Bayesian federal learning method based on double prior perception mechanism

Abstract

The invention discloses a Bayesian federated learning method based on a double prior perception mechanism, and relates to the technical field of federated learning. Aiming at defects and deficiencies in an existing FL system, a Bayesian federal learning method for evaluating client data information amount and model quality at the same time through double prior mechanisms is provided. The method comprises the following steps: 1, designing a double-priori mechanism, optimizing an FL system framework based on double priori, and reducing the influence of data isomerism; on one hand, model prior is introduced in a client selection stage, the model quality of clients is systematically evaluated, and the clients with high model quality are screened to participate in aggregation; and on the other hand, data prior is introduced in the model aggregation stage, the data information amount of the client is quantified, and the model performance and the model convergence rate are improved. 2, designing a global algorithm which is dominated by a server and is responsible for initialization, client selection, posterior aggregation and model broadcasting; and 3, designing a client algorithm, and taking local posteriori estimation and client selection as the core.

Description

Technical Field

[0001] This invention belongs to the field of federated learning technology, specifically relating to a Bayesian federated learning method that simultaneously evaluates the amount of client data information and the quality of the model through a dual prior mechanism. Background Technology

[0002] With the development of mobile internet, IoT, and AI technologies, data is exhibiting characteristics of distributed storage and localized management. However, traditional centralized machine learning methods face limitations in practical applications due to constraints such as data privacy protection, security, and regulatory compliance. Federated learning (FL), as a distributed machine learning paradigm, achieves global model training without sharing raw data by training models locally on each client and aggregating the model parameters. It has broad application prospects in mobile intelligence, healthcare, financial risk control, and IoT edge computing.

[0003] However, FL systems commonly suffer from data heterogeneity issues during actual deployment. Data held by different clients typically exhibits non-independent and identically distributed (non-IID) characteristics, causing discrepancies between the local objective function of each client and the global optimization objective. In the model aggregation phase, existing technologies often employ deterministic aggregation strategies such as weighted averaging based on sample size. When there are significant differences in data distribution among clients, the update directions of the models uploaded by different clients may diverge significantly, and the aggregated updates are prone to deviating from the global optimum, leading to client drift, decreased convergence speed, training instability, and reduced model performance. Simultaneously, in the client selection phase, common methods such as random selection or full participation also have shortcomings: random selection struggles to effectively identify and filter out clients with poor update quality, while full participation significantly increases communication and computational overhead and may still introduce low-quality updates into the aggregation process, further exacerbating training fluctuations. In summary, existing FL processes lack effective characterization and utilization of client prior information in terms of client selection strategies and aggregation weight allocation mechanisms, making it difficult to achieve stable and efficient collaborative training in heterogeneous environments.

[0004] To address client drift caused by data heterogeneity, existing technologies primarily improve the optimization algorithm. For example, they introduce regularization terms into the client's local objective function to constrain local model updates (CN119294560A, CN119988019A); or they set control variables to correct local gradient bias (CN119761531A, CN119849602A), thereby improving training stability to some extent. However, these methods focus on regulating the optimization process and typically fail to systematically evaluate the amount of effective data information contained in the client and the quality of its local model updates. Therefore, they struggle to accurately reflect the actual differences in the contributions of different clients to global model training and to adaptively suppress and schedule unreliable updates during training.

[0005] Therefore, there is an urgent need for a mechanism that can adaptively evaluate the amount of client data and model quality, integrate relevant prior information into the modeling framework, and thereby achieve synergistic optimization of client selection strategy and aggregation weight allocation, so as to improve the training stability, convergence efficiency and model performance of federated learning under conditions of strong data heterogeneity. Summary of the Invention

[0006] This invention addresses the shortcomings and deficiencies of existing FL systems by proposing a Bayesian Federated Learning (Bayesian FL) method based on a dual-priority mechanism, aiming to solve the following technical problems: 1. In terms of prior design, existing solutions rely solely on single information such as data volume or model parameter differences to determine aggregation weights or select clients. They fail to systematically integrate multi-dimensional prior information, lack the ability to represent heterogeneous client data distribution in non-IID scenarios, and lack a systematic evaluation of client prior information.

[0007] 2. In terms of prior modeling and inference, existing technologies generally adopt fixed priors, which are difficult to adapt to dynamic changes in client data. Furthermore, they lack a unified Bayesian framework to effectively integrate multidimensional prior and posterior uncertainties. In addition, due to the involvement of complex integration or sampling operations, the computational complexity is high.

[0008] 3. Regarding client selection strategies, existing technologies lack a framework that unifies the modeling of data information volume and model quality, which often leads to client selection ignoring uncertainty clues. Aggregation weights also lack theoretical basis, which may cause low-value clients to dominate the aggregation process, affecting model performance and convergence rate.

[0009] The purpose of this invention is to construct a Bayesian FL framework based on dual priors by designing data priors and model priors to evaluate the amount of data information and model quality of the client respectively. This framework can filter out poor-quality models during aggregation and set aggregation weights according to the client's contribution, thereby significantly improving model performance and convergence rate in non-IID scenarios.

[0010] Technical solution To address the aforementioned technical problems, this invention proposes a Bayesian federated learning method based on a dual-prior mechanism. This method designs data priors and model priors to comprehensively evaluate the client's prior information from both data and model dimensions, guiding the client in selecting and aggregating weights. This significantly improves model performance and convergence rate in non-IID scenarios.

[0011] A Bayesian federated learning method based on a dual-priority perception mechanism is proposed, and a Bayesian FL system is designed, consisting of a server and a client set composed of several clients. Each client Maintain a local dataset The local datasets of all clients constitute the global dataset: Client Using local datasets Training Model Generate local posterior , representing the model In local dataset The posterior distribution; then the server obtains the client set. A subset of clients are selected to participate in model aggregation, and a global posterior is generated based on the local posterior aggregation of the clients. , representing the model In the global dataset The posterior distribution.

[0012] The Bayesian FL system transforms the FL optimization problem into a posterior estimation problem, estimating the local posterior on both the client and server sides. and global posterior To simplify calculations, a Gaussian distribution is used as an approximation. and : ,in They are and The mean, They are and covariance, It refers to the model parameter dimension.

[0013] The above solution is implemented using the following method and process: S1 designs a dual-priority mechanism, where the dual priors include data priors. and model prior The Bayesian FL system framework is optimized based on dual priors to reduce the impact of data heterogeneity. On the one hand, model priors are introduced during the client selection phase. Systematically evaluate the client On the one hand, the model quality is considered, and clients with high-quality models are selected for aggregation; on the other hand, data priors are introduced during the model aggregation phase. For the client The amount of data information is quantified, thereby dynamically adjusting the aggregation weight so that the aggregation weight is proportional to the amount of data information on the client side; by synergistically utilizing prior information in the two key stages of client selection and model aggregation, the model performance and model convergence rate are improved.

[0014] S2 employs a global algorithm, led by the server, which is responsible for initialization, client selection, posterior aggregation, and model broadcasting.

[0015] S3 designs client-side algorithms with local posterior estimation and client selection as the core.

[0016] Step S1 is as follows: S1 employs a dual prior mechanism, as detailed below: 1) Data Priors: Data Prior For quantitative clients The amount of data information, taking into account the amount of data on the client side. and label distribution information entropy Design data prior: . The larger the value, the stronger the client. The higher the amount of data information, the more it indicates that the client... Local posterior global posterior Their contribution is even greater.

[0017] in, The information entropy of label distribution is defined as: The uniformity of label distribution characterizes client diversity, where... Represents the set of all possible labels. This indicates a specific tag category. For tag categories In local dataset The probability of it.

[0018] For indicator functions, when The time value is Otherwise, the value is ,in Indicates the client Local dataset The The label category of each sample.

[0019] 2) Model Priors: Model Prior Used to evaluate clients The quality of the model, taking into account the client Local posterior covariance traces ,and With global posterior KL divergence : Model Prior The higher the value, the higher the quality of the client's model.

[0020] in, It is a local posterior. With global posterior The KL divergence, this metric is used to measure Compared to The offset.

[0021] Covariance The trace is used to quantify the magnitude of uncertainty in the model.

[0022] Step S2 is as follows: S2 employs a global algorithm, primarily driven by the server, responsible for initialization, client selection, posterior aggregation, and model broadcasting. The specific steps are as follows: S2.1 Global Post-hoc Initialization and Broadcast; The server initialization global post-validation is and broadcast to all clients. .

[0023] S2.2, Local training on the client side; Each client Using their respective local datasets Training models in parallel And use the Laplace approximation to estimate the local posterior. . S2.3 Client Evaluation and Selection; Client Based on local posterior Computational model prior The server collects all clients' data. And select the set of clients participating in the aggregation through the client selection step: .

[0024] S2.4, Local post-hoc upload; The clients participating in the aggregation will each have their own local posterior. Uploaded to the server.

[0025] S2.5, Data Prior Normalization; The server normalizes the prior data from the clients participating in the aggregation: .

[0026] S2.6, Global Posterior Weighted Aggregation; The server is based on a set of normalized data priors. The set of partial post-hoc data uploaded by the client Calculate the global posterior Covariance and mean: , This leads to a new global posterior distribution. .

[0027] S2.7, Global Model Broadcast; The server sends to all clients Broadcasting a new global posterior distribution .

[0028] S2.8, Iteration termination condition; Repeat steps S2.1 to S2.7 until the maximum number of training rounds is reached or the global model converges.

[0029] Step S3 is as follows: S3 designs a client-side algorithm, with local posterior estimation and client selection as its core. The specific steps are as follows: S3.1, Local model initialization; Client Receive global post-hoc broadcast from server and the model Initialize to .

[0030] S3.2, Local Training and Local Posterior Estimation; Client Based on local dataset Local training is performed using the Laplace approximation, and the local posterior is estimated. .

[0031] S3.3, Model Prior Calculation and Upload; Client-based local posterior Priors for the computational model: and will Uploaded to the server.

[0032] S3.4, Client selects, server executes; The server's set of model priors for all received clients Sort in descending order and select the model with the highest prior value. Several clients participated in this round of model aggregation: .in , Represents the selection set Before sorting Model Prior The corresponding set of clients, set Size is ,Right now and .

[0033] S3.5, Local post-hoc upload; The selected client will obtain the local posterior from this round of training. Uploaded to the server for global model aggregation.

[0034] Furthermore, the steps for local training of the S3.2 Laplacian approximation specifically include: S3.2.1, MAP estimation, using the Stochastic Gradient Descent (SGD) algorithm on the local dataset. Optimize the objective function to obtain the model. MAP estimation: ,in It is a client The likelihood distribution represents the likelihood distribution for The loss function; This is the regularization loss caused by global distribution.

[0035] S3.2.2 Covariance Estimation: To reduce computational overhead, the empirical Fisher information matrix is ​​used. Estimating covariance Furthermore, a diagonal matrix is ​​used to approximate and reduce computational complexity: .

[0036] S3.2.3, Local Posterior Construction. Combining the MAP estimation results with the covariance estimation, the local posterior is obtained. ,in .

[0037] Technical effect The significant advancements of this invention lie in its use of Bayesian estimation to design a systematic set of client-side prior metrics, and the design of a Bayesian FL framework based on the proposed prior information. This enables effective model training and client-side prior information awareness, thereby improving the model performance and convergence rate of the FL system. Specifically, this invention offers the following advantages: 1. By using Bayesian estimation, the uncertainty of the model can be estimated while training the model. At the same time, the maximum a posteriori probability (MAP) estimation is used instead of the maximum likelihood estimation (MLE) method in the traditional FL system, which can improve the convergence rate by utilizing the information of the prior distribution.

[0038] 2. Through data prior and model prior design, the quality of the model trained by the client and its contribution to the global model can be better evaluated, and the client selection strategy design and model aggregation weight design are optimized.

[0039] 3. By using a Gaussian distribution to approximate the true posterior, the computational complexity is simplified while estimating the optimal model, avoiding complex integration and sampling calculations. At the same time, the Laplace approximation is used to estimate the local posterior, reducing the complexity of the Gaussian representation and improving computational efficiency.

[0040] 4. A Bayesian FL framework based on a dual prior mechanism was designed to improve model performance and convergence rate. Attached Figure Description

[0041] Figure 1 This is the Bayesian FL system framework diagram of the present invention, i.e., the interaction logic framework diagram of its various components. Figure 2 This is a flowchart of the global algorithm of the present invention. Figure 3 This is a flowchart of the client algorithm of the present invention. Figure 4 This is a diagram verifying the effect of an embodiment of the present invention. Figure 5 Table 1: Symbol Definition Table Detailed Implementation like Figure 1 As shown, the Bayesian FL system of this invention includes a central server (hereinafter referred to as "server") and A client set consisting of [number] clients Each client Maintain a local dataset The local datasets of all clients constitute the global dataset: Client Using local datasets Training Model Generate local posterior , representing the model In local dataset The posterior distribution. Then the server (Server) obtains the client set... A subset of clients are selected to participate in model aggregation, and a global posterior is generated based on the local posterior aggregation of the clients. , representing the model In the global dataset The posterior distribution.

[0042] The Bayesian FL system of this invention transforms the FL optimization problem into a posterior estimation problem, estimating the local posterior on both the client and server sides. and global posterior To simplify calculations, this invention uses a Gaussian distribution to approximate the representation. and : ,in They are and The mean, They are and covariance, It refers to the model parameter dimension.

[0043] The core innovation of the S1 invention system lies in the design of a dual-priority mechanism, wherein the dual priors include data priors. and model prior The details are as follows: 1) Data Priors: Data Prior For quantitative clients The amount of data information, taking into account the amount of data on the client side. and label distribution information entropy Design data prior: . The larger the value, the stronger the client. The higher the amount of data information, the more it indicates that the client... Local posterior global posterior Their contribution is even greater.

[0044] in, The information entropy of label distribution is defined as: The uniformity of label distribution characterizes client diversity, where... Represents the set of all possible labels. This indicates a specific tag category. For tag categories In local dataset The probability of it; For indicator functions, when The time value is Otherwise, the value is ,in Indicates the client Local dataset The The label category of each sample.

[0045] 2) Model Priors: Model Prior Used to evaluate clients The quality of the model, taking into account the client Local posterior covariance traces ,and With global posterior KL divergence : Model Prior The higher the value, the higher the quality of the client's model.

[0046] in, It is a local posterior. With global posterior The KL divergence, which is the metric used in this invention to measure... Compared to The offset; Covariance The present invention uses this indicator to quantify the magnitude of uncertainty in the model.

[0047] This invention optimizes the Bayesian FL system framework based on the aforementioned dual priors, thereby reducing the impact of data heterogeneity. On one hand, model priors are introduced during the client selection phase. Systematically evaluate the client The model quality is assessed to select clients with higher-quality models for aggregation; on the other hand, data priors are introduced during the model aggregation phase. For the client The amount of data information is quantified, thereby dynamically adjusting the aggregation weights to ensure that the aggregation weights are proportional to the amount of data information on the client side. By collaboratively utilizing prior information in the two key stages of client selection and model aggregation, model performance and convergence rate can be improved.

[0048] The S2 global algorithm is server-driven, responsible for initialization, client selection, posterior aggregation, and model broadcasting. Its overall process is as follows: Figure 2 As shown, the specific steps are as follows.

[0049] S2.1 Global Posteriori Initialization and Broadcast. The server initializes the global posteriori as follows: and broadcast to all clients. .

[0050] S2.2, Local training on the client side. Each client... Using their respective local datasets Training models in parallel And use the Laplace approximation to estimate the local posterior. . S2.3 Client Evaluation and Selection. Client Based on local posterior Computational model prior The server collects all clients' data. And select the set of clients participating in the aggregation through the client selection step: .

[0051] S2.4, Partial Posteriori Upload. Clients participating in the aggregation will upload their respective partial posterioris. Uploaded to the server.

[0052] S2.5, Data Prior Normalization. The server normalizes the prior data of the clients participating in the aggregation: S2.6, Global Posterior Weighted Aggregation. The server uses a set of normalized data priors. The set of partial post-hoc data uploaded by the client Calculate the global posterior Covariance and mean: , This leads to a new global posterior distribution. .

[0053] S2.7, Global Model Broadcast. The server broadcasts the model to all clients. Broadcasting a new global posterior distribution .

[0054] S2.8, Iteration Termination Condition. Repeat steps S2.1 to S2.7 until the maximum number of training rounds is reached or the global model converges.

[0055] The S3 client algorithm focuses on local posterior estimation and client selection. Its algorithm flow is as follows: Figure 3 As shown, the specific steps are as follows.

[0056] S3.1 Local model initialization. Client Receive global post-hoc broadcast from server and the model Initialize to .

[0057] S3.2, Local Training and Local Posterior Estimation. Client Based on local dataset Local training is performed using the Laplace approximation, and the local posterior is estimated. .

[0058] S3.3, Model Prior Calculation and Upload. The client is based on local posterior. Priors for the computational model: and will Uploaded to the server.

[0059] S3.4 Client Selection (Server Execution). The server selects the set of model priors for all received clients. Sort in descending order and select the model with the highest prior value. Several clients participated in this round of model aggregation: .in , Represents the selection set Before sorting Model Prior The corresponding set of clients, set Size is ,Right now and .

[0060] S3.5, Local Posterior Upload. The selected client uploads the local posterior obtained from this round of training. Uploaded to the server for global model aggregation.

[0061] Furthermore, the steps for local training of the S3.2 Laplacian approximation include: S3.2.1, MAP estimation. Using the Stochastic Gradient Descent (SGD) algorithm on the local dataset... Optimize the objective function to obtain the model. MAP estimation: ,in It is a client The likelihood distribution represents the likelihood distribution for The loss function; This is the regularization loss caused by global distribution.

[0062] S3.2.2 Covariance Estimation. To reduce computational cost, the empirical Fisher information matrix is ​​used. Estimating covariance Furthermore, a diagonal matrix is ​​used to approximate and reduce computational complexity: .

[0063] S3.2.3, Local Posterior Construction. Combining the MAP estimation results with the covariance estimation, the local posterior is obtained. ,in .

[0064] Example The embodiment verifies the effectiveness and advancement of the proposed method in improving model performance and accelerating model convergence through a simulation experiment. The simulation dataset used is the CIFAR-10 dataset, a classic computer vision dataset containing 60,000 32x32 pixel color images in 10 categories (including 50,000 training images and 10,000 test images), covering common objects such as airplanes, cars, birds, and cats.

[0065] The example uses Python 3.10 for simulation experiments and runs on a computing system equipped with an AMD EPYC 9754 processor (18 virtual CPUs), an NVIDIA RTX 4090D graphics card, and 60 GB of memory.

[0066] The model in this example uses a lightweight three-layer convolutional neural network (CNN) for classification: the input undergoes three 3×3 convolutions + ReLU activations + 2×2 max pooling, with the number of feature channels increasing sequentially from 32 to 64 and remaining constant; then the features are flattened, followed by two fully connected layers with ReLU (64 neurons each), and finally a linear layer with 10 outputs to obtain the classification result. The cross-entropy loss function is used during training.

[0067] Effect comparison and verification Representative existing algorithms in the field of FL include: (1) FedAvg (2017) is the standard baseline method of FL, which randomly selects client models and averages them to generate a global model; (2) FedCross (2024) optimizes the impact of data heterogeneity through a multi-model cross-aggregation mechanism; (3) FedAS (2024) is a personalized federated learning method that explicitly models and handles the differences between shared models and personalized models.

[0068] The effectiveness verification of the embodiments is as follows: Figure 4 As shown, the method proposed in this invention achieves the best training results on the CIFAR-10 simulation dataset used: (1) The proposed method converged to an accuracy of 76.7% after 200 rounds, which is the highest model performance compared to other algorithms (FedAvg: 57.9%, FedCross: 69.9%, FedAS: 72.0%), indicating that the proposed method improves model performance; (2) The proposed method quickly achieves and maintains a high accuracy rate, while other methods have a slower increase in accuracy, larger curve oscillations, and obvious instability, indicating that the proposed method improves the model convergence rate.

Claims

1. A Bayesian federated learning method based on a dual-priority perception mechanism, characterized in that, Design a Bayesian FL system, including a server and A client set consisting of [number] clients Each client Maintain a local dataset The local datasets of all clients constitute the global dataset: ; Client Using local datasets Training Model Generate local posterior , representing the model In local dataset The posterior distribution; then the server obtains the client set. A subset of clients are selected to participate in model aggregation, and a global posterior is generated based on the local posterior aggregation of the clients. , representing the model In the global dataset The posterior distribution of; The Bayesian FL system transforms the FL optimization problem into a posterior estimation problem, estimating the local posterior on both the client and server sides. and global posterior To simplify calculations, a Gaussian distribution is used as an approximation. and : ,in They are and The mean, They are and covariance, It refers to the model parameter dimension.

2. The Bayesian federated learning method based on a dual-priority perception mechanism according to claim 1, characterized in that, The steps include: S1 designs a dual-priority mechanism, where the dual priors include data priors. and model prior The Bayesian FL system framework is optimized based on dual priors to reduce the impact of data heterogeneity. On the one hand, model priors are introduced during the client selection phase. Systematically evaluate the client On the one hand, the model quality is considered, and clients with high-quality models are selected for aggregation; on the other hand, data priors are introduced during the model aggregation phase. For the client The amount of data information is quantified, thereby dynamically adjusting the aggregation weight so that the aggregation weight is proportional to the amount of data information on the client. By leveraging prior information in two key stages—client selection and model aggregation—model performance and convergence rate can be improved. S2 designs a global algorithm, led by the server, responsible for initialization, client selection, posterior aggregation, and model broadcasting; S3 designs client-side algorithms with local posterior estimation and client selection as the core.

3. The Bayesian federated learning method based on a dual-priority perception mechanism according to claim 2, characterized in that, Step S1 is as follows: S1 employs a dual prior mechanism, as detailed below: 1) Data Priors: Data Prior For quantitative clients The amount of data information, taking into account the amount of data on the client side. and label distribution information entropy Design data prior: ; The larger the value, the stronger the client. The higher the amount of data information, the more it indicates that the client... Local posterior global posterior Their contribution is even greater; in, The information entropy of label distribution is defined as: The uniformity of label distribution characterizes client diversity, where... Represents the set of all possible labels. This indicates a specific tag category. For tag categories In local dataset The probability of it; For indicator functions, when The time value is Otherwise, the value is ,in Indicates the client Local dataset The The label category of each sample; 2) Model Priors: Model Prior Used to evaluate clients The quality of the model, taking into account the client Local posterior covariance traces ,and With global posterior KL divergence : Model Prior The higher the value, the higher the quality of the client's model; in, It is a local posterior. With global posterior The KL divergence, this metric is used to measure Compared to The offset; Covariance The trace is used to quantify the magnitude of uncertainty in the model.

4. The Bayesian federated learning method based on a dual-priority perception mechanism according to claim 2, characterized in that, Step S2 is as follows: The S2 design uses a global algorithm, which is server-driven and responsible for initialization, client selection, posterior aggregation, and model broadcasting. The specific steps are as follows: S2.1 Global Post-hoc Initialization and Broadcast; The server initialization global post-validation is and broadcast to all clients. ; S2.2, Local training on the client side; Each client Using their respective local datasets Training models in parallel And use the Laplace approximation to estimate the local posterior. ; S2.3 Client Evaluation and Selection; Client Based on local posterior Computational model prior The server collects all clients' data. And select the set of clients participating in the aggregation through the client selection step: ; S2.4, Local post-hoc upload; The clients participating in the aggregation will each have their own local posterior. Uploaded to the server; S2.5, Data Prior Normalization; The server normalizes the prior data from the clients participating in the aggregation: ; S2.6, Global Posterior Weighted Aggregation; The server is based on a set of normalized data priors. The set of partial post-hoc data uploaded by the client Calculate the global posterior Covariance and mean: , Thus, a new global posterior distribution is obtained. ; S2.7, Global Model Broadcast; The server sends to all clients Broadcasting a new global posterior distribution ; S2.8, Iteration termination condition; Repeat steps S2.1 to S2.7 until the maximum number of training rounds is reached or the global model converges.

5. The Bayesian federated learning method based on a dual-priority perception mechanism according to claim 2, characterized in that, Step S3 is as follows: S3 designs a client-side algorithm, with local posterior estimation and client selection as its core. The specific steps are as follows: S3.1, Local model initialization; Client Receive global post-hoc broadcast from server and the model Initialize to ; S3.2, Local Training and Local Posterior Estimation; Client Based on local dataset Local training is performed using the Laplace approximation, and the local posterior is estimated. ; S3.3, Model Prior Calculation and Upload; Client-based local posterior Priors for the computational model: and will Uploaded to the server; S3.4, Client selects, server executes; The server's set of model priors for all received clients Sort in descending order and select the model with the highest prior value. Several clients participated in this round of model aggregation: ;in , Represents the selection set Before sorting Model Prior The corresponding set of clients, set Size is ,Right now and ; S3.5, Local post-hoc upload; The selected client will obtain the local posterior from this round of training. Uploaded to the server for global model aggregation.

6. The Bayesian federated learning method based on a dual-priority perception mechanism according to claim 5, characterized in that, in, The specific steps for local training using the Laplace approximation in S3.2 include: S3.2.1, MAP estimation; using the Stochastic Gradient Descent (SGD) algorithm on the local dataset. Optimize the objective function to obtain the model. MAP estimation: ,in It is a client The likelihood distribution represents the likelihood distribution for... The loss function; The loss is due to the regularization caused by global distribution; S3.2.2 Covariance Estimation: To reduce computational overhead, the empirical Fisher information matrix is ​​used. Estimating covariance Furthermore, a diagonal matrix is ​​used to approximate and reduce computational complexity: ; S3.2.3, Local Posterior Construction. Combining the MAP estimation results with the covariance estimation, the local posterior is obtained. ,in .

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