Apparatus and method for optical neural network

Abstract

The present invention relates to devices and methods for optical neural networks. The present invention provides an optical neural network, which is constructed based on photonic integrated circuits to perform neuromorphic computing. In the optical neural network, matrix multiplication is implemented using one or more optical interference units, which can apply arbitrary weighted matrix multiplication to an array of input optical signals. Nonlinear excitation is achieved by optical nonlinear units, which can be based on nonlinear optical effects, such as saturable absorption. These calculations are implemented optically, resulting in high computing speed and low power consumption in the optical neural network.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to U.S. Application No. 62,344,621, filed on June 2, 2016, entitled “METHODS AND DESIGN OF OPTICAL NEURAL NETWORK,” which is incorporated herein by reference in its entirety. Background Art

[0003] Existing computers based on the von Neumann architecture are generally more power hungry and less efficient than their biological counterparts - the central nervous system - for a wide range of tasks, such as perception, communication, learning, and decision making. With the ever-increasing amounts of data associated with big data processing, it is beneficial to develop computers that can learn, combine, and analyze large amounts of information quickly and efficiently. For example, speech recognition software (such as Apple's Siri) is typically executed in the cloud because the computations involved are generally too challenging for the hardware in mobile phones.

[0004] One way to address the shortcomings of the von Neumann computing architecture is to develop artificial neural networks (ANNWs). ANNWs generally simulate the signal processing architecture in the brain and have received widespread attention recently. ANNWs can greatly improve speech recognition, visual object recognition, object detection, and many other fields, such as drug discovery and genomics. Traditional artificial neural networks generally use electronic architectures, such as application-specific integrated circuits (ASICs) and field-programmable gate arrays (FPGAs). However, the computing speed and power efficiency achieved with these hardware architectures are still limited by electronic clock rates and ohmic losses. Summary of the invention

[0005] Embodiments of the present technology generally relate to artificial neural networks. In one example, an apparatus for implementing an artificial neural network includes an input waveguide array that receives an optical signal of a first array. An optical interference unit is in optical communication with the input waveguide array to perform a linear transformation of the optical signal of the first array to an optical signal of a second array. The apparatus also includes an optical nonlinear unit that is in optical communication with the optical interference unit to perform a nonlinear transformation on the optical signal of the second array to generate an optical signal of a third array. A detector array is in optical communication with the optical nonlinear unit to detect the optical signal of the third array.

[0006] In another example, a method for artificial neural network computing includes receiving an optical signal of a first array with an input waveguide array. The method also includes interfering the optical signal of the first array using an optical interference unit in optical communication with the input waveguide array to linearly transform the optical signal of the first array into an optical signal of a second array. The method also includes nonlinearly transforming the optical signal of the second array using an optical nonlinear unit in optical communication with the optical interference unit to generate an optical signal of a third array. The method also includes detecting the optical signal of the third array.

[0007] In yet another example, an optical neural network includes an input waveguide array that receives an optical signal of a first array. The network also includes a plurality of interconnected Mach-Zehnder interferometers (MZIs) that are in optical communication with the input waveguide array to linearly transform the optical signal of the first array into an optical signal of a second array by interference in the optical signal of the first array. Each of the plurality of MZIs includes a first phase shifter configured to change a splitting ratio of the MZI; and a second phase shifter configured to shift a phase of an output of the MZI. The network also includes a saturable absorber array that is in optical communication with the plurality of interconnected MZIs to nonlinearly transform the optical signal of the second array into an optical signal of a third array. Each saturable absorber in the saturable absorber array receives a corresponding optical signal in the optical signal of the second array. The network also includes a detector array that is in optical communication with the optical nonlinear unit to detect the optical signal of the third array.

[0008] It should be recognized that all combinations of the foregoing concepts and the additional concepts discussed in detail below (if such concepts are not mutually inconsistent) are considered to be part of the inventive subject matter disclosed herein. Specifically, all combinations of the claimed subject matter appearing at the end of this disclosure are considered to be part of the inventive subject matter disclosed herein. It should also be recognized that terms explicitly used herein that may also appear in any disclosure incorporated by reference should be given the meaning most consistent with the specific concepts disclosed herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Those skilled in the art will appreciate that the drawings are primarily for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily drawn to scale; in some cases, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate understanding of different features. In the drawings, the same reference numerals generally refer to the same features (e.g., functionally similar and / or structurally similar elements).

[0010] Figure 1 Schematic diagram showing an optical neural network based on photonic integrated circuits.

[0011] Figure 2A and Figure 2B A schematic diagram showing an optical interference unit 200 that can be used in an optical neural network, which is substantially similar to Figure 1 The optical neural network shown in FIG.

[0012] Figure 3 A schematic diagram showing a control circuit that can be used in an optical neural network, which is essentially similar to Figure 1 The optical neural network shown in FIG.

[0013] Figure 4A Schematic diagram showing an optical neural network including an input layer, multiple hidden layers, and an output layer.

[0014] Figure 4B Shown in Figure 4A Schematic diagram of the hidden layer implementing SVD decomposition in the optical neural network shown in FIG.

[0015] Figure 4C Shown in Figure 4A Schematic diagram of a hidden layer in an optical neural network using a Mach-Zehnder interferometer (MZI) for optical linear transformation.

[0016] Figure 4D Schematic diagram showing an optical neural network using interconnected MZIs and implementing vowel recognition.

[0017] Figure 5 The optical response of a nonlinear cell based on saturable absorption is shown.

[0018] Fig. 6A and Figure 6B Illustration of an optical bistability that can be used in an optical nonlinear unit in an optical neural network, which is essentially similar to Figure 1 The optical neural network shown in FIG.

[0019] Figure 7 A schematic diagram of an optical nonlinear unit including a tunable ring resonator is shown.

[0020] Figure 8 A schematic diagram of an optical nonlinear unit including a Mach-Zehnder interferometer is shown.

[0021] Figures 9A-9D Illustration of an optical neural network using an optical nonlinear unit including a ring resonator.

[0022] Fig.10 Schematic diagram showing a recurrent optical neural network.

[0023] Fig.11A Schematic diagram showing an optical neural network comprising multiple columns of interconnected MZIs.

[0024] Fig. 11B Microscope image of an experimentally fabricated 5×5 unit cell on-chip optical interference cell.

[0025] Fig.12 Shown in Fig.11A and Fig. 11B The decision boundary for a neural network trained on a simple 2-dimensional 3-class classification problem is shown in Figure 2.

[0026] Fig.13A An optical micrograph of 22 optical interference elements on a die fabricated experimentally is shown.

[0027] Fig. 13B yes Fig.13A Schematic illustration of an optical neural network shown in FIG.

[0028] Fig. 13C is Fig.13A Schematic illustration of a single phase shifter used in an MZI in an optical neural network is shown in FIG.

[0029] Fig.14A The correction rates for the vowel recognition problem with various phase encoding errors (σF) and light detection errors (σD) are shown.

[0030] Figures 14B-14E Simulated and experimental vowel recognition results are shown for a training matrix without errors. DETAILED DESCRIPTION

[0031] Overview

[0032] Optical neural networks (ONNWs) provide a promising way to overcome the limitations of computational efficiency and power consumption in microelectronic and hybrid opto-electronic implementations. ONNWs (generally referred to as artificial neural networks) typically include an input layer, at least one hidden layer, and an output layer. In each layer, information is propagated through the neural network by linear combinations (e.g., matrix multiplications) followed by application of nonlinear activation functions to the results of the linear combinations. When training an artificial neural network model, data can be fed into the input layer and the output is calculated by a forward propagation step. The parameters can then be optimized by a backward propagation process. The weighted parameters (i.e., elements of the matrix) of each synapse are optimized by a backward propagation process.

[0033] In ONNWs, linear transformations (and certain nonlinear transformations) can be performed at the speed of light and detected at rates exceeding 100 GHz in photonic networks, and in some cases, with minimal power consumption. For example, ordinary lenses can perform Fourier transforms without any power consumption, and certain matrix operations can also be performed optically without consuming power. However, implementing these transformations with bulky optical components (such as optical fibers and lenses) can be challenging due to the lack of phase stability and the difficulty of integrating a large number of neurons (e.g., on the order of millions of neurons) in the network. Integrated photonics can solve this problem by providing a scalable architecture for large, phase-stable optical transformations.

[0034] The devices and methods described herein use on-chip, coherent optical neuromorphic computing techniques based on photonic integrated circuits. In general, the operations in neuromorphic computing techniques can be decomposed into a series of linear and nonlinear transformations of the input optical signal. In this technique, matrix multiplication (i.e., linear transformation) is implemented using one or more optical interferometers that can multiply arbitrary weighted matrices ω by ω. i is applied to the ith signal in the input optical signal. The nonlinear excitation is achieved by an optical nonlinear unit, which may be based on a nonlinear optical effect, such as saturable absorption.

[0035] Optical neural networks based on photonic integrated circuits have several advantages. First, the high speed, high bandwidth, and low crosstalk achievable in photons are well suited to ultrafast artificial neural network processors. In addition, the high electro-optical conversion efficiency of photonic devices allows such implementations to match or outperform comparable electronic systems with low energy usage. Using existing technologies in quantum optical devices and on-chip nanophotonic circuit fabrication, it is feasible to design variable on-chip ONNW architectures.

[0036] Figure 1 A schematic diagram of an optical neural network 100 based on a photonic integrated circuit is shown. The network 100 includes an electronic interface 110 to encode a digital signal 105a, such as an image signal for image recognition or a speech signal for speech recognition, into an array of optical signals 105b. Various encoding schemes can be used here. For example, the digital signal 105a can be encoded into a polarization form of the optical signal 105b. In another example, the digital signal 105a can be encoded into a phase (or time delay) of the optical signal 105b. In yet another example, the digital signal 105a can be encoded into an intensity of the optical signal 105b. In yet another example, the digital signal 105a can be encoded into a wavelength of the optical signal 105b.

[0037] The array of optical signals 105b is guided to a photonic integrated circuit (PIC) 120 through an array of input waveguides 122. As used herein, the term "waveguide" may include any structure capable of guiding an optical signal in a confined manner. For example, a waveguide may include an optical fiber, a semiconductor waveguide fabricated in a substrate, a photonic crystal structure configured to guide an optical signal, or any other suitable structure. The PIC 120 includes an optical interference unit 124 (also referred to as a matrix product unit 124) to perform a linear transformation of the array of optical signals 105b. In other words, the array of optical signals 105b is treated as a vector (e.g., X), and the optical interference unit 124 acts as a matrix (e.g., M) that is multiplied by the vector, i.e., MX. The matrix multiplication generates an optical signal 105c, which is guided to an optical nonlinear unit 126 through an array of output waveguides 128.

[0038] In some cases, the optical interference unit 124 connects each input waveguide 122 to all output waveguides 128. In other words, the input waveguides 122 and the output waveguides 128 are fully connected. In some cases, the optical interference unit 124 connects a subset of the input waveguides in the array of input waveguides 122 to a full subset of the output waveguides in the output waveguides 128. For example, two input waveguides in the array of input waveguides 122 can be fully connected to two output waveguides in the array of output waveguides 128. In practice, any other number of fully connected waveguides can also be used.

[0039] The optical nonlinear unit 126 is configured to perform a nonlinear excitation function on the optical signal 105c and generate an optical signal 105d. The detector array 130 is used in the network 100 to detect the optical signal 105d and generate a detected signal 105e. The detected signal 105e is converted back into a large number of parallel electronic signals 105f by the electronic interface 140.

[0040] Figure 2A and Figure 2B Schematic diagram of an optical interference unit 200 that can be used in the optical neural network 100 described above is shown. Generally, the optical interference unit 200 functions to perform matrix multiplication on an array of optical signals. Figure 2A Three examples of optical interference cells 220a, 220b and 220c are shown in FIG. In practice, any other type of interference cell capable of performing a linear transformation may be used.

[0041] In one example, the optical interference unit 200 may include a photonic crystal 220a. Figure 2BAs shown in , the photonic crystal 220a includes a substrate 222a and a two-dimensional (2D) array of holes 224b defined in the substrate 222a. The size (e.g., diameter and spacing) of the holes 224a and the material of the substrate 222a can be configured so that interference of optical signals is transmitted into the photonic crystal 220a. More information about using photonic crystals for optical signal interference can be found in U.S. Patent Application Publication No. US 20100226608A1, entitled "Multimode interference coupler for use with slot photonic crystal waveguides", which is incorporated herein by reference in its entirety.

[0042] In some cases, optical interference unit 200 may include one photonic crystal 220a. In other cases, optical interference unit 200 may include an array of photonic crystals that may receive an array of N optical modes, perform a linear transformation on the received optical modes, and then output an array of N optical modes.

[0043] exist Figure 2B In the embodiment of the present invention, the photonic crystal 220a includes an array of holes 224a. Other configurations may also be used. For example, the photonic crystal 220a may include an array of microdisks disposed on a substrate 222a. In another example, the photonic crystal 220a may include a stack of thin films, in which case the photonic crystal 220a may be a one-dimensional (1D) photonic crystal. The length of the photonic crystal 220a may be substantially equal to or greater than 20 μm (e.g., about 20 μm, about 30 μm, about 50 μm, about 100 μm, about 200 μm, about 30 μm, about 500 μm or greater, including any value and sub-ranges between these values). The diameter of each hole 224a may be substantially equal to or greater than 20 nm (e.g., about 20 nm, about 30 nm, about 50 nm, about 100 nm, about 200 nm, about 300 nm or greater, including any value and sub-ranges between these values). In some cases, the pitch d of the array of holes 224a can be substantially equal to the wavelength λ of the optical signal propagating in the photonic crystal 220a divided by the refractive index n of the photonic crystal 220a. p , that is, d = λ / n p In some cases, substrate 222a can be made of silicon or any other suitable material.

[0044] The photonic crystal 220a can be coated with a phase change material to change the optical path length of the photonic crystal 220a. The change in optical path length can in turn change the interference of optical signals propagating in the photonic crystal 220a. This can adjust the weight parameters of each hidden layer in the generated optical neural network.

[0045] In another example, the optical interference unit 200 includes an array of interconnected Mach-Zehnder interferometers (MZIs) 220b. Each MZI splits an input optical signal into a first arm and a second arm, and then combines the optical signals from the two arms for interference. Each MZI also includes a first phase shifter and a second phase shifter, the first phase shifter is configured to change the splitting ratio of the MZI, and the second phase shifter is configured to shift the phase of one output of the MZI. Figures 4A-4D Further details of using the MZI in the optical interference cell 200 are described.

[0046] In yet another example, the optical interference unit 200 may include a multimode interferometer (MMI) 220c. The MMI may include a single-mode waveguide receiving an input optical signal and an array of multimode waveguides for the received optical signals to interfere with each other. The multimode waveguide has many guided modes, each of which has a different propagation constant. Because the mode is an eigenmode, the modes propagate independently of each other. When the multimode interference is excited by the input optical signal, the field distribution can be decomposed into eigenmodes. Even if there is usually no energy exchange between these eigenmodes, they propagate at different speeds, generating interference patterns that vary along the length of the multimode waveguide. More information about multimode interference can be found in U.S. Patent No. 9,097,852B2, entitled "Multi-mode interference device", which is incorporated herein by reference in its entirety.

[0047] Figure 3 Shown can be used in Figure 1 Schematic diagram of control circuit 300 in optical neural network 100 is shown in FIG. Control circuit 300 includes controller 310 that provides digital control signals, which are converted into analog control signals by digital-to-analog converter (DAC) 320. Buffer amplifier 330 is used in control circuit 300 to amplify the analog control signal before applying the signal to photonic integrated circuit 305. Photonic integrated circuit 305 can be connected to Figure 1 The photonic integrated circuit 120 shown in FIG. 1 and described above is substantially the same.

[0048] In practice, the control circuit 300 can be used to train an optical neural network including a photonic integrated circuit 305. For example, the photonic integrated circuit 305 can include an array of interconnected MZIs, each of which includes a phase shifter that controls the splitting ratio of the MZI and another phase shifter that controls the phase of the output. The control circuit 300 can then control the phase imposed by each phase shifter to achieve different matrix transformations. In other words, the control circuit 300 can change the elements M(i, j) (also called weight parameters) of the transformation matrix M implemented by the optical interference unit in the photonic integrated circuit 305.

[0049] During the training process, a set of test data points with expected outputs can be sent to the optical neural network. The expected outputs are then compared to the actual outputs. In the event of any discrepancies, the control circuit 300 can then change the phase settings of the photonic integrated circuit 305 so that the photonic integrated circuit 305 produces the expected results. After determining the phase settings that produce the expected results, the optical neural network can then be used to process unknown data points.

[0050] Alternatively, the weight parameters can be trained separately on an electronic computer. The weight parameters can then be programmed into the optical neural network via thermal phase shifters (e.g. when MZIs are used in optical interferometers) or hard-coded into the optical neural network via phase change materials.

[0051] Optical neural network using Mach-Zehnder interferometer

[0052] Figures 4A-4C A schematic diagram of an optical neural network 400 using a Mach-Zehnder interferometer (MZI) for optical linear transformation is shown. Figure 4A The optical neural network 400 is shown to include an input layer 410, a sequence of hidden layers 420(1), 420(2), ..., and 420(n) (collectively referred to as hidden layers 420), and an output layer 430. Each layer includes a plurality of neurons (in Figure 4A For example, the input layer 410 includes four neurons 411, 412, 413, and 414 (also referred to as nodes). In some cases, such as by Figure 4A Each node indicated by a circle in FIG. 1 may include a waveguide (e.g., input waveguide 122), and the arrows between the columns of circles may be photonic circuits that perform linear and / or nonlinear transformations (e.g., Figure 1 Similarly, the output layer 430 includes four neurons 431, 432, 433 and 434. In practice, any other number of neurons may be used for each layer. Figure 4AAs can be seen in FIG. 4 , each neuron in the input layer 410 is connected to all four neurons in the first hidden layer 420 (1). Similarly, each neuron in the first hidden layer 420 (1) is connected to all four neurons in the second hidden layer 420 (2), and so on.

[0053] In the optical neural network 400, in each layer (e.g., 420), information is propagated by linear combination (e.g., matrix multiplication) followed by application of a nonlinear activation function. In this network 400, a vector of optical signals can be represented as:

[0054]

[0055] Among them, E j is the electric field at waveguide j (in Figure 4B ) The matrix-vector product Z i =W i-1 X is performed by an optical interferometer unit and the activation function f(Z(i)) is implemented using an optical nonlinear unit. The units of network 400, optical interferometers and nonlinear units can be tiled to implement a deep learning network.

[0056] In network 400, matrix-vector products and nonlinear excitations may be evaluated every Ln / c seconds, where L is the physical length of network 400, n is the refractive index, and c is the speed of light. For example, network 400 may have a length L of approximately 1 cm, with a refractive index of approximately 3, thereby providing an evaluation time of approximately 100 ps (also referred to as forward propagation time). During this forward propagation time, a total number of D input vectors may propagate through network 400, yielding a total bandwidth of Dc / nL. Thus, the operations generated at a clock rate may easily exceed tens of gigahertz. This clock rate may be limited only by the rate at which optical signals may be converted into electrical signals (e.g., approximately 100 GHz in current technology).

[0057] In addition to the ultra-fast forward propagation, the computation time associated with evaluating the matrix-vector product scales linearly with the matrix size N. Increasing the size of the matrix from N to N+1 corresponds to adding one waveguide to the network 400. For this system, the number of operations per second is R = 2m·N 2 10 11 Operations / second, where m is the number of layers in the neural network 400.

[0058] Figure 4BEach hidden layer 420 is shown to include an optical interference unit 425 and an optical nonlinear unit 426 to implement a singular value decomposition (SVD) scheme to achieve an arbitrary linear transformation of the input optical signal. In the SVD scheme, a general real matrix (M) can be decomposed into M = USV*, where U is an m×m unitary matrix, S is an m×n diagonal matrix with non-negative real numbers on the diagonal, and V* is the complex conjugate of the n×n unitary matrix V. Figure 4B The optical interferometer unit 425 shown in FIG. 4 includes a first MZI array 421 to implement matrix multiplication using a matrix V, an array of attenuators 422 (or amplifiers) to implement matrix multiplication using a matrix S, and a second MZI array 423 to implement matrix multiplication using a matrix U. In this way, the optical interferometer unit 425 can apply matrix multiplication to the input signal using the matrix M, where M=USV*.

[0059] Matrix multiplication implemented in this way does not consume any power in principle. This leads to high energy efficiency of neural network 400.

[0060] The diagonal elements λ of the matrix S i These are usually referred to as the singular values ​​of the matrix M. The usual convention is to list the singular values ​​in descending order. In this case, the diagonal matrix S is uniquely determined by M. The diagonal matrix S can be obtained using a set of optical amplifiers. An optical amplifier is a device that directly amplifies an optical signal without converting it into an electrical signal. An optical amplifier can include a laser with or without an optical cavity (such as a traveling wave amplifier or a single channel amplifier), or a laser in which feedback from the cavity is suppressed. In the optical neural network 400, each optical amplifier is applied to an output node and amplifies or attenuates the signal by a constant factor λ. i .

[0061] The optical nonlinear unit 426 may include an array of saturable absorbers 427. Alternatively, the optical nonlinear unit 426 may include an array of bistable materials. In general, for an input intensity I in , the light output intensity from the optical nonlinear unit 426 is given by the nonlinear function I out =f(I in ) is given.

[0062] Figure 4C Schematic diagram of an optical interference unit 425 and an optical nonlinear unit 426 is shown. The optical interference unit 425 includes an interconnected MZI 428. Each MZI 428 includes two input waveguides 442a and 442b, two arms 444a and 444b, and two output waveguides 446a and 446b. Each MZI 428 also includes a phase shifter 445a disposed on one arm 444a and another phase shifter 445b disposed on one output waveguide 446a.

[0063] Each phase shifter can be implemented with a heater that heats the waveguide that applies an electric field to the electrode of the waveguide. Phase shifter 445a applies a phase θ and can control the splitting ratio between the signals transmitted by the two output waveguides 446a and 446b. Phase shifter 445b applies a phase φ and can control the phase delay between the signals transmitted by the two output waveguides 446a and 446b. With this configuration, each MZI can perform a unitary transformation on the optical signals received by the two input waveguides 442a and 442b, which can be written as:

[0064]

[0065] Figure 4D An optical neural network 400 is shown, illustrating an optical interference unit 425 and a nonlinear unit 426. Each optical interference unit 425 includes an interconnected MZI, and each nonlinear unit 426 includes an array of waveguides containing saturable absorbers or bistable materials. One optical interference unit 425 and one nonlinear unit 426 form a layer 420 that propagates an optical signal. In practice, the sequence of layers 420 forms a photonic integrated circuit that can receive, for example, a speech signal from a speaker and then process the received speech signal to recognize the content of the speech signal, i.e., speech recognition.

[0066] Optical Nonlinear Unit

[0067] In the neuromorphic techniques described herein, optical nonlinear units (e.g. Figure 1 126 or Figures 4A-4D Specifically, the optical nonlinear unit can use up the input power I through the nonlinear function f in , becomes the output power, making I out =f(I in ):

[0068] In one example, the optical nonlinearity can be based on saturable absorption. Without being bound by any particular theory or mode of operation, the nonlinear function of a saturable absorber can be written as:

[0069]

[0070] Where σ is the absorption cross section, τ s is the radiation lifetime of the material forming the absorber, T m is the maximum transmittance of the saturable absorber, T 0 is the initial transmittance, I 0 is the peak incident intensity. Figure 5 The optical response of a nonlinear cell based on saturable absorption is shown. The saturable absorber used in this cell can be, for example, a dye or a semiconductor quantum dot.

[0071] Fig. 6A and Figure 6B The diagram illustrates optical bistability that can be used for optical nonlinear units. Fig. 6A Schematic diagram of a photonic crystal 600 with optical bistability is shown. The photonic crystal 600 includes a low-index dielectric substrate 610 (n L ~1.5) in a high-index dielectric rod 620 (e.g., n H In some cases, the pitch of the array of rods 620 is represented by a, and the radius of each rod in the array of rods 620 is r=a / 4.

[0072] Figure 6B Show Fig. 6A The optical response of the photonic crystal is shown in . Without being bound by any particular theory or mode of operation, the nonlinear relationship of the photonic crystal 600 can be written as:

[0073]

[0074] Among them, I 0 is the characteristic intensity of the photonic crystal 600, and δ is a parameter that depends on the geometry of the photonic crystal 600. More information about optical bistable photonic crystals can be found in Soljacic et al., "Optimal bistable switching in nonlinear photonic crystals", PHYSICAL REVIEW E 66, 055601 (R), 2002, which is incorporated herein by reference in its entirety.

[0075] Figure 7 A schematic diagram of an optical nonlinear cell 700 using a tunable ring resonator 720 is shown. The cell 700 includes an input waveguide 710 that receives input light. The input waveguide 710 is briefly coupled to the ring resonator 720. A probe waveguide 730 is also briefly coupled to the ring resonator 720 to split a portion of the input light to a detector 740. Based on the detected signal, the detector 740 generates a control signal to tune the ring resonator 720. For example, the control signal can change the resonant wavelength of the ring resonator 720 so as to change the optical response of the ring resonator 720. The transmittance of the cell 700 also depends on the power of the input light in order to implement a nonlinear excitation function in a neural network.

[0076] Figure 8A schematic diagram of an optical nonlinear cell 800 using a Mach-Zehnder interferometer is shown. The cell 800 includes an input waveguide 810a that receives input light and splits the input light into two arms 820a and 820b. A phase shifter 830 is provided on the arm 820b to apply an adjustable amount of phase shift. The light from the two arms 820a and 820b is combined at the output waveguide 810b. A portion of the light propagating in the arm 820b is transmitted to and detected by the detector 840. Depending on the detected signal, the detector 840 can generate a control signal to control the amount of phase shift applied by the phase shifter 830.

[0077] Figures 9A-9D An optical neural network 900 using a ring resonator-based optical nonlinear unit 924 is shown. The optical neural network 900 includes an input layer 910, a sequence of hidden layers 920, an output layer 930, and a detection layer 940. Each hidden layer 920 includes an optical interference unit 922 and an optical nonlinear unit 924.

[0078] Fig. 9B A schematic diagram of an optical nonlinear unit 924 is shown, which can be used with Figure 7 The optical nonlinear unit 700 shown in and described above is substantially similar. Fig. 9C 9 is a graph of the output power of the ring resonator in the optical nonlinear unit 924 versus wavelength detuning and derivative. Fig.9D The optical output power (P out ) to input power (P in ). A family of curves can be realized by configuring a single optical nonlinear unit.

[0079] In the optical nonlinear unit 924, the light incident on the optical cavity is detected by the photodetector, which then drives the optical cavity non-resonantly. This opto-electronic component can implement a range of high-speed nonlinear excitation functions, including ReLU and S-shaped, such as Fig.9D Different nonlinear functions can be selected by applying a bias voltage that causes the Lorentz transfer function (see Fig. 9C ) shifts, thereby modifying the input-output power relationship.

[0080] Recurrent Optical Neural Networks

[0081] Fig.10 Schematic diagram of a recursive optical neural network 1000 that can circulate an optical signal at an output layer. The optical neural network 1000 includes an optical interference unit 1010 and an optical nonlinear unit 1020 to form a hidden layer. Fig.10Only one hidden layer is shown, but multiple hidden layers can be used. At the output, the optical signal is transmitted to the switch 1030, which sends part of the received signal to the readout unit 1040 for detection and sends another part of the received signal back to the optical interference unit 1010 for another round of linear transformation (and then to the optical nonlinear unit 1020 for nonlinear excitation). By wrapping the optical signal from the output layer of the optical neural network 1000 back to the input layer, the same physical hardware can be used to achieve larger transformations with a smaller number of weights. This recursive configuration can be used to efficiently construct deep neural networks, that is, neural networks with a large number of hidden layers.

[0082] In one example, the optical signal at the output layer is sent directly back to the input layer for another round of transformation. In another example, the optical signal at the output layer can be converted into an electrical signal, which is then sent to a light source (not shown). The electrical signal can be used as a control signal to control the light source to transmit an optical signal substantially similar to the optical signal at the output layer. In other words, the light source regenerates the output optical signal. This configuration can reduce possible losses or distortions during optical transmission back to the input layer.

[0083] Characterizing Optical Neural Networks Using Photonic Integrated Circuits

[0084] Fig.11A Schematic diagram of an optical neural network 1100 is shown, and the optical neural network 1100 includes a plurality of columns of interconnected MZIs 1110 (0), 1110 (1), ... and 1110 (L). In addition to each MZI 1120 also including two loss-balancing phase shifters 1125, the MZIs 1120 in each column 1110 are connected to Figure 4C The MZI shown in FIG. 11 is substantially similar. One loss-balanced phase shifter is disposed on an arm of the MZI 1120 and another loss-balanced phase shifter is disposed on an output waveguide of the MZI 1120 . Fig. 11B Microscope image of an experimentally fabricated 5×5 unit cell on-chip optical interference cell.

[0085] Fig.12 Shown in Fig.11A and Fig. 11B The decision boundary for a simple 2D 3-class classification problem trained on a neural network is shown in . The three classes of data are labeled Fig.12 In training, batch forward propagation and backpropagation are used to optimize the parameters. Fig.12 The classification results for two input units, 3 output units and 1 hidden layer are shown, showing an error rate of less than 8%. In another round of training, 786 input units, 6 output units and 1 hidden layer were used. Similarly, an error rate of less than 10% was achieved.

[0086] Fig.13A An optical micrograph of an experimentally fabricated 22-mode, on-chip optical interferometer cell is shown. The physical regions of the optical neural network program are highlighted in gray. The system acts as an optical field programmable gate array, which can be a test bed for optical experiments. Fig. 13B Yes Fig.13A Schematic representation of an optical neural network 1300 of an optical interference unit shown in FIG. The optical neural network 1300 implements both matrix multiplication and matrix amplification entirely in an optical manner. Fig. 13C Schematic illustration of the transmission curves of a single phase shifter in a Mach-Zehnder interferometer (MZI) and the internal phase shifters used to tune the MZI.

[0087] The optical neural network 1300 includes an input waveguide array 1305 to receive an input mode and transmit the input mode to a SU(4) core 1310, which includes an array of interconnected MZIs. A non-unitary diagonal matrix multiplication core (DMMC) 1320 is coupled to the SU(4) core 1310. The DMMC 1320 includes vertical columns of MZIs. One input waveguide of each MZI is connected to the SU(4) core 1310. One output waveguide of each MZI is coupled to, for example, an optical nonlinear unit, while the other output waveguide is blocked. Alternatively, the output waveguide can be coupled to a detector 1330 to detect a portion of the signal transmitted by the output waveguide. In this way, the DMMC 1320 can change the overall intensity (or power) of the optical signal received by the neural network 1300.

[0088] The SU(4) 1310 core implements operators U and V through a Givens rotation algorithm that decomposes a unitary matrix into several sets of phase shifters and beam splitters, while the DMMC 1320 implements operator S by controlling the splitting rate of the DMMC interferometer to add or remove light to or from the optical mode relative to a reference amplitude. In this way, the combination of SU(4) 1310 and DMMC 1320 can perform SVD decomposition.

[0089] Vowel recognition was performed on the neural network 1300. To prepare the training and test data sets, 360 data points were used. Each data point included four logarithmic area scaling coefficients for a phoneme. The logarithmic area scaling coefficients or feature vectors represent the power contained in different logarithmically spaced frequency bands and are derived by calculating the Fourier transform of the speech signal multiplied by the Hamming window function. The 360 ​​data points were generated by 90 different people speaking 4 different vowel phonemes. Half of these data points were used for training and the remaining half were used to test the performance of the trained optical neural network 1300. The matrix parameters were trained using the standard back propagation algorithm using the stochastic gradient descent method on a conventional computer.

[0090] A coherent optical neural network 1300 is implemented using a programmable nanophotonic processor comprising an array of 56 Mach-Zehnder interferometers (MZIs) and 213 phase-shifting elements, such as Fig.13A Each interferometer consists of two evanescent mode waveguide couplers sandwiching an internal thermo-optical phase shifter that controls the splitting ratio of the output modes, followed by a second modulator that controls the relative phase of the output modes. By controlling the phase propagated by these two phase shifters, given a controlled incident phase on the two electromagnetic input modes of the MZI, these MZIs perform all rotations in the SU(2)Lie group. For example, the nanophotonic processor can be manufactured with OPSIS Foundry in a silicon-on-insulator photonics platform.

[0091] The fidelity of the measurements was 99.8 ± 0.003% for the 720 optical interferometers and DMMC cores used in the experiments. In this analog computer, the fidelity is limited by practical non-ideal conditions, such as (1) the limited accuracy of the optical phase that can be set using a custom 240-channel voltage source with 16 bits of voltage resolution per channel; (2) light detection noise; and (3) thermal crosstalk between phase shifters, which effectively reduces the number of bits of resolution used to set the phase. As with digital floating-point operations, these values ​​exhibit a certain number of bits of precision, with limited dynamic range and noise in the optical intensity causing effective truncation errors.

[0092] In this demonstration, the nonlinear transformation I out =f(I in ) is a method in the electronic domain that measures the intensity of the optical mode output on the photodetector array and converts the signal I out Here, f models the mathematical function associated with a real saturable absorber (e.g., a dye, semiconductor, or graphene saturable absorber, or a saturable amplifier) ​​that can be integrated directly into the waveguide after each optical interference stage of the circuit. For example, given an input intensity I 0 , we can solve T from equation (3) above m (I 0 ), the output intensity can be adjusted according to I out =I 0 ·T m (I 0 )calculate.

[0093] After programming the nanophotonic processor to implement an optical neural network architecture consisting of 4 layers of optical interferometers with 4 neurons in each layer, the neural network was used on a vowel recognition test set. The network correctly recognized 138 / 180 (76.7%) cases, compared to 165 / 180 (91.7%) in simulation.

[0094] Fig.14AThe phase encoding errors (σ F ) and light detection error (σ D ), the definitions of these two variables can be found in the Methods section. The solid lines are contours of the different levels of percent accuracy. Figures 14B-14E Simulation and experimental vowel recognition results for error-free training matrices are shown. Fig. 14B In the vowel A is pronounced. Fig. 14C In the vowel B. Fig.14D In the vowel C is pronounced. Fig.14E In the middle, pronounce the vowel D.

[0095] Since the optical neural network 1300 processes information in the analog signal domain, the architecture may be prone to computational errors. Photodetection and phase encoding are the main sources of error in the optical neural network presented here. In order to understand the role of phase encoding noise and photodetection noise in the ONNW hardware architecture and develop their accuracy model, different levels of phase encoding noise (σ F ) and light detection noise (σ D ) to digitally simulate the performance of the trained matrix. The percentage of accuracy versus σ F and σ D The distribution of Fig.14A middle, Fig.14A Serves as a guide to understanding the experimental performance of optical neural networks.

[0096] Implementing higher precision analog-to-digital converters in the photodetector arrays and voltage controllers can bring the performance of optical neural networks close to that of digital computers. Known techniques can be applied to design photodiode arrays to achieve significantly higher dynamic ranges, such as using logarithmic or multi-stage gain amplifiers. Solving these manageable engineering problems can further improve the accuracy performance of optical neural networks to achieve accuracy percentages approaching the performance of error-corrected digital computers.

[0097] Processing big data at high speed and low power is perhaps the core challenge in the field of computer science, and in fact, most of the power and processors in data centers are spent on performing forward propagation (test time prediction). Moreover, the low forward propagation speed limits the application of artificial neural networks in many fields including self-driving cars, which require high-speed and parallel image recognition.

[0098] Compared to the electronic computer architecture of the prior art, the optical neural network architecture described in this article takes full advantage of high detection rate, high sensitivity photon detectors to achieve high-speed, energy-efficient neural networks. Once the parameters have been trained and programmed on the nanophotonic processor, the forward propagation calculations are performed optically on the passive system. In this embodiment, maintaining the phase modulator setting consumes only a small amount of power on the order of about 10mW per modulator on average. In addition, the phase can be set with non-volatile phase change materials, which does not consume any power to maintain. Using this change, the total power consumption can be limited only by the physical size, the spectral bandwidth of the dispersion components (THz) and the light detection rate (e.g., about 100GHz). In principle, such a system can be at least 2 orders of magnitude faster than electronic neural networks (which are limited to GHz clock rates).

[0099] In an optical neural network with N nodes, implementing m layers of N×N matrix multiplications and operating at a typical 100 GHz light detection rate, the number of operations per second of the system can be:

[0100] R=2m×N 2 ×10 11 Operation / s (5)

[0101] The ONN power consumption during operation can be controlled by the light intensity to trigger the optical nonlinearity and achieve a sufficiently high signal-to-noise ratio (SNR) at the photodetector. In the optical nonlinear unit, the threshold power p for triggering saturable absorption can be assumed to be around 1 mW / cm 2 For example, a dye may have a power of approximately 0.3 mW / cm 2 To about 1mW / cm 2 Graphite can have a threshold power of about 0.5 mW / cm 2 To about 0.8mW / cm 2 The threshold power.

[0102] Since the cross section A of the waveguide is about 0.2 μm × 0.5 μm, the total power of the operating system is estimated to be: P ~ NmW. Therefore, the energy of each operation of the optical neural network can be calibrated as R / P = 2m × N × 10 14 Operation / Joule (or P / R = 5 / mN fJ / operation). If optical bistability is used instead of saturable absorption as the initiating nonlinear phenomenon, almost the same energy performance and speed can be achieved. Even for very small neural networks, the above power efficiency is at least 3 orders of magnitude higher than the power efficiency in conventional electronic CPUs and GPUs, where P / R ~ 1pJ / operation (excluding the power spent on data movement), while conventional image recognition tasks typically involve tens of millions of training parameters and thousands of neurons (mN ~ 10 5). These factors suggest that for standard problem sizes, the optical neural networks described in this paper can be tens of millions of times more efficient than conventional computers. In fact, the larger the neural network, the greater the advantage of using optics, because evaluating an N×N matrix in electronics takes O(N 2 ) energy, while in optics, in principle no energy is used.

[0103] Optical neural networks also allow new methods to train artificial neural network parameters. On conventional computers, parameters are trained using backpropagation and gradient descent. However, for some artificial neural networks, the effective number of parameters substantially exceeds the number of different parameters (including recurrent neural networks (RNNs) and convolutional neural networks (CNNs)), and it is well known that training using backpropagation may be inefficient. In particular, the recursive nature of RNNs makes them in fact extremely deep artificial neural networks (depth = sequence length), while in CNNs, the same weight parameters are repeatedly used in different parts of the image to extract features.

[0104] In an optical neural network, an alternative method to directly obtain the gradient of each different parameter can be implemented without backpropagation. This method can use forward propagation and finite difference methods on an optical neural network.

[0105] In this method, the gradient ΔW for different specific weight parameters in the artificial neural network is ij It can be obtained by two forward propagation steps, which are to calculate J(W ij ) and J(W ij +δ ij ), followed by the evaluation of ΔWij=J(W ij +δ ij )-J(W ij ) / δ ij (This step requires only two operations.) On a conventional computer, this scheme is not advantageous because the forward propagation (evaluating J(W)) is typically computationally expensive. However, in an optical neural network, each forward propagation step is computed in constant time (limited by the light detection rate, which can exceed 100 GHz), and the power consumption is only proportional to the number of neurons. Moreover, using this on-chip training scheme, the unitary matrix can be easily parameterized and trained.

[0106] Regarding the physical size of the proposed optical neural network, current technology enables optical neural networks with over 1000 neurons. For example, photonic circuits with up to 4096 optical components can be fabricated. 3-D photonic integration can enable even larger optical neural networks by adding another spatial degree of freedom. Moreover, by feeding the input signal (e.g., an image) in multiple batches over time (rather than all at once), a much larger effective neural network can be achieved with a relatively small number of physical neurons.

[0107] in conclusion

[0108] Although various embodiments of the present invention have been described and illustrated herein, it will be easy for those skilled in the art to conceive of various other devices and / or structures for performing functions and / or obtaining results and / or one or more advantages described herein, and each of these variations and / or improvements is considered to be within the scope of the embodiments of the present invention described herein. More specifically, it will be easy for those skilled in the art to recognize that the meanings of all parameters, dimensions, materials and configurations described herein are exemplary, and the actual parameters, dimensions, materials and / or configurations will depend on the specific application of the teachings of the present invention. Those skilled in the art will recognize or be able to use only routine experiments to clarify many equivalents of the specific embodiments of the present invention described herein. Therefore, it is to be understood that the aforementioned embodiments are presented only by way of example, and within the scope of the appended claims and their equivalents, embodiments of the present invention can be practiced in a different manner from that specifically described and claimed. The embodiments of the present invention disclosed herein relate to each individual feature, system, article, material, kit and / or method described herein. In addition, if these features, systems, articles, materials, kits and / or methods are not mutually inconsistent, any combination of two or more of these features, systems, articles, materials, kits and / or methods is included within the scope of the present invention disclosed herein.

[0109] Likewise, the concepts of each of the present invention may be embodied as one or more methods, examples of which have been provided. The actions performed as a part of the method may be sequenced in any suitable manner. Therefore, embodiments of the actions performed in a sequence different from that illustrated may be constructed, which may include performing some actions simultaneously, even if shown as sequential actions in the illustrated embodiment.

[0110] All definitions, as defined and used herein, should be understood against dictionary definitions, definitions in documents incorporated by reference, and / or ordinary meanings of the defined terms.

[0111] The indefinite articles "a" and "an" as used in the specification and claims should be understood to mean "at least one" unless explicitly indicated to the contrary.

[0112] The phrase "and / or" used in the specification and claims should be understood to mean "either or both" of the elements so connected, i.e., in some cases the elements are present jointly, and in other cases the elements are present separately. Multiple elements listed with "and / or" should be interpreted in the same manner, i.e., "one or more" elements are so connected. In addition to the elements explicitly identified by the "and / or" clause, other elements may optionally be present, whether related or unrelated to those elements explicitly identified. Thus, as a non-limiting example, a reference to "A and / or B" when used in conjunction with an open language such as "comprising" may refer to only A (optionally including elements other than B) in one embodiment; to only B (optionally including elements other than A) in another embodiment; to both A and B (optionally including other elements) in yet another embodiment; and so on.

[0113] "Or" used in the specification and claims should be understood to have the same meaning as "and / or" defined above. For example, when separating each item in a list, "or" or "and / or" should be interpreted as inclusive, i.e., including at least one of many elements or lists of elements, but also including more than one, and optionally, including additional unlisted items. Only when explicitly indicated as the opposite term, such as "only one" or "exactly one" or when used in the claims, "consisting of..." refers to including exactly one element of many elements or lists of elements. Generally, the term "or" used in this article will only be interpreted as indicating mutually exclusive solutions (i.e., "one or the other but not both") when it is preceded by exclusive terms such as "or", "one of...", "only one of..." or "exactly one of...". "Substantially comprising" will have the same ordinary meaning as used in the field of patent law when used in the claims.

[0114] As used in the specification and claims, the phrase "at least one" when referring to a list of one or more elements should be understood to mean at least one element selected from any one or more elements in the list of elements, but not necessarily including at least one of all elements explicitly listed in the list of elements, and not excluding any combination of elements in the list of elements. This definition also allows elements to be optionally present in addition to those elements explicitly identified in the list of elements indicated by the phrase "at least one", regardless of whether they are related or unrelated to those elements explicitly identified. Therefore, as a non-limiting example, "at least one of A and B" (or equivalently "at least one of A or B" or equivalently "at least one of A and / or B") can refer to at least one A, optionally including more than one, but B does not exist (and optionally including elements other than B); in another embodiment, at least one B, optionally including more than one, but A does not exist (optionally including elements other than A); in yet another embodiment, at least one A, optionally including more than one, and at least one B, optionally including more than one (optionally including other elements), etc.

[0115] In the claims and in the above description, all transitional phrases, such as "comprising," "including," "carrying," "having," "containing," "involving," "holding," "composed of," and the like, are to be understood as open ended, i.e., meaning including, but not limited to, including. Only the transitional phrases "consisting of" and "consisting essentially of," respectively, are closed or semi-closed transitional phrases, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

1. A device for implementing an artificial neural network, the device comprising: an electronic interface that encodes a digital signal into the optical signal of the first array; an input waveguide array, the input waveguide array receiving the optical signal of the first array; an optical interferometer in optical communication with the input waveguide array to perform a linear transformation of an optical signal of the first array into an optical signal of a second array; as well as an output waveguide array in optical communication with the optical interference unit to guide the optical signal of the second array, wherein at least one input waveguide in the input waveguide array is in optical communication with each output waveguide in the output waveguide array through the optical interference unit.

2. The device according to claim 1, wherein: The optical interference unit comprises: A plurality of interconnected Mach-Zehnder interferometers (MZIs), each of the plurality of interconnected MZIs comprising: a first phase shifter configured to change a splitting ratio of the MZI; and A second phase shifter is configured to shift a phase of an output of the MZI.

3. The device according to claim 2, wherein: The plurality of interconnected MZIs are configured to perform a linear transformation of the optical signal of the first array by singular value decomposition (SVD).

4. The device according to claim 2, wherein: The plurality of interconnected MZIs include: a first set of MZIs that perform a unitary transform of the optical signals of the first array to generate transformed optical signals of the first array; and a second group of MZIs, the second group of MZIs being in optical communication with the first group of MZIs, each MZI in the second group of MZIs receiving a corresponding transformed optical signal from the transformed optical signal of the first array and transmitting a first output to a nonlinear unit, wherein a second output of each MZI in the second group of MZIs is optically blocked so as to change a total intensity of the transformed optical signal of the first array and perform a non-unitary diagonal matrix multiplication of the transformed optical signal of the first array.

5. The device according to claim 1, wherein: The optical interference unit comprises: a plurality of interconnected MZIs that perform a unitary transformation of the optical signals of the first array; and An array of optical attenuators or amplifiers in optical communication with the plurality of interconnected MZIs to vary the strength of the first array of optical signals after the plurality of interconnected MZIs.

6. The device according to claim 1, wherein: The optical interference unit includes a photonic crystal network.

7. The apparatus of claim 6, further comprising a phase change material coated on at least one photonic crystal in the photonic crystal network.

8. The device according to claim 1, wherein: The optical interference unit includes a two-dimensional (2D) array of ring resonators.

9. The device according to claim 1, wherein: The optical signals of the first array include a first number of optical signals, the optical signals of the second array include a second number of optical signals, and the first number is different from the second number.

10. The apparatus according to claim 1, further comprising: An optical nonlinear unit in optical communication with the optical interference unit to perform a nonlinear transformation on the optical signals of the second array to generate optical signals of a third array.

11. The device according to claim 10, wherein: The optical nonlinear unit includes a saturable absorber array, each saturable absorber in the saturable absorber array being configured to absorb a corresponding optical signal among the optical signals of the second array.

12. The device according to claim 10, wherein: The optical nonlinear unit includes an array of bistable optical switches, each bistable optical switch in the array of bistable optical switches receives a corresponding optical signal of the optical signals of the second array.

13. The apparatus according to claim 10, wherein: The optical nonlinear unit includes a ring resonator array, and each ring resonator in the ring resonator array receives a corresponding second optical signal from the interference unit.

14. The apparatus according to claim 10, further comprising: A detector array is in optical communication with the optical nonlinear unit to detect the optical signal of the third array.

15. The apparatus according to claim 14, further comprising: A control circuit is operatively coupled to the optical interference cell, the optical nonlinear cell and the detector array to adjust a setting of at least one of the optical interference cell or the optical nonlinear cell based at least in part on the optical signals of the third array detected by the detector array.

16. The apparatus of claim 14, further comprising: At least one optical channel is in optical communication with the optical nonlinear unit to direct at least a portion of the optical signal of the third array back to the input waveguide array.

17. The apparatus according to claim 14, wherein: The detector array generates an array of electrical signals in response to detecting the optical signals of the third array, and the device further comprises: a light source in optical communication with the input waveguide array; and A feedback circuit transmits the electrical signal array to the light source, and the light source emits a fourth array of optical signals based on the electrical signal array.

18. A method for artificial neural network calculation, the method comprising: receiving the optical signal of the first array with an input waveguide array; interfering the optical signal of the first array using an optical interferometer in optical communication with the input waveguide array to linearly transform the optical signal of the first array into an optical signal of a second array; directing the optical signal of the second array using an output waveguide array, wherein at least one input waveguide in the input waveguide array is in optical communication with each output waveguide in the output waveguide array through the optical interferometer; as well as Nonlinear excitation is performed on the optical signal of the second array using an optical nonlinear unit.

19. The method according to claim 18, wherein: The optical signal interfering with the first array comprises: Propagate the optical signal of the first array through a plurality of interconnected Mach-Zehnder interferometers (MZIs); changing a splitting ratio of at least one MZI among a plurality of interconnected MZIs; and A phase of an output of the at least one MZI is shifted.

20. The method according to claim 19, wherein: Propagating the optical signal of the first array through the plurality of interconnected MZIs includes performing a linear transformation on the optical signal of the first array by singular value decomposition (SVD).

21. The method according to claim 19, wherein: Propagating the optical signal of the first array through the plurality of interconnected MZIs comprises: performing a unitary transform of the optical signal of the first array with a first set of MZIs to generate a transformed optical signal of the first array; and The total intensity of the transformed optical signal of the first array is changed by a second group of MZIs in optical communication with the first group of MZIs, each MZI in the second group of MZIs receives a corresponding transformed optical signal from the transformed optical signal of the first array and transmits a first output to a nonlinear unit, wherein a second output of each MZI in the second group of MZIs is optically blocked.

22. The method according to claim 18, wherein: The optical signal interfering with the first array comprises: performing a unitary transformation of the optical signal of the first array with a plurality of interconnected MZIs; and An optical signal of the first array is attenuated or amplified with an array of optical attenuators in optical communication with the plurality of interconnected MZIs.

23. The method according to claim 18, wherein: The optical signal interfering with the first array comprises: The optical signal of the first array is propagated through the photonic crystal network.

24. The method according to claim 23, further comprising: The phase of a phase change material coated on at least one photonic crystal in the photonic crystal network is changed to change the interference of the optical signals of the first array.

25. The method of claim 18, wherein: The optical signal interfering with the first array comprises: An optical signal of a first array is propagated through a two-dimensional (2D) array of ring resonators.

26. The method according to claim 18, wherein the optical nonlinear unit is used to perform nonlinear excitation on the optical signals of the second array to obtain the optical signals of the third array.

27. The method of claim 26, wherein performing nonlinear excitation comprises: At least one of the optical signals of the second array is attenuated with an array of saturable absorbers, each saturable absorber in the array of saturable absorbers being in optical communication with a corresponding one of the optical signals of the second array.

28. The method of claim 26, wherein performing nonlinear excitation comprises: The strength of at least one of the optical signals of the second array is varied with an array of optical bi-stable switches, each optical bi-stable switch in the array of optical bi-stable switches being in optical communication with a corresponding one of the optical signals of the second array.

29. The method of claim 26, further comprising: directing at least a portion of the optical signal of the third array back to the input waveguide array; as well as At least a portion of the optical signals of the third array are transformed using the optical interference element and the optical non-linear element.

30. The method of claim 26, further comprising: A setting of at least one of the optical interference element or the optical non-linear element is adjusted based at least in part on the optical signal of the third array.

31. An apparatus for implementing an artificial neural network, the apparatus comprising: an input waveguide array, the input waveguide array receiving the optical signal of the first array; an optical interferometer in optical communication with the input waveguide array to perform a linear transformation of an optical signal of the first array into an optical signal of a second array; as well as an output waveguide array in optical communication with the optical interference unit to direct the optical signal of the second array, wherein at least one input waveguide in the input waveguide array is in optical communication with each output waveguide in the output waveguide array through the optical interference unit; A nonlinear unit is provided for performing nonlinear excitation on the optical signal of the second array.

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