Method for improving calculation performance of optical reserve pool based on high-dimensional data input time delay

Abstract

The invention discloses an optical reserve pool calculation performance improvement method based on high-dimensional data input time delay, and the method specifically comprises the steps: integrating input information and input information at a previous moment, and expanding the integrated information into D-dimensional input data; uD is obtained according to the delay embedding theory, a data sequence composed of the D-dimensional data and diagonal elements multiplied by the sequence of the moment and the sequence of the previous moment is used as 2D-1-dimensional input data, a corresponding random mask should be expanded into a corresponding dimension, and then the dimension is multiplied by a scaling factor gamma to obtain S (t); training the obtained high-dimensional data in a reservoir layer, and in the training stage, driving a reservoir computer by using an input signal S (t) to generate a reservoir computer output signal y (t); and through the time delay light reserve pool, a ridge regression calculation method is adopted to obtain a prediction result. According to the method, prediction errors are greatly reduced, and the performance of a reservoir computing system is improved.

Description

Technical Field

[0001] The present invention belongs to the field of time-delay optical reservoir computing, and particularly relates to a method for improving the computing performance of time-delay optical reservoir computing based on high-dimensional data input. Background Art

[0002] Reservoir computing is a new neural network computing method introduced in the early 21st century, which is particularly suitable for processing time-related inputs and can exhibit leading performance in tasks such as speech recognition and time series prediction. The reservoir in the optoelectronic system was first proposed by Larger et al. and implemented through hardware. Different from traditional reservoirs that use complex random neural networks to process time series data, time-delay reservoirs simplify the network structure by introducing delay loops and effectively capture historical information in time series data, making them particularly suitable for dealing with time series problems with obvious time dependence. In a time-delay reservoir system, nonlinear nodes usually use modulators, such as phase modulators or Mach-Zehnder modulators, etc., to achieve the nonlinear effect in the loop. Time-delay optical reservoir computing based on semiconductor optical amplifiers has the advantages of strong parallelism, high computing rate, and low energy consumption, and has currently received extensive attention from scholars at home and abroad.

[0003] The traditional reservoir structure consists of three parts: an input layer, a reservoir layer, and an output layer. Among them, the input layer is used for information input; in the reservoir layer, information is processed and the node states are output. The node states are affected by the node states at the previous moment and can be memorized and stored within a certain period of time; the output layer collects the output node states and trains them to obtain appropriate weights. According to the previous signal input into the reservoir and output a predicted signal, it is a single-step prediction task. In order to achieve multi-step prediction on this basis, due to its complex nonlinearity and insufficient information, it is a challenging task to perform multi-step prediction only based on the nonlinear dynamic system of short-term time series. In recent years, the multi-step prediction research of time-delay reservoirs based on semiconductor lasers has input high-dimensional data. The dynamics of high-dimensional variables are intertwined with each other, which improves the nonlinearity of the system and enriches the information. Therefore, multi-step prediction tasks can be achieved, and the prediction effect is significantly improved compared with traditional reservoirs. Predicting future states based on short-term high-dimensional series is natural and important and can also be widely used in the real world.

[0004] Due to the time-varying and non-stationary nature of many real-world dynamic systems, recent short-term time series usually contain more information about their nearest future evolution than time series from the distant past. Even if long-term data is measured, the prediction effectiveness mainly depends on the recent short-term data. On the other hand, due to the dynamic intertwining of high-dimensional variables, the nonlinearity of the system is enhanced. Therefore, short-term but high-dimensional data can be used for prediction. Summary of the Invention

[0005] In view of the above problems, the present invention provides a method for improving the computational performance of a time-delay optical reservoir computer based on high-dimensional data input.

[0006] A method for improving the computational performance of a time-delay optical reservoir computer based on high-dimensional data input according to the present invention is specifically as follows:

[0007] Integrate the input information u(t) and the input information at previous times, and expand it into a D-dimensional input data; according to the delay embedding theory, we get U D = u(t), u(t - 1), …, u(t - D + 1), and use the data sequence composed of the diagonal elements of the multiplication of this D-dimensional data and the sequence at this moment and the previous moment as the 2D - 1-dimensional input data. The corresponding random mask should be expanded to the corresponding dimension, and then multiplied by the scaling factor γ to obtain S(t), S(t) = γ × U D × mask(t), γ adjusts the standard deviation of the mask, mask(t) represents the random mask, which is a D × N matrix, and N represents the number of virtual nodes, so as to meet the definition of matrix operations.

[0008] Input the obtained high-dimensional data into the reservoir layer for training. In the training stage, use the input signal S(t) to drive the reservoir computer to generate the output signal y(t) of the reservoir computer; if we want to predict L steps, the output weight is ω out ; After passing through the time-delay optical reservoir, in order to avoid overfitting, the method of ridge regression calculation is adopted to obtain the prediction result.

[0009] The response lasers in the reservoir are affected by optical feedback and optical injection, and the rate equation is expressed as:

[0010]

[0011] Where E r (t), N r (t) respectively represent the slow-varying electric field intensity and carrier density of the response laser, respectively represent the differentials of E r (t), N r (t) with respect to time t. α is the linewidth factor, i is the imaginary unit, G N is the gain parameter, N0 is the carrier density during the transparent period, ε is the saturation gain coefficient, τ p , τ s are the photon and carrier lifetimes respectively, τ is the delay time, J r is the injection current of the response laser, the second term represents the influence of information injection in the input layer on the laser, and the third term represents the influence when the laser is self-feedback, where v0 represents the output frequency of the response laser, and Δv s represents the frequency difference between the light source and the response laser, E s(t) is the signal after optical modulation, and k s is the injection intensity of the light source, and k f is the self - feedback intensity of the laser.

[0012] The beneficial technical effects of the present invention are as follows:

[0013] By expanding the input data into high - dimensions in the present invention, rich input information is added. Through non - linear combination, the non - linearity of the system is increased. After the training of the time - delay optical reservoir, the computational amount of the system is reduced, and the result of predicting multiple steps with a small error is achieved. The prediction error is greatly reduced, and the performance of the reservoir computing system is improved. Description of the Drawings

[0014] Figure 1 is the principle block diagram of the method for improving the computing performance of the time - delay optical reservoir based on high - dimensional data input of the present invention.

[0015] Figure 2 is the prediction error corresponding to 20 steps of one - dimensional input data and D - dimensional input data.

[0016] Figure 3 is the prediction error corresponding to 20 steps of 2D - 1 - dimensional input data. Detailed Embodiments

[0017] The following further elaborates on the present invention in detail with reference to the drawings and specific implementation methods.

[0018] A method for improving the computing performance of the time - delay optical reservoir based on high - dimensional data input in the present invention expands the input data into a high - dimensional sequence. According to the delay embedding theory, u(t), u(t - 1), …, u(t - D + 1) are composed into D - dimensions as high - dimensional input data, and the data sequence composed of the diagonal elements of the product of this D - dimensional data and the sequence at this moment and the previous moment is used as 2D - 1 - dimensional input data. The corresponding random mask should be expanded to the corresponding dimension, and then multiplied by the scaling factor γ to obtain S(t). The obtained high - dimensional data is trained in the reservoir layer. The data passes through the delay loop, and the matrix composed of the states of all data is used to train the output weights. When predicting L steps after u(t), the corresponding weights are L - dimensional to ensure the rationality of matrix operations. Finally, the target data is fitted through the trained weights to facilitate the comparison of the prediction results of high - dimensional data. Because the prediction effectiveness mainly depends on the recent short - term data, when D is large, this periodic oscillation becomes smaller, and the prediction error increases with the increase of L. Due to the sensitive dependence of chaotic input data on the initial conditions, when the value of L is large, the L - step ahead prediction is more difficult, and it is necessary to control the dimension of the input information and the prediction steps to make the final prediction result optimal.

[0019] Embodiment:

[0020] The present invention changes the one-dimensional input data to D-dimensional input data, enhancing the memory effect of time series prediction tasks in reservoir computing. By referring to past input signals to correct memory loss, the past input signals are integrated into D dimensions by the delay embedding theory as the input, i.e., U D =[u(t), u(t - 1), …, u(t - D + 1)], as Figure 1 shown. By changing the dimension D, that is, changing the number of past inputs, through the time-delay optical reservoir, the training results are obtained to evaluate the normalized mean square error of the time series prediction task, i.e., NMSE. In the input layer, the input information is weighted. To ensure that each node of the signal can match the same mask, the generation time of the mask is set to T, indicating that a complete mask exists between (n - 1)T < t < nT, and the number of masks changes according to the dimension of the signal quantity. After the information processing in the input layer is completed, it is injected into the reservoir layer. The response lasers in the reservoir are affected by optical feedback and optical injection, and the rate equations are as follows:

[0021]

[0022] where E r (t), N r (t) represent the slow-varying electric field intensity and carrier density of the response laser respectively, respectively represent the differentials of E r (t), N r (t) with respect to time t. α is the linewidth factor, i is the imaginary unit, G N is the gain parameter, N0 is the carrier density during the transparency period, ε is the saturation gain coefficient, τ p , τ s are the photon and carrier lifetimes respectively, τ is the delay time, J r is the injection current of the response laser, the second term represents the influence of information injection in the input layer on the laser, and the third term represents the influence when the laser has self-feedback. Among them, v0 represents the output frequency of the response laser, Δv s represents the frequency difference between the light source and the response laser, E s (t) is the optically modulated signal, k s is the injection intensity of the light source, k f is the self-feedback intensity of the laser.

[0023] After passing through the time-delay optical reservoir, to avoid overfitting, the ridge regression calculation method is adopted to obtain the prediction results. Judged by the normalized mean square error, as Figure 2As shown, the dot curve represents the 20-step prediction error obtained from the reservoir computing of one-dimensional input data. Obviously, as the number of prediction steps increases, the prediction result becomes worse and worse, and the value of NMSE shows periodic fluctuations. This periodic curve corresponds to the autocorrelation function of the original chaotic input data. The autocorrelation function of the Sante-Fe sequence signal shows periodic changes. The square curve represents the 20-step prediction error obtained from the reservoir computing of one-dimensional input data. As D increases, not only can the prediction error be reduced, but the periodic fluctuations of NMSE will also slow down. Moreover, due to the sensitive dependence of chaotic input data on initial conditions, the prediction error will increase with the increase of L, and it is more difficult to predict L steps ahead.

[0024] The data is transformed into D-dimensional data as input according to the delay embedding theory to enhance the memory effect of the time series prediction task in reservoir computing, which has a significant improvement compared to the traditional reservoir computing. However, by combining past data, the nonlinearity of the entire system can be enhanced, which can further improve the prediction error. Nonlinear transformation is performed on past input data, such as u(t)×u(t - 1), and the diagonal elements are taken. This processing method has much better effect than linear transformation. Finally, 2D - 1 dimensional input information is constructed for information weighting, and the prediction error can be obtained through reservoir computing, as Figure 3 shown. Overall, the prediction error still increases with the increase of L, but the periodic fluctuations presented by NMSE become less obvious, and the prediction result has been greatly improved. Even the prediction for the next 20 steps can be maintained below 0.1.

Claims

1. A method for improving the computational performance of a time-delay optical reservoir computer based on high-dimensional data input, characterized in that Specifically: Integrate the input information u(t) and the input information at previous times, and expand it into a D-dimensional input data; according to the delay embedding theory, we get U D = u(t), u(t - 1), …, u(t - D + 1), and use the data sequence composed of the diagonal elements obtained by multiplying the D-dimensional data by the sequence at this moment and the previous moment as the 2D - 1-dimensional input data. The corresponding random mask should be expanded to the corresponding dimension and then multiplied by the scaling factor γ to obtain S(t), S(t) = γ × U D × mask(t). γ adjusts the standard deviation of the mask. mask(t) represents the random mask and is a D × N matrix, where N represents the number of virtual nodes, to meet the definition of matrix operations; The obtained high-dimensional data is sent to the reservoir layer for training. During the training phase, the reservoir computer is driven by the input signal S(t) to generate the output signal y(t) of the reservoir computer. If we want to predict L steps, the output weight is ω out ; After passing through the time-delay optical reservoir, in order to avoid overfitting, the ridge regression calculation method is adopted to obtain the prediction result.

2. A method for improving the computing performance of a time-delay optical reservoir computing based on high-dimensional data input according to claim 1, characterized in that The response laser in the reservoir is affected by optical feedback and optical injection, and the rate equation is expressed as: where E r (t), N r (t) represent the slowly varying electric field strength and carrier density of the response laser respectively, respectively represent the derivatives of E r (t) and N r (t) with respect to time t; α is the linewidth factor, i is the imaginary unit, G N is the gain parameter, N0 is the carrier density during the transparency period, ε is the saturation gain coefficient, τ p , τ s are the photon and carrier lifetimes respectively, τ is the delay time, J r is the injection current of the response laser. The second term represents the influence of information injection in the input layer on the laser, and the third term represents the influence received during the self - feedback of the laser. Among them, v0 represents the output frequency of the response laser, Δv s represents the frequency difference between the light source and the response laser, E s (t) is the signal after optical modulation, k s is the injection intensity of the light source, k f is the self - feedback intensity of the laser.

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