Generative adversarial network design method based on quantum coupling

Abstract

The invention discloses a quantum coupling-based generative adversarial network design method. The method comprises the following steps of: respectively inputting real handwritten picture information of two domains; constructing a quantum machine learning model coupled with a quantum generative adversarial, so as to measure the judgment probability of the discriminator on the authenticity of the data and the quantum bit amplitude of the quantum patch generator; adjusting parameters of the quantum patch generator and the classic discriminator through a parameter sharing method, and capturing sharing features of the two similar domains; and meanwhile, the generator is constructed by using a patch type network design method, so that the number of quantum bits is reduced, and the training cost of the quantum network is reduced. According to the method, high-quality handwritten data generation can be realized, a new research direction is provided for the field adaptation aspect of quantum machine learning, relatively high classification precision of a cross-domain classifier can be realized, and a new possibility is developed for the development of a quantum generative adversarial network in the future.

Description

Technical Field

[0001] The present invention belongs to the technical field of application of quantum machine learning in domain adaptation, and specifically is a method for designing a generative adversarial network based on quantum coupling. Background Art

[0002] With the development of machine learning, domain adaptation between different data domains has become a major problem. Classifiers trained with hand-drawn images often have low classification effects on real photos. At this time, the joint distribution problem between domains becomes the focus. The joint distribution of multi-domain images is a probability density function that assigns a density value to each matching pair of images in different domains, such as images of the same scene in different modalities (such as color images and grayscale images), or images of the same person in different emotional states (such as happiness and sadness). Once the joint distribution of multi-domain videos is learned, it can be used to generate new image tuples. In addition to film and game production, joint distribution learning of images can be applied to domain adaptation.

[0003] Quantum computing, as a technology that uses the principles of quantum mechanics to process information, has been proven to provide solutions that surpass traditional computing methods for certain specific problems; however, the practical application of quantum computers still faces many challenges, such as hardware stability, algorithm design complexity, and sensitivity to noise.

[0004] In the field of quantum machine learning, generative adversarial networks (GANs), as a powerful data generation and processing tool, have shown great potential in image processing, data simulation, etc. However, applying it to the quantum field, especially combining the advantages of quantum computing for field adaptation, is a new research direction. The quantum version of generative adversarial networks (QGANs) can utilize the superposition and entanglement characteristics of quantum states, and theoretically can provide more efficient data processing capabilities. However, because quantum networks are limited by the number of quantum bits, more quantum bits will bring a huge training burden. Therefore, how to design a quantum network with low training cost and high training efficiency is a problem considered by the quantum network model of quantum coupled generative adversarial networks.

[0005] Compared with the existing technology, the technical differences are as follows: Technical comparison with patent CN116263972A "Image generation method and device based on quantum generative adversarial network"; Patent CN116263972A proposes an image generation method and device based on quantum generative adversarial networks, which aims to use quantum generative adversarial networks to generate images, apply them to the field of image processing technology, and generate expected images in quantum computing systems. This application proposes a design method for a generative adversarial network based on quantum coupling, which significantly reduces the training complexity and improves the accuracy of domain adaptation classifiers through optimized quantum circuit design and algorithm implementation. It is mainly used in quantum machine learning scenarios in domain adaptation to achieve high-quality handwritten data generation and cross-domain classification. There are essential differences in the application scenarios of the two.

[0006] Patent CN116263972A extracts the feature vector of the sample image in the training sample set, uses a quantum encoder to convert the feature vector into a quantum state, and obtains the image feature quantum state; according to the image feature quantum state, the generator and discriminator are trained. During the training process, the matrix density distance between the image feature quantum state and the generated quantum state and the fidelity of the discriminant quantum state are calculated to determine whether the convergence conditions are met. This application constructs a quantum machine learning model of a generative adversarial network based on quantum coupling, including two quantum patch generators and two classical discriminators; real and false pixel information is input into the classical discriminator, and the judgment probability is observed; a parameter layer sharing strategy is adopted to force the coupled network to share some parameters when updating the gradient to learn common features, so that the coupled generator learns to synthesize image pairs, and a softmax layer is added after the classical discriminator as a classifier to achieve domain adaptation classification accuracy. There are essential differences in the technical solutions of the two.

[0007] Patent CN116263972A uses a quantum encoder to calculate the distance between the feature vector and the standard feature vector in the standard database to determine the image feature quantum state, inputs it into the discriminator and uses the Pauli Z gate to measure the quantum bit to obtain the discrimination result, and judges the convergence condition based on the matrix density distance between the image feature quantum state and the generated quantum state and the fidelity of the discriminant quantum state. In this application, the quantum patch generator consists of at least two quantum subgenerators, which perform single quantum bit transformation and embed quantum entanglement by adjusting the rotation angle parameter θ; the classical discriminator is constructed using a classical neural network; the parameter layer sharing strategy is adopted during training optimization, and the first layer of the generator of the forced coupling network and the last few layers of the discriminator share weights; the optimization algorithm involves loading data into quantum registers, calculating the discriminator and generator losses, and updating parameters. There are essential differences between the two in terms of technical means.

[0008] Patent CN116263972A uses a small number of quantum bits to express quantum states in training, solving problems such as difficulty in training convergence, instability, and too small gradients, making the discriminator and generator stable. This application uses the patch method to build a quantum patch generator to generate a clearer handwriting data set, capture high-level features of images and share them, and improve the accuracy of domain adaptation; optimize quantum circuit design, use limited quantum computing resources, reduce computing time, and reduce computing complexity. There is an essential difference between the two in terms of technical effects.

[0009] Technical comparison with patent CN115700614A "A quantum generator, control method and quantum generative adversarial network"; Patent CN115700614A proposes a quantum generator, control method and quantum generative adversarial network, which aims to use quantum generators and quantum generative adversarial networks to generate data, solve the computational delay problem caused by the implementation of the generative model in the classical generative adversarial network based on classical computers, and is suitable for scenarios that require efficient data generation, such as data simulation, image processing and other fields. This application proposes a design method for a generative adversarial network based on quantum coupling, focusing on significantly reducing the training complexity and improving the accuracy of domain adaptation classifiers through optimized quantum circuit design and algorithm implementation. It is mainly used in quantum machine learning scenarios in domain adaptation to achieve high-quality handwriting data generation and cross-domain classification. There are essential differences in the application scenarios of the two.

[0010] The quantum generator of patent CN115700614A includes a random initialization module based on quantum logic gates and at least one layer of entanglement module. The random initialization module generates random variables, and the entanglement module performs entanglement operations to determine the generated data; the quantum generative adversarial network includes the quantum generator and the discriminator, and the generator and the discriminator can be trained separately while fixing each other's parameters. This application constructs a quantum machine learning model of a generative adversarial network based on quantum coupling, including two quantum patch generators and two classical discriminators; inputs real and false pixel information into the classical discriminator, and observes the judgment probability; adopts a parameter layer sharing strategy, and forces the coupled network to share some parameters when updating the gradient to learn common features, so that the coupled generator learns to synthesize image pairs; adds a softmax layer as a classifier after the classical discriminator to achieve domain adaptive classification. There is an essential difference between the two in terms of training methods.

[0011] Patent CN115700614A adds quantum circuits with randomly initialized parameters to the quantum generator to generate random data distribution; uses quantum gate combination circuits to solve the problem of network computing speed delay of classical generators. This application uses the patch method to build a quantum patch generator to generate a clearer handwriting data set; applies quantum generative adversarial networks to domain adaptation work, captures high-level features of images and shares them, and improves the accuracy of domain adaptation; optimizes quantum circuit design, reduces computing time, and reduces computing complexity. There are essential differences between the two in terms of technical effects and output content. Summary of the invention

[0012] To solve the above technical problems, the present invention proposes a generative adversarial network design method based on quantum coupling, which focuses on significantly reducing the training complexity and improving the accuracy of the domain adaptation classifier while maintaining high performance through optimized quantum circuit design and algorithm implementation.

[0013] To achieve the above object, the technical solution adopted by the present invention is: A method for designing a generative adversarial network based on quantum coupling comprises the following steps: S1. Build a quantum machine learning model based on quantum coupling generative adversarial network, including two quantum patch generators G1 and G2 for generating false pixel information, and two classical discriminators D1 and D2 for distinguishing real and false pixel information; S2, inputting the real pixel information and the false pixel information generated by the quantum patch generator into the classical discriminator, and observing the classical discriminator's judgment probability after inputting the real pixel data and the false data generated by the quantum patch generator; S3. The parameter layer sharing strategy is adopted during training optimization. The G1, G2 and D1, D2 parameter layers are divided into shared layers and common layers. During the training optimization process, the coupled network is forced to update the shared layer parameters of the corresponding parameter layers of G1, G2 and D1, D2 when updating the gradient. and Share it; S4. After repeating steps S2-S3 to reach the maximum number of iterations mum_epochs, an optimized quantum machine learning model based on quantum coupled quantum generative adversarial device is obtained. After the training is completed, the coupled generator learns to synthesize the corresponding image pairs without corresponding supervision; S5. Add a softmax layer after the classic discriminator to obtain two classifiers C1 and C2 to achieve domain adaptation classification accuracy.

[0014] As a further improvement of the present invention, in step S1, the adversarial network is composed of two identical patch-generated adversarial networks, and each patch-generated adversarial network is composed of a quantum patch generator and a classical discriminator.

[0015] As a further improvement of the present invention, in step S2, the quantum patch generator is composed of at least two quantum sub-generators, each sub-generator uses five quantum bits, one of which is used as a redundant bit to provide nonlinear characteristics for the measurement result, and each bit is input into the parameterized quantum circuit after passing through the coding layer; The circuit structure of the quantum patch generator includes a Y rotation gate and a controlled Z gate. By adjusting the rotation angle parameter θ, various single quantum bit transformations are performed and quantum entanglement is embedded. The classical discriminator is constructed using a classical neural network. The basic architecture includes an input layer, L hidden layers and an output layer, where L in the L hidden layers is ≥ 1.

[0016] As a further improvement of the present invention, it is characterized in that: in step S3, the parameter layer is defined as follows: and They are respectively distributed from the edge of the first field and the marginal distribution of the second domain The image extracted from and GAN 1 and GAN 2 The generator of is the random input of the generator; ; here and are the layer parameters of the generator, and yes and The number of parameter layers, the generator gradually decodes abstract high-level feature information to more specific details, the first layer decodes high-level semantics, and the last layer decodes low-level details, forcing and The first layer of has the same structure and shares weights. The shared weight constraint enforces the high-level semantics in and The last layer is unconstrained and implements the shared high-level features in different ways to deceive their respective discriminators. Similarly, suppose and It’s GAN 1 and GAN 2 The discriminant model, and yes and The layer parameters of the discriminator map the input image to a probability score, estimating the probability that the input image is real data. The first layer of the discriminant model extracts low-level features, and the last layer extracts high-level features, forcing and Having the same parameters of the last few layers is achieved by sharing the weights of the last few layers; .

[0017] As a further improvement of the present invention, in step S4, the optimization algorithm of the quantum machine learning model is as follows: S4-1. Initialize the common layer parameters of quantum generators G1 and G2 , , shared layer parameters , initialize the discriminator D 1 , D 2 Common parameters , , shared layer parameters ; S4-2, the real image data real_data 1 and real_data 2 Loading into quantum register and Set up two quantum registers with a size of N quantum bits. After normalizing the data, load the data into the two registers through quantum amplitude encoding to obtain the real data quantum state. , random noise fake_data 1 and fake_data 2 Loading into quantum register and ; S4-3. Random quantum states A pair of false quantum states are generated through two generators ; S4-4, use the discriminator to evaluate two pairs of true and false data respectively, and is the discrimination score of the discriminator for the real data and the generator output, Represents the overall parameters of the discriminator, and "=" indicates assignment: ; S4-5. The two generated false quantum states Denormalization obtains two classic data generated by the generator generate_data 1、2； S4-6. Calculate the discriminator loss ; ; Calculating the generator loss ; ; S4-7. Update the parameters of the generator's common layer and the discriminator normal layer parameters , is the learning rate, They are the updated gradient values ​​for the generator common layer, the discriminator common layer, the generator shared layer, and the discriminator shared layer: ; Update the parameters of the shared layers of the generator and discriminator and ; ; S4-8, repeat S4-2 to S4-7 until all data in the training set are input; S4-9. Repeat S4-2 to S4-8 until the maximum number of iterations mum_epochs is reached.

[0018] As a further improvement of the present invention, in step S5, the classifier classifies the image as follows: a softmax layer is added after the last layer of the discriminator, and the digital classification problem in the MNIST domain includes using images and labels in the MNIST domain and the QCoGAN learning problem includes using images in the MNIST domain and the USPS domain to train QCoGAN. The two classifiers are used to classify C1 in the MNIST domain and C2 in the USPS domain, respectively. The label information of the USPS domain is not used during the training process, and the adaptation of the classifier from USPS to MNIST is achieved using the same method.

[0019] The beneficial effects of the present invention are: 1) The method described in the present invention uses the patch method to build a quantum patch generator and uses a classical neural network to build a discriminator. Compared with the traditional generative adversarial network, the patch network architecture with a wider depth in this paper can capture more detailed information and generate a clearer handwriting data set; 2) The method described in this invention inherits the powerful functions of traditional GAN ​​and applies quantum generative adversarial networks to domain adaptation for the first time. The QCoGAN framework can effectively capture and share high-level features of images, while also effectively identifying low-level features. Compared with traditional methods, the accuracy of domain adaptation has been improved; 3) The invention introduces quantum computing methods to bring new possibilities for field adaptation, especially in the context of classical computer computing power approaching a bottleneck; the method described in the invention will greatly improve the application speed and effect of machine learning after the development and maturity of quantum computing technology in the future; 4) By optimizing the quantum circuit design, the method described in the present invention can more effectively utilize limited quantum computing resources, reduce computing time, and reduce the overall computational complexity, making quantum machine learning technology more practical and efficient in channel estimation in the field of wireless communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a network logic diagram of a generative adversarial network based on quantum coupling in an embodiment of the present invention; Figure 2 It is the basic structure of the quantum patch generator in the embodiment; Figure 3 is a schematic diagram of a quantum patch generator generating a number 0 in an embodiment; Figure 4 It is the classic discriminator structure in the embodiment; Figure 5 is a schematic diagram of coupling network parameter sharing in an embodiment; Figure 6 The model in the embodiment iterates one hundred times to generate a digital zero result; Figure 7 It is the effect of generating the number 1 in the embodiment; Figure 8 It is the effect of generating number 2 in the embodiment; Fig. 9 is the change curve of the loss function of the generator and the discriminator in the embodiment; Fig.10 This is the advantage of domain adaptation in the embodiments over the classical method. DETAILED DESCRIPTION

[0021] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments: The invention provides a method for designing a quantum-coupled generative adversarial network. Figure 1 As shown, the following steps are included: S1. Build a quantum machine learning model based on quantum coupling generative adversarial network, including two quantum patch generators for generating false pixel information and two classical discriminators for distinguishing real and false pixel information; S2, inputting the real pixel information and the false pixel information generated by the quantum patch generator into the classical discriminator, and observing the classical discriminator's judgment probability after inputting the real pixel data and the false data generated by the quantum patch generator; A method based on parameterized quantum circuits is used to design quantum patch generators, such as Figure 2 The figure shows that five quantum bits are used, of which the first bit is used as a redundant bit to provide nonlinear characteristics for the measurement result. Each bit is input into the parameterized quantum circuit after passing through the coding layer. The circuit structure mainly includes a Y rotation gate and a control Z gate. By adjusting the rotation angle parameter , which is able to perform a variety of single-qubit transformations. This structure successfully embeds quantum entanglement, a key quantum mechanism that allows qubits to exhibit rich interactions. This entanglement not only enhances the characterization capabilities of the circuit, but also enables it to accurately describe complex data distributions.

[0022] Considering that a single-layer structure may have limitations in its representation capabilities, we adopted a multi-layer superposition strategy to more effectively approximate and represent various complex quantum states. When this basic layer structure is repeated many times, approaching infinite layers, it achieves universality in quantum computing, which means that, from a theoretical point of view, it has the ability to generate or identify any quantum state.

[0023] At the same time, too few quantum bits cannot capture the specific features of the image. However, if you want to generate an image with clear features, you need to increase the number of quantum bits, which also greatly increases the training cost.

[0024] Therefore, the quantum patch generator is optimized using a quantum patch structure. The patch method greatly reduces the bit number requirements of quantum devices. The quantum patch generator mentioned above is used as a sub-generator, that is, a patch. Each sub-generator is responsible for generating a specific part of the final image. Finally, the outputs of each sub-generator are spliced ​​into the final output of the generator and input to the discriminator. Figure 3 What is shown is that 4 sub-generators generate 8*8 handwritten 0 images.

[0025] It is worth pointing out that since this structure uses simple quantum gates based on Pauli operators, these gates can be easily implemented on current quantum hardware. This not only ensures its theoretical rationality, but also means that it is highly feasible on actual quantum computing hardware.

[0026] The discriminator D is constructed by using a classical neural network. As a biologically inspired computational model, fully connected neural networks are the workhorse of deep learning. Various advanced deep learning models can be designed by combining FCNN with techniques such as convolutional layers, residual connections, or attention mechanisms. FCNN and its variants have surpassed other computational models in many machine learning tasks and achieved state-of-the-art performance.

[0027] The basic architecture of FCNN is as follows Figure 4 As shown, it includes the input layer, L Hidden Layers and output layer. The nodes in each layer are called "neurons". A typical feature of FCNN is The neurons in the layer are only allowed to connect to The left panel shows the basic structure of a fully connected neural network consisting of an input layer, a hidden layer, and an output layer. There are 2 neurons in the input layer and 5 neurons in the first hidden layer. The right panel shows the calculation rules of a single neuron. The neurons highlighted in the gray area are connected by Calculate, where represents the weight, refers to the output of the blue neuron, and is a predefined activation function.

[0028] S3. Use parameter layer sharing strategy during training optimization, and force coupled networks to share some parameters when updating gradients, so that they can learn common features. like Figure 5 As shown, the coupled network structure is composed of a pair of identical networks - GAN 1 and GAN 2 , each GAN is responsible for synthesizing images in a field, each white square represents a parameter layer, the first half represents the generator, and the second half represents the discriminator. During the training process, we force them to share some parameters, which allows them to learn to synthesize pairs of corresponding images without corresponding supervision.

[0029] set up and They are respectively distributed from the edge of the first field and the marginal distribution of the second domain The image extracted from and GAN 1 and GAN 2 The generator of is the random input of the generator; ; here and are the layer parameters of the generator, and yes and With the number of parameter layers, the generator gradually decodes abstract high-level feature information to more specific detail information, with the first layer decoding high-level semantics and the last layer decoding low-level details.

[0030] Since we want to share the same high-level features between two images from different domains, we enforce and The first layer of has the same structure and shares weights. This constraint enforces the high-level semantics in and The last layer is unconstrained and implements the shared high-level features in different ways to fool their respective discriminators.

[0031] Similarly, suppose and It’s GAN 1 and GAN 2 The discriminant model, and yes and The layer parameters.

[0032] like Figure 6 As shown, the network only iterates 100 times and the output effect is excellent. The effect of generating numbers 1 and 2 is as follows Figure 7 and Figure 8 As shown, the network loss changes as Fig. 9 As shown in Figure 1, the blue and yellow lines are the loss curves of the generators G1 and G2, respectively, and the green and red lines are the loss curves of the discriminators D1 and D2, respectively. They all reach convergence in about 150 iterations. The field adaptation performance of the present invention is compared with other methods. Fig.10 As shown, the classification accuracy of the present invention is superior to that of the general method.

[0033] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A method for designing a generative adversarial network based on quantum coupling, characterized in that: The following steps are involved: S1. Build a quantum machine learning model based on quantum coupling generative adversarial network, including two quantum patch generators G1 and G2 for generating false pixel information, and two classical discriminators D1 and D2 for distinguishing real and false pixel information; S2, inputting the real pixel information and the false pixel information generated by the quantum patch generator into the classical discriminator, and observing the classical discriminator's judgment probability after inputting the real pixel data and the false data generated by the quantum patch generator; S3. The parameter layer sharing strategy is adopted during training optimization. The G1, G2 and D1, D2 parameter layers are divided into shared layers and common layers. During the training optimization process, the coupled network is forced to update the shared layer parameters of the corresponding parameter layers of G1, G2 and D1, D2 when updating the gradient. and Share; S4. After repeating steps S2-S3 to reach the maximum number of iterations mum_epochs, an optimized quantum machine learning model based on quantum coupled quantum generative adversarial device is obtained. After the training is completed, the coupled generator learns to synthesize the corresponding image pairs without corresponding supervision; S5. Add a softmax layer after the classic discriminator to obtain two classifiers C1 and C2 to achieve domain adaptation classification accuracy.

2. The method for designing a quantum coupling-based generative adversarial network according to claim 1, characterized in that: In step S1, the adversarial network consists of two identical patch-generated adversarial networks, each of which consists of a quantum patch generator and a classical discriminator.

3. The method for designing a quantum coupling-based generative adversarial network according to claim 1, characterized in that: In step S2, the quantum patch generator is composed of at least two quantum sub-generators, each sub-generator uses five quantum bits, one of which is used as a redundant bit to provide nonlinear characteristics for the measurement result, and each bit is input into the parameterized quantum circuit after passing through the coding layer; The circuit structure of the quantum patch generator includes a Y rotation gate and a controlled Z gate. By adjusting the rotation angle parameter θ, various single quantum bit transformations are performed and quantum entanglement is embedded. The classical discriminator is constructed using a classical neural network. The basic architecture includes an input layer, L hidden layers and an output layer, where L in the L hidden layers is ≥ 1.

4. The method for designing a quantum coupling-based generative adversarial network according to claim 1, characterized in that: The parameter layer in step S3 is defined as follows: and They are respectively distributed from the edge of the first field and the marginal distribution of the second domain The image extracted from and They are the generators of GAN1 and GAN2 respectively, is the random input of the generator; ； here and are the layer parameters of the generator, and yes and The number of parameter layers, the generator gradually decodes abstract high-level feature information to more specific details, the first layer decodes high-level semantics, and the last layer decodes low-level details, forcing and The first layer of has the same structure and shares weights. The shared weight constraint enforces the high-level semantics in and The last layer is unconstrained and implements the shared high-level features in different ways to deceive their respective discriminators. Similarly, suppose and It is the discriminant model of GAN1 and GAN2. and yes and The layer parameters of the discriminator map the input image to a probability score, estimating the probability that the input image is real data. The first layer of the discriminant model extracts low-level features, and the last layer extracts high-level features, forcing and Having the same parameters of the last few layers is achieved by sharing the weights of the last few layers; 。 5. The method for designing a generative adversarial network based on quantum coupling according to claim 1, characterized in that: In step S4, the optimization algorithm of the quantum machine learning model is as follows, S4-1. Initialize the common layer parameters of quantum generators G1 and G2 , , shared layer parameters , initialize the common parameters of discriminators D1 and D2 , , shared layer parameters ; S4-2. Load the real image data real_data1 and real_data2 into the quantum register and Set up two quantum registers with a size of N quantum bits. After normalizing the data, load the data into the two registers through quantum amplitude encoding to obtain the real data quantum state. , load random noise fake_data1 and fake_data2 into quantum registers and ; S4-3. Random quantum states A pair of false quantum states are generated through two generators ; S4-4, use the discriminator to evaluate two pairs of true and false data respectively, and is the discrimination score of the discriminator for the real data and the generator output, Represents the overall parameters of the discriminator, "=" indicates assignment: ； S4-5. The two generated false quantum states Denormalization obtains two classic data generated by the generator generate_data 1、2； S4-6. Calculate the discriminator loss ; ； Calculating the generator loss ; ； S4-7. Update the parameters of the generator's common layer and the discriminator normal layer parameters , is the learning rate, They are the updated gradient values ​​for the generator common layer, the discriminator common layer, the generator shared layer, and the discriminator shared layer: ； Update the parameters of the shared layers of the generator and discriminator and ; ； S4-8, repeat S4-2 to S4-7 until all data in the training set are input; S4-9. Repeat S4-2 to S4-8 until the maximum number of iterations mum_epochs is reached.

6. The method for designing a quantum coupling-based generative adversarial network according to claim 1, characterized in that: In step S5, the classifier classifies the image as follows: a softmax layer is added after the last layer of the discriminator, and the digital classification problem in the MNIST domain is solved jointly, including using images and labels in the MNIST domain and the QCoGAN learning problem, including using images in the MNIST domain and the USPS domain to train the QCoGAN. The two classifiers are used to classify C1 in the MNIST domain and C2 in the USPS domain, respectively. The label information of the USPS domain is not used in the training process. The adaptation of the classifier from USPS to MNIST is achieved in the same way.

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