetic device according to any one of claims 1 to 6,
a learning data storage unit that stores learning data including at least a plurality of the input data;
a learning unit that learns the learning parameter by inputting the learning data stored in the learning data storage unit into the learning model;
a learning parameter storage unit that stores the learning parameter as a result of learning by the learning unit;
Machine learning device. A discrimination device that outputs a discrimination result for discrimination data using the learning model generated by the machine learning device according to claim 8,
a discrimination data acquisition unit that acquires the discrimination data;
a discrimination processing unit that outputs the discrimination result based on the output value from the learning model by inputting the discrimination data acquired by the discrimination data acquisition unit into the learning model;
Discriminator.

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