Single-layer phase-controlled diffraction deep neural network optimization method

Abstract

The present invention proposes a single-layer phase-controlled diffraction deep neural network optimization method, which belongs to the field of diffraction optics and deep learning technology. First, the physical structure parameters are set, including the wavelength of the incident light, the size of the diffraction unit, the size of the diffraction layer, and the distance between the diffraction layer and the input and output planes; according to the Rayleigh-Sommerfeld diffraction formula, the complex amplitude of the light wave propagating in the free space before and after the diffraction layer is numerically solved; the complex amplitude that passes through the diffraction layer and reaches the output plane is converted into light intensity and then normalized, and the regional intensity corresponding to each category is used to calculate the cross entropy loss function value; the stochastic gradient descent algorithm is used to implement the update of the diffraction layer parameters; finally, the single-layer phase-controlled diffraction deep neural network is applied to the classification task and the performance is tested. The present invention simplifies the cascaded diffraction layer structure without losing the model performance through an improved model optimization method, while effectively reducing the insertion loss and promoting the practical application of the diffraction deep neural network.

Description

Technical Field

[0001] The present invention relates to the field of diffraction optics and deep learning technology, and in particular to a single-layer phase-controlled diffraction deep neural network optimization method. Background Art

[0002] The revival and development of artificial intelligence technology has brought about profound changes in people's lifestyles. Artificial intelligence technology represented by deep learning has been widely used in various fields, such as face recognition, speech recognition and machine translation. However, the traditional von Neumann computing architecture based on the storage and computing separation mechanism can no longer adapt to the current rapidly growing large-scale matrix computing needs. The resulting problems such as storage wall and power wall have gradually become important factors restricting the further promotion and application of deep learning technology. Therefore, academia and industry have been actively exploring potential technologies for the next generation of computing architecture in the hope of overcoming the above shortcomings. In recent years, optical neural networks have received considerable attention, and optical computing is considered to be one of the most promising candidate technologies for the next generation of computing architecture due to its advantages such as high speed, high parallelism and low power consumption. Among the many optical neural network implementations, the diffractive deep neural network is considered to be a milestone. It has verified for the first time the possibility of all-optical methods to achieve complex pattern recognition tasks, and revealed the synergy between deep learning algorithm acceleration and optical inverse design.

[0003] However, the performance of the original diffraction deep neural network is still significantly behind that of the electrical neural network. At present, many improvement methods have been proposed to improve the classification performance of the diffraction deep neural network, but few studies have noticed that insufficient optimization is one of the reasons for the performance degradation of the original diffraction deep neural network. In addition, the original diffraction deep neural network requires multiple cascaded diffraction layers to achieve high classification accuracy, and each diffraction layer, as an optical device, will inevitably introduce insertion loss in actual use, and the more layers there are, the more proportional the insertion loss. Therefore, overcoming the performance degradation caused by insufficient optimization and the increase in insertion loss caused by the cascade of multiple diffraction layers are problems that need to be urgently solved in the practical application of diffraction deep neural networks. Summary of the invention

[0004] The present invention aims to solve the technical problems in the related art at least to a certain extent.

[0005] To this end, the purpose of the present invention is to propose a single-layer phase-controlled diffraction deep neural network optimization method. Through the improved optimization method, the cascaded diffraction layer is simplified to a single-layer structure without losing performance, and at the same time, the insertion loss is effectively reduced, thereby promoting the practical application of the diffraction deep neural network.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a single-layer phase-controlled diffraction deep neural network optimization method, the method comprising the following steps: (1) physical structure parameter setting, wherein the parameters include the incident light wavelength λ, the diffraction unit size s, the diffraction layer size N×N, and the distance d between the diffraction layer and the input plane and the output plane; (2) optical diffraction calculation, according to the Rayleigh-Sommerfeld diffraction formula, a direct integration algorithm based on fast Fourier transform is used to numerically solve the complex amplitude of the light wave propagating in the free space before and after the diffraction layer; (3) calculation of the phase control effect of the diffraction layer, calculating the output complex amplitude of the light wave after passing through the diffraction layer; (4) output normalization and loss function calculation, converting the complex amplitude reaching the output plane into the corresponding light intensity I, performing normalization processing, and then calculating the value of the loss function; (5) gradient backpropagation and parameter update, calculating the gradient according to the calculated loss value and backpropagating to update the diffraction layer phase control parameters; (6) performance testing, applying the designed single-layer phase-controlled diffraction deep neural network to classification tasks and testing the performance.

[0007] Furthermore, the discrete form of the Rayleigh-Sommerfeld diffraction formula is:

[0008] in U in and U out are the complex amplitudes on the front and back planes, respectively, (x i ,y j ) and (x m ,y n ) are points on the front and back planes respectively and m, n = 1, 2, ..., N, and z l-1 and z l are the positions of the front and back planes, respectively, z l -z l-1 is the distance between adjacent planes, Δξ and Δη are the dimensions of the diffraction unit in the horizontal and vertical directions, respectively, and k=2π / λ is the wave number; the direct integration algorithm based on fast Fourier transform is: O=IFFT2{FFT2{U}*FFT2{G}}ΔξΔη, where FFT2{·} and IFFT{·} represent two-dimensional fast Fourier transform and two-dimensional inverse fast Fourier transform, respectively, and U is U in After zero padding, the size of the matrix is ​​2N-1×2N-1, G is a matrix of size 2N-1×2N-1 composed of g, and the symbol * represents the Hadamard product; the N×N area at the bottom right of the output matrix O is the target output.

[0009] Furthermore, the phase regulation effect of the diffraction layer can be expressed as: surf_out =U surf_in*exp(jφ), where U surf_in and U surf_out They represent the complex amplitudes reaching the diffraction layer and after passing through the diffraction layer respectively, and φ is the phase control parameter of the diffraction layer.

[0010] Furthermore, the normalization process is to normalize the light intensity obtained on the output plane without changing the light intensity distribution, specifically including but not limited to maximum value normalization, that is, I'=I / max{I}; the loss function is a cross entropy function, specifically: in m is the number of batch training, l is i represents the non-overlapping area of ​​each category on the output plane, y n is the label of the corresponding input sample.

[0011] Furthermore, the stochastic gradient descent algorithm is used to realize gradient back propagation and update the diffraction layer phase control parameters.

[0012] Furthermore, the single-layer phase-controlled diffraction deep neural network was applied to MNIST and Fashion-MNIST classification, and the classification performance was tested.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] The present invention improves the optimization process by introducing output normalization and loss function replacement in the parameter optimization of the diffraction deep neural network, and fully explores the task fitting ability of the diffraction deep neural network, so that the number of diffraction layers can be reduced to one without losing performance. At the same time, the insertion loss caused by multiple diffraction layers can also be reduced, which facilitates the practical application of the diffraction deep neural network. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments, wherein:

[0016] Figure 1 This is a schematic diagram of the process flow of the single-layer phase-controlled diffraction deep neural network optimization method proposed in the present invention;

[0017] Figure 2 This is a working schematic diagram of the single-layer phase-controlled diffraction deep neural network proposed in the present invention;

[0018] Figure 3 The training classification accuracy curve and test confusion matrix of the single-layer phase-controlled diffraction deep neural network proposed in the present invention on the MNIST and Fashion-MNIST data sets;

[0019] Figure 4This is a test example of the single-layer phase-controlled diffraction deep neural network proposed in the present invention on the MNIST and Fashion-MNIST data sets; DETAILED DESCRIPTION

[0020] In order to enable those skilled in the art to better understand the method proposed in the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain the present invention, but should not be understood as limiting the present invention. In the drawings, the same reference numerals represent the same or similar components, or the same or similar steps.

[0021] In response to the problems existing in the background technology, the present invention proposes a single-layer phase-controlled diffraction deep neural network optimization method. Through the improved model optimization method, the cascaded diffraction layer structure is simplified to a single layer without losing performance, and at the same time, the insertion loss is effectively reduced, thereby promoting the practical application of the diffraction deep neural network.

[0022] The optimization method process of the present invention is as follows Figure 1 As shown, the specific steps include:

[0023] (1) Physical structure parameter settings, wherein the parameters include the wavelength of the incident light being 0.45 mm, the size of the diffraction unit being 0.4 mm, the size of the diffraction layer being 200×200, and the distance between the diffraction layer and the input plane and the output plane being 30 mm;

[0024] (2) Optical diffraction calculation: According to the Rayleigh-Sommerfeld diffraction formula, a direct integration algorithm based on fast Fourier transform is used to numerically solve the complex amplitude of the light wave propagating in the free space before and after the diffraction layer. The discrete form of the Rayleigh-Sommerfeld diffraction formula is: in U in and U out are the complex amplitudes on the front and back planes, respectively, (x i ,y j ) and (x m ,y n ) are points on the front and back planes respectively and m, n = 1, 2, ..., 200, and z l-1 and z l are the positions of the front and back planes, respectively, z l -z l-1 is the distance between adjacent planes, Δξ and Δη are the dimensions of the diffraction unit in the horizontal and vertical directions respectively, and k=2π / λ is the wave number. The direct integration algorithm based on fast Fourier transform is:

[0025] O = IFFT2{FFT2{U}*FFT2{G}}ΔξΔη, where FFT2{·} and IFFT{·} represent two-dimensional fast Fourier transform and two-dimensional inverse fast Fourier transform, respectively, and U is U in After zero padding, the size of the matrix is ​​399×399. G is a 399×399 matrix composed of g. The symbol * represents the Hadamard product. The 200×200 area at the bottom right of the output matrix O is the target output.

[0026] (3) Calculation of the phase regulation effect of the diffraction layer, which is to calculate the output complex amplitude of the light wave after passing through the diffraction layer. The phase regulation effect of the diffraction layer can be expressed as: surf_out =U surf_in *exp(jφ), where U surf_in and U surf_out denote the complex amplitudes reaching the diffraction layer and after passing through the diffraction layer, respectively, and φ is the phase control parameter of the diffraction layer;

[0027] (4) Output normalization and loss function calculation: After converting the complex amplitude reaching the output plane into the corresponding light intensity I, normalization processing is performed, and then the value of the loss function is calculated. The normalization processing is to normalize the light intensity obtained at the output plane without changing the light intensity distribution, specifically including but not limited to maximum value normalization, that is, I'=I / max{I}; the loss function is a cross entropy function, specifically: in m is the number of batch training, l is i represents the non-overlapping area of ​​each category on the output plane, y n is the label of the corresponding input sample;

[0028] (5) Gradient back propagation and parameter update: the gradient is calculated according to the calculated loss value and the stochastic gradient descent algorithm is used to implement gradient back propagation and update the diffraction layer phase control parameters;

[0029] (6) Performance test: build a single-layer phase-controlled diffraction deep neural network such as Figure 2 As shown in the figure, the test is applied to MNIST and Fashion-MNIST classification respectively. The test process specifically includes:

[0030] 1) MNIST classification

[0031] ① Set the physical structure parameters, as shown above;

[0032] ② The 60,000 samples in the data set are divided into training set and validation set in a ratio of 8:2, and the test set contains 10,000 samples. All samples are used as input of the diffraction deep neural network in the form of amplitude modulation. Figure 2As shown in the figure, a single-layer diffraction deep neural network is built and then trained and optimized. The training parameters include: the number of iterations is 50, the number of small batch training is 128, and the initial learning rate is between 0.1 and 1. The classification accuracy curve of the training process is shown in Figure 3 (a)

[0033] ③After training, the optimized diffraction deep neural network is tested on the test set. The classification confusion matrix on the test set is as follows: Figure 3 As shown in (b), the randomly selected test samples are as follows Figure 4 It can be observed that, using the optimization method proposed in the present invention, a single-layer diffractive deep neural network can achieve a test classification accuracy of 93.99% on the MNIST dataset, which exceeds the classification performance of the 5-layer diffractive deep neural network in the original study.

[0034] 2) Fashion-MNIST Classification

[0035] ① Set the physical structure parameters, as shown above;

[0036] ② The 60,000 samples in the data set are divided into training set and validation set in a ratio of 8:2, and the test set contains 10,000 samples. All samples are used as the input of the diffraction deep neural network in the form of phase modulation. Figure 2 As shown in the figure, a single-layer diffraction deep neural network is built and then trained and optimized. The training parameters include: the number of iterations is 50, the number of small batch training is 128, and the initial learning rate is between 0.1 and 1. The classification accuracy curve of the training process is shown in Figure 3 (c)

[0037] ③After training, the optimized diffraction deep neural network is tested on the test set. The classification confusion matrix on the test set is as follows: Figure 3 As shown in (d), the randomly selected test samples are as follows Figure 4 It can be observed that, using the optimization method proposed in the present invention, a single-layer diffractive deep neural network can achieve a test classification accuracy of 80.94% on the Fashion-MNIST dataset, achieving the same level of classification performance as the 5-layer diffractive deep neural network in the original study.

[0038] The present invention improves the optimization process by introducing output normalization and loss function replacement in the parameter optimization of the diffraction deep neural network, and fully explores the task fitting ability of the diffraction deep neural network, so that the number of diffraction layers can be reduced to one without losing performance. At the same time, the insertion loss caused by multiple diffraction layers can also be reduced, which facilitates the practical application of the diffraction deep neural network.

[0039] In combination with the description and practice of the present invention disclosed herein, other embodiments of the present invention are easy to think of and understand for those skilled in the art. The embodiments described in detail above are considered to be exemplary only, and those skilled in the art may modify the technical solutions recorded in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and the true scope and gist of the present invention are defined by the claims.

Claims

1. A single-layer phase-controlled diffraction deep neural network optimization method, characterized in that: The method comprises the following steps: (1) Setting of physical structure parameters, wherein the parameters include the wavelength λ of the incident light, the size s of the diffraction unit, the size N×N of the diffraction layer, and the distance d between the diffraction layer and the input plane and the output plane; (2) Optical diffraction calculation: According to the Rayleigh-Sommerfeld diffraction formula, a direct integration algorithm based on fast Fourier transform is used to numerically solve the complex amplitude of light waves propagating in free space before and after the diffraction layer; (3) Calculation of the phase regulation effect of the diffraction layer, and calculation of the output complex amplitude of the light wave after passing through the diffraction layer; (4) Output normalization and loss function calculation: After converting the complex amplitude reaching the output plane into the corresponding light intensity I, normalization is performed, and then the value of the loss function is calculated; (5) Gradient back propagation and parameter update: calculate the gradient according to the calculated loss value and back propagate it to update the diffraction layer phase control parameters; (6) Performance testing: Apply the designed single-layer phase-controlled diffraction deep neural network to the classification task and test the performance.

2. The optimization method according to claim 1, characterized in that: The discrete form of the Rayleigh-Sommerfeld diffraction formula is: in U in and U out are the complex amplitudes on the front and back planes, respectively, (x i ,y j ) and (x m ,y n ) are points on the front and back planes respectively and m, n = 1, 2, ..., N, and z l-1 and z l are the positions of the front and back planes, respectively, z l -z l-1 is the distance between adjacent planes, Δξ and Δη are the dimensions of the diffraction unit in the horizontal and vertical directions, respectively, and k=2π / λ is the wave number; the direct integration algorithm based on fast Fourier transform is: O=IFFT2{FFT2{U}*FFT2{G}}ΔξΔη, where FFT2{·} and IFFT{·} represent two-dimensional fast Fourier transform and two-dimensional inverse fast Fourier transform, respectively, and U is U in After zero padding, the size of the matrix is ​​2N-1×2N-1, G is a matrix of size 2N-1×2N-1 composed of g, and the symbol * represents the Hadamard product; the N×N area at the bottom right of the output matrix O is the target output.

3. The optimization method according to claim 1, characterized in that: The phase regulation effect of the diffraction layer can be expressed as: U surf_out =U surf_in *exp(jφ), where U surf_in and U surf_out They represent the complex amplitudes reaching the diffraction layer and after passing through the diffraction layer respectively, and φ is the phase control parameter of the diffraction layer.

4. The optimization method according to claim 1, characterized in that: The normalization process is to normalize the light intensity obtained on the output plane without changing the light intensity distribution, specifically including but not limited to maximum value normalization, that is, I'=I / max{I}; the loss function is a cross entropy function, specifically: in i=0,...,C-1, m is the number of small batch training, l i represents the non-overlapping area of ​​each category on the output plane, y n is the label of the corresponding input sample.

5. The optimization method according to claim 1, characterized in that: The stochastic gradient descent algorithm is used to realize gradient back propagation and update the diffraction layer phase control parameters.

6. The optimization method according to claim 1, characterized in that: The single-layer phase-controlled diffraction deep neural network was applied to MNIST and Fashion-MNIST classification, and the classification performance was tested.

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