CN114707629A - Matrix calculation method based on light scattering and optical neural network - Google Patents
Matrix calculation method based on light scattering and optical neural network Download PDFInfo
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Abstract
The application discloses a matrix calculation method based on light scattering and an optical neural network, wherein the matrix calculation method based on light scattering comprises the steps of 1, decomposing a matrix W into a unitary matrix and a diagonal matrix; step 2, constructing a matrix calculation unit based on light scattering; step 3, performing electro-optical conversion on the input characteristic vector to obtain N paths of optical signals; step 4, inputting the N paths of optical signals into a matrix calculation unit to realize multiplication of the input eigenvector and the matrix W; after the optical signal passes through the matrix calculation unit, the arbitrary vector matrix multiplication can be performed at the light speed, and almost no optical loss exists. The all-optical neural network based on the matrix computing unit can effectively reduce the number of optical devices for realizing the operation of the neural network, and can provide an implementation scheme with smaller size, lower energy consumption, larger bandwidth, better robustness and higher operation speed for realizing the artificial neural network.
Description
Technical Field
The application belongs to the field of neural network computing, and particularly relates to a matrix computing method based on light scattering and an optical neural network.
Background
With the wide application of deep learning technology, Artificial Intelligence (AI) has achieved great success in machine vision, automatic driving, clinical diagnosis, and the like. However, the increase in computing power of integrated circuit chips as carriers for training and executing artificial intelligence models is gradually slowing, and the demand of artificial neural networks for computing power is gradually failing to meet. Integrated circuit chips based on von neumann architecture have a structurally formidable drawback that they separate programs and data when performing operations, resulting in a tidal data load between the memory and the computing unit, which reduces the computing rate and increases the computing power consumption. At present, researchers mainly solve the problem by continuously improving the integration level of a chip and performing methods such as memory operation, but as the size of a transistor is reduced, the performance of the transistor is increasingly influenced by the quantum effect. In addition, the existing neural network algorithm has low matching degree with the in-memory calculation method, and both the existing neural network algorithm and the in-memory calculation method limit the application of the in-memory calculation method.
An optical-based artificial neural network can overcome the above-mentioned shortcomings of integrated circuit-based artificial neural networks. Compared with electrical transmission, optical transmission has the advantages of high speed, large bandwidth, low delay, low energy consumption, high parallelism and the like. Therefore, the optical neural network can exert the advantages of the photon technology, and is expected to break through the bottleneck of the traditional electrical neural network.
In 2017, an MIT research team provides a structure based on a Mach-Zehnder interferometer array, so that matrix operation of an optical neural network is realized, and an on-chip neural network chip is built by using the structure. By reusing the neural network chip, they realize a four-input neural network and realize the recognition of four vowel signals. The optical neural network uses 56 Mach-Zehnder interferometer arrays and 213 phase shifters, the network scale is large, when input signals are increased, a large number of MZIs and phase shifters are needed, and the process difficulty is large. In 2018, Lin et al proposed a diffraction-based photon depth neural network, the all-optical diffraction depth neural network (D)2NN) consists of multiple layers of diffractive surfaces that can perform computational tasks at the speed of light. D2The training of the NN is completed by a computer, after the training is completed, a 3D model of each diffraction layer is completed through a Poisson surface reconstruction method, then the diffraction surface is printed by a 3D printer, and the classification task of handwritten numbers and fashion article images is completed. The diffraction device of the scheme has a large size, can only complete a specific machine learning task, and cannot be reconstructed.
The patent with application publication number CN 112232504 a provides a photonic neural network, which relates to the basic structure of a photonic matrix computing unit, and the patent provides a matrix computing unit based on MZI array, where each MZI is composed of a 2 × 2 directional coupler and a phase shifter, and the number of devices is large in practical use, and when the device is disturbed by the outside, the stability of the device is low, and the robustness of the whole neural network is poor. The patent with application publication number CN 111680796 a provides a photonic neural network device on chip based on cascade optical coupler, a chip and an application method thereof, wherein a matrix calculation unit of the photonic neural network device is formed by the cascade optical coupler and lacks a nonlinear unit, so that power consumption of the neural network may be increased and calculation performance may be reduced.
In combination with the above, a matrix computing unit with compactness, high integration level and good robustness is needed to implement an all-optical neural network.
Disclosure of Invention
The technical problem to be solved by the application is to provide an optical matrix calculation method based on light scattering, optical matrix calculation is realized by using an optical device, and a matrix calculation unit which has large bandwidth, low power consumption, runs at light speed and can be used for an optical neural network is realized on a chip.
The invention discloses a matrix calculation method based on light scattering, which comprises the following steps:
step 1, decomposing a matrix W into a unitary matrix and a diagonal matrix;
Step 4, inputting the N paths of optical signals into a matrix calculation unit to obtain a multiplication result of the input eigenvector and the matrix W;
further, the light scattering module is obtained by carrying out reverse design on the photonic device by a concomitant method.
Further, in step 1, the matrix W is decomposed into a unitary matrix and a diagonal matrix, specifically:
decomposing a matrix W into two unitary matrixes and a diagonal matrix by using a matrix singular value decomposition method, wherein a function expression of the matrix W is represented by the following formula:
W＝U∑VT
wherein, W is an M multiplied by N matrix, U is an M multiplied by M matrix, V is an N multiplied by N matrix, and U and V are unitary matrixes, which satisfies UUT＝I，VVTI, Σ is a diagonal matrix.
In step 2, the matrix calculation unit comprises a first light scattering module, a phase shifter array and a second light scattering module; the first light scattering module, the phase shifter array and the second light scattering module are sequentially connected, U and V are respectively represented by the first light scattering module and the second light scattering module, and sigma is represented by the phase shifter array.
N rows of optical signals are input into the first light scattering module for operation, then input into the phase shifter array, and finally output by the second light scattering module to realize multiplication of an optical vector and an arbitrary matrix. The matrix calculation unit has the advantages of small size, high integration level, low loss, high operation speed and the like.
Further, in step 1, the matrix W is decomposed into a unitary matrix and a diagonal matrix, specifically:
the matrix W is decomposed into N-1 unitary matrices and N diagonal matrices, and the function expression is as follows:
W＝∑N·V·∑N-1…∑2·V·∑1
where V is the unitary matrix, ΣiRepresents a diagonal matrix, i ═ 1, 2 … N.
In step 2, the matrix calculation unit comprises N-1 light scattering modules and N phase shifter arrays; the light scattering module and the phase shifter array are arranged at intervals, and the light scattering module is connected with the phase shifter array. The matrix calculation unit has the advantages of programmability, high robustness and the like.
The invention also provides an optical neural network based on light scattering, which comprises a laser array, an electro-optic modulator array, a plurality of hidden layers and a photoelectric detector array which are sequentially connected; wherein the hidden layer comprises a matrix calculation unit and an optical nonlinear unit; the output end of the matrix calculation unit is connected with the input end of the optical nonlinear unit; the nonlinear unit of the invention adopts a saturable absorber or a nonlinear refractive material.
The laser array generates N paths of light with light intensity of IinThe incoherent light source is input to an electro-optical modulator array, normalization processing is carried out on input characteristic vectors, the electro-optical modulator array modulates normalized data onto N paths of optical signals and outputs the N paths of optical signals to a hidden layer, a matrix calculation unit in the hidden layer can carry out matrix operation on the N paths of optical signals, an optical nonlinear unit carries out nonlinear operation on the N paths of optical signals and performs the function of a nonlinear activation function, and the operation performance of a neural network can be improved; the photoelectric detector array comprises N photoelectric detectors which are respectively in one-to-one correspondence with the N output optical signals of the last hidden layerThe method is used for detecting the output light intensity to obtain the calculation result of the optical neural network.
Further, a matrix calculation unit in the optical neural network comprises a first light scattering module, a phase shifter array and a second light scattering module; the first light scattering module, the phase shifter array and the second light scattering module are connected in sequence.
Further, a matrix calculation unit in the optical neural network comprises N-1 light scattering modules and N phase shifter arrays; the light scattering module and the phase shifter array are arranged at intervals, the light scattering module is connected with the phase shifter array, and N is equal to the dimension of the input eigenvector.
Compared with the prior art, the method has the following advantages: the optical matrix calculation unit adopted in the matrix calculation method provided by the application consists of the light scattering module and the phase shifter array, and compared with the MZI array realization matrix calculation in the prior art, the light scattering module is more compact in size and is easier to integrate on a chip; the light scattering module is subjected to reverse optimization design by using an accompanying method, so that the optical performance is better, and the loss is lower;
the matrix calculation unit formed by cascading the multistage light scattering unit and the phase shifter array has the programmable characteristic, can be repeatedly used on a chip to complete different matrix operations, and has high robustness and strong anti-interference capability; compared with the matrix multiplication operation realized in a circuit, the optical matrix calculation unit provided by the application has lower power consumption and higher operation speed, can effectively improve the operation speed and the energy consumption ratio of the neural network, and is more in line with the development trend of the neural network. The all-optical neural network can effectively shorten the calculation time and reduce the calculation loss through optical calculation.
Drawings
Fig. 1 is a schematic diagram of a matrix calculation unit in an embodiment of the present application.
Fig. 2 is a schematic diagram of a matrix calculation unit in the second embodiment of the present application.
Fig. 3 is a graph of simulation results for a four-input four-output light scattering module.
Fig. 4 is a schematic diagram of the optical neural network structure of the present application.
FIG. 5 is a flow chart of the present application for data classification of Iris data sets using a two-layer neural network.
Figure 6 is a test accuracy graph of data classification for iris data sets.
Detailed Description
Example one
The matrix calculation method based on light scattering comprises the following steps:
step 1, decomposing a matrix W into a unitary matrix and a diagonal matrix;
decomposing a matrix W into two unitary matrices and a diagonal matrix by using a matrix Singular Value Decomposition (SVD) method, wherein a function expression of the matrix W is represented by the following formula:
W＝U∑VT
wherein, W is an M multiplied by N matrix, U is an M multiplied by M matrix, V is an N multiplied by N matrix, and U and V are unitary matrixes, which satisfies UUT＝I，VVTI, U and V are characterized by two light scattering modules, respectively; Σ is a diagonal matrix with diagonal elements being singular values, characterized by a shifter array.
and constructing a matrix calculation unit based on light scattering according to the matrix decomposed by adopting a matrix Singular Value Decomposition (SVD) method. As shown in fig. 1, the matrix calculation unit includes a first light scattering module, a phase shifter array and a second light scattering module, the first light scattering module, the phase shifter array and the second light scattering module are sequentially connected through a waveguide, U and V are respectively represented by the first light scattering module and the second light scattering module, and Σ is represented by the phase shifter array; the light scattering module is obtained by reverse design of a photonic device by a companion method, and has good optical performance and low loss.
The first light scattering module and the second light scattering module are both used for realizing vector unitary matrix multiplication of N paths of optical signals, the phase shifter array comprises N phase shifters, the N phase shifters respectively correspond to the optical signals output by the first light scattering module one by one to realize vector diagonal matrix multiplication of the optical signals, and the optical signals output by the N phase shifters respectively enter the second light scattering module; and the random matrix operation is realized by optimizing the specific parameters of the light scattering module and the phase shifter array.
Fig. 3 is a diagram showing simulation results of a four-input four-output light scattering module. The light scattering module is reversely designed by using an adjoint algorithm, and the simulation size is 4 multiplied by 4 mu m2The simulation result is a relative refractive index distribution diagram of the light scattering module, and the color shade represents the relative refractive index. The simulation optimization result can be exported to be a GDS file which is used as a layout of the light scattering module, and a foundation is laid for the design of the optical neural network chip.
Specifically, a high-power laser array is adopted to generate N paths of light with the light intensity of IinAnd the incoherent light source is used for normalizing the input characteristic vectors in the data set and modulating the input characteristic vectors to N paths of optical signals by using the amplitude electro-optical modulator to realize the electro-optical conversion of the input characteristic vectors.
Step 4, inputting the N paths of optical signals into a matrix calculation unit to realize multiplication operation of the eigenvector and the matrix W;
in the matrix calculation unit, N paths of incoherent light are used as input light sources, and in the output waveguide, the light intensities of different wavelengths can be directly added due to the incoherent property of the light. The calculation expression is as follows:
in the formula IoutTo output light intensity, IinFor the input light intensity, W is a matrix represented by a matrix computing unit, WijIs the weight of the matrix W.
Example two
The matrix calculation method based on light scattering comprises the following steps:
step 1, decomposing a matrix W into a unitary matrix and a diagonal matrix;
specifically, the matrix W is decomposed into N-1 unitary matrices and N diagonal matrices, and the function expression is as follows:
W＝∑N·V·∑N-1…∑2·V·∑1
where V is a unitary matrix that can be characterized using a light scattering module, Σi(i ═ 1, 2 … N) represents a diagonal matrix, which can be characterized using N respective shifter arrays; the number of diagonal matrices is equal to the dimension of the input feature vector.
when the matrix W is decomposed into N-1 unitary matrixes and N diagonal matrixes, a matrix calculation unit is constructed based on light scattering; as shown in fig. 2, the matrix calculation unit includes N-1 light scattering modules and N phase shifter arrays; the light scattering module and the phase shifter array are arranged at intervals, and the light scattering module is connected with the phase shifter array through a waveguide. Wherein the light scattering module is obtained by carrying out reverse design on the photonic device by a concomitant method.
The N paths of optical signals can realize arbitrary matrix multiplication operation through the cascade phase shifter and the optical scattering module.
Step 4, inputting the N paths of optical signals into a matrix calculation unit to realize multiplication operation of the eigenvector and the matrix W;
EXAMPLE III
The optical neural network based on light scattering is an all-optical neural network, fig. 4 is a schematic structural diagram of an all-optical neural network chip of the present application, and includes a laser array, an electro-optical modulator array, a plurality of hidden layers and a photodetector array, which are connected in sequence, where the hidden layers include a matrix calculation unit and an optical nonlinear unit; the output end of the matrix calculation unit is connected with the input end of the optical nonlinear unit; the matrix calculation unit is obtained by decomposing a matrix into a unitary matrix and a diagonal matrix, representing the unitary matrix by using a scattering unit, and representing the diagonal matrix by phase-shifting array in the matrix calculation method.
The electro-optical modulator array comprises N amplitude modulators in one-to-one correspondence with N paths of input optical signals, the matrix calculation unit can perform any vector matrix operation on the N paths of optical signals, the optical nonlinear unit can perform nonlinear operation on the N paths of optical signals, the nonlinear activation function is executed, and the operation performance of the neural network can be improved. The photodetector array comprises N photodetectors in one-to-one correspondence with the N output optical signals of the last hidden layer.
Using high power laser array to generate N paths of light with light intensity IinThe incoherent light source is used for normalizing input characteristic vectors in a data set, modulating data to be classified to N paths of optical signals by using an electro-optical modulator array, wherein the light intensity of the optical signals is in direct proportion to the data to be classified, and the amplitude of signals loaded to the first hidden layer is as follows:
wherein xiFor the i-th path normalized input signal, X0The matrix calculation unit in the first hidden layer is used for calculating to obtain:
obtaining the output Y of the first hidden layer after passing through the nonlinear operation unit in the first hidden layer1，Y1Also as an input signal X1Loading into a second hidden layer:
in the formula f (z)i) Is a nonlinear activation function realized by simulation of an optical nonlinear device, and finally outputs N paths after calculation of L hidden layersThe light signal is detected by the photoelectric detector to output light intensity Y, and the calculation result of the optical neural network is obtained.
The optical neural network of the present invention is used for classification with specific data. Figure 5 shows a flow diagram of a neural network implementing data classification using iris datasets containing a total of 150 data in 3 classes, 50 data in each class, with 4 features per record: the length of the calyx, the width of the calyx, the length of the petals and the width of the petals can be used for predicting which variety of iris flowers belong to by the 4 characteristics, the iris flowers comprise three varieties of wild iris, iris discolor and north American iris, and x is shown in figure 5i(i ═ 1, 2, 3, 4) are each 4-term features of the dataset, hi(i ═ 1, 2, 3, 4) are 4 neurons in the neural network, respectively, yi(i is 1, 2, 3) is the output of the neural network, and the input vector passes through a weight matrix W1And W2And obtaining the output of the neural network after operation.
The iris data set is used as an input characteristic vector, the dimension N of the input characteristic vector is 4, the characteristic of each data is normalized and then input into the electro-optical modulator array, four paths of optical signals are output into the hidden layers, and the photoelectric detector array detects the intensity of output light in the output waveguide through the operation of the two hidden layers to judge the type of iris. Fig. 6 is a diagram of the test result, and the test accuracy can reach 0.87 when the training time is 1000.
The size of the optical matrix calculating unit is more compact, and the optical matrix calculating unit is easier to integrate on a chip; the second matrix calculation unit is cascaded with the phase shifter array by utilizing a multi-stage light scattering unit, has the programmable characteristic, can be repeatedly used on a chip to complete different matrix operations, and has high robustness and strong anti-interference capability; the light scattering module is designed in a reverse optimization mode by using a following method, so that the optical performance is better, and the loss is lower. Compared with the existing on-chip optical neural network technology, the all-optical neural network provided by the application reduces the number of optical devices for realizing the operation of the neural network, and can provide an implementation scheme with smaller size, lower energy consumption, larger bandwidth, better robustness and higher operation speed for realizing the neural network.
Claims (10)
1. The matrix calculation method based on light scattering is characterized by comprising the following steps:
step 1, decomposing a matrix W into a unitary matrix and a diagonal matrix;
step 2, constructing a matrix calculation unit based on light scattering according to the decomposed matrix, wherein the matrix calculation unit comprises a light scattering module and a phase shifter array; the light scattering module is used for representing a unitary matrix, and the phase shifter array is used for representing a diagonal matrix;
step 3, performing electro-optical conversion on the input characteristic vector to obtain N paths of optical signals; where N is equal to the dimension of the input feature vector.
And 4, inputting the N paths of optical signals into a matrix calculation unit to realize multiplication of the input eigenvector and the matrix W.
2. The method of claim 1, wherein the light scattering module is derived from photonic back-engineering by a concomitant method.
3. The method for calculating a matrix based on light scattering according to claim 1 or 2, wherein the matrix W is decomposed into a unitary matrix and a diagonal matrix in step 1, specifically:
decomposing a matrix W into two unitary matrixes and a diagonal matrix by using a matrix singular value decomposition method, wherein a function expression of the matrix W is represented by the following formula:
W＝U∑VT
wherein, W is an M multiplied by N matrix, U is an M multiplied by M matrix, V is an N multiplied by N matrix, and U and V are unitary matrixes, which satisfies UUT＝I，VVTI, Σ is a diagonal matrix.
4. The method of claim 3, wherein the matrix calculation unit in step 2 comprises a first light scattering module, a phase shifter array and a second light scattering module;
the first light scattering module, the phase shifter array and the second light scattering module are sequentially connected, U and V are respectively represented by the first light scattering module and the second light scattering module, and sigma is represented by the phase shifter array.
5. The method for calculating a matrix based on light scattering according to claim 1 or 2, wherein the matrix W is decomposed into a unitary matrix and a diagonal matrix in step 1, specifically:
the matrix W is decomposed into N-1 unitary matrixes and N diagonal matrixes, and the function expression is as follows:
W＝∑N·V·∑N-1…∑2·V·∑1
where V is the unitary matrix, ΣiRepresents a diagonal matrix, i ═ 1, 2 … N.
6. The method of claim 5, wherein the matrix calculation unit in step 2 comprises N-1 light scattering modules and N phase shifter arrays;
the light scattering module and the phase shifter array are arranged at intervals, and the light scattering module is connected with the phase shifter array.
7. The optical neural network based on light scattering is characterized by comprising a laser array, an electro-optic modulator array, a plurality of hidden layers and a photoelectric detector array which are sequentially connected;
wherein the hidden layer comprises a matrix calculation unit and an optical nonlinear unit; the output end of the matrix calculation unit is connected with the input end of the optical nonlinear unit;
the laser array generates N paths of light with light intensity of IinThe incoherent light source is input to an electro-optical modulator array, normalization processing is carried out on input characteristic vectors, the electro-optical modulator array modulates normalized data onto N paths of optical signals and outputs the optical signals to a hidden layer, a matrix calculation unit in the hidden layer can carry out matrix operation on the N paths of optical signals, an optical nonlinear unit carries out nonlinear operation on the N paths of optical signals and executes nonlinear activation functionsThe photodetector array comprises N photodetectors which are respectively in one-to-one correspondence with the N paths of output optical signals of the last hidden layer and are used for detecting the light output intensity.
8. The optical neural network based on light scattering of claim 7, wherein the matrix computing unit in the optical neural network is the matrix computing unit as described in claim 4.
9. The optical neural network based on light scattering of claim 7, wherein the matrix calculation unit in the optical neural network is the matrix calculation unit as set forth in claim 6.
10. The optical neural network based on light scattering of claim 7, wherein the nonlinear element is a saturable absorber or a nonlinear refractive material.
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