Secure distributed SAR image data generation method based on split federated learning

Abstract

The invention discloses a secure distributed SAR (Synthetic Aperture Radar) image data generation method based on split federated learning, which belongs to the technical field of SAR images and specifically comprises the following steps: constructing a split federated learning model comprising a plurality of clients; on each client, splitting a locally held SAR image data set into a plurality of subsets by using a data segmentation algorithm; independently training a local generation model on a subset of each client by each client, and generating pseudo-synthetic aperture radar image data; by utilizing a federated learning framework, each client only updates and shares parameters of a local generation model to the central server; the central server aggregates the received model parameter updates and generates global model parameters; the central server distributes the global model parameters to all the clients, and each client updates a respective local generation model according to the global model parameters; repeating the steps until a preset number of training iterations is reached; the generalization ability and accuracy of the global model are improved.

Description

Technical Field

[0001] The present invention relates to the field of SAR image technology, and in particular to a secure distributed SAR image data generation method based on split federated learning. Background Art

[0002] Synthetic Aperture Radar (SAR) is an advanced remote sensing technology that is widely used in earth science research, disaster monitoring, military reconnaissance and other fields. SAR image data plays an irreplaceable role in many application scenarios due to its unique imaging mechanism and rich information content. However, with the rapid increase in the amount of SAR image data and the diversification of application requirements, how to efficiently and securely generate and process this data has become an important research topic.

[0003] Traditional SAR image data processing methods usually rely on centralized data processing centers, and all data needs to be transmitted to the data center for processing. This approach not only places extremely high demands on network bandwidth and storage capacity, but also poses a great security risk during data transmission. Once the data is leaked or tampered with, it may bring serious consequences.

[0004] In recent years, federated learning, as an emerging distributed machine learning framework, has provided new ideas for solving the above problems. Federated learning allows multiple participants to conduct collaborative learning by sharing model parameter updates instead of original data while keeping data locally stored. This approach can not only effectively protect data privacy, but also utilize the data resources of each participant to improve the training effect of the model.

[0005] Although federated learning has many advantages in theory, it still faces some challenges in practical applications. First, the complexity and high-dimensional characteristics of SAR image data make the direct application of federated learning algorithms face computing and communication challenges. Secondly, existing federated learning algorithms often assume that the data distribution of all participants is consistent, but in fact SAR image data from different sources may have significant differences, which will affect the generalization ability and training efficiency of the model. Split federated learning SFL is an emerging distributed learning technology that combines the advantages of federated learning and split learning. It improves the efficiency of model training and communication while protecting data privacy. It is suitable for a variety of scenarios that require distributed data collaborative learning. Therefore, the present invention proposes a secure distributed SAR image data generation method based on split federated learning. Summary of the invention

[0006] The purpose of the present invention is to provide a secure distributed SAR image data generation method based on split federated learning to solve the following technical problems:

[0007] SAR image data from different sources may have significant differences, which will affect the generalization ability and training efficiency of the model.

[0008] The purpose of the present invention can be achieved through the following technical solutions:

[0009] A secure distributed SAR image data generation method based on split federated learning includes the following steps:

[0010] Step 1: Build a split federated learning model, which includes a central server and multiple clients distributed in different geographical locations. Each client holds a part of the SAR image dataset, and the image datasets do not interact with each other.

[0011] Step 2: On each client, a data segmentation algorithm is applied to segment the locally held SAR image dataset into several subsets;

[0012] Step 3: Each client independently trains a local model based on a local data subset using a generative adversarial network to extract features and adjust parameters, and uses the local model to process new inputs to generate a pseudo synthetic aperture radar image as the output result;

[0013] Step 4: After each client completes a round of local optimization, it calculates the change in model parameters in the current iteration cycle. Using the federated learning framework, each client only shares the parameter updates of its locally generated model with the central server or other clients.

[0014] Step 5: The central server or other clients aggregate the received model parameter updates, verify the parameters, and generate global model parameters based on the federated average;

[0015] Step 6: The central server evaluates the performance of the newly generated global model parameters on the preset validation set, and distributes the global model parameters that have passed the evaluation to all clients. Each client updates its local generation model according to the global model parameters. After the client completes the local training, it calculates the change in the model parameters again and sends these updates back to the central server for the next round of aggregation.

[0016] Step 7: Repeat steps 3 to 6 until the predetermined number of training iterations is reached.

[0017] As a further solution of the present invention: when transmitting model parameter updates between each client and the central server, end-to-end encryption technology is used, differential privacy technology is introduced in the parameter update process of the locally generated model, and noise is added to the data sample.

[0018] As a further solution of the present invention: in step 2, the specific process of the data segmentation algorithm is:

[0019] Regard the entire SAR image dataset as an overall region Ω, calculate the average gray value and standard deviation of all pixel points within the region; divide the overall region into several sub-regions, and for each sub-region R i , calculate the average gray value μ i and standard deviation σ i；

[0020] The formula for calculating the average value is: μ = (∑x j ) / N, where x j is the gray value of the j-th pixel point within the sub-region R, and N is the number of pixel points within the sub-region;

[0021] The formula for calculating the standard deviation is: σ = √[(∑(x j -μ)^2) / (N - 1)];

[0022] Set a threshold T. When σ i > T, then perform splitting; otherwise, do not split; split the sub-region R i that meets the splitting condition into four smaller sub-regions R i1 , R i2 , R i3 , R i4 , and continue to determine whether each newly generated sub-region needs to be split until the σ values of all sub-regions are less than or equal to the threshold T;

[0023] For any two sub-regions A and B after splitting, if D(A, B) < S, then re-combine sub-regions A and B, where D represents the distance metric between the two regions, and S is a preset merging threshold.

[0024] As a further solution of the present invention: in the step 3, the process of generating pseudo-synthetic aperture radar image data is as follows:

[0025] Denoise, normalize, and enhance the original SAR image data, extract features from the preprocessed SAR image, where the features include texture features and spectral features, construct a generation model based on a generative adversarial network, use the extracted features as input, train the selected generation model, and for each subset D i , calculate the loss function L(θ), where θ represents the model parameters;

[0026]

[0027] where D is the discriminator, G is the generator, p data is the real data distribution, p zis the noise distribution; the model parameter θ is updated using the gradient descent method to minimize the loss function L(θ); and new pseudo SAR image data G(θ,z) is generated, where z represents a random noise vector.

[0028] As a further solution of the present invention: the training process of generating an adversarial network also includes:

[0029] Fixed the discriminator D and trained the generator G to maximize the probability of deceiving the discriminator;

[0030] The generator G is fixed and the discriminator D is trained to improve its ability to distinguish between real images and generated images;

[0031] The above two steps are repeated alternately until the Nash equilibrium is reached.

[0032] As a further solution of the present invention: in step 4, the process of parameter update sharing is:

[0033] The parameters are encrypted and transmitted via the TLS protocol. Each client uploads parameter updates at different time points. The central server receives the encrypted parameter updates from each client and stores them in an independent storage. The central server aggregates the parameter updates only after receiving a sufficient number of parameter updates.

[0034] As a further solution of the present invention: in step 5, the central server receives local updates from all clients and calculates the weighted average of these updates. The update of each client is assigned a different weight according to the size of its local data, and the calculated weighted average update is used to update the parameters of the global model.

[0035] As a further solution of the present invention: in step 6, the process of the client updating the respective local generation models according to the global model parameters is as follows:

[0036] Each client receives the latest global model parameters W from the central server t , where t represents the current iteration round. The client synchronizes the received global model parameters with the local model parameters. The formula is:

[0037] W local t =αW local t-1 +(1-α)W t ;

[0038] Among them, α is a weight coefficient between 0 and 1;

[0039] Using the updated local model parameters, the client continues to train the model on its local dataset; assuming the loss function is labeled l, the training process can be expressed as minimizing the loss function:

[0040] W local t+1 =argminl(W,D local );

[0041] Among them, D local It is the client's local dataset;

[0042] After completing local training, the client calculates the new model parameter update or gradient. Using the gradient descent method, the update can be expressed as: ΔW local t+1 =-ηabla W l(W local t ,Dlocal), where η is the learning rate, abla W l is the gradient of the loss function with respect to the model parameters;

[0043] The client updates the new model parameters again with ΔW local t+1 After encryption, it is uploaded back to the central server or other designated client.

[0044] Beneficial effects of the present invention:

[0045] The present invention constructs a federated learning model including multiple participants, and applies a data segmentation algorithm on each participant to split the locally held SAR image data set into several subsets, independently trains a local generative model on each subset, and uses a federated learning framework to aggregate and distribute global model parameters. This design not only avoids the direct sharing of original data and protects data privacy, but also enhances the security of the system by introducing end-to-end encryption technology and differential privacy technology. In addition, the method allows clients to be added or removed dynamically, thereby improving the scalability and flexibility of the system. By independently training the generative model on each subset, it is helpful to capture local features in the data, thereby improving the generalization ability and accuracy of the global model. At the same time, the computing resources of multiple clients are used for distributed training, which improves the efficiency and speed of data processing, and is particularly suitable for the processing of large-scale SAR image data sets. Overall, the present invention has significant advantages in protecting data privacy, improving system security, improving processing efficiency and flexibility, and provides an effective solution for distributed SAR image data generation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present invention will be further described below in conjunction with the accompanying drawings.

[0047] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] See also Figure 1 As shown, the present invention is a secure distributed SAR image data generation method based on split federated learning, which aims to improve the security and privacy protection capabilities of the model by utilizing multiple geographically dispersed data sources while ensuring the quality and diversity of the generated SAR images. The specific implementation process includes the following steps:

[0050] Step 1: Build a split federated learning model

[0051] Architecture design: Establish a system structure consisting of a central server and multiple geographically different clients, each of which has its own unique part of the SAR image dataset.

[0052] Data isolation: Ensure that the data sets between clients are independent of each other and do not exchange or share data in any form to enhance the privacy of the overall system.

[0053] Communication protocol: Develop secure and efficient communication protocols to ensure the security and reliability of data transmission during federated learning. This includes using encryption technology to protect data from being stolen or tampered with during transmission.

[0054] Step 2: Local dataset segmentation

[0055] Algorithm application: In each client, a specific data segmentation technique is used to divide the original SAR image set into several smaller subsets. This not only helps to speed up the subsequent processing flow, but also better adapts to the computing resource requirements of different scales.

[0056] Data preprocessing: Perform necessary preprocessing operations on the divided data subsets, such as standardization and denoising, to improve data quality and thus improve the training effect of the model.

[0057] Step 3: Local model training

[0058] Feature extraction and parameter adjustment: For each divided dataset, a generative adversarial network (GAN) is used as the basic framework to perform in-depth analysis and learning on the client side to extract key features and adjust the model parameter settings accordingly.

[0059] Pseudo image generation: New input samples are processed using the optimized local model to efficiently generate high-quality synthetic aperture radar images.

[0060] Hyperparameter tuning: During local training, the hyperparameters of the generative adversarial network, such as learning rate and batch size, are continuously adjusted to achieve the best training effect.

[0061] Step 4: Parameter Update Sharing

[0062] Change calculation: After completing a round of iterations, each client needs to calculate the changes in its model weights in this round.

[0063] Federated synchronization: Through a secure channel, only the calculated change information is sent to other participants instead of the actual data itself, or directly uploaded to the central node. This method effectively avoids the risk of sensitive information leakage.

[0064] Differential privacy: Differential privacy technology is introduced in the parameter update process to further protect the privacy of user data and prevent potential privacy leakage.

[0065] Step 5: Global model integration

[0066] Parameter aggregation: After receiving information from all participants, the central node is responsible for aggregating the information and determining the new round of global optimal solution based on specific rules (such as weighted average).

[0067] Performance Validation: In addition, the solution is thoroughly tested on a pre-prepared test set to confirm that it meets the established standard requirements.

[0068] Anomaly detection: During the parameter aggregation process, an anomaly detection mechanism is added to identify and eliminate possible anomalies or malicious updates to ensure the stability and security of the global model.

[0069] Step 6: Model parameter distribution and retraining

[0070] Result Feedback: Once it is confirmed that the current version has achieved the expected results, it will be distributed to all relevant parties.

[0071] Continuous Improvement: After receiving the latest guidelines, each site will continue to work on the next round using a similar process until a preset maximum number of iterations is reached.

[0072] Version management: Introduce a version management mechanism to record the update of model parameters in each round, so as to facilitate rollback or comparative analysis when necessary.

[0073] Step 7: Iterate until convergence

[0074] Repeat: The entire project will continue to repeat steps 3 to 6 until the predetermined number of training rounds is reached or no significant performance improvement is observed.

[0075] Dynamic adjustment: Dynamically adjust the training strategy according to the actual training situation, such as changing the learning rate, adjusting the batch size, etc., to accelerate the convergence process.

[0076] Monitoring and logging: Establish a comprehensive monitoring system to track training progress and performance indicators in real time, and record detailed log information for later analysis and troubleshooting.

[0077] Through the above series of links, this solution can fully utilize the advantages of cross-regional cooperation while ensuring data security, and promote the development of more accurate and reliable SAR image generation technology.

[0078] In a preferred embodiment of the present invention, in order to further enhance the security and privacy protection capabilities of the system, we use end-to-end encryption technology when transmitting model parameter updates between each client and the central server. This means that every communication sent from the client to the central server will be encrypted to ensure that even if the data is intercepted during transmission, it cannot be interpreted or tampered with by unauthorized third parties. This encryption mechanism provides a secure data transmission environment for the entire federated learning process, greatly reducing the risk of data leakage.

[0079] In addition, to improve the privacy of local data processing, we introduce differential privacy technology in the parameter update process of the local generation model. Differential privacy is a powerful privacy protection method that masks the contribution of individual data by making small, random modifications to the data (usually called adding noise), thereby protecting the user's private information from being leaked. In our method, every time the client updates its local model parameters, a certain amount of noise is injected into these parameters, so that even if the attacker has access to some model parameters, it is difficult to infer the specific data sample information.

[0080] At the same time, we also add noise directly to the data samples as another level of privacy protection. This method can further obfuscate the data characteristics, making it more difficult for any attempt to reverse engineer the original data by analyzing the model output. In this way, we not only protect the information of a single data point, but also enhance the privacy protection level of the entire dataset.

[0081] In another preferred embodiment of the present invention, in step 2, the specific process of the data segmentation algorithm is as follows:

[0082] Regard the entire SAR image dataset as an overall region Ω, and calculate the average gray value and standard deviation of all pixel points within the region; divide the overall region into several sub-regions, and for each sub-region R i , calculate the average gray value μ i and standard deviation σ i；

[0083] The formula for calculating the average value is: μ = (∑x j ) / N, where x j is the gray value of the j-th pixel point within the sub-region R, and N is the number of pixel points within the sub-region;

[0084] The formula for calculating the standard deviation is: σ = √[(∑(x j - μ)^2) / (N - 1)];

[0085] Set a threshold T. When σ i > T, then perform splitting; otherwise, do not split; split the sub-region R i that meets the splitting condition into four smaller sub-regions R i1 , R i2 , R i3 , R i4 , and continue to determine whether each newly generated sub-region needs to be split until the σ values of all sub-regions are less than or equal to the threshold T;

[0086] For any two sub-regions A and B after splitting, if D(A, B) < S, then re-combine sub-regions A and B, where D represents the distance metric between the two regions, and S is a preset merging threshold.

[0087] In another preferred embodiment of the present invention, it is characterized in that in step 3, the process of generating pseudo-synthetic aperture radar image data is as follows:

[0088] Denoise, normalize, and enhance the original SAR image data, extract features from the preprocessed SAR image, and the features include texture features and spectral features. Construct a generation model based on a generative adversarial network, use the extracted features as input, and train the selected generation model. For each subset D i , calculate the loss function L(θ), where θ represents the model parameters;

[0089]

[0090] where D is the discriminator, G is the generator, p data is the true data distribution, pz is the noise distribution; the model parameter θ is updated using the gradient descent method to minimize the loss function L(θ); and new pseudo SAR image data G(θ,z) is generated, where z represents a random noise vector.

[0091] In a preferred case of this embodiment, the training process of the generative adversarial network further includes:

[0092] First, we move to the first stage, where the discriminator D is fixed and we focus on training the generator G. In this stage, the task of the generator G is to generate SAR image data that is as realistic as possible, with the goal of maximizing the probability of fooling the discriminator D. In other words, the generator G tries to produce fake images that look like real SAR images, so that the discriminator D cannot distinguish which ones are real and which ones are created by the generator G. To achieve this, the generator G continuously adjusts its internal parameters to minimize a specific loss function through the back-propagation algorithm, which measures the difference between the distribution of generated images and real images.

[0093] Next, the training process enters the second stage, when it is the turn of the generator G to be fixed and the discriminator D to be trained. In this stage, the role of the discriminator D changes to a strict "quality inspector", and its task is to improve its ability to distinguish between real SAR images and fake images generated by the generator G. This means that the discriminator D needs to become more sensitive and able to capture even the slightest differences to correctly classify the source of the input image. Similarly, the discriminator D will also optimize its own parameters through backpropagation, but its goal is to maximize a different loss function, which reflects the accuracy of the discriminator D in classifying real and fake images.

[0094] These two stages are not carried out in isolation, but are executed alternately to form a closed-loop optimization process. In each iteration, the generator G and the discriminator D will adjust according to each other's current state. This mutually reinforcing competition mechanism drives the two to continue to evolve until they reach a state called Nash equilibrium. At the Nash equilibrium point, the quality of the images generated by the generator G is so high that the discriminator D can no longer effectively distinguish between the real and the fake. At the same time, the discriminator D becomes so powerful that it is difficult for the generator G to further improve its deception ability. At this point, we can assume that GAN training has reached a relatively stable and efficient working state, and can produce high-quality SAR image data.

[0095] In another preferred embodiment of the present invention, in step 4, the process of parameter update sharing is:

[0096] The parameters are encrypted and transmitted via the TLS protocol. Each client uploads parameter updates at different time points. The central server receives the encrypted parameter updates from each client and stores them in an independent storage. The central server aggregates the parameter updates only after receiving a sufficient number of parameter updates.

[0097] In another preferred embodiment of the present invention, in step 5, the central server receives local updates from all clients and calculates a weighted average of these updates, and the update of each client is assigned a different weight according to the size of its local data, and the calculated weighted average update is used to update the parameters of the global model.

[0098] In another preferred embodiment of the present invention, in step 6, the process in which the client updates the respective local generation models according to the global model parameters is as follows:

[0099] Each client receives the latest global model parameters W from the central server t , where t represents the current iteration round. The client synchronizes the received global model parameters with the local model parameters. The formula is:

[0100] W local t =αW local t-1 +(1-α)W t ;

[0101] Among them, α is a weight coefficient between 0 and 1;

[0102] Using the updated local model parameters, the client continues to train the model on its local dataset; assuming the loss function is labeled l, the training process can be expressed as minimizing the loss function:

[0103] W local t+1 =argminl(W,D local );

[0104] Among them, D local It is the client's local dataset;

[0105] After completing local training, the client calculates the new model parameter update or gradient. Using the gradient descent method, the update can be expressed as: ΔW local t+1 =-ηabla W l(W local t ,Dlocal), where η is the learning rate, abla W l is the gradient of the loss function with respect to the model parameters;

[0106] The client updates the new model parameters again with ΔW local t+1 After encryption, it is uploaded back to the central server or other designated client.

[0107] The above is a detailed description of an embodiment of the present invention, but the content is only a preferred embodiment of the present invention and cannot be considered to limit the scope of implementation of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A secure distributed SAR image data generation method based on split federated learning, characterized in that: It includes the following steps: Step 1: Construct a split federated learning model, which includes a central server and multiple clients distributed at different geographical locations. Each client holds a partial SAR image dataset, and there is no interaction between the image datasets; Step 2: On each client, apply a data splitting algorithm to split the locally held SAR image dataset into several subsets; Step 3: Based on the local data subsets, each client independently trains a local model using a generative adversarial network, performs feature extraction and parameter adjustment, and uses the local model to process new inputs, thereby generating pseudo-synthetic aperture radar images as output results; Step 4: After each client completes one round of local optimization, calculate the change in the model parameters within the current iteration cycle. Using the federated learning framework, each client only shares the parameter updates of its locally generated model with the central server or other clients; Step 5: The central server or other clients aggregate the received model parameter updates, verify the parameters, and generate global model parameters based on federated averaging; Step 6: The central server evaluates the performance of the newly generated global model parameters on a preset validation set, distributes the qualified global model parameters to all clients. Each client updates its local generated model according to the global model parameters. After the client completes local training, calculate the change in the model parameters again and send these updates back to the central server for use in the next round of aggregation; Step 7: Repeat Steps 3 to 6 until a predetermined number of training iterations is reached.

2. According to claim 1, a secure distributed SAR image data generation method based on split federated learning is characterized in that: When transmitting model parameter updates between each client and the central server, end-to-end encryption technology is adopted. Differential privacy technology is introduced during the parameter update process of the locally generated model, and noise is added to the data samples.

3. The secure distributed SAR image data generation method based on split federated learning according to claim 1 is characterized in that: In Step 2, the specific process of the data splitting algorithm is as follows: The entire SAR image data set is regarded as an overall region Ω, and the mean and standard deviation of the grayscale values ​​of all pixels in the region are calculated; the overall region is divided into several sub-regions, and for each sub-region R i , calculate the average gray value μ of its internal pixels i and standard deviation σ i ; The formula for calculating the average value is: μ=(∑x j ) / N, where x j is the gray value of the jth pixel in the sub-region R, and N is the number of pixels in the sub-region; The formula for calculating the standard deviation is: σ=√[(∑(x j -μ)^2) / (N-1)]; Set the threshold T, when σ i >T, the split is performed; otherwise, no split is performed; the sub-region R that meets the split condition is i Split into four smaller sub-regions R in a quadtree manner i1 ,R i2 ,R i3 ,R i4 , continue to determine whether to split each newly generated sub-region until the σ values ​​of all sub-regions are less than or equal to the threshold T; For any two sub-regions A and B after splitting, if D(A,B) < S, then re-combine sub-regions A and B, where D represents the distance metric between the two regions and S is a preset merging threshold.

4. The secure distributed SAR image data generation method based on split federated learning according to claim 1 is characterized in that: In Step 3, the process of generating pseudo-synthetic aperture radar image data is as follows: The original SAR image data is denoised, normalized and enhanced, and features are extracted from the preprocessed SAR image, including texture features and spectral features. A generative model is constructed based on a generative adversarial network, and the extracted features are used as input to train the selected generative model. For each subset D i , calculate the loss function L(θ), where θ represents the model parameters; Where D is the discriminator, G is the generator, and p data is the real data distribution, p z is the noise distribution; Use the gradient descent method to update the model parameter θ to minimize the loss function L(θ); generate new pseudo-SAR image data G(θ,z), where z represents a random noise vector.

5. The secure distributed SAR image data generation method based on split federated learning according to claim 4 is characterized in that: The training process of the generative adversarial network also includes: Fix the discriminator D and train the generator G to maximize the probability of deceiving the discriminator; Fix the generator G and train the discriminator D to improve its ability to distinguish real images and generated images; Alternate between the above two steps until a Nash equilibrium state is reached.

6. The secure distributed SAR image data generation method based on split federated learning according to claim 1 is characterized in that: In Step 4, the process of sharing parameter updates is as follows: Transmit the parameters after encryption through the TLS protocol. Each client uploads parameter updates at different time points. The central server receives the encrypted parameter updates from each client and stores them in an independent memory. Only when the central server receives a sufficient number of parameter updates does it aggregate the parameter updates.

7. The secure distributed SAR image data generation method based on split federated learning according to claim 1 is characterized in that: In step 5, the central server receives local updates from all clients and calculates a weighted average of these updates. Each client's update is assigned a different weight according to the size of its local data. The calculated weighted average update is used to update the parameters of the global model.

8. The secure distributed SAR image data generation method based on split federated learning according to claim 1 is characterized in that: In step 6, the process of the client updating its local generation model according to the global model parameters is as follows: Each client receives the latest global model parameters W from the central server t , where t represents the current iteration round. The client synchronizes the received global model parameters with the local model parameters. The formula is: W local t =αW local t-1 +(1-α)W t ; Among them, α is a weight coefficient between 0 and 1; Using the updated local model parameters, the client continues to train the model on its local dataset; Assuming the loss function is labeled as l, the training process can be expressed as minimizing the loss function: W local t+1 =argminl(W,D local ); Among them, D local It is the client's local dataset; After completing local training, the client calculates the new model parameter update or gradient. Using the gradient descent method, the update can be expressed as: ΔW local t+1 =-ηabla W l(W local t ,Dlocal), where η is the learning rate, abla W l is the gradient of the loss function with respect to the model parameters; The client updates the new model parameters again with ΔW local t+1 After encryption, it is uploaded back to the central server or other designated client.

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