JPH08202673A - Neural network and its learning method - Google Patents

Abstract

PURPOSE: To represent the reliability of the probability of a phenomenon on the neural network in addition to the probability and to obtain a neural network which is high in safety and reliability by enabling the output of a neuron to have a specific value corresponding to the potential at which the neuron is coupled. CONSTITUTION: This neural network is equipped with neurons N1-N3 which determine output values in probability according to input pulse signals and connections W13 and W23 which convert the outputs of the neurons N1-N3 into pulse signals and outputs the pulse signals as inputs to other neurons. The outputs of the neurons N1-N3 can have three values of 1, 0, and -1 according to potentials that the neurons N1-N3 input from the connections W12 and W23. Consequently, the neural network can be represented as, for example, (probability of phenomenon) = (probability that a neuron becomes 1)/(probability that the neuron becomes -1) and (reliability of probability of phenomenon) = (probability that the neuron is not 0), and the reliability of the probability can be represented on the network in addition to the probability of the phenomenon.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a stochastic neural network.

[0002]

2. Description of the Related Art In recent years, a large number of neural network models have been proposed in order to realize the functions such as poor pattern recognition and stochastic information processing of Neumann computers. However, compared with the information processing of living things, its ability is not sufficient at present, and it is a difficult task to express the stochastic uncertainty of a phenomenon or knowledge on a neural network.

Various methods have been proposed in the past for processing stochastic knowledge by a neural network. One of them is called a Boltzmann machine, and it is probabilistically determined whether or not to fire depending on the size of an input. A method using a neuron has been proposed.

A Boltzmann machine, which is an example of the above-described conventional neural network which operates stochastically, will be described below with reference to the drawings. The operation of the Boltz machine is shown, for example, in "Neural network information processing (published by Sangyo Tosho, pages 27-31, pages 55-64, issued June 20, 1988)" by Aso.

FIG. 7 is a block diagram of a Boltzmann machine.
There is no limit to the number of neurons, and the amount and complexity of information that can be processed increases by increasing the number and interposing a neuron commonly called a hidden layer in addition to the input / output neurons that are the gateways of information. However, here, in order to briefly explain the operation, the configuration is made up of three neurons. N1, N2, and N3 are neurons that take a 0 or 1 state. W12, W13, and W23 are connections between neurons. The state of a neuron is stochastically determined by the sum of the total input to the neuron and the threshold value unique to the neuron. The output of a neuron is determined by the state of the neuron and the integration of connections, and its output is input to another neuron. For example, when the state of N1 is 1, W1
If 2 is 0.5, the value of the signal output from N1 and input to N2 is 0.5. Further, the coupling is not one-way, and the output of N2 is similarly integrated with W12 and input to N1. Thus, for example, N2 has inputs from N1 and N3. At this time, the probability that the state of N2 becomes 1 is the relation of the sigmoid curve to the sum of the inputs and the threshold specific to N2. Correlates with. FIG. 4 shows the relationship between the input and the probability that the state will be 1. If random state changes continue according to this operation principle, the state of each neuron becomes 1 with a specific probability according to the connection. Note that a Boltzmann machine normally operates a parameter called temperature and undergoes a process called annealing. For the operation of such a Boltzmann machine, see, for example, “Neural Network Information Processing (Issue Book Issue, No. 27)” by Aso. Page-3
P. 1, issued June 20, 1988). "
By the principle described above, the Boltzmann machine can represent probabilistic knowledge as a network. For example, when N1 and N3 are 1, the probability that N2 will be 1 is uniquely determined, so that it is possible to perform processing such as obtaining the phenomenon occurrence probability when there are two pieces of evidence.

[0006]

However, with the above-mentioned structure, the reliability of the correlation between two neurons cannot be expressed on the network, and there is a drawback as described below.

[0007] First, even if the number of raw data which is the basis of the threshold value held by each neuron and the coupling value between neurons is insufficient, the same threshold value as when sufficient raw data is obtained. Or, it will be configured by the value of the combination, and there is no method to judge how reliable the phenomenon occurrence probability is. For example, as a result of observing the phenomenon corresponding to N1 independently, 7 times out of 10 times was 1 and 3 times was 0, so the threshold value of N1 is determined based on this raw data. In order to set the state of N1 to 1 with the probability of 0.7, the value of the input value with the probability of 0.7 may be set as the threshold value using FIG. However, it is impossible to determine whether the phenomenon occurrence probability is 0.7 with the raw data of at most 10 times, or the true probability is another value, but it happened to be 7 times 1 at this time. The true probability is 0.5, but it may happen to be 1 7 times, and in such a case, the probability expressed by the Boltzmann machine is different from the true probability. Therefore, it should be expressed in the network that the reliability of the determined threshold is low when the raw data is small as described above, but it is difficult to express the reliability by the Boltzmann machine. Therefore, the threshold value or the coupling value is determined in the same manner regardless of the number of observations 100 times or 10 times, and it is determined how much the answer obtained by the operation of the Boltzmann machine may deviate from the target phenomenon. It had the drawback of not being able to.

Second, since the value of reliability is not used when integrating two probabilities, it is impossible to distinguish the degree of influence from two neurons. For example, W23 is an uncertain combination based on the raw data of 10 observations, W23
Even if is a reliable combination of 100 observations, N
The weights of the degrees of influence that determine the states of 1 and N3 determine the state of N2 are equal, and the state of N2 obtained by integrating the two probabilities is not affected by the number of observations. Therefore, even if the reliability of a plurality of inputs in N2 is different, the state of N2 is determined to have the same weight.

[0009]

In order to solve the above-mentioned problems, a neural network of the present invention comprises a neuron that stochastically determines an output value according to an input pulse signal,
The output of the neuron is provided with a connection for converting the output of the neuron into a pulse signal and outputting the pulse signal so as to be an input of another neuron, and the output of the neuron is 1 or 0 or -1 depending on the potential input from the connection by the neuron. The feature is that it can take three values.

[0010]

In the neural network configured as described above, since the state of the neuron can take three values of 1, 0 and -1, for example, (probability of phenomenon) = (probability that neuron becomes 1) /
(Similarly, probability of becoming −1); (Probability of probability of phenomenon) = (Probability that neuron is not 0); and, in addition to probability of phenomenon, reliability of probability is expressed on the network. It becomes possible to do.

With this capability, it is possible to judge how reliable the prediction of the neural network is, for example, when predicting the safety factor of a phenomenon, and when the reliability of the prediction is low, a person makes a judgment. It is possible to realize flexible response such as taking corrective action or taking certain measures to secure the prediction, and it becomes possible to use a neural network having high safety and reliability.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A neural network according to an embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram of a neural network which is an embodiment of the present invention. The embodiments are intended to provide a neural network with high safety and reliability by expressing not only the probability of a phenomenon but also the reliability of the probability on a network.

There is no limit to the number of neurons, and the number and complexity of information that can be processed increases if the number is increased, but in the present embodiment, the configuration is made up of three neurons in order to briefly explain the operation.

N1, N2 and N3 are neurons which take the states of -1, 0 or 1. W13 and W23 are connections between neurons. The state of a neuron is stochastically determined by the total value of the inputs to that neuron. In the case of the Boltzmann machine, the threshold value of a neuron is treated as a value peculiar to the neuron, but in the present invention, the threshold value is defined as a neuron with a constant output of 1 connected to each neuron. N33 is a threshold neuron of N3, and W33
Is a combination that gives a threshold to N3.

Although threshold neurons are usually coupled to N1 and N2 as well, this embodiment will focus on the input / output of N3, and therefore these threshold neurons are not shown. .

The operation of the neural network configured as described above will be described below with reference to FIGS. 1, 2, 3, 4, 5, and 6.

When the output of N1 is 1, the coupling W13 inputs the value 1 from N1. The coupling holds two parameters a and b, respectively, and when the input is 1, the coupling generates a specific electric potential shown in the following equation and outputs this electric potential to N3 at this specific frequency.

(Potential V1) = (Parameter a); (Frequency) = (Parameter b); An example of the pulse signal output from the result W13 is shown in FIG.
(A). The pulse signal output from W13 is input to N3. The coupling puts a small amplitude sine wave on the output potential to clearly show that there is an output to the neuron. Therefore, even when the parameter a is 0, it is clearly distinguished from the case where no potential is output due to the presence of the sine wave. The output potential of W13 when the parameter a is 0 is shown in FIG. The amplitude V1 determined by the parameter a is 0, and the pulse generation frequency determined by the parameter b is the rate of the time when the sine wave is on the whole time.

It should be noted that this sine wave is to clearly show the existence of the output from the coupling, and is not necessarily a sine wave. For example, the same effect can be obtained with a triangular wave, and conversely, if a sine wave is transmitted to the neuron when there is no output, the same effect can be obtained.

Also, to indicate that there is no output, the combination is
It is also possible to send a potential that cannot be taken by the output potential of the connection to the neuron when there is no output so that when the potential is received, the neuron can recognize that there is no input from the connection.

Similarly, since there are also inputs from W23 and W33, the pulse potential input to N3 is the total value of the outputs of these three couplings. FIG. 3 shows an example of the total value of the pulse potentials input by N3. The pulse potential output to N3 is not always a positive potential, and a plurality of pulse potentials may be output to N3.
Since the timing of output to R3 is random, the waveform of the total value of the input pulse potentials of N3 is not a steady constant waveform but a random waveform.

The value of -1, 0 or 1 output by N3, that is, the state of N3 is determined by the pulse potential input by N3. When N3 inputs a pulse, that is, receives a signal applied with a sine wave, the state of N3 is 1-
It becomes 1. The state of N3 is 0 when there is no input pulse. The probability that the state of N3 becomes 1 or -1 is determined by the input pulse potential total value, and the probability that the state of N3 becomes 1 or -1 has a positive correlation. In this embodiment, this correlation is a sigmoid curve as shown in FIG. As a result, the state of N3 becomes -1 or 1 when a pulse is input, becomes 0 when no pulse is input, and each occurrence frequency becomes a constant value. An example of the state of N3 is shown in FIG.

The above-described operation of the neural network makes it possible to express the uncertainty of knowledge in the neural network. A neural network for weather forecasting will be described as an example of inference using this neural network.

N1 is a neuron indicating the presence of a rain cloud, N3
Is a neuron that indicates that it starts to rain within 1 hour. W13 is a combination indicating the correlation between rain clouds and rain, and the parameter a
Is the probability that it will rain within one hour when there is a rain cloud as knowledge, and parameter b represents the reliability of the knowledge. N3 indicates that it rains, does not know, and does not rain when the states are 1, 0, and -1, respectively. The purpose of this example is to predict the probability of rain within one hour when there is a rain cloud. Therefore, the output of N1 is always 1.

The smaller the parameter b, the more often N3 does not input a pulse, and the state of N3 is often zero. This condition indicates that we do not know if it will rain.

From the state of N3, the following three values can be obtained. CF indicates the reliability of knowledge used for judgment. P indicates the rainfall probability indicated by the knowledge possessed. P'is the probability used for the final judgment after considering the reliability.

CF = (time when N3 is 1 or -1) / (unit time); P = (time when N3 is 1) / (time when N3 is 1 or -1); P '= PxCF + 0.5x (1-CF); By obtaining these three values, it is possible to make a judgment with high safety and reliability. For example, when there is a rain cloud, even if the knowledge P possessed indicates that the rainfall probability is 0.9, if the confidence level CF of the knowledge is 0.1, then P ′ will be 0.54 and the rainfall probability. You can get a very realistic answer that you don't know because you lack knowledge.

Further, by observing the pulse waveform output from N3, even if P'is the same 0.5, a certain value of 0.
You can judge whether it is 5 or 0.5 that you do not know what the probability is, and if P'is certain 0.5 if the experiment can be digested unless it rains on 2 days 1 day, It is very useful in making realistic judgments, such as scheduling the schedule with certainty.

Further, when N2 is defined as a neuron showing another cause of rainfall, the pulse input to N3 is the total value of the pulses from the two neurons N1 and N2, and the waveform of each pulse has a specific value. Since the reliability is reflected in the form of the frequency of the electric potential, the state of N3 determined by the input of this summed pulse becomes a natural probability that integrates the two causes. That is, the probability indicated by the knowledge having a small reliability has a small influence on the integration probability of N3, and the integration of the probability considering the reliability, which has been difficult with the conventional neural network, can be easily realized. The knowledge referred to here is the parameter held by the bond.

Similarly, the threshold neurons N3 of N3
It is also possible to sum the pulse inputs from 33 and integrate the probabilities.

The natural integration of the probabilities received from the two neurons described above is possible because the coupling has two parameters of a specific electric potential and a specific frequency. Due to the existence of these two parameters, the probability of the knowledge and the reliability are clarified, and the evaluation of the knowledge itself, for example, whether or not the reliability needs to be increased, can be evaluated, which is very effective.

In this embodiment, the effect has been described for a neuron capable of outputting three values of 1, 0, -1 and a neural network having a connection for holding a specific potential and frequency. A large effect can be obtained even with a neural network that is equipped with a neuron that can output three values of 0 and -1, and a connection that holds a specific electric potential and frequency.

For example, even if the connection holds only the parameter a and the upstream neuron continues to output a specific potential to the downstream neuron, the value of the parameter a is set to 0 when the reliability of the connection is low. , A neural network having neurons capable of taking three outputs of -1, 0, and 1 can be obtained by using a neuron whose state becomes 0 when the potential input from the connection is 0. In such a neural network, since the state of the neuron becomes 0 when the reliability of the connection, that is, the knowledge is low, it is natural that the reliability of the probability can be obtained from the state of the neuron.

Even if the neuron can output only binary values of 1 and -1, if the connection gives a specific potential to the neuron at a specific frequency, the neuron outputs the potential from the connection. If the neuron is set to 1 with a probability of 0.5 when it is not received, it is possible to represent the P ′ in a pseudo manner with the probability that the state of the neuron is 1. Of course, such a neural network also takes reliability into consideration, and has the effect of safety and reliability that conventional neural networks do not have.

As described in this embodiment, 1, 0,
If the neural network is provided with a neuron that can output three values of -1 and a connection that holds a specific potential and frequency, the reliability of the connection can be more accurately reflected in the neuron, and the effect will be greater. .

Next, a method of learning the two parameters of the combination will be described. Although it is possible to empirically determine two parameters and perform inference using a neural network without using this learning method, the method described here can be used to easily and properly calculate the two parameter values of the combination. Can be obtained.

In order to carry out learning, first, raw data on which knowledge is based is prepared. Explaining the example of the neural network that infers the rainfall from the rain cloud described above, the past record of the presence or absence of rainfall 1 hour after the rain cloud is the raw data. Suppose this raw data is as follows.

It rained 1 hour after the rain cloud = 20 times; it did not rain 1 hour after the rain cloud = 5 times; When such raw data was obtained, parameters a and b were set as follows. If decided, the two parameters of W13 can be acquired very easily. One hour after the rain cloud, it means that N3 is 1 when N1 is 1.
It means that it was N3 and that it did not rain.
That was 1. In this learning method, the ratio of the number of times that the upstream neuron of the connection is 1 to the downstream neuron of the connection to the total number of times of the raw data is P. Therefore, in the rain cloud example above, P is 0.8.

(P) = (Number of rains: 20 times) /
(Total number of times: 25 times); Parameter a is inversely obtained from the state change rule of the neuron used in the neural network. As described above, the relationship between the input of the neuron and the probability that the neuron becomes 1 is a sigmoid curve as shown in FIG. 4, so that the parameter a is the value on the horizontal axis corresponding to P with P on the vertical axis. And

The parameter b is a value that has a positive correlation with the number of raw data, and the slope gradually becomes gentle and the value approaches 1 as the number of raw data increases. This makes it possible to obtain a value suitable for realistic inference that the reliability increases as the number of raw data increases. FIG. 6 shows an example of the relationship between the number of raw data and the parameter b.

The above-described learning of the connection is usually performed by treating the raw data as a teacher signal and modifying the parameters a and b of the connection at the learning stage of the neural network. At the learning stage, the neural network is constrained by raw data, and the connection between the constrained neurons is modified so that the parameters a and b become the values obtained by the above calculation method according to the constrained neuron values. Of. By using this method, from the raw data,
It is possible to generate knowledge of reliability corresponding to the number of raw data and express it as a neural network, and easily perform realistic inference considering the reliability of the knowledge.

In the present invention, the two eigenvalues held by the bond are the specific potential to be output and the specific frequency of outputting the potential, but they do not necessarily have to be these values directly. For example, the connection is made to hold two positive values, that is, a parameter c that shows a tendency to set the output neuron to 1 and a parameter d that shows a tendency to set the output neuron to 1.
It is also possible to obtain b.

(Parameter a) = (Parameter c) /
(Parameter d); (Parameter b) = (Parameter c) + (Parameter d); That is, the neural network has the same value as that of the present invention as long as the connection holds a parameter that indirectly determines a specific potential and frequency. is there.

The values of 1, 0, -1, etc. used in the present invention are the simplest values, and other values have the same effect as long as the basic principle of the present invention that the neuron takes a ternary state. Obtainable. For example, to take a ternary value of 2, 1, 0, or a ternary value of 2, 0, -2 is essentially 1, simply by adding an offset or increasing the value.
It can be seen to be similar to 0, -1. That is,
Even if the value of the output of the neuron and the sign of the positive and negative are different,
As long as the basic principle of the present invention that the neuron takes a ternary state, the neural network is equivalent to the present invention.

The method of multiplication, addition, and sum used in the present invention does not simply mean the accumulation of two numerical values, but includes a wide range of mathematically equivalent operations.

[0047]

Since the present invention is configured as described above, it has the following effects.

Since the state of the neuron can take three values of -1, 0, 1 in the neural network, for example, (probability of phenomenon) = (probability that neuron becomes 1) /
(Similarly, probability of becoming −1); (Probability of probability of phenomenon) = (Probability that neuron is not 0); and, in addition to probability of phenomenon, reliability of probability is expressed on the network. It becomes possible to do. With this ability, it is possible to judge how reliable the prediction of the neural network is, for example, in the case of predicting the safety factor of a phenomenon, and when the reliability of the prediction is low, a person can make a judgment or It is possible to implement a flexible response such as taking a certain measure to secure the prediction, and it becomes possible to use a neural network with high safety and reliability.

[Brief description of drawings]

FIG. 1 is a diagram showing a neural network of an embodiment.

FIG. 2A is a diagram showing an example of a pulse signal generated by the coupling. FIG. 2B is a diagram showing an example of a pulse signal generated by the coupling when the parameter a is 0.

FIG. 3 is a diagram showing an example of a total value of pulse signals input to a neuron.

FIG. 4 is a diagram showing an example of a relationship between a pulse potential input to a neuron and a probability that the neuron becomes 1.

FIG. 5 is a diagram showing an example of neuron states.

FIG. 6 is a diagram showing an example of the relationship between the number of raw data and the parameter b in the learning stage of neurons.

FIG. 7 is a block diagram of a Boltzmann machine that is an example of a conventional neural network.

[Explanation of symbols]

 N1 neuron N2 neuron N3 neuron W13 connection W12 connection W23 connection N33 threshold neuron W33 threshold neuron connection

Claims (4)

[Claims] 1. A neuron that stochastically determines an output value according to an input pulse signal, and a coupling that converts the output of the neuron into a pulse signal and outputs the pulse signal so as to be an input of another neuron. , A neural network characterized in that the output of the neuron can take three values of 1 or 0 or -1, depending on the potential input from the connection to the neuron. 2. When the output of an upstream neuron that provides an output to the connection is 1, the connection provides a specific potential as an output to a downstream neuron that provides the output, and the connection provides the downstream neuron. 2. The neural network according to claim 1, wherein the potential and its frequency are unique values of each of the connections forming the neural network. 3. A neuron that stochastically determines an output value according to an input pulse signal, and a coupling that converts the output of the neuron into a pulse signal and outputs the pulse signal so as to be an input of another neuron. , When the output of an upstream neuron that gives an output to the connection is 1, the connection gives a specific potential as an output to a downstream neuron which the output gives the output, and the potential given to the downstream neuron by the connection. Neural network characterized in that the frequency is a unique value of each of the connections that make up the neural network. 4. A neuron for probabilistically determining an output value according to an input pulse signal, and a coupling for converting the output of the neuron into a pulse signal and outputting the pulse signal so as to be an input of another neuron. , When the output of an upstream neuron that gives an output to the connection is 1, the connection gives a specific potential as an output to a downstream neuron which the output gives the output, and the potential given to the downstream neuron by the connection. The frequency is a learning method of the connection of the neural network, which is a unique value of each of the connections forming the neural network. When the output of is bound multiple times by the teacher signal, two neurons at both ends of the connection The parameter a, which determines the output potential of the downstream neuron whose pulse is output by the ron and the connection, and which has a positive correlation with the probability that the downstream neuron is 1 when the output of the upstream neuron is 1 as the teacher signal. And a parameter b that determines the frequency of output has a positive correlation with the number of times both upstream and downstream neurons are constrained by the teacher signal.