CN102034133A - Quantum neural network-based comprehensive evaluation method for multi-factor system - Google Patents

Abstract

A kind of integrated evaluating method of the multifactor system based on quantum nerve network, comprising the following steps: 1) set multiple feed-forward type quantum neurons of the multifactor system; 2) quantum register of a n quantum bits is prepared; 3) by quantum register | 0 amp; amp; gt; Or | 1 amp; amp; gt; As the receiver user because of the input of prime number,

It is exported for it

4) parallel computation operator O is set, the output quantum state of multifactor system comprehensive evaluation method is used for, evolution is updated to it; 5) until the variation before updated output quantum state and update is in the error range of permission, i.e., network state is stablized, and transmission information sequence corresponding to output quantum state at this time is the testing result of multifactor system.

Description

A kind of integrated evaluating method of the multifactor system based on quantum nerve network

Technical field

The present invention relates to complication system comprehensive evaluation field, especially a kind of integrated evaluating method of multifactor system.

Background technology

Integrated evaluating method commonly used in the traffic system evaluation both at home and abroad can be divided on the whole: expert assessment method, economic analysis method, operational research Methods and other mathematical methods etc.Neural network is because its massively parallel processing, fault-tolerance, self-organization and characteristics such as adaptive ability and association function, become the strong instrument of dealing with problems, to breaking through the bottleneck of existing science and technology, the non-linear complicated phenomenon that waits of more deep exploration has played great function, is widely used in many scientific domains.The researchist is applied to comprehensive evaluation to neural network model and also inquires into according to its characteristics.

Important component part as artificial intelligence, subjectivity when neural net method can be avoided determining the index weight, and by study to given sample mode, obtain the experience of evaluation experts, knowledge, subjective judgement reaches the tendency to target importance, when the objective system beyond needing sample mode is made comprehensive evaluation, this method just can be reproduced the experience of evaluation experts, knowledge and intuitive thought, thereby realize effective combination of quantitative test and qualitative analysis, guarantee the advantages of estimating such as objectivity preferably, in nearly 20 years, attracted a large amount of experts and scholars' sight.Yet along with the dark people who uses promotes and the emerging in large numbers day by day of practical problems, traditional neural network model that network structure is single has relatively also shown many disadvantages and deficiency gradually, for example intrinsic pace of learning slowly, catastrophe memory loss or the like.In order to overcome neural limitation and the deficiency of calculating, scholars wish to have new theory to combine with neural calculating, improve the neural calculated performance of calculating in itself.Thus, the neural calculating of quantum just grows up.

Nineteen ninety-five, professor Kak of the U.S. proposed the neural notion of calculating of quantum first, and some scholars have proposed quantum nerve network models such as quantum derivative neural network, quantum dot neural network, quantum entanglement neural network afterwards.Studies show that, quantum nerve network is owing to utilized quantum estimated performances such as quantum is parallel, quantum entanglement, be better than ANN in aspect performances such as memory capacity and processing speeds, have the parallel processing capability stronger and also can handle more large data collection than ANN, and can solve the unaccountable problem of some ANN, can't find the solution linear inseparable problem etc. as catastrophe memory loss problem, monolayer neural networks.In recent years, the research of quantum nerve network was active day by day, and in pattern-recognition, tangle aspects such as calculatings, approximation to function and obtain Preliminary Applications, report still rare but quantum nerve network is applied to Research of Comprehensive.

Kouda adopts a quantum phase shift door of simulation and two quantum controlled not-gates, has proposed the neural network based on the quantum door.This network complex representation quantum state by the simulation to the quantum door, demonstrates learning ability preferably.But learning algorithm is comparatively complicated, and is particularly when using the gradient coaching method, comparatively loaded down with trivial details to the calculating of plural arc tangent differentiate, not high for the network test accuracy of some classification problems, and net training time is longer.

Summary of the invention

For the deficiency that calculating is loaded down with trivial details, accuracy is not high, the training time is long of the evaluation method that overcomes existing multifactor system, the invention provides a kind ofly simplify calculatings, improve accuracy, the integrated evaluating method of shortening training time based on the multifactor system of quantum nerve network.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of integrated evaluating method of the multifactor system based on quantum nerve network, described integrated evaluating method may further comprise the steps:

1) a plurality of feed-forward type quantum neurons of the described multifactor system of setting, wherein, each neuronic structural similarity, be input as n position quantum bit, n is a natural number, it is n position quantum register, be output as 1 quantum register, the output of preceding m quantum neuron is imported as the feedforward of m+1 feedforward property quantum neuron simultaneously, m is a natural number, and the threshold value of feedforward property quantum neuron also is a n position quantum bit, and the connection weight of feed-forward type quantum neuron is the matrix of a n*n, the evolution operator F of feed-forward type quantum neuron is an operator that acts on the quantum register of n position, the evolution of control feed-forward type quantum neuron state;

2) quantum register of a n position quantum bit of preparation, the state of quantum neuron is U, U=0 or U=1 use respectively | and 0〉or | 1〉represent;

3) with quantum register | 0〉or | 1〉as the input of the factor number of this receiver user,

Be its output

4) set parallel computation operator O, use it for the output quantum state of multifactor system synthesis evaluation method, it is upgraded evolution;

5) variation before output quantum state after upgrading and the renewal is in the error range that allows, and promptly network state is stable, and the pairing transmission information sequence of output quantum state of this moment is the testing result of multifactor system.

As preferred a kind of scheme: in the described step 3), the multifactor detecting device of set amount sub neural network, function F (θ) obtains the up-to-date state of neuron according to neuronic phase angle, adopts the complex representation method, is expressed as:

F(θ)＝e ^iθ＝cosθ+sinθ·i. (7)

In the formula (7), with " 1 " expression | 0 〉, with " i " expression | 1 〉.

Further, in the described step 4), the set amount sub neural network is 3 layers of feedforward quantum nerve network, hidden layer adopts the described feed-forward type quantum neuron of step 1), output layer neuronal activation function adopts the S function, and linear function is adopted in modeling, the following expression of processing procedure:

${U_j}^{\left(p\right)}=S(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_j}^{\left(p\right)}{w}_{\mathrm{ij}}-{\mathrm{\θ}}_j)---\left(8\right)$

${V_j}^{\left(p\right)}=F(\frac{\mathrm{\π}}{2}{U_j}^{\left(p\right)}-2\mathrm{\πS}\left({\mathrm{\δ}}_j\right))---\left(9\right)$

y _j ^(p)＝Im(V _j ^(p)) (10)

${O_K}^{\left(p\right)}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y_j}^{\left(p\right)}{w}_{\mathrm{jk}}-{\mathrm{\θ}}_k---\left(11\right)$

Wherein: x _j ^(p)Represent i input of p sample, n is the number of input neuron, w _IjI neuron of expression input layer is to j neuronic weights of input hidden layer, θ _jBe hidden layer j neuronic threshold value, s () is the sigmoidal function, 0.5 π U _j ^(p)Be p sample hidden layer j neuronic control quantum bit phase, 2 π * S (δ _j) the corresponding neuronic work quantum bit phase of expression, Im is for asking imaginary part, V _j ^(p)Be the state that j neuron expression of p sample hidden layer comes out, y _j ^(p)Be j neuron real output value of p sample hidden layer, θ _kBe output layer k neuronic threshold value, w _JkJ neuron of expression hidden layer is to output layer k neuronic weights, O _K ^(p)Represent k output layer neuron output of p sample, m represents the number of hidden layer neuron;

Adopt the gradient coaching method that network is developed to train and calculate, the objective function of study is:

$J=\frac{1}{2}\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{(d_k^{\left(p\right)}-o_k^{\left(p\right)})}^2---\left(12\right)$

In the formula, For the desirable output of network, p are that pattern sample number, l are network output neuron number;

The adjustment formula of weights and phase shift parameters is as (13)-(15):

$\mathrm{\Δ}{w}_{\mathrm{jk}}={\mathrm{\η}}_w\underset{p=1}{\overset{p}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)}){\mathrm{gy}}_j^{\left(p\right)}---\left(13\right)$

$\mathrm{\Δ}{\mathrm{\δ}}_j={\mathrm{\η}}_{\mathrm{\δ}}\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)})w_{\mathrm{jk}}\mathrm{Im}\left(V_j^{\left(p\right)}\right)\mathrm{Im}\left(V_j^{\left(p\right)}\mathrm{gi}\right)S\left({\mathrm{\δ}}_j\right)(1-S\left({\mathrm{\δ}}_j\right))---\left(14\right)$

$\mathrm{\Δ}{w}_{\mathrm{jk}}={\mathrm{\η}}_k\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)})w_{\mathrm{jk}}{U}_j^{\left(p\right)}(1-U_j^{\left(p\right)})x_i^{\left(p\right)}\mathrm{Im}\left(V_j^{\left(p\right)}\right)\mathrm{Im}\left(V_j^{\left(p\right)}\mathrm{gi}\right)---\left(15\right)$

Wherein: η _wBe learning rate, η _δBe the phase shift regulation rate, θ _kRegard that having increased by one is output as 1 hidden layer neuron and weights between each output layer neuron of k as, with w _JkUpgrade together; θ _jRegarding as has increased weights that are output as between 1 input layer and j the hidden layer neuron, with w _IjUpgrade together.

Technical conceive of the present invention is: the present invention has proposed the computation model and the quantum nerve network comprehensive evaluation model of new quantum neuron on the basis of Kouda research, in the framework of quantum theory, explained neuronic information processing mechanism.Three layers of neuron models network and classical neuron models network that feedforward neural network contrast Kouda proposes that this model is formed, the result of test demonstrates this network and has learning ability preferably, training time is short, the computational accuracy height, afterwards, modeling detects the fast public traffic system implementation result and shows to the fast public traffic system Comprehensive Evaluation Problem to adopt network that this neuron forms, adopts the network of quantum neuron to have stronger generalization ability.

Quantum nerve network is constituted detecting device, receiver and the processor of multifactor system evaluation factor, its core is to adopt a plurality of feed-forward type quantum neurons that the multifactor system evaluation problem factor of carrying out is decomposed, thereby the structure that simplified system is estimated, network evolution utilizes quantum parallel computation characteristic to carry out fast seeking, reduces the complexity of multifactor system evaluation problem.

Beneficial effect of the present invention mainly shows: 1, constitute the multifactor system synthesis evaluation model of quantum nerve network by adopting a plurality of quantum neurons to substitute traditional BP neural network, multifactor network structure is simple, and complexity is low; 2, the multifactor system synthesis evaluation method of quantum nerve network is in the evolution of network state, can utilize quantum parallel computation characteristic to make optimizing speed by exponential raising, computer artificial result shows that the designed multifactor system synthesis evaluation method of the quantum nerve network performance of the present invention is better than classical neural net method; Adopt multifactor its performance of system synthesis evaluation method of a plurality of neuronic improved quantum nerve networks to be better than adopting the multifactor system synthesis evaluation method of single neuronic quantum nerve network.

Description of drawings

Fig. 1 is that quantum nerve network is used for the process flow diagram that multifactor system synthesis is estimated;

Fig. 2 is a feedforward property quantum neuron model;

Fig. 3 is that quantum nerve network is used for multifactor system synthesis evaluation model.

Embodiment

Below in conjunction with accompanying drawing the present invention is described further.

With reference to Fig. 1～Fig. 3, a kind of multifactor system synthesis evaluation method based on quantum nerve network, in the classic computer The Realization of Simulation this method, designed a kind of feedforward quantum neuron and shown multifactor receiver received signal, designed multifactor detecting device on this basis based on quantum nerve network with the quantum register tables.

The concrete steps that quantum nerve network is used for the implementation method that multifactor system synthesis estimates as shown in Figure 1, detailed process is as follows:

1): design a plurality of feed-forward type quantum neuron models

The designed single feedforward quantum neuron model of the present invention as shown in Figure 2, QNN is output as 1 quantum bit among the figure.

w ₁, w ₂..., w _n: the probability when going out state of activation for contiguous neuron is expressed; S (∑): probable value and the weights comprehensively received of ∑ wherein, do simple addition, S () is the sigmoidal function, and the integrated information of collecting is transformed in [0,1] scope, is the starting stage that produces control quantum bit phase; 0.5 π * U: the phase place that produces the control quantum bit.2 π * S (δ): the phase place of inside neurons state, δ is the adjusting parameter of phase place; F (θ): according to the control quantum bit, the state after neuron state changes adopts the complex representation method; M: observation, the probability during with the neuronal activation state is expressed, as neuronic information output.

Compare with traditional neural network, the structure of quantum nerve network is basic identical, and different is that it represents information with the quantum state phase place, and the effect of the weights of network is that phase place is rotated variation, excitation function is to the controlled non-door operation of phase place, by changing the purpose that quantum state reaches computing.

2): design and a kind ofly represent that with quantum register multifactor receiver comes received signal

Prepare a quantum register of being made up of n position quantum bit, neuronic input information is U, and U=0 or U=1 use respectively | 0〉or | 1〉represent.

3): design a multifactor detecting device of quantum nerve network

Suppose, if neuronic state is

The phase angle of this moment is 2 π S (δ) (S is the sigmoidal function, and δ regulates parameter), and is specific as follows:

If the control quantum bit is | 0〉(U=0), according to the account form of Fig. 2, the phase angle of neuron state becomes-2 π S (δ), and this moment, neuronic state was:

As can be seen, neuron state has identical observability with its initial state.From the angle of measuring, neuronic state does not change, if the control quantum bit is | 1 〉, then neuronic phase angle becomes

Neuronic state is:

This moment, neuronic state was reversed.

If control quantum bit

Neuron state is represented with formula (1), the principle of work of pressing controlled not-gate, and the probability when the gained neuron is activated state is:

$\cos \left(\frac{\mathrm{\π}}{2}{U}^2\right)\sin \left(2\mathrm{\πS}{\left(\mathrm{\δ}\right)}^2\right)+\sin \left(\frac{\mathrm{\π}}{2}{U}^2\right)\cos \left(2\mathrm{\πS}{\left(\mathrm{\δ}\right)}^2\right).---\left(4\right)$

Probability when being activated state by the neuron of Fig. 2 working method gained is:

$\cos \left(\frac{\mathrm{\π}}{2}{U}^2\right)\sin \left(2\mathrm{\πS}{\left(\mathrm{\δ}\right)}^2\right)\sin \left(\frac{\mathrm{\π}}{2}{U}^2\right)\cos \left(2\mathrm{\πS}{\left(\mathrm{\δ}\right)}^2\right)-2\sin \left(\frac{\mathrm{\π}}{2}U\right)\cos \left(2\mathrm{\πS}\left(\mathrm{\δ}\right)\right)\cos \left(\frac{\mathrm{\π}}{2}U\right)\left(2\mathrm{\πS}\left(\mathrm{\δ}\right)\right)---\left(5\right)$

Obviously, when U=1 and U=0, Fig. 2 simulates controlled not-gate fully, and in 0＜U＜1 o'clock, Fig. 2 only is the approximate simulation controlled not-gate, rather than simulates controlled not-gate fully, and both differ

$-2\sin \left(\frac{\mathrm{\π}}{2}U\right)\cos \left(2\mathrm{\πS}\left(\mathrm{\δ}\right)\right)\cos \left(\frac{\mathrm{\π}}{2}U\right)\left(2\mathrm{\πS}\left(\mathrm{\δ}\right)\right).---\left(6\right)$

Formula (6) is considered to be in the penalty term that the quantum neuron state is overturn fully, and function F among Fig. 2 (θ) obtains the up-to-date state of neuron according to neuronic phase angle, and the present invention adopts the complex representation method.

F(θ)＝e ^iθ＝cosθ+sinθ·i. (7)

Represent with " 1 " in the formula (7) | 0 〉, with " i " expression | 1 〉.

4): design a parallel computation operator and carry out EVOLUTIONARY COMPUTATION

Designing a parallel computation operator is O, parallel as follows with EVOLUTIONARY COMPUTATION:

Here mainly introduce 3 layers of feedforward quantum nerve network, the quantum neuron that hidden layer adopts a last joint to propose, output layer neuronal activation function is used for classification, adopts the S function, and linear function is adopted in modeling, the following expression of information processing process:

${U_j}^{\left(p\right)}=S(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_j}^{\left(p\right)}{w}_{\mathrm{ij}}-{\mathrm{\θ}}_j)---\left(8\right)$

${V_j}^{\left(p\right)}=F(\frac{\mathrm{\π}}{2}{U_j}^{\left(p\right)}-2\mathrm{\πS}\left({\mathrm{\δ}}_j\right))---\left(9\right)$

y _j ^(p)＝Im(V _j ^(p)) (10)

${O_K}^{\left(p\right)}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y_j}^{\left(p\right)}{w}_{\mathrm{jk}}-{\mathrm{\θ}}_k---\left(11\right)$

Wherein: x _j ^(p)Represent i input of p sample, n is the number of input neuron, w _IjI neuron of expression input layer is to j neuronic weights of input hidden layer, θ _jBe hidden layer j neuronic threshold value, s () is the sigmoidal function, 0.5 π U _j ^(p)Be p sample hidden layer j neuronic control quantum bit phase, 2 π * S (δ _j) the corresponding neuronic work quantum bit phase of expression, Im is for asking imaginary part, V _j ^(p)Be the state that j neuron expression of p sample hidden layer comes out, y _j ^(p)Be j neuron real output value of p sample hidden layer, θ _kBe output layer k neuronic threshold value, w _JkJ neuron of expression hidden layer is to output layer k neuronic weights, O _K ^(p)Represent k output layer neuron output of p sample, m represents the number of hidden layer neuron.

Adopt the gradient coaching method that network is developed to train and calculate, the objective function of study is:

$J=\frac{1}{2}\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{(d_k^{\left(p\right)}-o_k^{\left(p\right)})}^2---\left(12\right)$

In the formula,

For the desirable output of network, p are that pattern sample number, l are network output neuron number.

The adjustment formula of weights and phase shift parameters is as (13)-(15).

$\mathrm{\Δ}{w}_{\mathrm{jk}}={\mathrm{\η}}_w\underset{p=1}{\overset{p}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)}){\mathrm{gy}}_j^{\left(p\right)}---\left(13\right)$

$\mathrm{\Δ}{\mathrm{\δ}}_j={\mathrm{\η}}_{\mathrm{\δ}}\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)})w_{\mathrm{jk}}\mathrm{Im}\left(V_j^{\left(p\right)}\right)\mathrm{Im}\left(V_j^{\left(p\right)}\mathrm{gi}\right)S\left({\mathrm{\δ}}_j\right)(1-S\left({\mathrm{\δ}}_j\right))---\left(14\right)$

$\mathrm{\Δ}{w}_{\mathrm{jk}}={\mathrm{\η}}_k\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)})w_{\mathrm{jk}}{U}_j^{\left(p\right)}(1-U_j^{\left(p\right)})x_i^{\left(p\right)}\mathrm{Im}\left(V_j^{\left(p\right)}\right)\mathrm{Im}\left(V_j^{\left(p\right)}\mathrm{gi}\right)---\left(15\right)$

Wherein: η _wBe learning rate, η _δBe the phase shift regulation rate, θ _kRegard that having increased by one is output as 1 hidden layer neuron and weights between each output layer neuron of k as, with w _JkUpgrade together; θ _jRegarding as has increased weights that are output as between 1 input layer and j the hidden layer neuron, with w _IjUpgrade together.

5): the integrated evaluating method of on classic computer, realizing quantum nerve network

Application example is a fast public traffic system, and emulation adopts the matlab instrument to carry out building of model, and quantum nerve network is used model that multifactor system synthesis estimates as shown in Figure 3.

Under three kinds of situations, BRT is carried out comprehensive evaluation emulation, be respectively, quantum neuron model and traditional BP neural network model based on improved quantum nerve network model.The result of phantom error shows: under the identical situation of target error, the time required based on the integrated evaluating method simulation training of quantum nerve network is less than traditional BP neural network and quantum neuron far away, its result's relative error and maximum relative error are all less, extensive effect is best, so the evaluation model that proposes is increasing substantially the accuracy requirement that can satisfy comprehensive evaluation under the situation of learning efficiency again fully.

Claims (3)

1. integrated evaluating method based on the multifactor system of quantum nerve network, it is characterized in that: described integrated evaluating method may further comprise the steps:

1) a plurality of feed-forward type quantum neurons of the described multifactor system of setting, wherein, each neuronic structural similarity, be input as n position quantum bit, n is a natural number, it is n position quantum register, be output as 1 quantum register, the output of preceding m quantum neuron is imported as the feedforward of m+1 feed-forward type quantum neuron simultaneously, m is a natural number, and the threshold value of feedforward property quantum neuron also is a n position quantum bit, and the connection weight of feed-forward type quantum neuron is the matrix of a n*n, the evolution operator F of feed-forward type quantum neuron is an operator that acts on the quantum register of n position, the evolution of control feed-forward type quantum neuron state;

2) quantum register of a n position quantum bit of preparation, the state of quantum neuron is U, U=0 or U=1 use respectively | and 0〉or | 1〉represent;

3) with quantum register | 0〉or | 1〉as the input of the factor number of this receiver user,

Be its output

4) set parallel computation operator O, use it for the output quantum state of multifactor system synthesis evaluation method, it is upgraded evolution;

5) variation before output quantum state after upgrading and the renewal is in the error range that allows, and promptly network state is stable, and the pairing transmission information sequence of output quantum state of this moment is the testing result of multifactor system.

2. the integrated evaluating method of the multifactor system based on quantum nerve network as claimed in claim 1, it is characterized in that: in the described step 3), the multifactor detecting device of set amount sub neural network, function F (θ) obtains the up-to-date state of neuron according to neuronic phase angle, adopt the complex representation method, be expressed as:

F(θ)＝e ^iθ＝cosθ+sinθ·i. (7)

In the formula (7), with " 1 " expression | 0 〉, with " i " expression | 1 〉.

3. the integrated evaluating method of the multifactor system based on quantum nerve network as claimed in claim 1 or 2, it is characterized in that: in the described step 4), the set amount sub neural network is 3 layers of feedforward quantum nerve network, hidden layer adopts the described feed-forward type quantum neuron of step 1), output layer neuronal activation function adopts the S function, linear function is adopted in modeling, the following expression of processing procedure:

${U_j}^{\left(p\right)}=S(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x_j}^{\left(p\right)}{w}_{\mathrm{ij}}-{\mathrm{\θ}}_j)---\left(8\right)$

${V_j}^{\left(p\right)}=F(\frac{\mathrm{\π}}{2}{U_j}^{\left(p\right)}-2\mathrm{\πS}\left({\mathrm{\δ}}_j\right))---\left(9\right)$

y _j ^(p)＝Im(V _j ^(p)) (10)

${O_K}^{\left(p\right)}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y_j}^{\left(p\right)}{w}_{\mathrm{jk}}-{\mathrm{\θ}}_k---\left(11\right)$

Wherein: x _j ^(p)Represent i input of p sample, n is the number of input neuron, w _IjI neuron of expression input layer is to hidden layer j neuronic weights, θ _jBe hidden layer j neuronic threshold value, s () is the sigmoidal function, 0.5 π U _j ^(p)Be p sample hidden layer j neuronic control quantum bit phase, 2 π * S (δ _j) the corresponding neuronic work quantum bit phase of expression, Im is for asking imaginary part, V _j ^(p)Be the state that j neuron expression of p sample hidden layer comes out, y _j ^(p)Be j neuron real output value of p sample hidden layer, θ _kBe output layer k neuronic threshold value, w _JkJ neuron of expression hidden layer is to output layer k neuronic weights, O _K ^(p)Represent k output layer neuron output of p sample, m represents the number of hidden layer neuron;

Adopt the gradient coaching method that network is developed to train and calculate, the objective function of study is:

$J=\frac{1}{2}\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{(d_k^{\left(p\right)}-o_k^{\left(p\right)})}^2---\left(12\right)$

In the formula,

For the desirable output of network, p are that pattern sample number, l are network output neuron number;

The adjustment formula of weights and phase shift parameters is as (13)-(15):

$\mathrm{\Δ}{w}_{\mathrm{jk}}={\mathrm{\η}}_w\underset{p=1}{\overset{p}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)}){\mathrm{gy}}_j^{\left(p\right)}---\left(13\right)$

$\mathrm{\Δ}{\mathrm{\δ}}_j={\mathrm{\η}}_{\mathrm{\δ}}\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)})w_{\mathrm{jk}}\mathrm{Im}\left(V_j^{\left(p\right)}\right)\mathrm{Im}\left(V_j^{\left(p\right)}\mathrm{gi}\right)S\left({\mathrm{\δ}}_j\right)(1-S\left({\mathrm{\δ}}_j\right))---\left(14\right)$

$\mathrm{\Δ}{w}_{\mathrm{jk}}={\mathrm{\η}}_k\underset{p=1}{\overset{p}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}(d_k^{\left(p\right)}-o_k^{\left(p\right)})w_{\mathrm{jk}}{U}_j^{\left(p\right)}(1-U_j^{\left(p\right)})x_i^{\left(p\right)}\mathrm{Im}\left(V_j^{\left(p\right)}\right)\mathrm{Im}\left(V_j^{\left(p\right)}\mathrm{gi}\right)---\left(15\right)$

Wherein: η _wBe learning rate, η _δBe the phase shift regulation rate, θ _kRegard that having increased by one is output as 1 hidden layer neuron and weights between each output layer neuron of k as, with w _JkUpgrade together; θ _jRegarding as has increased weights that are output as between 1 input layer and j the hidden layer neuron, with w _IjUpgrade together.

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