Information processing system, control device, and program

Abstract

This information processing system includes: a physical system output generation device that, using as a reference physical system a physical system that generates one or more physical variables in response to an external force, receives an input of a set value of the external force to be applied to the reference physical system, applies an external force based on the set value to the reference physical system, acquires a physical variable generated by the reference physical system under application of the external force, and outputs information pertaining to the acquired physical variable; and a control device connected to the physical system output generation device. The control device determines the set value of the external force to be applied to the reference physical system on the basis of an output of an object that is a target of optimization processing, and updates a parameter of the object on the basis of the information pertaining to the physical variable generated by the reference physical system.

Description

Information processing systems, control devices, and programs

[0001] This invention relates to an information processing system, a control device, and a program.

[0002] Various methods have been devised to find solutions to optimization problems. For example, the problem of determining the weight parameters of a neural network can be considered an optimization problem. In this case, a known method (gradient method) is to use the difference between the output of the neural network given the input data and the correct answer for the input data as the loss function, differentiate this loss function for each weight parameter to find the gradient, and repeatedly add this gradient to the corresponding weight parameter.

[0003] Samuel L. Smith, Pieter-Jan Kindermans, Chris Ying, Quoc V. Le. Don't Decay the Learning Rate, Increase the Batch Size. 2017. ICLR 2018 (https: / / arxiv.org / abs / 1711.00489)

[0004] However, in the conventional optimization problems including gradient descent described above, numerous iterations are required for the weight parameters to converge, and solving these optimization problems currently takes a considerable amount of time. Therefore, there has been a strong demand for more efficient and faster optimization problem solving. For example, Non-Patent Document 1 attempts to speed up the solving of optimization problems by focusing on the relationship between batch size and learning rate.

[0005] This invention has been made in view of the above circumstances, and one of its objectives is to provide an information processing system, a control device, and a program that can solve optimization problems at a relatively high speed.

[0006] One aspect of the present invention, which solves the problems of the above-mentioned conventional example, is an information processing system comprising: a physical system output generation device that receives input of a set value of an external force to be applied to a physical system, which is a physical system that generates one or more physical variables in response to an external force, applies an external force based on the set value to the physical system, acquires the physical variables generated by the physical system under the applied external force, and outputs information relating to the acquired physical variables; and a control device connected to the physical system output generation device, wherein the control device is an object defined by parameter information and subject to optimization processing, and accepts input data and processes the input data The system includes: a storage unit that holds an object that outputs output information; an objective function calculation unit that inputs trial input data to the object, obtains output information for the trial input data, and calculates an objective function; a setting value determination unit that determines the setting value of the external force applied by the physical system output generation device to the reference physical system based on the calculated objective function; an information acquisition unit that acquires information relating to the physical variables generated by the reference physical system to which the external force has been applied according to the determined setting value from the physical system output generation device; and an update processing unit that updates the parameter information defining the object based on the information acquired by the information acquisition unit.

[0007] According to the present invention, by updating parameter information using sampling results from the response of a reference physical system, it becomes possible to perform optimization processes, including machine learning, quantum computing, and control of the physical system, at high speed without relying on numerical optimization methods.

[0008] This is a block diagram showing an example configuration of an information processing system according to an embodiment of the present invention. This is a configuration block diagram showing an example of a physical system response generation device of an information processing system according to an embodiment of the present invention. This is a schematic configuration block diagram showing an example of a physical system observation unit of an information processing system according to an embodiment of the present invention. This is an explanatory diagram showing an example of a physical system response used in an information processing system according to an embodiment of the present invention. This is a flowchart showing an overview of the operation of an information processing system according to an embodiment of the present invention. This is a functional block diagram showing an example of a control device according to an embodiment of the present invention. This is an explanatory diagram showing an example of a neural network targeted for machine learning in a control device according to an embodiment of the present invention. This is a flowchart showing an example of processing in an information processing system according to an embodiment of the present invention. This is an explanatory diagram showing the relationship between an information processing system according to an embodiment of the present invention and a conventional example. This is an explanatory diagram showing an example of operation when a different physical system is used in an information processing system according to an embodiment of the present invention.

[0009] Embodiments of the present invention will be described with reference to the drawings. The information processing system 1 according to an embodiment of the present invention is configured to include a physical response generation device 10 and a control device 20, as illustrated in Figure 1.

[0010] Here, the physical system response generation device 10 uses a physical system (hereinafter referred to as the reference physical system) that generates one or more physical variables in response to an external force. The physical system response generation device 10 receives input of a setting value for setting the external force, sets the external force to be applied to the reference physical system based on the setting value, measures the physical variables generated by the reference physical system, and outputs the result of the measurement as a response. This physical system response generation device 10 will be explained later with specific examples.

[0011] The control device 20 can be implemented using a general-purpose computer device and, as illustrated in Figure 1, is configured to include a control unit 21, a storage unit 22, and an interface unit 23.

[0012] The control unit 21 is a program control device such as a CPU, and operates according to a program stored in the storage unit 22. In the example of this embodiment, the control unit 21 stores parameters of an object (such as a model) to be the target of optimization information processing in the storage unit 22. If the model is a neural network, this parameter corresponds to information such as the weights of the neural network, and is a physical system different from the reference physical system (hereinafter referred to as the target physical system). If the target physical system is, for example, a quantum physical system, it corresponds to, for example, a state variable.

[0013] The control unit 21 inputs trial input data to the object and obtains output information for the trial input data. Here, if the object is a neural network, for example, the trial input data corresponds to the input data of the learning data set used for machine learning of the neural network. Also, if the object is a target physical system, the trial input data may be the parameter (such as a control parameter) itself that is the target of optimization in the target physical system.

[0014] The control unit 21 obtains an objective function based on the obtained output information. For example, if the object is a neural network, this objective function is the difference between the correct answer corresponding to the trial input data and the output information of the neural network as the object. Also, if the object is a target physical system, it can be calculated using the internal energy (obtained based on the output information) of the target physical system. In the case where the target physical system is a quantum physical system, this objective function may be calculated using the density matrix or the pseudo-probability density function of the target physical system.

[0015] The control unit 21 further determines a set value of an external force to be applied to the reference physical system of the physical system response generation device 10 based on the obtained objective function. An example of the determination of this set value will be described in detail later. Then, the control unit 21 acquires information related to the physical variable generated by the reference physical system to which the external force is applied according to the determined set value from the physical system response generation device 10, and updates the parameter information that defines the object based on the acquired information. The detailed operation of the control unit 21, including the example of the determination of the above set value, will be described later.

[0016] The storage unit 22 is a memory device, disk device, etc., and holds a program executed by the control unit 21. This program may be stored and provided in a computer-readable and non-transitory recording medium and then stored in this storage unit 22.

[0017] Further, the storage unit 22 also functions as a work memory of the control unit 21. Furthermore, in the present embodiment, parameter of an object to be processed is held in this storage unit 22.

[0018] The interface unit 23 includes a serial interface such as a USB interface and a network interface. This interface unit 23 is connected to the physical system response generator 10 and outputs information (set value, etc.) input from the control unit 21 to the physical system response generator 10. Also, this interface unit 23 outputs information output from the physical system response generator 10 to the control unit 21.

[0019] Also, in the example of the present embodiment, the interface unit 23, in accordance with an instruction input from the control unit 21, accepts parameters of an object to be optimized, such as information defining a neural network to be a machine learning target, from an external device and stores them in the storage unit 22, and also outputs the parameters, etc., stored in the storage unit 22 to the external device as a result of the optimization process.

[0020] [Example of Physical System Response Generator] Next, an example of the physical system response generator 10 will be described. The physical system response generator 10 according to the example of the present embodiment generates and responds with at least one physical variable (predetermined physical quantity) in response to an external force. This physical system response generator 10 holds a physical system (reference physical system CP) to be observed and includes an instruction receiving unit 11, a control unit 12, an external force applying unit 13, a physical system observing unit 14, and a response output unit 15, as illustrated in FIG. 2.

[0021] The reference physical system to be observed here is one in which the values ​​of predetermined physical quantities corresponding to its type change in response to the applied external force. Specifically, such a reference physical system is one in which, when it reaches a state of thermal equilibrium after the application of an external force (when the Helmholtz free energy of the observed physical system is minimized), the values ​​of the predetermined physical variables corresponding to the type of observed system differ depending on the applied external force.

[0022] The instruction receiving unit 11 receives input of a setting value for setting the external force from the control device 20 and outputs it to the control unit 12. Based on the setting value received by the instruction receiving unit 11, the control unit 12 controls the external force application unit 13 to apply the external force to the physical system.

[0023] The external force application unit 13 applies an external force to the physical system observation unit 14 according to the type of object being observed, in accordance with instructions input from the control unit 12. In one example of this embodiment, the reference physical system to be observed is a metallic magnetic parametron, and the external force is a magnetic field. In this example, the external force application unit 13 outputs a voltage signal of a magnitude instructed by the control unit 12 in order to control the strength of the magnetic field applied to the object being observed.

[0024] The physical system observation unit 14 reads the response of the object being observed (reference physical system) (physical variables generated in the reference physical system) under the application of a magnetic field based on the voltage signal output by the external force application unit 13. The method for reading this response is determined appropriately depending on the type of object being observed. For example, the outline of the physical system observation unit 14 when using a metallic magnetic material parametron as the object being observed is as follows.

[0025] The structure of a metallic parametron, the method of applying a magnetic field that induces a magnetization precession of frequency 1f, the behavior of a metallic parametron when an external magnetic field is applied, and the reading of the physical variables generated by the metallic parametron in response to the external force (in this example, the phase of the induced magnetization precession, which can be either 0 or π) are widely known, so only an overview will be provided here.

[0026] In other words, when a metallic magnetic parametron is used as the object of observation, the physical observation unit 14 is configured to include a first signal oscillator 141, a second signal oscillator 142, an amplifier 143, a coupler 144, a metallic magnetic parametron body 145, a signal filter 146, a third signal oscillator 147, and a mixer 148, as illustrated in Figure 3.

[0027] The first signal oscillator 141 generates and outputs an electrical signal (bias signal) with a frequency of 1f, having an amplitude corresponding to the voltage signal output by the external force application unit 13. This first signal oscillator 141 outputs a signal for 20 microseconds starting before the second signal oscillator 142, which will be described later, outputs a signal, and then stops outputting the signal.

[0028] The second signal oscillator 142 generates and outputs an electrical signal (an electrical signal with frequency 2f) for applying a magnetic field that induces magnetization precession with frequency 1f. The phase of the signal output by the second signal oscillator 142 may differ from the phase of the signal output by the first signal oscillator 141 by an amount corresponding to the voltage signal output by the external force application unit 13. Such a configuration can be realized using a widely known phase shifter. The second signal oscillator 142 starts outputting a signal 200 nanoseconds after the first signal oscillator 141 starts outputting a signal, and then outputs the signal for 2.3 milliseconds. The amplifier 143 amplifies the signal output by the second signal oscillator 142 at a specified amplification factor and outputs it.

[0029] The coupler 144 mixes the signal output by the second signal oscillator 142 and the signal output by the amplifier 143 and applies the resulting electromagnetic field to the metallic magnetic parametron body 145.

[0030] The metallic magnetic parametron body 145 includes, for example, magnetic dot parametrons made by processing yttrium iron garnet into dots, and has a structure for arranging these magnetic dot parametrons on a waveguide such as a coplanar line and applying a magnetic field based on the output signal from the coupler 144. The metallic magnetic parametron body 145 also includes an element for electrically reading out the magnetization precession of the magnetic dot parametrons using the Hall effect or the like. As already mentioned, the structure and operation of this metallic magnetic parametron body 145 are widely known, so a detailed explanation will be omitted here.

[0031] The signal filter 146 applies a low-pass filter and amplification to the voltage signal output by the metallic magnetic parametron body 145 (the voltage signal corresponding to the physical variable read from the metallic magnetic parametron), and outputs the resulting signal.

[0032] The third signal oscillator 147 outputs an electrical signal (reference signal) with frequency 1f. The mixer 148 mixes the signal output via the signal filter 146 with the reference signal output by the third signal oscillator 147, amplifies it, and outputs it as a parameter signal. In this embodiment, the first signal oscillator 141 stops outputting the bias signal, and then, after a certain period of time (while the second signal oscillator 142 is outputting a signal), the third signal oscillator 147 outputs an electrical signal with frequency 1f having at least one pulse, and information relating to at least one response is obtained. The period for obtaining information relating to the response is set in this way to take into account the period from the application of an external force until a thermal equilibrium state is reached.

[0033] In the example of the metallic magnetic parametron shown in Figure 3, the parameter signal output by the mixer 148 is a voltage signal. When it is higher than the threshold Vth (e.g., Vth = 0), it is determined that the phase of the magnetization precession is π, and when it is lower than the threshold Vth (e.g., Vth = 0), it is determined that the phase of the magnetization precession is 0.

[0034] The response output unit 15 outputs information relating to physical variables read from the observation target by the physical system observation unit 14. For example, if the observation target is a metallic magnetic parametron as described above, the physical variable generated in response to the external force is the phase of magnetization precession, and this phase is either 0 or π. Therefore, the information output by the response output unit 15 is either a voltage signal corresponding to phase 0, or a voltage signal corresponding to phase π, which is different from the aforementioned voltage signal. The response output unit 15 repeatedly reads these physical variables from the observation target multiple times (for example, about 70,000 times), calculates predetermined statistical values ​​(for example, arithmetic mean or maximum value) relating to them, and outputs these statistical values ​​to the control device 20 as information relating to the physical variables. Note that these statistical values ​​may be of different types depending on whether the physical variable is a discrete quantity (such as a voltage signal corresponding to either phase 0 or π) or a continuous quantity. In other words, in this embodiment, the information relating to the physical variables is information representing the acquired physical variables themselves, or information representing a function value (which may also be a statistical quantity) with the physical variables as variables.

[0035] In this example, the information output by the response output unit 15 differs depending on the bias signal. Specifically, if we show the relationship with the magnitude of the voltage signal output by the external force application unit 13 on the horizontal axis and the average of the voltage signals output by the mixer 148 on the vertical axis, we can see that there is a sigmoid function-like relationship, as illustrated in Figure 4. That is, the larger the amplitude of the bias signal, the more voltage signals representing a phase of π increase among the voltage signals corresponding to the multiple physical variables read out by the response output unit 15 (and therefore the average voltage signal becomes larger), while the smaller the amplitude of the bias signal, the more voltage signals representing a phase of 0 increase (and therefore the average voltage signal becomes smaller).

[0036] [Operation of the Physical System Response Generator] Here, we will explain the principle of optimizing the parameters of an object through the operation of the physical system response generator 10. For example, when determining the parameters (weights, etc.) of a neural network as an example of an object, the machine learning process of the neural network corresponds to maximizing the probability p(y) that the neural network outputs y under the latent variable z related to the input data. In other words, machine learning of a neural network corresponds to minimizing the Kullback-Leibler divergence, which represents how much the posterior probability qW(z|y) of the neural network being machine-learned differs from this probability p(y).

[0037] Here, the Kullback-Leibler divergence - F(y) is, It is expressed as, but by rearranging this equation, Thus, it can be expressed as the sum of the internal energy (first term) U and the posterior probability Shannon entropy (second term) S. This F can be correlated with the Helmholtz free energy F = U - TS (U: internal energy, T: temperature, S: entropy) in a physical system.

[0038] Therefore, the above equation can be interpreted as indicating that machine learning of neural networks can be performed using the Helmholtz free energy of some physical phenomenon instead of computational optimization. Specifically, by finding the weights W such that δF = 0 (thermal equilibrium), the posterior probability qW(z|y) of the neural network being machine-learned will be close to the probability p(y, z).

[0039] Furthermore, since the first term (internal energy U) here corresponds to the difference between the output and the correct answer (i.e., the loss function L), the weight W of the loss function L k The derivative (gradient) with respect to ij is ∂L / ∂W k ∂U / ∂W corresponds to ij kConsidering ij, this corresponds to the derivative of the internal energy, i.e., the external force. Here, k indicates that the weight is the weight related to the k-th layer of the neural network, and is different from an exponent.

[0040] Therefore, as a reference physical system, we use a thermodynamic system that transitions to a state of thermal equilibrium when an external force is applied (a system with a relatively short transition time is preferable), and perform the operation illustrated in Figure 5. In the state of thermal equilibrium, the Helmholtz free energy is minimized.

[0041] In other words, in a neural network targeted for machine learning, the above loss L is weighted W k The derivative value obtained when differentiating with respect to ij is obtained (S1), and the external force corresponding to this derivative value is applied to the reference physical system (S2). Then, when this reference physical system reaches a state of thermal equilibrium (δF = 0), the physical variables related to the reference physical system are detected (S3), and the weight parameter W is determined according to the detected response. k Update ij (S4). This completes the machine learning process for the neural network.

[0042] While physical variables may be detected only once, as mentioned above, since the reference physical system is a thermodynamic system, it is preferable to detect the physical variable multiple times, perform predetermined statistical calculations such as calculating the arithmetic mean, and output information related to the obtained statistical values.

[0043] The same applies to the case where the object to be optimized is a physical system (a physical system different from the reference physical system). If we consider the value obtained by differentiating the internal energy U of the target physical system with respect to the parameters of the target physical system, the response of the reference physical system when an external force proportional to this value is applied and it reaches thermal equilibrium corresponds to the corresponding parameter that minimizes the Helmholtz free energy F.

[0044] Furthermore, if the target physical system is a quantum physical system, instead of the internal energy U, a density matrix (or pseudo-probability density function) can be estimated by quantum state tomography of the target physical system. The expected value of the internal energy can then be calculated using this density matrix or pseudo-probability density function, and the external force to be applied to the reference physical system can be determined based on this expected value. In this case, it is possible to obtain the parameters that minimize the expected value of the Helmholtz free energy F of the quantum physical system.

[0045] In other words, according to the example of this embodiment, for any object, as long as a quantity corresponding to the internal energy that changes depending on the parameters can be defined, this reference physical system can be used to minimize the Helmholtz free energy F, that is, to obtain optimized parameters.

[0046] [Operation of the Control Device] Next, the operation of the control unit 21 of the control device 20 in this example will be described. In this embodiment, the control unit 21 executes a program stored in the storage unit 22 to perform object optimization processing. In this embodiment, the execution of this program by the control unit 21 realizes a configuration that functionally includes an objective function calculation unit 211, an external force specification unit 212, a response acquisition unit 213, and a parameter setting unit 214, as illustrated in Figure 6.

[0047] The objective function calculation unit 211 acquires or generates trial input data. Here, if the object to be optimized is a neural network, the trial input data is a set of training data consisting of input data and correct answers. If the object is a physical system, it may be the parameters of that physical system (for example, the variables themselves that represent the state of the physical system), and in this case, initially, they may be set randomly as long as the constraints of the physical system are satisfied.

[0048] The objective function calculation unit 211 receives trial input data for the object to be optimized and obtains an output value for the trial input data. If the object is a neural network, the operation of the objective function calculation unit 211 corresponds to inputting trial input data into the neural network and obtaining its output. If the object is a physical system, the operation of the objective function calculation unit 211 corresponds to determining the state of the physical system using trial input data and obtaining an output value for the physical system corresponding to that state.

[0049] For example, if the target physical system is a control system that includes at least one controlled object, the trial input data may be the magnitude of the external force applied to the controlled object in the target physical system. In this example, when inputting trial input data to the target physical system, the control unit 21, in its operation as the objective function calculation unit 211, controls the magnitude of the external force (e.g., voltage value) applied to the controlled object in the target physical system according to the trial input data. The control unit 21 then outputs the internal energy of the controlled object (kinetic energy, or the sum of the energy if there are multiple controlled objects) as the output value of the target physical system.

[0050] In another example, the target physical system is a quantum physical system, and the trial input data is a set of qubits. In this case, the output value that the target physical system outputs when trial input data is input is, for example, a density matrix obtained by quantum state tomography (the probability that a state is observed for each energy state).

[0051] The objective function calculation unit 211 calculates the objective function based on the output values ​​output by the object. Specifically, if the object is a neural network, the operation of this objective function calculation unit 211 corresponds to the process of calculating the difference (loss) between the output values ​​obtained by inputting trial input data into the neural network and the correct answer corresponding to the trial input data.

[0052] Also, when the object is the target physical system (including the case where it is a quantum physical system), the difference between the output value obtained from the target physical system, that is, the internal energy of the target physical system or the density matrix (or the pseudo-probability density function), and the value of the internal energy or density matrix that the target physical system should reach (that is, the target value) can be used as the objective function. Here, the target value such as the value of the internal energy or density matrix that the target physical system should reach is determined in advance.

[0053] The external force specifying unit 212 differentiates the objective function with respect to the parameters of the object. When there are a plurality of parameters for the object, the results of sequential differentiation with respect to each parameter are output.

[0054] For example, when the object is a neural network and the objective function is the loss L, the external force specifying unit 212 differentiates with respect to the parameter W of each weight included in the neural network to obtain the differential value (gradient) corresponding to each parameter. For example, if the neural network to be subjected to the learning process is an n-layer network, and the parameter of the weight between the i-th node of the k-th layer and the j-th node of the k + 1-th layer of this neural network is W k ij (k = 1, 2,..., n - 1), the external force specifying unit 212 calculates the differential value (gradient) ∂L / ∂W k ij for each of these weight parameters W k ij of the neural network that defines the neural network. k ij.

[0055] As described above, this operation can be performed by adopting a method similar to the widely known backpropagation method, so detailed description here is omitted.

[0056] Also, in this example (the example where the object is a neural network), the external force specifying unit 212 sequentially outputs information for setting an external force proportional to each obtained differential value ∂L / ∂W k ij to the physical system response generation device 10.

[0057] If the object is a target physical system, the external force specification unit 212 differentiates the internal energy (e.g., the kinetic energy of the controlled object) obtained by the objective function calculation unit 211 with respect to the parameters of the target physical system (e.g., the voltage value for applying an external force to the controlled object) to obtain the gradient of the internal energy corresponding to the parameters. Specifically, if the parameters indicate the magnitude of the external force applied to the target physical system, the external force specification unit 212 calculates the change in internal energy (derivative value, i.e., gradient) with respect to the change in the magnitude of the external force, and outputs information to the physical system response generation device 10 that sets an external force proportional to this derivative value. In this example as well, if there are multiple parameters, the external force specification unit 212 calculates the derivative value (gradient) of the internal energy corresponding to each parameter, and sequentially outputs information to the physical system response generation device 10 that sets an external force proportional to the calculated derivative value.

[0058] If the object is a target physical system and is a quantum physical system, the external force specification unit 212 uses the density matrix (or pseudo-probability density function), which is the output value of the target physical system, to determine the expected value of the internal energy. Furthermore, it calculates the derivative of this expected value with respect to the parameter (the amount of change in the expected value with respect to the change in the qubit, which is the parameter), and outputs information to the physical system response generation device 10 that sets an external force proportional to this derivative. In this example as well, if there are multiple parameters, the external force specification unit 212 determines the derivative (gradient) of the internal energy corresponding to each parameter, and sequentially outputs information to the physical system response generation device 10 that sets an external force proportional to the determined derivative.

[0059] The response acquisition unit 213 obtains information output by the physical system response generation device 10 after the external force specification unit 212 outputs information for setting the external force, and outputs it to the parameter setting unit 214. The information obtained by the response acquisition unit 213 here is a value corresponding to the parameter obtained by differentiating the objective function in setting the external force. The parameter setting unit 214 then sets the parameter (the parameter used when determining the differential value corresponding to the information) that corresponds to the information output by the external force specification unit 212 (information proportional to the differential value) from among the object's parameters, based on the information obtained by the response acquisition unit 213.

[0060] For example, if the object is a neural network, then the weight parameters W k Information R output by the physical system response generation device 10, which sets the external force using information proportional to the derivative value related to ij. k Upon receiving ij, the parameter setting unit 214 processes the information R k The corresponding weight parameter W is based on ij. k Set ij. For example, the parameter setting unit 214 sets this weight parameter W. k ij, information R k Set the value to the value obtained by multiplying ij by a predetermined proportionality constant C: W k ij = C・R k ij

[0061] In this example, the control unit 21 controls each weight parameter W k Regarding ij, the processing of each part is performed, and the weight parameter W k While updating ij, the updated weight parameter W k The value ij is stored in the memory unit 22, and the object is optimized. In other words, if the object is a neural network, machine learning is performed.

[0062] Furthermore, if the object is a target physical system, the parameter setting unit 214 sets the parameters of the target physical system (for example, the magnitude of the external force applied to the target physical system) based on the information output by the physical system response generation device 10.

[0063] Furthermore, if the object is a target physical system and is a quantum physical system, the parameter setting unit 214 sets the qubits of the quantum physical system based on the information output by the physical system response generation device 10.

[0064] The control unit 21 repeatedly executes the operations of the objective function calculation unit 211, the external force specification unit 212, the response acquisition unit 213, and the parameter setting unit 214 until the objective function calculated by the objective function calculation unit 211 becomes smaller than a predetermined value, or for a predetermined number of times.

[0065] [Operation] An example of the operation of the information processing system 1 according to an embodiment of the present invention will be described below. In the following description, the information processing system 1 will perform machine learning of a neural network as an optimization process. The neural network used as an example here will be a three-layer neural network as illustrated in Figure 7, and below, the connection weight between the i-th node of the first layer on the input side and the j-th node of the intermediate second layer will be W. 1 ij is the connection weight between the i-th node of the second layer and the j-th node of the third layer, which is the output layer, and W is the connection weight between the i-th node of the second layer and the j-th node of the third layer. 2 It is written as ij.

[0066] Here, the number of nodes in each layer may differ from one another. For example, in the example in Figure 7, the first layer has 784 nodes and the second layer has 128 nodes.

[0067] Furthermore, in the following example of this embodiment, we will describe an example of using this neural network to machine-learn a classifier that classifies handwritten single-digit numbers drawn on image data (28x28 image data) (generating a classifier that classifies images in the so-called MNIST database), and the output layer is a softmax function: This determines the N outputs Yn (n = 1, 2, ..., N) of the output layer. Note that Y is the weight W of the first layer. １ And the weight W of the second layer ２ (W １ , W ２ Each of these is a matrix (shown in bold in the formula), and using the input data X, It is written as follows.

[0068] The control device 20 of the information processing system 1 starts the process illustrated in Figure 8, and inputs the MNIST data, which is the training data, as trial input data to the neural network, which is the object to be optimized, and calculates the objective function (here, loss L) by the difference between the result and the predetermined correct answer related to the training data (S21).

[0069] The control device 20 further determines whether the loss L calculated in step S21 falls below a predetermined threshold (S22), and if it determines that it does not fall below the threshold (S22: No), the weight W １ , W ２ The parameter W of the added weight k While sequentially selecting each of ij (k=1,2) (S23), the selected weight parameter W k The derivative of the loss L obtained by differentiating it at ij (k=1,2) is ∂L / ∂W. k Calculate ij (S24).

[0070] The control device 20 performs this differential calculation using a method similar to the widely known backpropagation method, as already described.

[0071] The control device 20 calculates the differential value ∂L / ∂W obtained in step S24. k Information to set an external force proportional to ij is output to the physical system response generation device 10 (S25).

[0072] The physical system response generation device 10 holds, for example, a metallic magnetic parametron as an object to be observed for which it generates at least one physical variable that changes in response to an external force, and sets the external force based on information input from the control device 20 in a manner appropriate to this object to be observed. Specifically, in the example using a metallic magnetic parametron, the physical system response generation device 10 generates an electrical signal (bias signal) with a frequency of 1f having an amplitude corresponding to the voltage signal corresponding to the information for setting the external force output in step S25, and applies a magnetic field corresponding to this electrical signal to the metallic magnetic parametron for 20 microseconds, and then generates an electrical signal with a frequency of 2f 200 nanoseconds after the application of this magnetic field, and applies a magnetic field corresponding to this electrical signal to the metallic magnetic parametron (S26: Application of external force).

[0073] At this time, the metallic magnetic material parametron takes the state in which its Helmholtz free energy F is minimized, and in this state, the phase of the physical variable magnetization precession is either "0" or "π".

[0074] The physical response generation device 10 samples the phase of the magnetization precession of the metallic magnetic parametron multiple times (for example, about 70,000 times) (S27). According to widely known phase readout methods, this sampling result is obtained as a voltage signal with different voltage values ​​(for example, -V0 and +V0, respectively) depending on whether the phase is "0" or "π".

[0075] The physical response generation device 10 averages the sampling results obtained in step S27 (S28) and outputs the averaged result Vave as information to the control device 20 (S29).

[0076] The control device 20 multiplies this average result Vave by a predetermined proportionality constant C to obtain the derivative value ∂L / ∂W obtained in step S24. k Weight parameter W corresponding to ij k Update ij and store it in the memory unit 22 (S30): W k ij = C・Vave

[0077] The physical response generation device 10 and the control device 20 then perform the processing from steps S23 to S30 for all weight parameters included in the neural network that is the target of machine learning. The control device 20 then returns to step S21 and continues processing. Furthermore, in step S22, if the control device 20 determines that the loss L calculated in the immediately preceding step S21 is below a predetermined threshold (S22: Yes), it terminates the processing.

[0078] Figure 9 shows a comparison of the change in loss L for each update of weight W between an example of machine learning of a neural network using the information processing system 1 according to this embodiment and an example of machine learning using a conventional method.

[0079] As shown in Figure 9, according to the example of this embodiment (parametron), the loss L decreases rapidly within about 10 iterations and then gradually decreases thereafter. On the other hand, according to the conventional machine learning method (gradient descent), the loss L decreases slowly and monotonically, but even after 50 iterations, the result is similar to the loss L after 1 or 2 iterations in the example of this embodiment.

[0080] [When the object is a target physical system] Next, an example of the operation of the information processing system of this embodiment will be described, using the case where the object is a target physical system, particularly a quantum physical system, as an example. In this target physical system, constraints on the qubits are assumed to be set in advance.

[0081] In this example, the control device 20 sets N-bit qubits Qi (i = 1, 2...) which are the parameters themselves, as trial input data. These qubits may be initially set randomly. The control device 20 then obtains the objective function (in this case, the density matrix) as the output of the target physical system.

[0082] The control device 20 further calculates the expected value E of the internal energy of the target physical system using the obtained density matrix. It then checks whether this expected value falls below a predetermined threshold, and repeats the process as long as it is determined that it does not fall below the threshold.

[0083] The control device 20 calculates the derivative ∂E / ∂Qi by differentiating the calculated expected value E with respect to the i-th qubit Qi (i = 1, 2...). This derivative is a numerical derivative and can be obtained by dividing the difference between the current expected value E and the previous expected value E in the iterative process by the difference between the current qubit Qi and the corresponding previous qubit Qi.

[0084] The control device 20 outputs information to the physical system response generation device 10 that sets an external force proportional to the derivative value ∂E / ∂Qi obtained here. The operation of the physical system response generation device 10 at this time is the same as in the example already described, so a repeated explanation will be omitted. The physical system response generation device 10 outputs information to the control device 20 regarding the response of the reference physical system when the external force set by the above information is applied.

[0085] The control device 20 updates the i-th qubit Qi, which is a parameter corresponding to the differential value ∂E / ∂Qi used to set the external force, based on the information output by the physical system response generation device 10. Specifically, the control device 20 can set the value of qubit Qi based on whether the value of the information output by the physical system response generation device 10 exceeds a predetermined threshold.

[0086] The following steps are performed by the physical system response generation device 10 and the control device 20 for each qubit to set up a new qubit Qi (i = 1, 2, ...). The control device 20 then finds an objective function corresponding to the newly set qubit Qi, calculates the expected value of the internal energy of the target physical system using this objective function, and repeats the process of calculating the derivative until it determines that the calculated expected value E falls below a predetermined threshold.

[0087] [Variations of the Physical System] In the explanation so far, the physical system has been described as being one, but this embodiment is not limited to this. For example, the physical system response generation device 10 may have multiple physical systems (for example, P systems) to be observed. In this example, if the object to be optimized is a neural network, the control device 20 instructs the physical system response generation device 10 to apply external forces corresponding to the P derivative values ​​of each of the P weight parameters of the loss L, which is the objective function of the neural network.

[0088] The physical system response generator 10 then applies an external force corresponding to each of the P observed objects, and performs multiple samplings on the physical variables generated by each observed object to calculate the average. The physical system response generator 10 outputs information representing the average of the values ​​of the physical variables obtained from each observed object, and the control device 20 determines the corresponding weight parameter based on the information output by the physical system response generator 10 corresponding to that weight parameter. That is, if the i-th derivative value among the P derivative values ​​corresponds to the weight parameter Wi, the control device 20 updates the weight parameter Wi based on the average value of the physical variables obtained from the observed object to which the external force corresponding to the i-th derivative value was applied. In this example, the weight parameters are updated at a maximum of P values ​​at a time.

[0089] [Examples where input changes over time] Also, if the training data is input moment by moment, it is not possible to optimize for the dataset, so instead of minimizing the Helmholtz free energy, one can try to minimize the time integral of the Helmholtz free energy.

[0090] For example, let V(x, t) be an external field that changes over time, and let A[ρ, v] be a quantity equivalent to the action integral. Considering this, we aim to minimize this quantity A[ρ,v]. Specifically, the above action integral for an anisotropic physical system with a movement cost M: Regarding this, by using variational calculus and considering the condition for minimizing A[ρ,v], we obtain the Fokker-Planck equation. We obtain this. Here, T is the temperature of the heat bath, k B is the Boltzmann constant. M is the covariance matrix of the dynamical variable x. The probability density flow u* represented by this Fokker-Planck equation is, It can be expressed as follows. Here, if we write the mobility tensor as Mmob, The first and second terms on the right-hand side of the equation defining this probability density flow u* are based on thermodynamic laws, and from a machine learning perspective, the first term corresponds to gradient descent. The second term on the right-hand side represents the effects of batch learning, etc. Furthermore, the third term on the right-hand side is a term not found in conventional machine learning theory.

[0091] Therefore, in this example of this embodiment, the physical system response generation device 10 uses a physical system corresponding to this probability density flow u*. As an example, we consider the orientation M of multiple (as many as the number of weight parameters) electron spins of a magnetic material over time, as in a spin glass. Then, as the physical system corresponding to the above probability density flow u*, the time change of the orientation of these electron spins is We use the physical system given by . Here, M is a vector quantity with as many components as there are weight parameters, each representing the direction of the electron spin corresponding to the weight parameter. Here, γ is the gyrometric ratio, which is 1.76 × 10⁻⁶. 11 s -1 T -1 Let's assume that h is a random external field, and its autocorrelation is Let's assume that (where δ(τ) is the delta function). Furthermore, α represents the relaxation constant, which defines the time it takes for the magnitude of the time change of M to decay. Here, the larger α is, the faster the decay.

[0092] In this example, the control device 20 uses, for example, a two-layer neural network as the object to be optimized, with the first layer having 10 nodes, and the weight parameter W is applied to the input data. １ ｉ (Here, i = 1, 2, ..., 10) are multiplied, and a nonlinear function is applied to each to obtain the value of each node. The second layer (output layer) has 196 (14 × 14) nodes, and its j-th node (here, j = 1, 2, ..., 196) is the weight parameter W of the i-th node in the first layer. ２ ｉｊ (W of this weight parameter) ２ ｉｊ Let i be determined by multiplying by a 10x196 matrix and summing over i, for example using the softmax function.

[0093] The control device 20 sequentially inputs the training data as input data to the neural network, and the squared error between the output layer value and the correct data corresponding to the training data used as input data is defined as the objective function, which is the loss L, and the weight parameters W of the loss L are defined as follows: １ ｉ , W ２ ｉｊ Information that sets the external force, proportional to the derivative value of each of these factors, is output to the physical system response generation device 10.

[0094] Then, the physical system response generation device 10 in this example determines Heff (which is a vector having components corresponding to the differential values ​​for each of the multiple weight parameters) based on the information that sets the external force, and samples the amount of change in M ​​when it is applied to the physical system multiple times (for example, about 70,000 times). During this sampling, the amount of change in M ​​will decay over time according to a time (relaxation time) determined by the relaxation constant α.

[0095] The physical response generation device 10 averages the obtained sampling results for each component of M (for each value of M corresponding to each weight parameter), and outputs the result of this average to the control device 20 as information for updating the weight parameters.

[0096] The control device 20 updates the weight parameter corresponding to the average result included in the information output by the physical system response generation device 10. Here, the weight parameter W １ ｉ , W ２ ｉｊ You may update each of these by setting it to the corresponding average result mentioned above.

[0097] Furthermore, in this process, the physical system response generator 10 may use multiple physical systems in which the relaxation constant α is different for each weight parameter (group of weight parameters). In this example as well, each physical system considers the spins M of multiple particles (as many as there are weight parameters), and as a physical system corresponding to the probability density flow u* already explained, the time evolution of the spin is We assume that the physical system is given by [formula], but the relaxation constant α is different for each corresponding weight parameter (group of parameters).

[0098] As an example, the physical system response generation device 10 has a weight parameter W １ ｉ As the corresponding physical system, we use a physical system where α = α1 (therefore, in this physical system, M, Heff, and h are 10-dimensional vectors), and the weight parameter W ２ ｉｊ As the corresponding physical system, we use a physical system where α = α2 ≠ α1 (in this physical system, M, Heff, and h are 10 × 196-dimensional vectors). In this case, the value of α may be set to be smaller the closer to the output layer (i.e., the decay per unit time becomes smaller and the relaxation time becomes longer): α2 < α1.

[0099] The relationship between these relaxation constants α1 and α2 may be determined experimentally. For example, Figure 10 shows an example of using the above two-layer neural network to perform machine learning on MNIST images. Figure 10 shows a heatmap (Figure 10(a)) with α1 on the vertical axis and α2 on the horizontal axis, plotted so that it approaches black when the loss is low, and a comparison of the outputs (B), (C), (D) after machine learning with 100 training data points with the correct answer (A) (Figure 10(b)). As illustrated here, in this example, machine learning proceeds in the region α1 > α2, and in particular in this example, α1 ~ 1 × 10 -1degree, α2~1×10 -3 The efficiency of machine learning is relatively high when the values ​​are within a certain range. In fact, when α1 > α2, the output after machine learning with 100 training data points (B) is close to the correct answer, whereas when α1 = α2 and α1 < α2, machine learning is not achieved in this example (C), (D).

[0100] However, this applies only to this example; in practice, the relaxation constants for each group of weight parameters can be determined experimentally.

[0101] In the examples described so far, we have discussed the use of a metallic magnetic material parametron as the object of observation, and also explained the use of a spin system, but other types of objects may also be used as objects of observation.

[0102] 1 Information processing system, 10 Physical system response generation device, 11 Instruction receiving unit, 12 Control unit, 13 External force application unit, 14 Physical system observation unit, 15 Response output unit, 20 Control device, 21 Control unit, 22 Storage unit, 23 Interface unit, 141 First signal oscillator, 142 Second signal oscillator, 143 Amplifier, 144 Coupler, 145 Metal magnetic parametron body, 146 Signal filter, 147 Third signal oscillator, 148 Mixer, 211 Objective function calculation unit, 212 External force specification unit, 213 Response acquisition unit, 214 Parameter setting unit.

Claims

1. An information processing system comprising: a physical system output generation device that receives input of a set value of an external force to be applied to a physical system, which is a physical system that generates one or more physical variables in response to an external force, applies an external force based on the set value to the physical system, acquires the physical variables generated by the physical system under the applied external force, and outputs information relating to the acquired physical variables; and a control device connected to the physical system output generation device, wherein the control device comprises: a storage unit that holds an object which is defined by parameter information and is the subject of optimization processing, accepts input data, and outputs output information for the input data; an objective function calculation unit that inputs trial input data to the object, obtains output information for the trial input data, and calculates an objective function; a setting value determination unit that determines the set value of the external force to be applied to the reference physical system by the physical system output generation device based on the calculated objective function; an information acquisition unit that acquires information relating to the physical variables generated by the reference physical system under the applied external force based on the determined setting value from the physical system output generation device; and an update processing unit that updates the parameter information defining the object based on the information acquired by the information acquisition unit. An information processing system that includes this.

2. An information processing system according to claim 1, wherein the object to be optimized is a neural network model defined by weight information as parameter information, and the setting value determination unit calculates a derivative value obtained by differentiating the objective function with respect to the parameter information, and determines a setting value for the external force to be applied to the reference physical system according to the derivative value.

3. An information processing system according to claim 1, wherein the target of optimization is a target physical system that generates at least one output value, and the objective function is the internal energy of the target physical system.

4. An information processing system according to claim 1, wherein the target of optimization is a target physical system that generates at least one output value, the target physical system is a quantum mechanical physical system, and the objective function is the density matrix or pseudo-probability density function of the target physical system.

5. A control device connected to a physical system output generation device, which uses a physical system that generates one or more physical variables in response to an external force as a reference physical system, receives input of a set value of an external force to be applied to the reference physical system, applies the external force based on the set value to the reference physical system, acquires the physical variables generated by the reference physical system under the applied external force, and outputs information relating to the acquired physical variables, comprising: a storage unit that holds an object which is defined by parameter information and is the subject of optimization processing, accepts input data, and outputs output information for the input data; an objective function calculation unit which inputs trial input data to the object, obtains output information for the trial input data, and calculates an objective function; a set value determination unit which determines the set value of the external force to be applied to the reference physical system by the physical system output generation device based on the calculated objective function; an information acquisition unit which acquires information relating to the physical variables generated by the reference physical system under the applied external force based on the determined set value from the physical system output device; and an update processing unit which updates the parameter information defining the object based on the information acquired by the information acquisition unit.

6. An information processing system comprising: a physical system output generation device that receives input of a set value of the external force to be applied to each of the multiple reference physical systems, each of which generates one or more physical variables in response to an external force, applies the external force based on the set value to the corresponding reference physical system, acquires the physical variables generated by the corresponding reference physical system under the applied external force, and outputs information relating to the acquired physical variables; and a control device connected to the physical system output generation device, wherein the control device has multiple layers, each having multiple nodes, that accept input data and output output information for the input data, and is the target of optimization processing; a storage unit that holds weight parameters between nodes in different layers included in the neural network; an objective function calculation unit that inputs trial input data to the neural network, obtains output information for the trial input data using the weight parameters, and calculates an objective function; and a setting value determination unit that determines the set value of the external force to be applied to each of the multiple reference physical systems of the physical system output generation device based on the calculated objective function. An information processing system comprising: an information acquisition unit that acquires information relating to physical variables generated by each of the plurality of reference physical systems to which an external force is applied according to the determined setting value from the physical system output generation device; an update processing unit that updates a portion of the weight parameters held by the storage unit using information relating to physical variables generated by a first reference physical system, which is one of the reference physical systems, from the information acquired by the information acquisition unit, and updates a portion of the weight parameters held by the storage unit, which is different from the updated weight parameters, using information relating to physical variables generated by a second reference physical system, which is different from the first reference physical system, from the information acquired by the information acquisition unit, to update the weight parameters of the neural network.

7. An information processing system according to claim 6, wherein the relaxation constants of the first reference physical system and the second reference physical system are different from each other.

8. An information processing system according to claim 7, wherein the relaxation constant of the first reference physical system is set to have a longer relaxation time than the relaxation constant of the second reference physical system, and the update processing unit updates the weight parameters among the weight parameters held by the storage unit that relate to the first layer to which input data is input, using information relating to the physical variables generated by the first reference physical system, and updates the weight parameters among the weight parameters held by the storage unit that relate to the first layer to which input data is input, using information relating to the physical variables generated by the second reference physical system.

9. A program that causes a computer connected to a physical system output generation device to function as a physical system output generation device, which takes a physical system that generates one or more physical variables in response to an external force as a reference physical system, receives input of a set value of an external force to be applied to the reference physical system, applies the external force based on the set value to the reference physical system, acquires the physical variables generated by the reference physical system under the applied external force, and outputs information relating to the acquired physical variables, the computer being connected to the computer as a physical system output generation device, which takes a physical system that generates one or more physical variables in response to an external force as a reference physical system, receives input of a set value of an external force to be applied to the reference physical system, applies the external force based on the set value, acquires the physical variables generated by the reference physical system under the applied external force, and outputs information relating to the acquired physical variables, the computer being connected as a physical system output generation device, which takes a physical system that generates one or more physical variables in response to an external force as a reference physical system, receives input of a set value of an external force to be applied to the reference physical system, applies the external force based on the set value, acquires information relating to the physical variables generated by the reference physical system under the applied external force based on the set value, and updates the parameter information defining the object based on the information acquired by the acquisition means.

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