JPH0438556A - Data processor - Google Patents

Abstract

PURPOSE:To suppress the number of neurons at an irreducible minimum by dividing the neurons of a neural layer in each data processing part into neuron groups composed of the fixed number of neurons and making the respective neuron groups as mentioned above correspondent to the neurons of the neural layer in the next step in a neural network. CONSTITUTION:A front step processing part 10 and a rear step processing part 120 are composed of input layers 31, 34, intermediate layers 32, 35 and output layers 33 and 36. The neurons of the input layer 31 is divided into neuron groups a1 or the like. The neuron group a1 is composed of four neurons n16, n26 or the like. Adjacent neuron groups a1 and a2 share the two neurons. The other neuron groups are similarly constituted as well. The neuron group a1 or the like is made correspondent to the neuron n16 or the like of the intermediate layer 32. The neurons of the intermediate layer 32 is divided into the neuron groups composed of four neurons as well. The respective neuron groups of the intermediate layer 32 are made correspondent to the respective neurons of the output layer 34.

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Field of Application] The present invention relates to a data processing device based on the concept of neural arbiter software.

[Conventional technology]

The neural network in this type of data processing device is constructed in a layered manner by providing nerve cell models (hereinafter referred to as neurons) in parallel as shown in FIG. Neurons in each layer are connected to all neurons in adjacent layers to input and output data. That is, in neuron 1, externally input data It, Iz
,I.

...In respectively has weights WI, W2, W3...W
n is multiplied, and data O corresponding to the comparison result between the sum total and the threshold value θ is output.

Various methods are possible for this comparison, but for example, if the normalization function 1 [f] is adopted, output data 0 will be expressed as 0=1 (ΣWnln-θ]...(1) In other words, when ΣWn-In is equal to or higher than the threshold value 6, the neuron fires and the output data 0 becomes "l", and Σ
When Wn・In is smaller than the threshold θ, output data 0 is “0”
becomes.

A conventional neural network is constructed by arranging such neurons in parallel to form a neural layer and connecting these neural layers in series.

The neural layer is, for example, Rosenplant (Ros
3 like the Berceptron proposed by
It consists of layers: an input layer, a hidden layer, and an output layer, with neurons in each layer synapsing to all neurons in other adjacent layers.

[Problem to be Solved by the Invention] In such a data processing device, neurons in the input layer must be arranged in multiple stages in order to process input data, but neurons in the output layer do not substantially output processing results. Since only a few steps are required, a relatively small number is sufficient. However, until now, there has been no established theory on how to determine the number of neurons in the hidden layer, and the same number of neurons has usually been provided for all neural layers. As a result, the number of neurons becomes enormous, and there is a problem in that not all neurons are used efficiently.

The present invention was devised to solve these conventional problems, and it is an object of the present invention to provide a data processing device configured with the minimum number of neurons necessary for processing purposes.

[Means for Solving the Problems] A data processing device according to the present invention is provided with a plurality of mutually independent data processing sections each having a plurality of stages of neural layers, and each data processing section has a certain number of neurons in the neural layer. The neurons are divided into groups of neurons,
Some neurons in each neuron group also belong to adjacent neuron groups, and each neuron group corresponds to neurons in the next neural layer, and the number Nn of neurons in the n-th neural layer is N−. ((J″
T;TTv)/(J-7-v))2.

However, N, l-6 is the number of neurons in the (n-1)th stage, a
is the number of neurons in one neuron group, and ■ is the number of neuron columns that also belong to another adjacent neuron group.

1 Example] The present invention will be explained below with reference to illustrated embodiments.

FIG. 1 shows a character recognition system having a data processing device according to an embodiment of the present invention.

This character recognition system includes a video camera 10, a preprocessing device 20, a data processing device 100, a postprocessing device 40, and a display 5o. A video camera 10 is provided for inputting characters and is connected to a preprocessing device 20. The preprocessing device 2o is, for example, a conventionally known image processing device, and filters input character data.
This is binarized, and feature data (for example, number of end points, number of branch points, etc.) of this input character is extracted, and this feature data is output to the data processing device 100. The data processing device 100 configures a neural network as described later, recognizes characters based on the character characteristic data input from the preprocessing device 20, and sends data corresponding to the recognition results to the postprocessing device 40. Output. The recognition signal is, for example, a character code, and the post-processing device 40 stores this output data as, for example, word processing data, and outputs it to the display 50 at the same time. The display 50 is, for example, a CR
It consists of a data processing device l.

The characters recognized by O are displayed on the screen.

The neural network that constitutes the data processing device 100 is configured as part of, for example, hardware of a computer. This data processing device 100 is schematically represented in FIG. 1, and includes a pre-processing section 110 and a post-processing section 120.

The pre-processing section 110 has nine data processing sections as described later, but in FIG. 1, there are three data processing sections 111.
112.113 are shown.

On the other hand, the post-processing section 120 consists of one data processing section.

In this embodiment, each data processing unit has three neural layers. To explain the configuration of the data processing unit using the data processing unit 111 as an example, the data processing unit 111 has an input layer 31 as a neural layer, an intermediate layer 3
2 and an output layer 33, and the intermediate layer 32 is disposed between the input layer 31 and the output layer 33. Each layer 31.32.3
3 each has a large number of neurons n, and the input layer 31
The neurons n in the hidden layer 32 are connected to all the neurons n in the hidden layer 32, and the neurons n in the hidden layer 32 are connected to all the neurons n in the output layer 33.

Other data processing units 112, 113, etc. are also the data processing unit 11.
It has the same configuration as 1. The post-processing unit 120 also has a similar configuration, and includes an input layer 34, a middle layer 35, and an output layer 36, in which neurons n in the input layer 34 are connected to all neurons n in the middle layer 35, and the neurons n in the middle layer The 35 neurons n are connected to all neurons n of the output layer 36. The number of neurons in the input layer 34 of the post-processing unit 120 is equal to the sum of the numbers of neurons in each output layer 33 of the pre-processing unit 110, and each neuron in each output layer 33 is coupled to one neuron in the input layer 34.

FIG. 2 shows three-dimensionally the configurations of the front-stage processing section 110 and the rear-stage processing section 120. In this embodiment, the pre-processing section 110 has nine data processing sections as described above, but in this figure, there are four data processing sections 111.112.1.
Only 13.114 are shown. Further, as described above, each neuron in the output layer 33 of each data processing unit of the front-stage processing unit 110 is connected to the input layer 33 of the rear-stage processing unit 120, respectively.
connected to one neuron. In other words, the neurons of the output layer 33 of the pre-processing section 110 and the post-processing section 1
There is a one-to-one correspondence with the twenty neurons of the input layer 34. The number of input layers 34 of the post-processing section 1.20 is the same as the number of data processing sections of the pre-processing section 110 (in the case of this embodiment, 9
) is divided into regions e, f, g, h, 1, L k, 1, m, and each of these regions is divided into the output layer 33 of each data processing section 111112.113.114 of the pre-processing section 110, respectively. handle.

Each neuron n is defined as (
1] Output “1” or “0” data based on the second normalization function. The neuron n is composed of, for example, an operational amplifier, and the weight Wn by which data input to each neuron n is multiplied is obtained, for example, by a variable resistor connected to the input terminal of the operational amplifier. Further, the dark value function is realized by a switching element or the like. That is, by changing the magnitude of the variable resistance according to the output data of each neuron, the weight Wn is changed, the output data is corrected, and learning is performed.

FIG. 3(a), (b), and (c) show the input layer 31 and the intermediate layer 3.
2 and an output layer 33 schematically. The number of neurons decreases in the order of input layer 31, intermediate layer 32, and output layer 33. Here, for ease of explanation, the number of neurons in the input layer 31 is 64, the number of neurons in the intermediate layer 32 is 49, and the number of neurons in the output layer 33 is 36.

Furthermore, in the input layer 31, neurons in each layer are arranged in eight directions in the horizontal and vertical directions, in the intermediate layer 32, seven neurons are arranged in the horizontal and vertical directions, and in the output layer 33, neurons are arranged in the horizontal and vertical directions. There are 6 arrays. Here, the position of the neuron in the lower left corner of the diagram is taken as the origin, and the neuron located i-th from the left and third from the bottom is nl.

Each neuron in the input layer 31 fires in response to character feature data obtained via the video camera 10. For example, n
The Euler number is expressed by the combination of firings of ll nil, ... n81, and n1□, n2□, ... nIl□
Suppose that the area is expressed by the combination of firings. That is, the firing pattern of the neurons in the input layer 31 is determined according to the input character.

On the other hand, in the output layer 33, for example, a neuron ni on a diagonal line connecting neurons in the lower left corner and the upper right corner.

Numerical values are represented by (neurons surrounded by dashed lines). That is, 1 to 6 neurons on this diagonal
A numerical value of 4 is represented. As will be described later, this value indicates the result of clustering the characters input from the video camera 10 using a predetermined method, that is, the cluster.

Input layer 34, intermediate layer 35, and output layer 3 of post-processing section 120
6 has the same configuration as the input layer 31, intermediate layer 32, and output layer 33 of the pre-processing section 110, but has different functions. That is, in the post-processing unit 120, clusters related to input characters are input to the input layer 34 from the pre-processing unit 110, and
The output layer 36 outputs a character code corresponding to the input character. This character code is shown in Figure 3 (C)
For example, as in the example shown in , it is represented by neurons on a diagonal line connecting neurons in the lower left corner and the upper right corner.

As will be described later, multivariate analysis is performed in each data processing unit of the first-stage processing unit 110, and a plurality of clustering data based on this multivariate analysis is input to the second-stage processing unit 120, and multivariate analysis is performed. Character recognition is performed.

Next, the correspondence between neurons in each layer, that is, the neural layer, will be explained.

In each layer, neurons are divided into neuron groups each consisting of a fixed number of neurons, and in this embodiment, one neuron group consists of four neurons. To explain the input layer 31, as shown in FIG. 3(a), for example, the neuron group at is the neuron n16sn.
Ha~nl? From %n2f, neuron group a2 is neuron nZ&, n3b, nzl, ILff? Each consists of Similarly, by shifting the neuron groups a3, am, a5, and a to the right in the figure by 1 new
m,;3f is defined. Each of these neuron groups a,
~a.

are the neurons n16, nl, n of the hidden layer 32, respectively.
36, n46, nsh, n hhs n T&. That is, the neuron group of the input layer 31 is
In this case, the lower left neuron of this neuron group corresponds to the neuron (n , , ) at the same coordinates as the neuron n + 6) in the case of the knee group a1.

Similarly to the input layer 31, the neurons in the intermediate layer 32 are divided into neuron groups, and each neuron group is composed of four neurons. Each neuron group corresponds to a neuron in the output layer 33 in exactly the same manner as described above.

As understood from FIG. 3(a), some of the neurons in each neuron group also belong to adjacent neuron groups. Specifically, for example, neurons n26 and nzt of neuron group a1 are adjacent to neuron group a21t' on the right side.

also belongs to neuron group a, neurons n16, n
Z& also belongs to the lower adjacent neuron group a8. Thus, each neuron group overlaps other neighboring neuron groups.

Here, the number of neurons in the input layer 31 is Ni, which is 7131
Let a be the number of neurons in a neuron group in , and let V be the number of columns of neurons that also belong to another adjacent neuron group. Assuming that the number of neuron groups in the input layer 31 is X, the following equation holds true as understood from FIG.

(('r-v) ,

Since each neuron group in the input layer 31 corresponds one-to-one to one neuron in the intermediate layer 32, the number X of neuron groups in the input layer 31 is equal to the number of neurons in the intermediate layer 32. Therefore, if the number of neurons in the intermediate layer 32 is set as Nm, then Nm = ((rFrT-v) / (√a-V)
+2 (2).

Generalizing this relationship, the number of neurons N in the n-th neural layer is N-□ ((F lower T
] v)/(√a-V))2 (3). however,
N7-1 is the number of neurons in the 221 layer of the (n-1)th stage.

The number of neurons in the input layer 31 is determined by the processing content for input data. That is, in the case of character recognition, for example, the number of neurons in the input layer 31 is determined depending on the type of character feature data. - On the other hand, the number of neurons in the output layer 33 is determined by the output content. In the above-described character recognition system, clusters of feature data are determined in the front-stage processing section 110, and clusters are determined on the basis of the type of character code of the character in the rear-stage processing section 120. Therefore, depending on the processing content of this data processing device, the input layer 31
．． 34 and the number of neurons in the output layer 33, 36 are determined. On the other hand, the number of neurons in the intermediate layer 32, 35 is determined by the number of neurons in the input layer 31, the number of neurons in the neuron group, etc., as shown in equation (2). Of course, the relationship between the number of neurons in the hidden layer 32.35 and the output layer 33.36 is also the same as that between the input layer 31.34 and the hidden layer 32.36.
35, and must satisfy equation (3).

Therefore, as shown in FIG. 1 and FIGS. 3(a) to (C), three neural layers are not necessarily provided in each of the pre-processing section 110 and the post-processing section 120, but there are two or more intermediate layers. In some cases, layers are provided so that the number of neural layers is four or more. Next, we will explain how to determine the calendar number of the neural layer.

As described above, the number Ni of neurons in the input layer 31.34 and the number No of neurons in the output layer 33.36 are determined depending on the purpose of the data processing device. On the other hand, the number a of neurons included in a neuron group and the number V (overlap rate) of columns of neurons that also belong to another adjacent neuron group are determined experimentally. For example, a is "4" and V is "l" (in this case, the overramp rate is 50%). Now, the number of neurons Ni in the input layer 31
, the number a of neurons in the neuron group and the overlap rate V are determined, then the number N2 of neurons in the second layer (first intermediate layer) is determined by equation (3). Once the number N2 of neurons in the second layer is determined, (3) the number N of neurons in the second to third layers (second intermediate layer) is similarly determined.

However, this calculation is continued until the number of neurons in the (n+1)th layer becomes smaller than the number of neurons No in the output layer 33, and the nth layer becomes an intermediate layer immediately before the output layer 33.35.

Next, character recognition learning in this embodiment will be explained.

In this embodiment, the first data processing unit 111 receives Euler's number, area, and number of groups as feature data from the preprocessing device 20, and performs clustering on these feature data. That is, the first data processing section 11
1 determines which cluster the input characters, such as kanji and hiragana, belong to using parameters such as Euler's number, area, and number of groups. Classify into. For example, "tree j and one tree" are classified into the same cluster. This kind of rastering, as explained later,
This is done by inputting printed characters from a video camera IO and learning them.

Similarly, the second data processing unit 112
, the stroke distributions in the horizontal direction, vertical direction, upward slope to the right, and upward slope to the left are input, and clustering is performed on these stroke distributions. The third data processing device 113 receives the number of branch points with the number of branches 3, the number of branch points with the number of branches 4, and the number of end points as input from the preprocessing device 20, and performs clustering on these. Before character recognition is learned by inputting feature data and performing clustering on the feature data, even if character data is input to the data processing device 30, the neurons in each output layer 33 of the pre-processing section 110 are Does not ignite. This neuron is
The learning ends when the firing becomes possible and a predetermined firing pattern corresponding to the input character data is exhibited. In this learning, each output layer 33 is connected to a post-processing device 40, and the clustering results output from the output layer 33 are displayed on the CRT 50. The characters inputted from the video camera IO are printed letters as described above, and clusters related to each feature data are predetermined for each printed letter.

That is, learning is performed until the pre-processing section 110 outputs a predetermined cluster according to the input character.

In a state where learning is completed, the input layer 31 and the output layer 33 exhibit a firing pattern that is artificially determined as described above in accordance with the input character data. It is estimated that the firing patterns in each of the input layer 31, intermediate layer 32, and output layer 33 change smoothly across these layers 31, 32, and 33. Therefore, in this embodiment, the middle layer 3 is designed so that the firing patterns in these layers change smoothly during the learning process.
2 and the output layer 33 are changed. Furthermore, in a state where learning is completed, as described above, one data processing unit has the number of intermediate layers determined based on equation (3), but only one intermediate layer is provided at the start of learning.

In a state where one intermediate layer 32 is provided in this manner, whether or not a neuron in the intermediate layer 32 should fire is determined by considering the firing of a plurality of corresponding neurons in the input layer 31 and the output layer 33.

That is, if a predetermined proportion or more of neurons among corresponding neurons in the input layer 31 and output layer 33 fire or should fire, the intermediate layer 3
It is determined that neurons No. 2 have a tendency to fire, and the weights of certain neurons in the intermediate layer 32 and the output layer 33 are increased to obtain such firing.

A method for determining whether or not neurons in the intermediate layer should fire will be specifically explained with reference to FIGS. 5(a) to 5(c). Note that FIG. 5(a) shows the firing pattern of the input layer 31, FIG. 5(b) shows the firing pattern of the intermediate layer 32, and FIG. 5(c) shows the firing pattern of the output layer 33. indicates a neuron that is firing, and a white circle indicates a neuron that is not firing. In this example, the input layer 31 exhibits a firing pattern as shown in the figure depending on the input character feature data, and the output layer 33 exhibits a firing pattern as shown in the figure to output a cluster corresponding to the character feature data. Must exhibit a pattern. In other words, the firing pattern of the illustrated input layer 31 is uniquely determined by the input characters, and the firing pattern of the output layer 33 is the one when learning is completed.

On the other hand, the tendency of the firing pattern of the intermediate layer 32 is determined according to the firing patterns of the input layer 31 and the output layer 33, as will be described later.

The correspondence between neurons in each layer when determining the tendency of such a firing pattern is the same as that described using FIGS. 3(a) to 3(C).

However, in the intermediate layer 32, each neuron n++s n, 1. , net, n77 to 2,
Each of the four neurons in the input layer 31 corresponds to
Regarding the output layer 33, each corner neuron nl
l, n 61% n l 6, n66 corresponds. In addition, each neuron n located at the periphery in the intermediate layer 32
il, ni7, n IJ% n 7j respectively correspond to the four neurons of the input layer 31 as described above, but regarding the output layer 33, the neuron n of the intermediate layer 32 corresponds.

For neuron n -n+, ni+, middle layer 32
neuron ni? For neuron n(r16,
ni6 and neuron n of the intermediate layer 32 correspond to neurons n l (J-11 and nlj, and neuron n7j of the intermediate layer 32 correspond to neurons n61j-11 and n6j, respectively.

In this embodiment, neurons in the intermediate layer 32 are determined to have a tendency to fire when, for example, 40% or more of the corresponding neurons in the input layer 31 and the output layer 33 are firing. In the example of FIG. 5(b), neurons in the input layer 31 and output layer 33 corresponding to neuron n26 in the intermediate layer 32 (a total of 8 neurons in areas a2 and f2)
out of 3 neurons), 3 neurons are firing.

Therefore, it is determined that the neuron n26 of the intermediate layer 32 has a tendency to fire. Also, among the neurons in the input layer 31 and the output layer 33 corresponding to the neuron nls in the intermediate layer 32 (six neurons in total in areas g and h), two neurons are firing. Therefore, the neuron n13 of the intermediate layer 32 has no tendency to fire. Therefore, it is determined that neurons in the intermediate layer 32 tend to exhibit a firing pattern as shown in FIG. 5(b).

In character recognition learning in this embodiment, the weight of each neuron in the intermediate layer 32 and output layer 33 is increased by a predetermined value so that the firing pattern thus obtained is obtained.

To specifically explain this increase in weight using FIG. 7,
If the output data 0 of neuron 1 in the intermediate layer is the value at the time of firing (for example, "1"), the data input from the firing neuron among the neurons in the input layer connected to neuron 1 ( For example, the synaptic weights for "r2" and '(3j) (in this case, "W2" and 'W3J) are increased by, for example, 5%. The synaptic weights of neurons in the output layer are also processed in the same way, as described above. The synaptic weight for the middle layer neuron that is determined to fire is increased by, for example, 5%.

Therefore, the weights of the intermediate layer 32 and the output layer 33 are increased so that the firing pattern changes most smoothly among the input layer 31, intermediate layer 32, and output layer 33. Here, if each neuron in the input layer 31 and output layer 33 is set to fire at the same frequency as possible for all input characters, each neuron in the intermediate layer 32 can also fire equally. This makes it possible to prevent a drop to the local minimum, and each neuron in the intermediate layer 31 fires substantially equally. That is, it is possible to avoid the generation of neurons that do not fire, and the neurons in the intermediate layer 32 can be made to work efficiently.

The increase in synaptic weight during one learning session changes as shown in Figure 6 with respect to the number of learning sessions, and the entire system is gradually learned through multiple learning sessions, and at the end of the learning process, fine adjustments are made due to minute changes. can be done. Also, the rapid increase in initial weights increases the learning speed.

In this way, when the learning with one hidden layer is completed, a new second hidden layer is added, and the predetermined number of corresponding neurons is added in the same manner for this second hidden layer. The synaptic weights in the second hidden layer and the layer connected to the output side of the second hidden layer (the output layer or the first hidden layer) are increased in consideration of whether more than a certain number of neurons fire. Thus, the weight distribution for the case of four layers is obtained. The same applies to the case of five or more layers.

Such addition of intermediate layers is performed until the number of intermediate layers reaches the number determined based on (3) 2 above.

When learning is completed, the input layer 31 and the output layer 3
3 exhibits a firing pattern that is artificially determined according to the input character.

After the learning of the first-stage processing section 110, the learning of the second-stage processing section 120 is performed. This is performed by connecting the upstream processing section 110 to the downstream processing section 120 as shown in FIG. 1, and similarly to the learning of the upstream processing section 110, it is performed while increasing the number of intermediate layers one by one. In the first stage learning of the post-processing unit 120, the characters input from the video camera IO are printed characters, and the post-processing unit 120 performs character recognition based on clusters of feature data input to the input layer 34. .

Then, when the character code corresponding to this character is output from the output layer 36, the first stage learning ends. Thereafter, handwritten characters are input, and a second stage of learning is performed using the same method. In learning by inputting handwritten characters, characters similar to printed characters are initially input, but as learning progresses, characters in various fonts are input, and learning is performed up to a predetermined stage.

In the example, as explained with reference to FIGS. 3(a) to (C), the number of neurons included in one neuron group is four, but the number is not limited to this. Any number can be selected depending on. Further, the number a of neurons in the neuron group and the O'Hara ratio V do not need to be the same values from the input layer to the output layer.

In other words, when a large number of hidden layers are provided, in order to make each group of neurons in the last hidden layer correspond to each neuron in the output layer in an I-to-I manner, this last hidden layer has neurons that are different from the other hidden layers. It may be necessary to have a number a or an overlap ratio V.

Further, the output layer 36 does not need to be configured to represent a character code by neurons on the diagonal, and may be configured to define a recognized character by all neurons.

Furthermore, in the above embodiment, each layer has a square shape, and the neurons are arranged like the eyes of the base, but this arrangement is conceptual, and in reality, it is not physically arranged like this. Not necessarily. So, for example, neurons can be constructed from computer memory;
In such a case, the physical arrangement of neurons in memory does not matter at all.

Furthermore, the present invention can be applied not only to character recognition but also to graphic recognition or speech recognition.

(Effects of the Invention) As described above, according to the present invention, it is possible to obtain the effect that a data processing device can be configured by the minimum group of neurons necessary for a processing purpose.

[BRIEF DESCRIPTION OF THE DRAWINGS] FIG. 1 is a schematic configuration diagram showing a character recognition system to which an embodiment of the present invention is applied; FIG. Figures 3 (a), (b), and (c) are conceptual diagrams showing neurons in the input layer, intermediate layer, and output layer, Figure 4 is a diagram showing the overlamp relationship of each neuron group, and Figure 5 (a). ), (b), and (c) are conceptual diagrams showing the firing distribution of neurons in the input layer, middle layer, and output layer. Figure 6 is a graph showing the relationship between the number of learning times and weight changes. Figure 7 is a graph showing the neuron firing distribution. It is a conceptual diagram showing an example. 1, n...Neuron 31.34 32.35 33.36 21.1 Input layer Middle layer Output layer 113.114...Data processing section

Claims (2)

[Claims] (1) A data processing device equipped with a multi-stage neural layer consisting of a plurality of neurons that fire and output predetermined data based on the result of performing predetermined processing on input data, the multi-stage neural layer comprising: A plurality of mutually independent data processing units each having a neural layer are provided, the neurons of the neural layer of each data processing unit are divided into neuron groups each consisting of a certain number of neurons, and some neurons in each neuron group are adjacent to each other. It also belongs to a neuron group, and each neuron group corresponds to a neuron in the next neural layer, and the number N_n of neurons in the n-th neural layer is N_n={((√N_n_−_1−v)/( √av)
A data processing device characterized by being determined according to the formula }^2. However, N_n_-_1 is the number of neurons in the (n-1)th stage, a is the number of neurons in one neuron group, and v is the number of columns of neurons that also belong to another adjacent neuron group. (2) A first-stage processing section consisting of a plurality of mutually independent data processing sections and a second-stage processing section having at least one data processing section, and the output data of the first-stage processing section is input to the second-stage processing section. Claim 1 characterized by
The data processing device described in Section 1.