JPH0680505B2 - Learning method for multilayer neural network - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Outline] A learning method for learning a multi-layer neural network, in which an excitatory load and an inhibitory load are provided in an intermediate layer, and an input pattern is input to the first layer to perform self-learning. , A first layer for nonlinearly processing an input pattern and a pattern from this first layer for the purpose of automatically forming elements that specifically react to the input pattern and improving redundancy and generalization ability. Regarding the excitable load that can be learned for all V ⁽¹⁾ , and the restrainable load that can be learned for computing the pattern from the monitor cell, the excitatory load and the inhibitory load OR circuit for obtaining the sum of each operation pattern, computed and a second layer of non-linear processing a pattern determined by the OR circuit, a predetermined load pattern V ⁽²⁾ from the second layer, and these calculation A third layer consisting of OR circuit for obtaining the sum of the pattern, performs non-linear processing calculates the sum of the pattern V ⁽²⁾ from the pattern V ⁽¹⁾ and the second layer from the first layer, as a result It said second layer a pattern of a monitor cell for calculating the inhibitory load (intermediate layer), excitatory appropriate based on the pattern V ⁽¹⁾ and pattern V of the second layer ⁽²⁾ from the first layer The value of the load is updated (increment / decrement ⁾ , and based on the sum of the pattern V ⁽¹⁾ from the first layer and the sum of the pattern V ⁽²⁾ of the second layer, the applicable inhibitory load (4) is It is configured to perform self-learning to update (increment / decrement) the value. In addition, the load is updated (incremented / decremented) by a pattern corresponding to the error with respect to the load of the third layer, and error correction learning can be performed.

[Industrial application field]

The present invention relates to a learning method for learning a multi-layered neural network, and more particularly to a learning method for a multi-layered neural network configured to provide an intermediate layer for self-learning and error learning.

[Problems to be Solved by Conventional Techniques and Inventions]

In recent years, a back propagation method, an error correction method, etc. have been proposed as a learning method for a robot manipulator to which a multilayered neural network that models the cerebellum is applied. The backpropagation method is excellent in that the middle layer can be learned with the same algorithm as the last layer, but the number of memorable input patterns and redundancy (normal even if a part of a cell fails due to learning) Is not yet sufficient in terms of generalization ability (the ability to perform various actions) and generalization ability (the ability to obtain a similar output when an input pattern that is different from the learned input pattern, but similar to the learned input pattern). There is. In addition, the error correction method has a problem in that learning is performed only in the final layer, and the structure of the intermediate layer is fixed based on the a priori knowledge, and cannot be self-learned.

According to the present invention, an excitatory load and an inhibitory load are provided in the middle layer, and an input pattern is input to the first layer for self-learning, whereby elements that specifically react to the input pattern are automatically formed and redundant. Its purpose is to improve sex and generalization ability.

[Means for solving the problem]

 Means for solving the problems will be described with reference to FIG.

In FIG. 1, the first layer is for performing non-linear processing 1 on the input pattern.

The second layer (intermediate layer) has a learnable excitatory load 2 for computing all patterns V ⁽¹⁾ from the first layer, and a learning for computing patterns from the monitor cell 6. Possible inhibitory load 4, excitatory load 2 and inhibitory load 4
A summing circuit 3 for calculating the sum of the patterns calculated for and, and a non-linear processing 5 for the patterns calculated by the summing circuit 3.

The third layer is composed of a summing circuit 8 which calculates a predetermined load 7 on the pattern V ⁽²⁾ from the second layer and calculates the sum of these calculated patterns.

The monitor cell 6 includes the pattern V ⁽¹⁾ and the second pattern from the first layer.
Non-linear processing is performed by summing the patterns V ⁽²⁾ from the layers,
The resulting pattern is the restraining load 4 of the second layer (intermediate layer).
Is calculated.

[Action]

According to the present invention, as shown in FIG. 1, the first layer performs non-linear processing on an input pattern and sends out a pattern V ⁽¹⁾ , and the second layer sends an excitable load 2 to these patterns V ^(1). and results of calculation, and calculates the sum of the calculation result of the inhibitory load 4 to the pattern of the monitor cell 6, to further feed the pattern V ⁽²⁾ performs a nonlinear process 5, the third layer is the pattern V ^{( 2) The} load 7 is calculated and the sum is calculated to output the output pattern (for example, FIG. 7 T
n) is output. At this time, based on the pattern V ^{(1) to} the second layer and the pattern V ⁽²⁾ from the second layer, the value of the excitatory load 2 of the element of the second layer is updated (increment / decrement), In addition, the monitor cell 6 is a pattern from the first layer.
Based on the sum of V ⁽¹⁾ and the pattern V ⁽²⁾ from the second layer,
Update the value of the restraining load 4 of the element of the 2nd layer (increment / decrement)
However, by suppressing the number of firing elements, self-learning (forming elements that react specifically to the input pattern) is performed. Further, with respect to the load 7 of the third layer, learning for updating (increment / decrement) so as to correct the error is performed (see FIGS. 7 and 8).

Therefore, by inputting the input pattern to the first layer and self-learning the excitatory load 2 and the inhibitory load 4 provided in the intermediate layer, the wiring adapted to the input is automatically performed, and the input pattern is connected to the input pattern. Elements (cells) that react specifically
Can be formed, and at the same time, redundancy and universal power can be obtained. Further, the error correction learning is performed on the load 7 of the third layer which is the final layer.

[Embodiment] Next, the configuration and operation of one embodiment of the present invention will be sequentially described in detail with reference to FIGS. 1 to 8.

In FIG. 1, the first layer is composed of elements that perform nonlinear processing 1 on the input pattern. This non-linear processing 1
For example, non-linear processing represented by the following formula is performed.

The second layer (intermediate layer) is a plurality of elements having excitatory load 2, sum circuit 3, inhibitory load 4, and nonlinear processing 5 (for example, 500).
Individual)). Here, the sum circuit 3 calculates the sum of the value obtained by calculating the excitatory load 2 for all the patterns V ⁽¹⁾ from the first layer and the value obtained by calculating the inhibitory load 4 for the pattern from the monitor cell 6. It is the basis.

The third layer is composed of a summing circuit 8 that calculates a predetermined load (a load that has been subjected to error correction learning) 7 on the pattern V ⁽²⁾ from the second layer and calculates the sum of these calculated patterns.

The monitor cell 6 includes the pattern V ⁽¹⁾ and the second pattern from the first layer.
Non-linear processing is performed by obtaining the sum of patterns V ⁽²⁾ from the layers.

FIG. 2 shows an example of the constitution of one element (cell) in the second layer of FIG. Here, Vj ⁽¹⁾ is the pattern from the first layer, Vi ⁽²⁾ is the pattern output from the second layer, Wij is the excitatory load, Wig
Represents an inhibitory load, Σ represents a sum circuit, θi represents a threshold, and ∫ represents nonlinear processing.

Next, the overall concept of the present invention will be described with reference to FIG.

In FIG. 3, signal is an input (joint angle and its velocity) about an ideal trajectory of a plane two-joint manipulator as shown in FIG. 7 described later.

The Gaussian filter is a Gaussian filter, and as will be described later with reference to FIG. 4, a phase width Δa (= 40 °) and an interval of 10 from the input pattern as shown in the upper part of FIG.
This is to extract a signal component consisting of °.

The first layer comprises the non-linear processing of FIG.

The second layer (intermediate layer) has the structure shown in FIG.
It is a layer that executes self-organization.

The third layer has the structure shown in FIG. 1 and the third layer, and error-corr
This is the layer that executes ection (error correction learning).

The monitor cell 6 includes the pattern V ⁽¹⁾ and the second pattern from the first layer.
The second layer (intermediate layer) is suppressed based on the pattern V ⁽²⁾ from the layer.

An example of generating an input pattern to be input to the first layer will be described with reference to FIG.

FIG. 4A shows the operation of the Gaussian filter. This is that of the plane 2 joint manipulator of FIG.
As shown in the joint angle θ in the upper part of Fig. 4 (c), -60 ° to + 60 ° (range of joint angle) Δa = 40 ° (half width) When the number of filters = 16, Fig. 4 (b) Input the joint angle θ instructed as shown in, and enter 16 Gaussian filters (half-value width Δa
= 40 °, 16 = a total of 16 Gaussian filters with intervals = 10 °) to generate an input pattern with a total of 16 elements. In addition, similarly for the speed shown in FIG.
An input pattern having a total of 24 elements is generated by the 24 Gauss filters (a total of 24 Gauss filters having a half width Δv = 240 degrees and an interval of 50 degrees / second). In the case of the plane two-joint manipulator shown in FIG. 7, since there are two sets of joint angles and velocities shown in FIG. 5, a total of (16 + 24) × 2 = 80 input patterns are shown in FIG. Input in the 1st layer). The pattern V ⁽¹⁾ that has been subjected to the nonlinear processing described above for the input patterns of these 80 input elements is input to the second layer.

Next, the self-learning of the second layer (intermediate layer) will be described in detail by using the fifth equations (1) to (4).

In FIG. 5, τdwij ⁽²⁾ / dt on the left side of equation (1) indicates the increment of excitatory load, τdwig / dt on the right side of equation (2) indicates the increment of inhibitory load, and equation (3) Vg on the left-hand side of FIG. 4 shows the suppression pattern from the monitor cell 6, and Vi ^{(2) in} equation (4) shows the pattern from the second layer. Also, τ is the time constant, c ₁ , c ₂
Indicates a learning parameter that determines the learning speed and the convergence value.
The procedure of self-learning will be described below.

First, the excitatory load wij ⁽²⁾ of the equation (1) and the inhibitory load wig of the equation (2) are initially given randomly (for example, uniform random numbers).

Second, the input pattern that has passed through the Gaussian filter shown in FIG. 4 (for example, the joint angle (θ ₁ , the joint angle of the plane two-joint manipulator,
θ ₂ ), velocity (V ₁ , V ₂ ) generated input pattern with 80 elements) undergoes non-linear conversion by the non-linear processing 1 of the first layer, and the pattern V ^{(1 )} .

Thirdly, based on the values of the excitatory load wij ⁽²⁾ and the inhibitory load wig, which are initially set at random for the pattern V ⁽¹⁾ for the second layer, the second pattern is calculated according to the equation (4). Generate the pattern V ⁽²⁾ output from the second layer. here,
θi is a threshold.

Fourthly, according to the equation (1), the increment of excitatory load “Δwi
j ⁽²⁾ ". The increment" Δw represented by this equation (1)
"ij ⁽²⁾ " (increased synapse value) fired an element in the second layer (cell, Vi ⁽²⁾ ) and an element in the first layer (cell, Vj ⁽¹⁾ ). Sometimes it is proportional to the product, on the other hand, it decreases when some element of the second layer is not firing or when there is no input from the first layer. Initially set to random excitatory load wij ⁽²⁾ Also, by inputting various specific input patterns and performing repeated learning and updating,
The connection of the second layer is automatically formed so as to converge to a stable equilibrium state where the value in the parenthesis on the right side of Expression (1) becomes zero.

Fifth, the inhibitory load increment “Δwig” is performed by the equation (2). The increment “Δwig” represented by this equation (2) is
A certain element of the second layer (cell, Vi ⁽²⁾ is fired, and the sum of output patterns Vi ⁽¹⁾ from the first layer and the sum of patterns Vj ⁽²⁾ from the second layer are more than a predetermined threshold θ ₀ . Is also large,
Proportional to the product. On the other hand, it decreases when a certain element of the second layer is not firing or when the sum is small. Even if initially set to random suppressive load wig, by inputting various peculiar input patterns and performing learning and updating, stability such that the value in the parenthesis on the right side of equation (2) becomes zero The suppression of the second layer is automatically controlled so as to converge to the equilibrium state. That is, when the elements (cells) of the second layer (intermediate layer) are overly ignited, Vg of the equation (3) becomes large, and the inhibitory load becomes large according to the equation (2), and the total number of firings of the second layer is increased. Control to suppress. On the other hand, when the total number of ignitions is small, it is controlled to increase. Further, when the value of the pattern V ⁽²⁾ from the second layer becomes smaller, V ⁽²⁾ applied to the right side of the equations (1) and (2) reduces the excitatory load and the inhibitory load. The increment is controlled to be small.

Next, FIG. 6 schematically shows a simulation result of a response example of the intermediate layer (second layer). The horizontal axis represents the input pattern, and the vertical axis represents the type of cell (element). The horizontal bar in the figure indicates a fired cell, that is, a cell that specifically reacts to the input pattern. From this response example, it is found that the detected cells (elements) of the input pattern were formed substantially uniformly (90% or more) corresponding to the input pattern. Further, it can be seen that the detected cells (elements of the second layer) are distributed from those that respond to one input pattern to those that respond to several similar input patterns.

Next, a configuration and a simulation result when the present invention is applied to a planar two-joint manipulator will be described with reference to FIGS. 7 and 8.

FIG. 7 shows an application example when the present invention is applied to a plane two-joint manipulator. The mechanical model of this controlled object can be expressed by the following equation.

A (θ) + B (θ,) + C (θ) = T Here, each term on the left side represents an inertial term, a centripetal and Coriolis force term, and a gravity term. Further, T on the right side is torque. In the simulation, the mass of the arm M ₁ = M ₂ = 5.0 kg and the length L ₁ = L ₂ = 0.3 m. As an ideal trajectory, it lasts 1 second 4
Different types were adopted, and the simulation time interval was 0.02 seconds. Therefore, 50 patterns are presented in the configuration of FIG. 1 for one trajectory. Feedback gain Kp
= 1.0 and speed Kv = 3.0. In each element (cell) of the first layer in FIG. 1, the angle and the angular velocity are already described in FIG. 4 (b).
80 discrete patterns were given through a Gaussian filter. For each joint, 40 pieces (angle: 16 pieces, each speed: 24
Individual).

8A and 8B show the arm angle θ ₁ and the arm angle θ _2.
For, the result of learning about a single trajectory is shown. The horizontal axis represents the number of times of learning, and the vertical axis represents the normalized RMSE (square of mean square error). Note that FIG. 8C shows the RMSE after 60 learnings. Here, N ⁽²⁾ is the number of cells in the intermediate layer (second layer).

〔The invention's effect〕

As described above, according to the present invention, the input pattern is input to the first layer, the excitatory load 2 and the inhibitory load 4 provided in the intermediate layer (second layer) are self-learned, and applied to the input. Since the configuration that automatically connects the wires is adopted, it is possible to form elements (cells) that specifically react to the input pattern in a self-learning manner and to have redundancy and generalization ability. You can Furthermore, the third layer, which is the final layer
The error correction learning can be performed by learning the layer weight 7. By applying a multilayer neural network that performs self-learning of the intermediate layer and error correction learning of the final layer to a feedback system, for example, as shown in FIG. 7, the multilayer neural network according to the present invention is learned according to the learning from the feedback system. Transition to feedforward system by network.

[Brief description of drawings]

FIG. 1 is a block diagram of the principle of the present invention, FIG. 2 is an example of the element structure of the second layer, FIG. 3 is an overall explanatory diagram of the present invention, FIG. 4 is a Gaussian filter explanatory diagram, and FIG. Learning operation explanatory diagram,
FIG. 6 is a response example of the intermediate layer, FIG. 7 is an explanatory diagram of an application example of the present invention, and FIG. 8 is a learning explanatory diagram of an application example of the present invention. In the figure, 1 and 5 are nonlinear processing, 2 is excitatory load, 3 and 8 are sum circuits, 4 is inhibitory load, 6 is monitor cell, and 7 is load.

Claims (2)

[Claims] 1. A learning method for learning a multi-layer neural network, comprising first means for nonlinearly processing an input pattern.
A layer, a learnable excitatory load means (2) for computing all patterns V ⁽¹⁾ from the first layer, and a learning for computing patterns from the monitor cell (6) Restrainable load means (4) and the excitable load means (2)
And a second circuit including a summing circuit (3) for calculating the sum of the patterns calculated by the suppressing load means (4) and a means (5) for nonlinearly processing the patterns calculated by the summing circuit (3). A third layer including a load means (7) for calculating a predetermined load on the pattern V ⁽²⁾ from the second layer, and a summing circuit (8) for obtaining the sum of the calculated patterns; Non-linear processing is performed by obtaining the sum of the pattern V ⁽¹⁾ from the first layer and the pattern V ⁽²⁾ from the second layer, and the resulting pattern is the restraining load means of the second layer (intermediate layer). The pattern V ⁽¹⁾ from the first layer and the pattern V ⁽²⁾ from the second layer are provided with the monitor cell (6) for calculating (4 ⁾
Pattern V ⁽² values and updates (down increment-min) of the corresponding excitatory load means in proportion to the product (2), the sum of the pattern V ⁽¹⁾ from the first layer from the second layer ^{) And} the pattern V from the second layer ⁽²⁾
Inhibitory load means (4) applicable in proportion to the integrated value of
A learning method for a multilayer neural network characterized by being configured to perform self-learning for updating (incrementing / decrementing) the value of. 2. The weight means (7) of the third layer is configured to update (increment / decrement) the weight means (7) by a pattern corresponding to the error amount so that the error learning can be performed. A learning method for a multilayer neural network according to item (1).