JP7394451B2 - Photonics classifier and classification method - Google Patents

Description

Application of Article 30, Paragraph 2 of the Patent Act - On August 19, 2019, website: https://doi. org/10.1364/OE. 27.024914 and https://www. osapublishing. org/oe/viewmedia. cfm? Published in Optics Express, Vol. uri=oe-27-18-24914&seq=0. 27, No. 18, p. 24914-24922 (https://doi.org/10.1364/OE.27.024914 - A publication published on September 2, 2020, Optics Express, 2019, Vol. 27, No. 18, p.24914-24922 ・Slides for research presentations at Asia Communications and Photonics Conference (ACP) 2019 held on November 2, 2020 ・On January 31, 2020, posted on the website Site: https://www.ofcconference.org/library/images/ofc/PDF/2020/OFC-2020-Abstracts-013120.pdf

The present invention relates to the field of optical computing.

Data classification is one of the important fields in statistics and is widely applied in various fields. With the development of AI technology, classification methods using machine learning are being studied. Currently, most neural networks are realized using computer programming. However, since neural networks require large-scale matrix operations and nonlinear function operations, they consume large amounts of computational resources and energy, are difficult to speed up, and are expensive. For this reason, the application of photonics technology is being considered.

US Patent No. 10268232

However, neural networks require nonlinear functional operations. Therefore, there are computer programming methods that simulate nonlinear functions. Achieving nonlinear functions in photonics technology requires nonlinear optical devices such as saturable absorbers, which are difficult to manufacture and scale up, require high optical power input, and are expensive. .

In order to solve the above problems, the photonics classifier according to the present invention shifts the phase of the corresponding optical signal according to N parameters (where N is an integer of 4 or more) corresponding to each sample data. An interferometer array including N Mach-Zehnder interferometers receives a phase-shifted optical signal, shifts the phase of the optical signal passing through each of the plurality of Mach-Zehnder interferometers connected in a grid, N×M interferometers (where M is an integer greater than or equal to N) output to a port, the plurality of Mach-Zehnder interferometers including N×M Mach-Zehnder interferometers; a photodetector that detects the optical power of the optical signal output from the port, and the phase shifted by each Mach-Zehnder interferometer of the N×M interferometer is associated with the correct classification result for each sample data. It can be calibrated to find the maximum optical power at the port.

The above photonics classifier further includes an input waveguide into which an optical signal of a single wavelength is input, and a splitter which branches the input optical signal into N waveguides and outputs it to an interferometer array.

In the above photonics classifier, the splitter includes a plurality of Mach-Zehnder interferometers, and by shifting the phase of the optical signal passing through each of the plurality of Mach-Zehnder interferometers, the splitter splits the input optical signal into N components at a predetermined ratio. The phases branched into the waveguide and shifted by each Mach-Zehnder interferometer are calibrated so that the optical power of the input optical signal is branched at a predetermined ratio.

In the above photonics classifier, the input waveguide, splitter, interferometer array, N×N interferometer, and photodetector are integrated on a photonics chip.

In the photonics classifier described above, the photonics chip is composed only of linear optical devices.

The photonics classifier described above further includes a controller that performs calibration by machine learning outside the photonics chip.

The above photonics classifier further includes a controller on the photonics chip that performs calibration by machine learning.

The above photonics classifier further comprises one or more other photonics chips, wherein the total number of Mach-Zehnder interferometers included in the interferometer array of each photonics chip is equal to the number of parameters corresponding to each sample data. , one controller collectively performs the calibration for each photonics chip.

In the photonics classifier described above, the Mach-Zehnder interferometer shifts the phase of the optical signal using thermo-optic or electro-optic effects.

The photonics classification method according to the present invention uses N Mach-Zehnder interferometers (N is an integer of 4 or more) included in an interferometer array to detect a corresponding optical signal according to N parameters corresponding to each sample data. A step of shifting the phase, and receiving the optical signal with the phase shifted by the N×M interferometer (where M is an integer greater than or equal to N), and passing it through each of the plurality of Mach-Zehnder interferometers connected in a grid pattern. shifting the phase of an optical signal and outputting it to N ports, the plurality of Mach-Zehnder interferometers including N×M Mach-Zehnder interferometers; The step of detecting the optical power of the output optical signal and the phase shifted by each Mach-Zehnder interferometer of the N×M interferometer are performed by detecting the maximum optical power at the port associated with the correct classification result for each sample data. calibrating to be detected.

According to embodiments of the present invention, the classification operation is a hardware process, so it is fast, can be recalibrated without rebuilding the hardware, and can be used for other classification operations. Also, unlike the case where data is placed on the intensities of lasers of different wavelengths that do not interfere (non-coherent), it operates with a single wavelength optical input even if there are many input parameters, and does not require high optical power for detection. First, it has good sensitivity because it can detect coherent optical signals.

FIG. 2 is a block diagram of a photonics classifier according to an embodiment of the invention. An example of a configuration in which two photonics chips are controlled by one external controller 50 is shown. An example of the configuration of the photonics chip 100 when N=4 is shown. An example of the configuration of the splitter 10 when N=4 is shown. An example of the phase distribution of each MZI of the N×N interferometer 30 before machine learning is shown. The optical power at each port of each sample data with the phase distribution shown in FIG. 5 is shown. An example of the phase distribution of each MZI of the N×N interferometer 30 after machine learning is shown. The optical power at each port of each sample data with the phase distribution shown in FIG. 7 is shown. It shows the probability that the maximum optical power is detected when the relative difference for determining the maximum optical power is changed. It shows the probability that the maximum optical power is detected when the relative difference for determining the maximum optical power is changed. Machine learning was performed on 90 samples out of 150 samples, and recognition was verified using the remaining 60 samples using the obtained phase distribution.The results are shown below. An example of handwritten digits 0 to 9 from the MNIST dataset is shown. An example of a photonics chip with N=16 is shown. The relationship between the handwritten numeric label and the optical power of each port after learning, and the relationship between the handwritten numeric label and the port where the maximum optical power is to be detected are shown. An example of handwritten digits 0 to 9 from the MNIST dataset is shown. The classification results are shown for a total of 10,000 samples, 1,000 each of handwritten digits 0 to 9 in the MNIST dataset.

FIG. 1 is a block diagram of a photonics classifier according to an embodiment of the invention. When parameters corresponding to individual sample data are input, the photonics classifier outputs a signal indicating the classification to which the parameters belong.

The photonics classifier shown in FIG. 1 includes a photonics chip 100, which is an optical device in which a waveguide, an interferometer, etc. are arranged, and an external controller 50 that controls elements on the photonics chip 100 using electrical signals. The photonics chip 100 can be integrated as a monolithic circuit, and for example, including a photodetector, can be integrated on a 220 nm SOI (Silicon on Insulator) substrate. The external controller 50 is, for example, an electronic circuit or a computer-controlled driver capable of executing algorithms.

In the photonics chip 100, a splitter 10, an interferometer array 20, an N×N interferometer 30, and a photodiode (PD) array 40 are arranged in order from the left in FIG. solid line). Parameters corresponding to individual sample data are input from the external controller 50 to the interferometer array 20, and a signal indicating the classification to which the parameter belongs is output from the PD array 40 to the external controller 50.

A continuous wave of a single wavelength is input to the photonics chip 100 from a light source. The splitter 10 splits the input light into N waveguides at a predetermined ratio of optical power. The ratio can be adjusted from the external controller 50, and may be equally divided or may be any ratio. It is desirable that the error in the ratio be within 10%. N represents an integer of 4 or more. FIG. 1 shows four waveguides for ease of presentation.

The optical signal split by the splitter 10 is input to the interferometer array 20 through N waveguides. The interferometer array 20 has N interferometers, and for example, a Mach-Zehnder interferometer is used. Each interferometer in interferometer array 20 outputs two signals whose phases are shifted according to parameters input by external controller 50. Therefore, interferometer array 20 outputs 2N signals to N×N interferometer 30 through 2N waveguides. FIG. 1 shows eight waveguides for ease of presentation.

The N×N interferometer 30 includes N×N interferometers connected in a grid pattern. Each interferometer has two inputs and two outputs, and the input side (left side in Figure 1) and output side (right side in Figure 1) of the NxN interferometer 30 are connected to 2N waveguides. be done. Each interferometer of the N×N interferometer 30 outputs two optical signals whose phases are shifted with respect to the two input optical signals. The amount to shift is controlled by an external controller 50 and calibrated by machine learning starting from an initial value. The optical signal output from the N×N interferometer 30 is input to the PD array 40.

The PD array 40 has 2N photodiodes connected to each waveguide, converts optical power into an electrical signal, and outputs the electrical signal to the external controller 50. To detect the light, a photodiode is used, eliminating the need for nonlinear processing with a nonlinear optical device such as a saturable absorber.

The external controller 50 detects the maximum optical power at the photodiode connected to the port associated with the correct classification result among the output ports of the N×N interferometer 30 for the parameters input to the interferometer array 20. The phase of each interferometer of the N×N interferometer 30 is calibrated using a predetermined algorithm so that the phase of each interferometer of the N×N interferometer 30 is adjusted. That is, an appropriate phase is machine learned to show the desired classification for the sample data. After performing machine learning, when the parameters corresponding to the sample data are input to the interferometer array 20, a photodiode connected to the port associated with the correct classification result among the output ports of the N×N interferometer 30 The maximum optical power is detected at

FIG. 2 shows a configuration example in which two photonics chips 100 and 200 are controlled by one external controller 50. An example of classification is the variety classification of Iris (iris), which will be described later, and is classified into three varieties based on four parameters: the length and width of the sepals and the length and width of the petals. The number of parameters representing each sample varies depending on the target to be classified, and if the number is larger than the value of N in the photonics chip 100, classification may be performed by controlling multiple photonics chips with one external controller 50. I can do it. For example, when the value of N of the photonics chip 100 is 4, using the configuration shown in FIG. 2, it is possible to classify samples when there are eight parameters representing each sample. As another configuration example, instead of providing one N×N interferometer 30 for each of the photonic chips 100 and 200 as shown in FIG. 2, one 2N×2N interferometer is provided, and the It may be connected to the waveguide from the interferometer array 20, and may be connected to the waveguide to the PD array 40 of the photonics chips 100 and 200 on the output side.

FIG. 3 shows an example of the configuration of the photonics chip 100 when N=4. Among the components of the photonics chip 100 shown in FIG. 1, the splitter 10, interferometer array 20, and N×N interferometer 30 are shown, and the PD array 40 is omitted.

The N×N interferometer 30 includes 4×4 Mach-Zehnder interferometers (MZI) (i, j) (i=0 to 3, j=0 to 3) and the diagonal lines of four adjacent MZIs among them. There are a total of 3×3 MZI(i,j)' (i=0 to 2, j=0 to 2), one at the top. N is the number of MZIs connected to the interferometer array 20 on the input side and the PD array 40 on the output side, in other words, the number of rows of the outermost MZI. Not only N×N structures, but also N×M, M≧N (outermost MZIs are N in the row direction (vertical direction) and M in the column direction (horizontal direction)). good. In the embodiment, an "N×N interferometer" having an N×N structure will be described, but more generally, it will be expressed as an "N×M interferometer" (where M is an integer greater than or equal to N).

As shown in the bottom of FIG. 3, each MZI has two waveguides 31, 32 and two phase shifters 33, 34. Two signals are input from the left side of the figure, and two signals are input from the right side of the figure. is output. The portions where the two waveguides 31 and 32 are shown close to each other before and after the two phase shifters 33 and 34 are couplers, and the two optical signals are coupled. When light of the same wavelength with a phase difference is combined, interference fringes are observed. The phase shifters 33 and 34 are controlled by the external controller 50 so that the phase difference between the signals output from the waveguides 31 and 32 of the MZI(i,j) becomes φ(i,j). The MZI has a thermo-optic effect or an electro-optic effect, and when the respective control voltages are applied to the phase shifters 33 and 34, the electric field from the electrodes gives heat and changes the respective phases of the optical signals passing through the waveguides 31 and 32. change. Phase difference φ(i,j) of each output signal of MZI(i,j)(i=0~3,j=0~3) and MZI(i,j)'(i=0~2,j= The phase differences φ(i,j)' of the respective output signals of 0 to 2) are collectively indicated as <φ> above the N×N interferometer 30 in FIG. <φ> is calibrated by machine learning starting from an initial value.

A splitter 10 and an interferometer array 20 are provided on the input side of the N×N interferometer 30, and a PD array 40 (not shown) is provided on the output side.

FIG. 4 shows an example of the configuration of the splitter 10 when N=4. The splitter 10 is composed of three Mach-Zehnder interferometers (MZI) 11 to 13. MZI11-13 have the same structure as shown in the bottom of FIG. Light is input to the upper left waveguide of MZI11, and no light is input to the lower left waveguide, but after being coupled by an internal coupler, the light is split into two, and the light is input to the upper right and lower right waveguides of MZI11. Light is output from. No light is input to the upper left waveguide of MZI12 and the lower left waveguide of MZI13, but light is input from MZI11 to the lower left waveguide of MZI12 and the upper left waveguide of MZI13, so the light is coupled by the internal coupler and then split. Optical signals are output from a total of four waveguides on the right side of MZIs 12 and 13. By controlling the voltage applied to the phase shifters 33 and 34 of each MZI from the external controller 50, the phase difference of the optical signals passing through the two waveguides 31 and 32 of each MZI is changed, and the waveguides on the right side of MZIs 12 and 13 are The optical power of the optical signal output from can be adjusted. The phase of each MZI for giving desired weighting to the optical power can be determined by machine learning together with the phase of each MZI of the N×N interferometer 30.

Returning to FIG. 3, the optical signal split by the splitter 10 is input to the interferometer array 20. The interferometer array 20 has four Mach-Zehnder interferometers (MZI) 21-24. MZIs 21-24 have the same structure as shown at the bottom of FIG. The phase shifters 33 and 34 of each MZI are controlled by the external controller 50 so that the MZIs 21 to 24 each output an optical signal with a phase difference corresponding to the parameters x ₁ to x ₄ (generally represented as <x> in FIG. 3). controlled.

0 to 7 shown on the output side of the N×N interferometer 30 are port IDs. After machine learning is performed, the port ID of the port with the highest optical power indicates the classification result for <x> input to the interferometer array 20. For example, in the above-mentioned Iris product classification example, three product classifications are obtained from four parameters, so port IDs 1, 3, and 5 are used as an example. In other words, machine learning of <φ> is performed for the sample <x> so that the optical power is maximized at the port ID (one of 1, 3, and 5 as an example) corresponding to the correct product type.

There are various machine learning algorithms, but as an example, the modified Bacteria Foraging Algorithm (modified BAF) is shown in pseudo code.

initialize φ _i,k
initialize δ=f(φ _i,k )
do
for (j: 0→N _C )
{
for (i: 0→S)
{
initialize θ
φ _i,k =φ _i,k +Δ・θ
δ'=f(φ _i,k )
if (δ'<δ)
{
δ=δ'
m=0
do
φ _i,k =φ _i,k +Δ・θ
δ'=f(φ _i,k )
m=m+1
while (δ'<δ &&m<=N _S )
}//end if
}//end i
sort δ in ascending order
sort φ _i,k
reproduce φ _i/2:S,k
}//end j
While (δ<δ ₀ )

In this specification, φ is used with a different definition only in this pseudocode. φ _k is a vector from k=1 to M, that is, a point in M-dimensional space (in the example of FIG. 3, it corresponds to the number of MZIs included in the N×N interferometer 30, so M=16+9=25) . First, φ _k for S bacteria, that is, φ _i,k , i=1 to S, k=1 to M, are randomly initialized (in the example of FIG. 3, each MZI of the N×N interferometer 30 initialize the phase (phase difference) with a random value). Obtain the output y(φ _i,k ) for each bacterium (in the example of FIG. 3, <x> is given and the optical power of ports 0 to 7 is measured). Assuming that the value to be output (in the example of FIG. 3, the measured optical power of ports 0 to 7 where the optical power of the port that shows the correct classification result for <x> is the maximum) is y ₀ , y The error between (φ _i,k ) and y ₀ (in the example of Fig. 3, the sum of the squared differences between the measured optical power and the optical power to be measured for ports 0 to 7) is δ (in the pseudocode above, δ=f(φ _i,k ) and δ′=f(φ _i,k )). Each bacterium moves along a random direction vector θ with steps Δ (φ _i,k =φ _i,k +Δ·θ in the above pseudocode) until the upper limit number of iterations is reached while the error decreases. Unless otherwise specified, repeat from obtaining the output y(φ _i,k ) for each bacterium described above. Sort the δ of each bacterium in ascending order (sort δ in ascending order in the pseudocode above), and replace the bacteria in the latter half with the bacteria in the first half with a smaller error (reproduce φ _{i/2:S in the pseudocode above). ,k} , i/2:S represents "i/2" to "S"). Repeat until the error reaches the termination criterion δ ₀ . To put it simply in the example of FIG. 3, S initial values of <φ> are prepared, and <φ> with a small error from the desired result is searched for.

Here, an example will be shown in which Iris type classification is performed using a photonics classifier having the photonics chip 100 having the configuration shown in FIG. 3. Table 1 shows the Iris dataset (partially omitted), which is often used as sample data for machine learning. There is data for 50 samples each of three types of iris (Setosa, Versicolor, and Virginica). Four characteristic quantities (length and width of sepals and petals) were measured.

For each sample, x ₁ to x ₄ are normalized as described below, and set in the phase shifter of each MZI of the interferometer array 20, and machine learning is performed a total of 150 times.
x ₁ = 2π × (value of sepal length of the sample - minimum value of sepal length among 150 samples) / (maximum value of sepal length among 150 samples - 150 samples) (minimum length of inner sepal)
x ₂ = 2π×(Value of sepal width of the sample - Minimum value of sepal width among 150 samples)/(Maximum value of sepal width among 150 samples - Sepal width among 150 samples) (minimum width of )
x ₃ = 2π × (value of petal length of the sample - minimum value of petal length among 150 samples) / (maximum value of petal length among 150 samples - 150 samples) (minimum length of inner petal)
x ₄ = 2π × (value of petal width of the sample - minimum value of petal width among 150 samples) / (maximum value of petal width among 150 samples - petal among 150 samples) (minimum width of )

In the phase shifter of each MZI of the N×N interferometer 30, for example, as shown in FIG. 5, <φ> is randomly set as an initial value in the range of −0.3π to 0.3π. The bar graphs of 4, 3, 4, 3, 4, 3, and 4 in each column shown as 1 to 7 in FIG. Initial values set for 4, 3, 4, 3, 4, 3, and 4 MZIs are shown in order from the left.

FIG. 6 shows the classification results before machine learning, and shows the phase distribution of the N×N interferometer 30 shown in FIG. 5. Parameters corresponding to each sample data are input to the interferometer array 20 and output to each port. The magnitude of the optical power is shown in gray scale. The scale at the bottom of Figure 6 is continuous: red around 0.0 to 0.5, orange around 0.5 to 1.0, yellow around 1.0 to 1.5, green around 1.5 to 0.4, light blue around 0.4 to 0.5, and blue around 0.5 to 0.7. is changing. The numerical value on this scale represents the ratio of optical power between ports, with the total optical power of eight ports being 1.0. In the upper part of FIG. 6, the sample number is plotted on the vertical axis and the port ID is plotted on the horizontal axis, and the samples are color-coded according to this scale.

Sample numbers 1 to 50 (variety Setosa) are mostly light blue at port ID 0, orange at port IDs 2 and 5, yellow at port IDs 1 and 6, and red at port IDs 3, 4, and 7, which is 40 at port ID 0. -50%, others indicate that optical power of about 0-15% was detected.

Sample numbers 51 to 100 (variety Versicolor) are mostly green for port IDs 0 and 2, orange for port IDs 4 to 6, and red for port IDs 1, 3, and 7, which is 15 to 40% for port IDs 0 and 2. "Other" indicates that optical power of about 0 to 10% was detected.

Sample numbers 101 to 150 (variety Virginica) are mostly blue at port ID 2, yellow at port ID 0, orange at port IDs 4, 5, and 7, and red at port IDs 1, 3, and 6; -70%, others indicate that optical power of about 0-15% was detected.

Before machine learning, the difference between ports with strong and weak optical power is small for the Setosa variety, and there are two ports with relatively strong optical power for the Versicolor variety, so they are not clearly classified.

FIG. 7 shows an example of the phase distribution of each MZI of the N×N interferometer 30 after machine learning. For sample numbers 1 to 50, 51 to 100, and 101 to 150, the mechanical Shows the value obtained by learning. FIG. 8 shows the value of <φ>, inputting parameters corresponding to each sample data to the interferometer array 20, color-coding the magnitude of the optical power output to each port, and displaying the results in gray scale. Indicate by display. The color scheme of the lower scale in FIG. 8 is the same as the lower scale in FIG. In the upper part of FIG. 8, the sample number is plotted on the vertical axis and the port ID is plotted on the horizontal axis, and the samples are color-coded according to this scale.

Sample numbers 1 to 50 (variety Setosa) are mostly blue for port ID 1, green for port ID 3, orange for port IDs 2 and 7, and red for port IDs 0 and 4 to 6, which is 50 to 70 for port ID 1. %, about 15 to 40% for port ID 3, and about 0 to 15% for others.

Sample numbers 51 to 100 (variety Versicolor) are mostly blue at port ID 3, light blue at port ID 5, orange at port ID 1, and red at port ID 0, 2, 4, 6, and 7, which is 50 at port ID 3. It shows that the optical power was detected at around 70%, around 40-50% at port ID 5, and around 0-10% at other ports.

For sample numbers 101 to 150 (variety Virginica), port ID 5 is blue, port ID 3 is green, and port IDs 0 to 3, 4, 6, and 7 are mostly red; this is about 50 to 70% for port ID 5. This indicates that optical power of approximately 15 to 40% was detected for port ID 3, and approximately 0 to 5% for the others.

After machine learning, the maximum optical power is detected at port IDs 1, 3, and 5 for sample numbers 1 to 50, 51 to 100, and 101 to 150, respectively, and correct classification results for the samples can be read.

How to determine the maximum optical power at the output port of the N×N interferometer 30 is as follows. If the difference between the maximum optical power Pmax detected at a certain port and the optical power P detected at other ports among the optical powers detected at each port is greater than the product of r and Pmax, then If so, use it as the maximum optical power. 9 and 10 show the probability that the maximum optical power is detected when the relative difference for determining the maximum optical power is set to r=0, r=0.05, and r=0.1. r=0 means that if the value is even slightly larger than the others, it will be used as the maximum optical power. In FIGS. 9 and 10, whether the maximum optical power was detected was checked once every ten to twenty times machine learning was performed. In other words, machine learning was performed a total of 70,000 to 80,000 times. The inner graph in FIG. 9 is an expanded range of 90 to 100% accuracy, and the inner graph of FIG. 10 is an expanded range of 80 to 100% accuracy and 3500 to 3800 checks. If the relative difference with the optical power of other ports when determining the maximum optical power and the number of machine learning operations are appropriately determined, classification results can be obtained with high probability.

Figure 11 shows the results of performing machine learning on 90 samples out of 150 samples and verifying recognition on the remaining 60 samples using the obtained phase distribution, color-coded using the same scale as in Figures 8 and 10. Shown in grayscale. The left side of FIG. 11 shows the results of machine learning performed on 90 samples out of 150 samples, and are as follows.

Sample numbers 1 to 30 (variety Setosa) are mostly blue for port ID 1, green for port ID 3 and 5, orange for port ID 2, and red for port ID 0, 4, 6, and 7, which is 50 for port ID 1. Indicates that optical power was detected at ~70%, approximately 15-40% for port IDs 3 and 5, and approximately 0-10% for others.

Sample numbers 31 to 60 (variety Versicolor) are mostly blue at port ID 3, light blue at port ID 5, orange at port ID 1, and red at port ID 0, 2, 4, 6, and 7, which is 50 at port ID 3. It shows that the optical power was detected at around 70%, around 40-50% at port ID 5, and around 0-10% at other ports.

For sample numbers 61 to 90 (variety Virginica), port ID 5 is blue, port ID 3 is light blue, port ID 1 is orange, and port IDs 0, 2, 4, 6, and 7 are mostly red. Indicates that optical power was detected at ~70%, approximately 40-50% for port ID 3, and approximately 0-10% for others.

That is, it can be seen that for sample numbers 1 to 30, 31 to 60, and 61 to 90, the maximum optical power is detected at port IDs 1, 3, and 5, respectively.

The right side of Figure 11 shows the results of verifying recognition with the remaining 60 samples using the obtained phase distribution, and for sample numbers 1 to 20, 21 to 40, and 41 to 60, the color display is almost the same as the left side of Figure 11. ing. Therefore, using samples different from those used for machine learning, for sample numbers 1 to 20, 21 to 40, and 41 to 60, the maximum optical power was detected at port IDs 1, 3, and 5, respectively, that is, correctly. You can see that it has been classified. The recognition probability was 98.3% when r=0%, 98.3% when r=5%, and 91.7% when r=10%.

Next, handwritten digits 0 to 9 (labeled 0 to 9) were classified using the MNIST dataset, which is often used as sample data for machine learning. FIG. 12 is an example of sample data of handwritten digits 0 to 9 included in the MNIST dataset. Each sample data has 28x28 pixels.

Although the photonics chip shown in FIG. 3 has N=4, the photonics chip shown in FIG. 13 with N=16 was used here. Although FIG. 13 does not show all waveguides to simplify the expression, the number of waveguides on the output side of the splitter 10, interferometer array 20, and N×N interferometer 30 is 16, 32, and 32, respectively. It's a book. In this case, the number of parameters that can be input to the interferometer array 20 is 16, so the 28 x 28 pixels are divided into 4 x 4 pixels, and the 7 x 7 4 x 4 pixels are convolved (summed) to form the interferometer array. Entered 20. The port IDs on the output side of the N×N interferometer 30 in FIG. 13 are 0 to 31, so for the ten handwritten numbers 0 to 9 shown in FIG. , 13, 15, 17, and 19, machine learning was performed so that the maximum optical power was detected.

The left side of FIG. 14 shows a color-coded grayscale representation of the relationship between the handwritten numeric label and the optical power of each port after learning. The color scheme is the same as the scale at the bottom of Figure 6. The right side of FIG. 14 shows the relationship between the handwritten numeric label and the port where the maximum optical power should be detected. The port where the maximum optical power should be detected is shown in white, and the other ports are shown in black.

Handwritten digit 0 is blue for port ID 1, green for port ID 3, 7, and 11, yellow for port ID 15, orange for port ID 5, 13, and 17, and red for other ports, which is 50 to 70% for port ID 1. This indicates that optical power of approximately 15 to 40% was detected for port IDs 3, 7, and 11, and approximately 0 to 15% for other ports.

The handwritten number 1 is blue for port ID 3, green for port ID 1, 5, and 17, yellow for port ID 9, 15, orange for port ID 7, 11, and 19, and red for other ports. It shows that optical power of about 70% was detected, about 15 to 40% for port IDs 1, 5, and 17, and about 0 to 15% for other ports.

Handwritten numeral 2 is blue for port ID 5, light blue for port ID 3, green for port IDs 9 and 19, yellow for port ID 13, orange for port IDs 1, 11, 15, and 17, and red for other ports. This indicates that optical power was detected at approximately 50 to 70% for port ID 3, approximately 40 to 50% for port ID 3, approximately 15 to 40% for port ID 9 and 19, and approximately 0 to 15% for other ports.

Handwritten numeral 3 is blue for port ID 7, green for port ID 1, 11, 15, and 19, yellow for port ID 13, 27, orange for port ID 3, 5, and 17, and red for other ports; This indicates that optical power of about 50 to 70% was detected, about 15 to 40% for port IDs 1, 11, 15, and 19, and about 0 to 15% for other ports.

Handwritten digit 4 is blue for port ID 9, green for port ID 3, 5, and 19, yellow for port ID 11, 13, and 15, orange for port ID 7, and red for other ports, which is 50 to 70% for port ID 9. This indicates that optical power of approximately 15 to 40% was detected for port IDs 3, 5, and 19, and approximately 0 to 15% for other ports.

The handwritten numeral 5 is blue for port ID 11, green for port IDs 1 and 7, yellow for port IDs 13, 15, and 17, orange for port ID 3, and red for other ports.This is about 50 to 70% for port ID 11. This indicates that optical power of approximately 15 to 40% was detected for port IDs 1 and 7, and approximately 0 to 15% for other ports.

Handwritten numeral 6 is blue for port ID 13, green for port ID 3, 5, and 11, yellow for port ID 19, orange for port ID 15, 19, and red for other ports.This is about 50 to 70% for port ID 13. This indicates that optical power of approximately 15 to 40% was detected for port IDs 3, 5, and 11, and approximately 0 to 15% for other ports.

The handwritten numeral 7 is blue for port ID 15, green for port IDs 3, 5, 7, 11, 17, and 19, and red for other ports. , 11, 17, and 19, optical power of about 15 to 40% was detected, and the others showed that optical power of about 0 to 5% was detected.

The handwritten number 8 is blue for port ID 17, green for port IDs 1, 3, 7, and 15, yellow for port IDs 5, 11, and 19, and red for other ports. This shows that optical power of about 15 to 40% was detected for ID1, 3, 7, and 15, and about 0 to 15% for the others.

The handwritten numeral 9 is blue for port ID 19, green for port ID 3, 5, 9, and 15, yellow for port ID 17, orange for port ID 1, 7, 11, and 13, and red for other ports; This indicates that optical power of about 50 to 70% was detected, about 15 to 40% for port IDs 3, 5, 9, and 15, and about 0 to 15% for other ports.

That is, only the white part on the right side of FIG. 14 is shown in blue at the corresponding position on the left side of FIG. Therefore, it can be seen that machine learning was performed so that the maximum optical power was detected at the port corresponding to each handwritten digit.

Next, we used a non-convolution method to classify handwritten digits 0 to 9 using the MNIST dataset. In the above, machine learning was performed on 10 samples using the photonics chip with N=16 shown in FIG. 13, but here, the photonics chip 100 with N=4 shown in FIG. Machine learning was performed on the samples. The sample data of handwritten digits 0 to 9 included in the MNIST dataset are not only shown in Figure 12, but also include various handwritings for each digit as shown in Figure 15 (this is due to the data used as samples). (partially).

Since the number of parameters that can be input to the interferometer array 20 in the photonics chip 100 shown in FIG. The external controller 50 repeats the process of controlling the 14×14 photonics chips by one external controller 50, or inputting the input to the interferometer array 20 of one photonics chip and obtaining the output from the PD array 40. .

When performing machine learning on 10,000 samples, the feature matrix A is a matrix with 10,000 rows and 14 x 14 x 8 columns (outputs of port IDs 0 to 7 for each 14 x 14 photonics chips). If the classification result y is a matrix with 10,000 rows (number of samples) and 10 columns (number of output ports for indicating the classification result), then use a matrix w with 14 x 14 x 8 rows and 10 columns. Then, the linear separation of y is expressed as Aw=y
It can be expressed as. That is, the processing by the N×N interferometer 30 on the optical signal can be expressed by linear calculation. The fixed value matrix w is obtained, for example, by machine learning using an external electronic circuit, a personal computer, or the like. Separation can be performed using the photonics chip 100 and only by matrix operations as described above, without using a nonlinear function.

Since embodiments according to the present invention can be expressed by matrix operations as described above, they are not limited to the number of input parameters of a photonics chip, and can be applied to classifications having a larger number of input parameters.

The processing in the photonics chip above is
y=w・sin(x)・Πsin(φ)
It can be expressed as , and does not include calculations by nonlinear optical devices. Here, y is the output, w is the weighting by the splitter, x is the input data, sin represents the characteristic of the MZI, and w·sin(x) represents the feature vector. Πsin(φ) represents processing by an N×N interferometer (linearly separated portion).

In this way, the photonics classifier according to embodiments of the present invention is applicable even when the number of parameters representing each sample exceeds the number of parameters that can be input to the photonics chip.

Table 2 shows the relationship between the correct label of each sample and the label recognized by the photonics classifier for about 1000 handwritten digits 0 to 9 in the MNIST dataset. The number of samples is concentrated on the diagonal line from the upper left to the lower right, indicating that most of the samples were correctly recognized. The probability of correct recognition is 88.93%.

Furthermore, FIG. 16 shows the classification results for a total of 10,000 samples, 1,000 each of handwritten digits 0 to 9 in the MNIST dataset. The horizontal axis indicates sample numbers, and each number corresponds to 1000 samples of handwritten digits from 0 to 9 in order from the smallest number to the largest number. The vertical axis indicates port IDs 0 to 9 for each sample. In FIG. 16, the magnitude of the output optical power is color-coded in gray scale, and the optical power increases from black to white. The fact that white areas are concentrated diagonally from the top left to the bottom right indicates that most of the images were correctly recognized. The probability of correct recognition is 91.72%.

Although the preferred embodiments of the present invention have been described in detail above, the present invention is not limited to such specific embodiments, and various modifications and changes can be made within the scope of the present invention as set forth in the claims. It is possible. For example, the external controller 50 shown in FIG. 1 may be mounted on the photonics chip 100.

The present invention can be used for various classification problems.

10 Splitter 20 Interferometer array 30 N×N interferometer 33, 34 Phase shifter 31, 32 Waveguide 40 Photodiode array 50 External controller 100, 200 Photonics chip

Claims (11)

Using N input parameters (N is an integer of 4 or more) obtained by normalizing each sample data, N Mach-Zehnder shifts the phase of the corresponding optical signal and outputs 2N optical signals. an interferometer array comprising interferometers, each Mach-Zehnder interferometer outputting two sinusoidal optical signals having a phase difference indicated by the input parameter;
an N×M interferometer that receives the 2N phase-shifted optical signals, shifts the phase of the optical signal passing through each of the plurality of Mach-Zehnder interferometers connected in a grid pattern, and outputs the phase-shifted optical signals to 2N ports; (However, M is an integer greater than or equal to N), and the plurality of Mach-Zehnder interferometers include N×M Mach-Zehnder interferometers, and the optical signal is classified by passing through the N×M interferometers. an N×M interferometer, in which the operation by the N×M interferometer is completed and the processing by the N×M interferometer corresponds to one matrix operation;
a photodetector that detects the optical power of the optical signals output from the 2N ports;
and performs learning so that the maximum optical power is detected at the port associated with the correct classification result for each sample data regarding the phase shifted by each of the Mach-Zehnder interferometers of the N×M interferometer. A photonics classifier that does not require nonlinear processing because classification is completed by later detecting the optical power. an input waveguide into which an optical signal of a single wavelength is input;
further comprising a splitter that branches the input optical signal into N waveguides and outputs it to the N Mach-Zehnder interferometers of the interferometer array, the splitter including a plurality of Mach-Zehnder interferometers, By shifting the phase of the optical signal passing through each of the plurality of Mach-Zehnder interferometers, the input optical signal is branched into N waveguides at a predetermined ratio, and the phase shifted by each Mach-Zehnder interferometer is The optical power of the input optical signal is calibrated to be split at a predetermined ratio, and the splitter is not split equally, but the phase of each Mach-Zehnder interferometer is determined by learning to determine a predetermined ratio for accurate classification. The photonics classifier according to claim 1, wherein is included in the learning parameters. 2. The photonics classifier according to claim 1, wherein the N×M interferometer completes the classification operation after performing processing corresponding to one 2N×2N matrix operation. 3. The photonics classifier of claim 2, wherein the input waveguide, the splitter, the interferometer array, the NxM interferometer, and the photodetector are integrated on a photonics chip. The photonics classifier according to claim 4, further comprising a controller outside the photonics chip that performs calibration by machine learning. The photonics classifier according to claim 4, further comprising a controller on the photonics chip that performs calibration by machine learning. one or more other photonics chips, the total number of Mach-Zehnder interferometers included in the interferometer array of each photonics chip is equal to the number of parameters corresponding to each sample data, and one controller 6. The photonics classifier of claim 5, wherein the calibration for photonics chips is performed collectively. The photonics classifier according to any one of claims 1 to 7, wherein the Mach-Zehnder interferometer shifts the phase of an optical signal using a thermo-optic effect or an electro-optic effect. 5. The photonics classifier according to claim 1, wherein the photoelectrically converted signal whose optical power is detected by the photodetector is not further processed in an electric circuit or fed back to the interferometer array. The photonics chip is composed only of linear optical devices, and the calculation is completed only by light propagation without feeding back the electric signal obtained by the photodetector to the input via an electric circuit. The photonics classifier according to item 4. N Mach-Zehnder interferometers (N is an integer of 4 or more) included in the interferometer array shift the phase of the corresponding optical signal using N input parameters obtained by normalizing each sample data. the step of outputting 2N optical signals, each Mach-Zehnder interferometer outputting two sine wave optical signals having a phase difference indicated by the input parameter, and outputting 2N optical signals so as to enable accurate classification; The branching ratio of the optical signal input to each Mach-Zehnder interferometer is determined by learning.
The 2N phase-shifted optical signals are received by an N×M interferometer (where M is an integer greater than or equal to N), and the optical signals that pass through each of the plurality of Mach-Zehnder interferometers connected in a grid pattern are shifting the phase and outputting to 2N ports, the plurality of Mach-Zehnder interferometers including N×M Mach-Zehnder interferometers, and by passing the optical signal through the N×M interferometers; a step in which the calculation for classification is completed, the processing by the N×M interferometer corresponds to one matrix calculation, and the interference state setting of the N×M interferometer reflects the result of learning; ,
detecting the optical power of the optical signals output from the 2N ports with a photodetector;
Regarding the phase shifted by each of the Mach-Zehnder interferometers of the N×M interferometer, learning is performed so that the maximum optical power is detected at the port associated with the correct classification result for each sample data, and after learning, the optical a step in which classification is completed by detecting power, so nonlinear processing is not necessary;
A photonics classification method comprising:

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