JP2017059071A - Optimization device, optimization method and optimization program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To optimize a weighting factor of each connection path of DNN (Deep Neural Network).SOLUTION: An optimization device 10 optimizes a learning apparatus which connects layers in a multistage manner including one or more nodes outputting an arithmetic result according to inputted data. The optimization device applies value of a factor which is set for a connection path between nodes included in different layers to a lattice point of a lattice model, generates a specific function of the lattice model using value of weight connecting the lattice points of the lattice model as input value on the basis of characteristics that input data and output data indicate, causes a quantum calculation device 13 obtaining a ground state of the lattice model in which value of the specific function becomes the minimum value by use of the quantum fluctuations to calculate a value of the lattice point in the ground state of the generated specific function, and outputs value of the factor corresponding to the value of the lattice point.SELECTED DRAWING: Figure 4

Description

  The present invention relates to an optimization device, an optimization method, and an optimization program.

  2. Description of the Related Art In recent years, a deep learning technique for learning language recognition and image recognition using a DNN (Deep Neural Network) having neurons connected in multiple layers (hereinafter sometimes referred to as nodes) has been known. . In such a DNN, nodes in different layers are connected to each other through connection paths in which predetermined weight coefficients are individually set, and a value output by a certain node is used as a weight coefficient set in the connection path. The value corrected in (1) is transmitted to the nodes of other layers.

  In order to allow such DNN to learn features such as language and images, a weighting factor set for each connection path is tried so that DNN can appropriately extract features of input data using a back-propagation method. An error-setting method is used. However, with such a method, the amount of calculation increases as the number of nodes and the number of layers increase, and therefore it is difficult to optimize the weighting factor of each connection path so that the features of the input data can be appropriately extracted. It becomes.

  On the other hand, a quantum computing technique that achieves parallelism on a scale that cannot be achieved by conventional computing devices by using superposition of quantum mechanical states has been studied. For example, as a technique of such quantum computation, there is a technique for obtaining an optimal solution for a predetermined condition, a period of input information, and the like at a higher speed than a conventional computing device by superposing a plurality of inputs. Proposed.

Japanese Patent No. 5354233

"Information Processing Using Quantum Mechanics", Go Kato, Artificial Intelligence 2014 May "Quantum Deep Learning", Nathan Wiebe, Ashish Kapoor, and Krysta M. Svore, Microsoft Research, Redmond, WA (USA), Internet <http://arxiv.org/pdf/1412.3489v1.pdf>, 2015 Search 18th of March

  However, a quantum calculation method for optimizing the weighting factor of each connection path of DNN has not been proposed so far. For this reason, learning of DNN requires a lot of time and computational resources.

  The present application has been made in view of the above, and an object thereof is to provide an optimization device, an optimization method, and an optimization program for optimizing the weighting coefficient of each connection path of a DNN.

  The optimization device according to the present application is an optimization device that performs optimization of a learning device in which layers including one or more nodes that output an operation result according to input data are connected in multiple stages, and are applied to different layers. The value of the coefficient set for the connection path between the included nodes is applied to the lattice points of the lattice model, and the weight value for connecting the lattice points of the lattice model is determined based on the characteristics indicated by the input data and the output data. A lattice function in the ground state of the generated characteristic function is generated in a quantum computing device that generates a specific function of the lattice model as an input value and obtains a ground state of the lattice model having a minimum characteristic function value using quantum fluctuations. A value of the point is calculated, and the value of the coefficient corresponding to the value of the grid point is output.

  According to one aspect of the embodiment, there is an effect that the weighting coefficient of each connection path of the DNN can be optimized.

FIG. 1 is a diagram illustrating an example of optimization processing according to the embodiment. FIG. 2 is a diagram illustrating an example of a learning device. FIG. 3 is a diagram for explaining the input and output of a node included in the learning device. FIG. 4 is a diagram illustrating an example of a functional configuration included in the optimization apparatus according to the embodiment. FIG. 5 is a diagram for explaining an example of an Ising model generated by the optimization apparatus according to the embodiment. FIG. 6 is a diagram for explaining an example of processing executed by the quantum computation device according to the embodiment. FIG. 7 is a diagram for explaining an example of processing executed by the optimization apparatus according to the embodiment.

  Hereinafter, a mode for carrying out an optimization apparatus, an optimization method, and an optimization program according to the present application (hereinafter referred to as “embodiment”) will be described in detail with reference to the drawings. Note that the optimization apparatus, the optimization method, and the optimization program according to the present application are not limited by this embodiment. In the following embodiments, the same portions are denoted by the same reference numerals, and redundant description is omitted.

[1. Optimization process)
First, an example of the optimization process according to the embodiment will be described with reference to FIG. FIG. 1 is a diagram illustrating an example of optimization processing according to the embodiment. In FIG. 1, an optimization apparatus 10 that performs a predetermined operation on input input data and optimizes a learning device Le that outputs output data is taken as an example, and features of the input data are appropriately extracted. An example of an optimization process for optimizing the learning device Le so that the learning can be performed will be described.

  First, the learning device Le optimized by the optimization device 10 will be described. For example, FIG. 2 is a diagram illustrating an example of a learning device. For example, as shown in FIG. 2A, the learning device Le is a DNN in which a plurality of nodes n (for example, neurons) that output calculation results for input data are connected in multiple stages. Specifically, the learning device Le includes an input layer IL for inputting input data, one or a plurality of intermediate layers ML for extracting features of the input data, and an output layer OL for outputting output data corresponding to the input data. Have.

  The input layer IL, the intermediate layer ML, and the output layer OL each have one or more nodes n. Each node n is sequentially connected from the node n included in the input layer IL to the node n included in the output layer OL via the node n included in the intermediate layer ML. For example, as illustrated in FIG. 2B, each node n of the input layer IL is connected to one or more nodes n included in the intermediate layer ML, and is included in the intermediate layer ML. n is connected to one or more nodes among the nodes n included in the output layer OL. That is, the learning device Le has a configuration in which nodes n are connected in multiple stages from the input device IL to the output layer OL, as shown in FIG.

  Here, a coupling coefficient (that is, a weight value) is set in each connection path that connects the nodes n, and the calculation result output by a certain node n is based on the value of the coupling coefficient. transmitted to n. For example, when the coupling coefficient “ω” is set in the connection path connecting the node n of the input layer IL and the node n of the intermediate layer ML, the node n of the input layer IL is output to the node of the intermediate layer ML. A value obtained by adding the coupling coefficient “ω” to the calculated result is input. Then, the node n in the intermediate layer ML outputs a calculation result based on the input value.

For example, FIG. 3 is a diagram illustrating the input and output of a node included in the learning device. For example, as shown in FIG. 3A, if a value input to a certain node n is x _j and a value output by the node n when the value x _j is input is y _j , y _j is As shown in FIG. 3B, it can be expressed by the following formula (1).

Here, f (x _j ) is a function that outputs a value corresponding to the value x _j . For example, a logistic sigmoid function expressed by the following equation (2), a hyperbolic tangent function expressed by the following equation (3), ReLU (Rectified Liner Unit) shown in Formula (4).

Here, as shown in FIG. 3C, when each node n is connected in multiple stages, the data x _j input to the node n _j is connected to the output of each node included in the lower layer. This is the sum of the values obtained by integrating the coupling coefficients set for the path. More specifically, the data x _j input to the node n _j has a value represented by the following equation (5) as shown in (D) in FIG. Here, b _j described in Expression (5) is a predetermined constant, y _i is a value output from the lower nodes n _{1 to} n _i , and ω _ij is from node n _i to node n _This is the value of the coupling coefficient set in the connection path to _j . Incidentally, as will become apparent in the following description, the optimization apparatus 10, in the overlapping state values of the coupling coefficient, for calculating the optimum value of coupling coefficient, in Formula (5), the omega _ij bracket Surrounded by notation.

  Such a learning device Le can learn features such as images, sentences, videos, and voices. For example, the learning device Le learns the characteristics of a cat, and when a cat is photographed in a part of an image input as input data, an image that emphasizes the cat portion of the input image is displayed. It can be output as output data. Note that the output data output from the learning device Le is not limited to the above-described form. For example, data indicating whether or not a cat is included in the image may be output. That is, the learning device Le can output arbitrary information as long as it is information indicating the characteristics included in the input data.

  Here, as a learning method of the learning device Le, for example, a back propagation method or the like is known. For example, in the back-propagation method, when the predetermined input data 101 is input to the learning device Le, the output layer is set so that the error between the data to be output to the learning device Le and the output data 102 actually output is eliminated. The coupling coefficient of each connection path is corrected from the OL side. However, in such a learning method, it becomes difficult to correct the coupling coefficient as the number of nodes and the number of layers increase.

  Therefore, the optimization apparatus 10 outputs the value of the coupling coefficient of the learning device Le that has appropriately learned the characteristics of the input data. Specifically, the optimization apparatus 10 receives input data input to the learning device Le and output data that the learning device Le that has learned the characteristics of the input data will output. Further, the optimization apparatus 10 applies the coupling coefficient value set for each connection path to each lattice point of the lattice model, and based on the characteristics indicated by the received input data and output data, A specific function of the lattice model in which a coefficient indicating the interaction of the two, that is, a weight value for connecting the lattice points is set is generated. Then, the optimization apparatus 10 causes the quantum calculation apparatus that obtains the ground state of the lattice model having the minimum characteristic function value using the quantum fluctuation to calculate the value of the lattice point in the ground state of the generated characteristic function. The calculated value of the grid point is output as the value of the coupling coefficient.

  That is, the optimization apparatus 10 maps the coupling coefficient of the learning device Le to the lattice points in the Ising model. Further, the optimization device 10 sets a coefficient indicating an interaction between lattice points based on the condition of the coupling coefficient of the learning device Le that outputs the acquired output data from the acquired input data. Then, the optimization apparatus 10 applies a quantum calculation apparatus that performs calculation using the characteristics of quantum fluctuation, such as quantum annealing, to the state where the characteristic function of the generated lattice model, that is, the value of the Hamiltonian becomes the minimum value, that is, the Ising model. Calculate the ground state.

  Thereafter, the optimization device 10 performs inverse mapping of the coupling coefficient values from the ground state of the Ising model calculated by the quantum computing device, and optimizes the regenerated coupling coefficient values for the acquired input data and output data. The obtained coupling coefficient, that is, the coupling coefficient of the learning device L3 that has learned the characteristics of the input data is output. Note that the optimization apparatus 10 does not necessarily have to hold the learning device Le itself. That is, the optimization device 10 only needs to optimize the connection coefficient of the learning device Le, and may not be an information processing device that operates as the learning device Le.

  Returning to FIG. 1, an example of optimization processing by the optimization apparatus 10 will be described along the flow. First, in the example shown in FIG. 1, the optimization apparatus 10 is an apparatus that optimizes the learning device Le in which layers including one or more nodes that output an operation result according to input data are connected in multiple stages. It is. For example, the optimization apparatus 100 acquires the feature data 100. The feature data 100 is data including features to be learned by the learning device Le. For example, in the example illustrated in FIG. 1, the feature data 100 includes input data 101 and output data 102. The input data 101 and the output data 102 are, for example, images obtained by photographing animals including animals and fruits.

  Here, the output data 102 is an image created in advance as an image to be output when the input data 101 is input to the learning device Le. For example, in a case where the learning device Le learns the appearance characteristics of the cat and emphasizes the contrast of the range in which the cat is photographed in the input image, the operator contrasts the cat among the subjects included in the input data 101. Is generated as output data 102. Note that the feature data 100 includes a plurality of sets of input data and output data in addition to the input data 101 and the output data 102.

  In such a case, the optimization apparatus 10 acquires input data 101 and output data 102 as the feature data 100 (step S1). In such a case, the optimization apparatus 10 executes an optimization process for optimizing the coupling coefficient of the learning device Le so that the output data 102 is output when the input data 101 is input. More specifically, the optimization apparatus 10 maps the coupling coefficient between the nodes of the learning device Le to each node, and sets a weight value for connecting the nodes based on the input data and the output data ( Step S2). That is, the optimization apparatus 10 generates a Hamiltonian that is a characteristic function of the Ising model based on the features indicated by the input data 101 and the output data 102, that is, the features that the learner Le learns.

  Hereinafter, an example of processing in which the optimization apparatus 10 generates a Hamiltonian of the Ising model will be described. In the following description, an example of a process for mapping the coupling coefficient of the learning device Le to the Ising model will be described. However, the optimization apparatus 10 uses a lattice model of any dimension such as a Heisenberg model or an XY model (that is, n A Hamiltonian in which the coupling coefficient of the learning device Le is mapped to the dimension vector model) may be generated.

For example, the Ising model Hamiltonian is expressed by the following equation (6). Here, H in equation (6) is a Hamiltonian indicating the total energy of the Ising model, S _i is the value of lattice point _i , S _j is the value of lattice point _j , and J is the lattice A coefficient indicating the interaction between points. Note that S _i and S _j take a value of ± 1.

  Here, assuming that the value of J varies between lattice points, the Hamiltonian can be expressed by the following equation (7).

Here, the optimization apparatus 10 maps the coupling coefficient between the nodes to the value “1” or “−1” of each lattice point in the Ising model. For example, the optimization apparatus 10 applies combinations of coupling coefficient values set for all connection paths included in the learning device Le to different lattice points. When performing such a mapping, the optimization apparatus 10, expressed a combination of the values of all of the coupling coefficients contained in the learner Le at each ω ₁ ~ω _n, the omega ₁ maps the lattice points S ₁ the omega ₂ maps to the lattice point _{S 2,} the same applies to other combinations, each mapped to a separate grid points _S 1 to S _n.

  Further, the optimization apparatus 10 sets a coefficient value J indicating an interaction between the respective lattice points based on the input data 101 and the output data 102. For example, when the learning device Le that outputs the output data 102 when the input data 101 is input, the optimization device 10 uses the same value for the coupling coefficient mapped to two grid points. The coefficient value J indicating the interaction between the two lattice points is set to a negative value. On the other hand, when the learning device Le that outputs the output data 102 when the input data 101 is input, the optimization device 10 uses the 2 if the values of the coupling coefficients mapped to the two grid points are different. The coefficient value J indicating the interaction between the two lattice points is set to a positive value.

  Further, the optimization apparatus 10 changes the absolute value of the coefficient value J according to the relative strength of the condition as to whether the values of the coupling coefficients are the same or different. For example, when the optimization apparatus 10 wants to make the condition that the values of the coupling coefficients mapped to two grid points are the same, the coefficient indicating the interaction between the two grid points. As the value J, a value having an absolute value smaller than the absolute value of the coefficient indicating the interaction between other lattice points is set.

  A more specific example will be described. For example, the optimization apparatus 10 prepares a learning device Le having such a combination of coupling coefficients for each combination of coupling coefficients, and inputs the input data 101 to each learning device Le. Further, the optimization device 10 identifies a learning device Le whose output data is the same as or similar to the output data 102 among the learning devices Le. Then, the optimization apparatus 10 determines the value of the coefficient indicating the interaction between the lattice points so that the absolute value of the value of the lattice point mapping the combination of the coupling coefficients included in the identified learner Le becomes a large value. do.

  In addition, the optimization apparatus 10 also specifies a set of coupling coefficients of the learning device Le that outputs data that is the same as or similar to the output data 102 for other input data and output data included in the feature data 100, The value of the coefficient indicating the interaction between the lattice points is changed so that the absolute value of the value of the lattice point to which the identified combination of coupling coefficients is mapped becomes a large value. As a result, the optimization apparatus 10 allows the value of the combination coefficient combination that reproduces the feature indicated by the input data 101 and the output data 102 included in the feature data 100 to be larger than the values of the other combination coefficient sets. The value of the coefficient indicating the interaction between the lattice points is set.

  Here, the Ising model having the Hamiltonian generated by the optimization device 10 has a ground state that minimizes the energy of the entire system. In such a ground state, the value of each lattice point is a value that realizes the condition set as an interaction between the lattice points as much as possible, that is, a value optimized with respect to the optimization condition. However, it takes time to calculate such a ground state by classical calculation.

  Therefore, the optimization device 10 causes the quantum computing device that performs quantum computation using quantum fluctuations to search the ground state of the Ising model having the generated Hamiltonian. For example, the optimization device 10 includes a quantum computing device including a plurality of qubits that can reproduce an arbitrary connection relationship. Then, the optimization device 10 maps each Ising model lattice point to each qubit of the quantum computing device, and maps a coefficient indicating an interaction between each Ising model lattice point to each qubit interaction. Let Then, the optimization apparatus 10 searches for the ground state of the system to which the Ising model is mapped using the technique of quantum annealing.

For example, the quantum computing device searches the ground state of the Ising model by temporally evolving from an overlapped state where the values of each qubit are uniform to the Ising model indicated by the generated Hamiltonian (step S3). Here, the ground state of the Ising model generated by the optimization device 10 is such that the value of the grid point to which the combination of coupling coefficients capable of appropriately extracting the feature indicated by the feature data 100 is mapped is greater than the value of the other grid point. Also grows. For this reason, the optimizing device 10 identifies the lattice point having the largest value from the calculation result of the quantum computing device, and outputs a set of coupling coefficients mapped to the identified lattice point. For example, the optimization apparatus 10 outputs a coupling coefficient list indicating the coupling coefficient values ω _{11 to} ω _jj mapped to the identified lattice points (step S4).

  Note that the process of searching the ground state of the Ising model generated by the optimization device 10 is not limited to the above description. For example, in quantum computation, an adiabatic model such as a lattice model and a circuit model using an arbitrary quantum circuit are equivalent. For this reason, since quantum computation using quantum annealing is equivalent to a quantum circuit that continuously operates a quantum gate, the optimization apparatus 10 uses an Ising model represented by the generated Hamiltonian as a quantum circuit that combines quantum gates. Can be optimized by any hardware that reproduces. For example, the optimization apparatus 10 may search the ground state of the generated Ising model using a quantum calculation apparatus that performs quantum calculation using nuclear magnetic resonance, quantum dots, Josephson elements, ion traps, photons, and the like. .

  In addition, the optimization device 10 can arbitrarily set each grid point in any manner as long as it can maximize the value of the grid point to which the combination of coupling coefficients that appropriately extract the feature indicated by the feature data 100 is mapped. A coefficient indicating an interaction between them may be set. For example, the optimization apparatus 10 calculates a difference between the input data 101 and the output data 102 and specifies a combination coefficient combination of the learning device Le that reproduces the calculated difference. Then, the optimization apparatus 10 sets a coefficient indicating the interaction between the lattice points so that the absolute value of the value of the update store to which the identified set is mapped is larger than the values of the other lattice points. May be.

  In the above description, the optimization apparatus 10 maps all combinations of the values of the coupling coefficients of the learning device Le to the lattice points. However, the embodiment is not limited to this, and the optimization apparatus 10 may map a set of coupling coefficient values to lattice points with an arbitrary granularity. For example, the optimization apparatus 10 maps a set of coupling coefficient values to lattice points for each layer included in the learning device Le. Further, the optimization apparatus 10 sets the connection relation of the lattice points mapping the combination of the coupling coefficient values according to the connection relation of each layer. For example, the optimization apparatus 10 connects a grid point to which a set of coupling coefficient values for the output layer is mapped to a grid point to which a set of coupling coefficient values for the intermediate layer is mapped.

  Then, when the input data 101 is input, the optimization device 10 maps the combination of the coupling coefficients of each layer so as to reproduce the coupling coefficient of the learning device Le that outputs the same or similar data as the output data 102. The coefficient indicating the interaction between the lattice points is set so that the value of the lattice point becomes larger than the other lattice points.

For example, the optimization system 10, the layers included in the learning unit Le and _L 1 ~L _n, the combination of values of the coupling coefficient between the nodes comprised in the layer _{L i + 1} in the layer _{L i} omega _{Li, When} represented _{by 1} to ω _{Li, n} , ω _{Li, 1} is mapped to the lattice point S _{Li, 1} , ω _{Li, 2} is mapped to the lattice point S _{Li, 2} , and other combinations are also individually separated in the same manner. Are mapped to lattice points S _{Li, 1 to} S _{Li, n} . Further, the optimization apparatus 10 represents ω _{Li + 1,1} as ω _{L + 1,1} to ω _{L + 1 , n, where} the combination of the coupling coefficient values of the nodes included in the layer L _{i + 1} and the nodes included in the layer L _{i + 2} is represented by ω _{L + 1,1} to ω _{L + 1 , n.} Map to the lattice point S _{Li + 1,1} , map ω _{Li + 1,2} to the lattice point S _{Li + 1,2} , and similarly map the other combinations to the individual lattice points S _{Li + 1,1 to} S _{Li + 1, n} . .

Moreover, the optimization apparatus 10 sets the connection of each lattice point according to the connection relation for each layer. For example, the optimization unit 10, the layer _L grid points coupling coefficient is mapped to _{i S Li, 1 ~S Li,} n and a layer _{L i +} grid point coupling coefficients are mapped in _{1 S Li + 1,1 ~S Li +} 1 _{, N} are connected to each other. Then, the optimization apparatus 10 sets a coefficient indicating an interaction between the lattice points S _{Li, 1 to} S _{Li, n} and the lattice points S _{Li + 1,1 to} S _{Li + 1, n} to a predetermined value. The value of the coefficient may be a constant or a value corresponding to a function of the node as shown in Expression (1).

In addition, the optimization apparatus 10 uses other values of grid points to which a set of grid points included in the learning device Le that outputs the same or similar output data as the output data 102 when the input data 101 is input. The coefficient indicating the interaction between the lattice points is manipulated so that the value is larger than the value of the lattice points. For example, when the learning device Le that outputs output data that is the same as or similar to the output data 102 when the input data 101 is input, the optimization device 10 includes ω _{Li, x} and ω _{Li + 1, y.} The interaction between the lattice points is shown so that the value of the lattice point S _{Li, x} mapped to ω _{Li, x} and the value of the lattice point S _{Li + 1, y} mapped to ω _{Li + 1, y} becomes large. Manipulate the coefficients.

  The ground state of the Hamiltonian generated as a result of the above-described processing includes values of a plurality of lattice points to which a set of coupling coefficients of each layer included in the learning device Le that has most appropriately learned the feature indicated by the feature data 100 is mapped. The value is larger than the value of the grid point. As a result, for each layer, the optimization apparatus 10 identifies the lattice point having the largest value in the ground state among the lattice points mapping the combination of coupling coefficients, and includes the combination of coupling coefficients indicated by the identified lattice points. A coupling coefficient list can be output.

  As described above, the optimization apparatus 10 maps a set of coupling coefficients to lattice points, and generates an Ising model Hamiltonian in which a coefficient value indicating an interaction between lattice points is set according to a feature to be learned. Then, the optimization device 10 causes the quantum computing device to calculate the generated ground state of the Hamiltonian, and outputs a set of coupling coefficients based on the value of each lattice point in the calculated ground state. As a result, the optimization apparatus 10 can optimize the coupling coefficient using the quantum calculation even when the learning device Le includes many nodes, and thus shortens the time required for learning of the learning device Le. can do.

In other words, the optimization apparatus 10 puts the combination of coupling coefficients set in the connection path between the nodes into a superposed state, and changes the observation probability of each superposed coupling coefficient set according to the feature to be learned. Let More specifically, as indicated by the bracket notation in Equation (5), the optimization apparatus 10 performs the calculation with the values of the coupling coefficients ω _{ij in} an overlapping state. Then, the optimization apparatus 10 outputs the finally observed combination coefficient set. For this reason, the optimization apparatus 10 can optimize a coupling coefficient using a quantum calculation, without using a back propagation method etc. and calculating | requiring a coupling coefficient by trial and error.

  Further, the optimization apparatus 10 puts the combination of coupling coefficients into a superposed state, changes the observation probability according to the feature, and outputs the finally observed combination of coupling coefficients. As a result, the optimization apparatus 10 simultaneously determines whether or not the feature has been successfully extracted for each combination of coupling coefficients, so that the combination of output coupling coefficients can be prevented from falling into a so-called local solution. it can. Further, the optimization device 10 can prevent overlearning of the learning device Le.

  Here, when the learner Le learns features by learning for each layer, pre-training, or the like, the performance of the entire learner Le may be reduced. However, the optimization apparatus 10 puts all combinations of coupling coefficients included in the learning device Le into a superposed state. For this reason, the optimization apparatus 10 can obtain | require the coupling coefficient of the learning device Le optimized more in the whole learning device Le rather than the learning device Le optimized by the learning for every layer, pre-training, etc.

[2. Optimization device configuration)
Next, the configuration of the optimization apparatus 10 according to the embodiment will be described with reference to FIG. FIG. 4 is a diagram illustrating an example of a functional configuration included in the optimization apparatus according to the embodiment. As shown in FIG. 4, the optimization device 10 is connected to the input device 20 and the output device 30. The optimization apparatus 10 includes an acquisition unit 11, a generation unit 12, a quantum calculation device 13, and an output unit 17. The quantum computation device 13 includes a state reproduction unit 14, an operation unit 15, and an observation unit 16. The state reproduction unit 14 includes a plurality of quantum bits 14a to 14d.

  The input device 20 is an input device for inputting the feature data 10 to the optimization device 10. For example, the reading device can read the feature data 100 from a recording medium such as an HDD (Hard Disk Drive) or a flash memory. It is. For example, when the input device 20 reads the feature data 100 from a recording medium such as a flash memory, the input device 20 outputs the read feature data to the optimization device 10.

  For example, the output device 30 is realized by a monitor, a printer, or the like, and receives the coupling coefficient list including the values of the coupling coefficients of the learning device Le optimized by the optimization device 10 with respect to the feature indicated by the feature data 100. An output device that displays or prints a received coupling coefficient list.

  When acquiring the feature data 100 from the input device 20, the acquisition unit 11 extracts input data 101 included in the feature data 100 and output data 102 corresponding to the input data 101, and the extracted input data 101 and output data 102 are extracted. Are output to the generation unit 12.

  The generation unit 12 applies a set of values of coupling coefficients between nodes included in the learning device Le to lattice points of the Ising model, and based on the characteristics indicated by the input data 101 and the output data 102, each lattice of the Ising model Generate a Hamiltonian with coefficients set to indicate the interaction between points. For example, the generation unit 12 generates an Ising model having a number of grids that can map all combinations of coupling coefficient values according to the number of nodes included in the learning device Le. Further, when mapping the set of coupling coefficients for each layer, the generation unit 12 generates an Ising model having a number of dimensions corresponding to the number of nodes included in each layer and the connection relationship between the layers. Then, the generation unit 12 maps a combination of coupling coefficient values to each lattice point of the generated Ising model.

  In addition, the generation unit 12 sets a coefficient value indicating an interaction between the lattice points based on the characteristics of the input data 101 and the output data 102 received from the acquisition unit 11. For example, when the generation unit 12 inputs the input data 101 received from the acquisition unit 11, the generation unit 12 specifies a combination coefficient value set included in the learning device Le that outputs the same or similar data as the output data 102. The value of the coefficient indicating the interaction between the respective grid points is set so that the value of the grid point mapping the identified set is larger than the values of the other grid points.

For example, FIG. 5 is a diagram for explaining an example of an Ising model generated by the optimization apparatus according to the embodiment. In the example illustrated in FIG. 5, an example of processing for mapping a set of three coupling coefficients to the lattice points S _i , S _j , and S _k is described. For example, generator 12 maps the set i of the coupling coefficient to the lattice point S _i, mapping the set j of the coupling coefficient to S _j, maps a set k of the coupling coefficient in S _k.

  Subsequently, the generation unit 12 prepares learning devices Le having combinations of coupling coefficients i to k, and inputs the input data 101 to each learning device Le. Then, the generation unit 12 compares the data output from each learning device Le with the output data 102 received from the acquisition unit 11, and identifies the combination coefficient combination of the learning devices Le that output the same or similar data. Then, the generation unit 12 sets the coefficient value indicating the interaction between the lattice points so that the values of the lattice points obtained by mapping the set of coupling coefficients of the specified learning device Le are the same.

For example, when the generation unit 12 inputs the input data 101 to each learning device Le, the learning device Le having the combination coefficient set i and the learning device Le having the combination coefficient set j are connected to the output data 102. When the same or similar data is output, the following processing is executed. First, the generation unit 12 sets the value of the coefficient value J _ik indicating the interaction between the lattice point S _i mapped with the coupling coefficient set _i and the lattice point S _k mapped with the coupling coefficient set k. Decrease. In addition, the generation unit 12 increases the values of the coefficients J _ij and J _kj indicating the interaction between the lattice point S _j to which the coupling coefficient set j is mapped and other lattice points.

  Further, the generation unit 12 performs the above-described processing for each set of the input data 101 and the output data 102 included in the feature data 100. Then, the generation unit 12 outputs the Ising model generated as a result of the above-described processing to the quantum calculation device 13.

  Returning to FIG. 4, the description will be continued. The quantum computing device 13 is a so-called quantum computer that uses quantum computation to search the ground state of the Ising model indicated by the Hamiltonian generated by the generating unit 12. For example, the quantum computing device 13 has a plurality of qubits 14a to 14d that can hold a plurality of values in a superposed state, and can reproduce the state of the Ising model using each qubit 14a to 14d. A reproduction unit 14 is included.

  When the operation unit 15 of the quantum computing device 13 receives the Hamiltonian generated by the generation unit 12, the operation unit 15 determines the qubits 14a to 14d included in the state reproduction unit 14 and the coupling coefficient between the qubits 14a to 14d. By controlling, the ground state of the Ising model indicated by the Hamiltonian received from the generation unit 12 is quantum-calculated.

  For example, the qubit can be set to the state shown by the following equation (8). When the qubit in the state shown in Expression (8) is observed, the probability of observing the value “0” is a power of the absolute value of α, and the probability of observing the value “1” is the power of the absolute value of β. It becomes.

  Here, α and β shown in the equation (8) are complex numbers that satisfy the following equation (9).

  First, the operation unit 15 sets a uniform state for each of the qubits 14a to 14d as an initial state. For example, the operation unit 15 sets the state shown in the following expression (10) for each qubit 14a to 14d. When the state shown in Expression (10) is set, when each of the qubits 14a to 14d is observed individually, 0 or 1 is observed with the same probability.

  Then, the operation unit 15 temporally develops the states of the qubits 14a to 14d from the initial state to the state indicated by the Hamiltonian generated by the generation unit 12, so that the Ising model indicated by the Hamiltonian generated by the generation unit 12 is displayed. Search ground state.

For example, the operation unit 15 sets an interaction between qubits based on the value of J _ij . Then, the operation unit 15 develops the state of the qubit 14a over time. When the time development described above is sufficiently performed, the states of the qubits 14a to 14d become the ground state of the Ising model indicated by the Hamiltonian generated by the generation unit 12. For example, when the state of the qubit 14a is expressed by Equation (3), the values of α and β gradually change based on the value of J _ij due to time evolution. And the observation part 16 can observe the ground state of an Ising model by observing the state of each quantum bit 14a-14d developed in time. Then, the observation unit 16 outputs to the output unit 17 the ground state of the identified Ising model, that is, the value of each qubit 14a to 14d when observed.

  Here, the concept of processing executed by the quantum computation device 13 will be described with reference to FIG. FIG. 6 is a diagram for explaining an example of processing executed by the quantum computation device according to the embodiment. In the example shown in FIG. 6, the Hamiltonian value in the Ising model generated by the generation unit 12 is set to the value of each lattice point with the Hamiltonian value on the vertical axis and the combination of the values of each lattice point on the horizontal axis. Each value combination is indicated by a solid line.

  For example, the quantum computing device 13 sets the superposed state of values that can take the values of the quantum bits 14a to 14d. As a result, the quantum computation device 13 reproduces all combinations of the values of the lattice points in the Ising model, as indicated by the dotted circles in FIG. Then, as indicated by the dotted arrows in FIG. 6, the quantum computing device 13 causes the state of each qubit 14a to 14d to evolve into a state indicated by the Hamiltonian of the Ising model generated by the generation unit 12, Reproduce the Hamiltonian value for each combination of values between grid points. Such processing is performed while the qubits 14a to 14d are kept in the quantum state.

  Here, the state in which the value of the Hamiltonian takes the minimum value is the most stable state in the system. For this reason, when the qubits 14a to 14d that are sufficiently developed in time with the quantum state maintained are observed, a state ω in which the value of the Hamiltonian is minimum may be observed as shown in FIG. Is expensive. Therefore, the quantum computing device 13 observes the value of each of the qubits 14a to 14d that has been sufficiently developed while maintaining the quantum state, so that the value of the Hamiltonian is minimized without falling into a minimum value. Specify the value of each grid point.

  Returning to FIG. 4, the description will be continued. When the output unit 17 receives the values of the qubits 14 a to 14 d observed by the observation unit 16, the output unit 17 outputs a coupling coefficient list including the optimized coupling coefficients to the output device 30 based on the values. For example, the output unit 17 sets the value of each qubit 14a to 14d as the value of the lattice point of the Ising model corresponding to each qubit 14a to 14d. The output unit 17 obtains optimized data by inverse mapping output data from each lattice point of the Ising model, and outputs a coupling coefficient list including a combination of coupling coefficients corresponding to the acquired data. Output to 30. For example, when the value of a certain lattice point is “1” and the value of another lattice point is “−1”, the output unit 17 sets a combination coefficient that is mapped to the lattice point having a value of “1”. Is output to the output device 30.

[3. Flow of processing executed by optimization device]
Next, the flow of processing executed by the optimization apparatus 10 according to the embodiment will be described with reference to FIG. FIG. 7 is a diagram for explaining an example of processing executed by the optimization apparatus according to the embodiment. First, the optimization apparatus 10 acquires input data 101 and output data 102 (step S101). Further, the optimization apparatus 10 maps the set of coupling coefficients between the nodes to the lattice points of the Ising model (step S102). Further, the optimization apparatus 10 sets a coefficient value indicating an interaction between lattice points of the Ising model based on the characteristics indicated by the input data 101 and the output data 102 (step S103).

  Then, the optimization apparatus 10 causes the quantum bits of the quantum computer 13 to evolve over time into the ground state of the Ising model (step S104). Also, the optimization apparatus 10 acquires the ground state of the Ising model by observing the qubits that have evolved over time (step S105). Then, the optimization apparatus 10 outputs, as an optimization result, data obtained by inversely mapping the observation result, that is, a coupling coefficient list including a combination of coupling coefficients mapped to the lattice point having the largest value (step S106). finish.

[4. (Modification)
The optimization apparatus 10 according to the above-described embodiment may be implemented in various different forms other than the above-described embodiment. Therefore, in the following, another embodiment of the optimization device 10 will be described.

[4-1. About Ising model)
Note that the optimization apparatus 10 described above maps a set of coupling coefficients to each lattice point of the Ising model, and a weight value that connects the lattice points based on the characteristics indicated by the input data 101 and the output data 102. It was set. However, the embodiment is not limited to this. For example, the optimization apparatus 10 may map a combination of coupling coefficients to a model other than the Ising model. When such processing is executed, the optimization apparatus 10 can obtain a continuous value instead of a binary value such as “+1” or “−1”.

[Calculation of 4-2.1 layer only]
Moreover, the optimization apparatus 10 mentioned above calculated the coupling coefficient about all the connection paths which the learning device Le has. However, the embodiment is not limited to this. For example, the optimization apparatus 10 may calculate a coupling coefficient for a connection path between any one layer and another layer.

[4-3. Others]
Here, the optimization apparatus 10 may perform processing in consideration of dummy paths that are not used when the learning device Le is actually operated. For example, the optimizing device 10 may put the combination of coupling coefficients set in all connection paths including the dummy path into a superposed state, and calculate the optimal coupling coefficient group by quantum calculation.

  Further, the optimization apparatus 10 may perform processing in consideration of convolution. For example, the optimizing device 10 does not only superimpose not only the combination of coupling coefficients in which the value of the coupling coefficient set to the connection path is changed but also the combination of coupling coefficients that are convolved between different nodes. You can do it. That is, the optimization apparatus 10 obtains combinations of coupling coefficient values set for all connection paths for each convolution mode, and obtains all combinations of combinations of coupling coefficients obtained for all convolution modes. You may be in a superposition state.

[4-4. (Hardware configuration)
The optimization device 10 described above has the quantum calculation device 13 that searches the ground state of the Ising model indicated by the Hamiltonian. However, the embodiment is not limited to this. For example, the optimization apparatus 10 may include only the acquisition unit 11, the generation unit 12, and the output unit 17, and may cause the quantum computation device 13 installed outside to search for a ground state.

  Among the functional configurations of the optimization device 10, the processing performed by the acquisition unit 11, the generation unit 12, and the output unit 17 is an integrated circuit such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array). May be realized. The processing performed by the acquisition unit 11, the generation unit 12, and the output unit 17 is stored in a storage device inside the optimization device 10 by a processor such as a CPU (Central Processing Unit) or an MPU (Micro Processing Unit), for example. The optimization program may be realized by executing a RAM (Random Access Memory) as a work area.

[5. effect〕
As described above, the optimization apparatus 10 is an apparatus that performs optimization of the learning device Le in which layers including one or more nodes that output an operation result corresponding to input data are connected in multiple stages, and includes a node n The value of the coefficient indicating the interaction between the lattice points of the lattice model is applied to the lattice points of the lattice model by applying the coupling coefficient value set for the connection path between them to the lattice points of the lattice model. Generate a specific function of the lattice model with. Further, the optimization device 10 causes the quantum calculation device 13 that obtains the ground state of the lattice model having the minimum value of the characteristic function using the quantum fluctuation to calculate the value of the lattice point in the ground state of the generated characteristic function. . Then, the optimization apparatus 10 outputs the value of the coupling coefficient corresponding to the value of the grid point.

  As a result, the optimization apparatus 10 can optimize the coupling coefficient using the quantum calculation even when the learning device Le includes many nodes, and thus shortens the time required for learning of the learning device Le. can do. Further, the optimization device 10 causes the quantum calculation device 13 that obtains the ground state of the lattice model having the minimum value of the characteristic function using the quantum fluctuation to calculate the value of the lattice point in the ground state of the generated characteristic function. Therefore, it is possible to prevent the value of the coupling coefficient from falling into a local solution. That is, the optimization apparatus 10 can prevent overlearning of the learning device Le.

  Further, the optimization apparatus 10 applies the combination of the coupling coefficient values set for all the connection paths included in the learning device to the lattice points of the lattice model. For this reason, the optimization apparatus 10 can obtain | require the value of the coupling coefficient of the optimized learning device Le.

  Further, the optimization apparatus 10 applies a combination of coupling coefficient values set in a connection path between a node included in a predetermined layer and another node to a lattice point of the lattice model. For this reason, the optimization apparatus 10 can obtain | require the value of the optimized coupling coefficient for every layer.

  In addition, the optimization apparatus 10 uses the combination of the coupling coefficient values set in the connection path between the node included in the predetermined layer and the other node as the node included in the other layer connected to the predetermined layer. A combination of coefficient values set in a connection path with another node is applied to a lattice point connected to the applied lattice point. For this reason, since the optimization apparatus 10 can obtain | require the value of the coupling coefficient optimized for every layer, considering the performance in the whole learning device Le, it can prevent overlearning.

  Further, the optimization device 10 connects each connection path of the learning device Le that outputs data that is the same as or similar to the output data 102 when the input data 101 is input among the lattice points to which the combination of the coupling coefficient values is applied. The value of the weight for connecting the grid points is set so that the value of the grid point fitted with the value of the coupling coefficient set for is close to a predetermined value. For this reason, the optimization apparatus 10 can obtain | require the coupling coefficient of the learning device Le which learned the characteristic which the input data 101 and the output data 102 show appropriately.

  As described above, some of the embodiments of the present application have been described in detail based on the drawings. It is possible to implement the present invention in other forms with improvements.

  Moreover, the above-mentioned “section (module, unit)” can be read as “means”, “circuit”, and the like. For example, the generation unit can be read as generation means or a generation circuit.

DESCRIPTION OF SYMBOLS 1 Control system 10 Optimization apparatus 11 Acquisition part 12 Generation part 13 Quantum calculation apparatus 14 State reproduction part 14a-14d Qubit 15 Operation part 16 Observation part 17 Output part 20 Input apparatus 30 Output apparatus

Claims (7)

An optimization device that optimizes a learning device in which layers including at least one node that outputs an operation result according to input data are connected in multiple stages,
Apply the value of the coefficient set for the connection path between nodes in different layers to the lattice points of the lattice model, and connect the lattice points of the lattice model based on the characteristics of the input data and output data Generate a specific function of the lattice model with the value of
A quantum computing device that obtains a ground state of a lattice model having a minimum value of a characteristic function using quantum fluctuations, and calculates a value of a lattice point in the ground state of the generated characteristic function,
The optimization apparatus, wherein the coefficient value corresponding to the value of the grid point is output. The optimization device includes:
The optimization apparatus according to claim 1, wherein a combination of coefficient values set for all connection paths included in the learning device is applied to a lattice point of the lattice model. The optimization device includes:
The optimization apparatus according to claim 1, wherein a combination of coefficient values set in a connection path between a node included in a predetermined layer and another node is applied to a lattice point of the lattice model. The optimization device includes:
The combination of the coefficient values set in the connection path between the node included in the predetermined layer and the other node is used as the connection path between the node included in the other layer connected to the predetermined layer and the other node. The optimization apparatus according to claim 3, wherein the set combination of coefficient values is applied to a grid point connected to the fitted grid point. The optimization device includes:
Coefficient values set for each connection path of a learning device that outputs data that is the same as or similar to the output data when the input data is input among the lattice points to which the combination of the coefficient values is applied. The optimization device according to any one of claims 1 to 4, wherein a value of a weight for connecting the lattice points is set so that a value of the lattice point fitted with a value approaches a predetermined value. . An optimization device that optimizes a learning device in which layers including one or more nodes that output an operation result corresponding to input data are connected in multiple stages,
Receiving input data to be input to the learning device and output data to be output to the learning device when the input data is input;
Apply the value of the coefficient set for the connection path between nodes in different layers to the lattice points of the lattice model, and connect the lattice points of the lattice model based on the characteristics of the input data and output data Generate a specific function of the lattice model with the value of
A quantum computing device that obtains a ground state of a lattice model having a minimum value of a characteristic function using quantum fluctuations, and calculates a value of a lattice point in the ground state of the generated characteristic function,
The optimization method is characterized in that the value of the coefficient corresponding to the value of the grid point is output. A computer having an optimization device that optimizes a learning device in which layers including one or more nodes that output operation results corresponding to input data are connected in multiple stages,
Receiving input data to be input to the learning device and output data to be output to the learning device when the input data is input;
Apply the value of the coefficient set for the connection path between nodes in different layers to the lattice points of the lattice model, and connect the lattice points of the lattice model based on the characteristics of the input data and output data Generate a specific function of the lattice model with the value of
A quantum computing device that obtains a ground state of a lattice model having a minimum value of a characteristic function using quantum fluctuations, and calculates a value of a lattice point in the ground state of the generated characteristic function,
An optimization program for executing a process of outputting the value of the coefficient corresponding to the value of the grid point.

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