Geometric topology-aware federated learning method and system for strong heterogeneous data

Abstract

The geometric topology perception federated learning method and system facing strong heterogeneous data belong to the field of data processing, which comprises: a client performs optimal transmission-based geometric perception distillation; the client performs error-novelty coupling-based sample selection; and a server performs adaptive topology boundary-based prototype alignment. The present application realizes strategic improvement of precision in a severe non-IID scene, balances communication efficiency and edge deployment friendliness, strengthens active elimination of low mastery area and cross-round knowledge redundancy, can effectively adapt to medical image joint diagnosis, cross-bank financial modeling, multi-factory industrial quality inspection and multi-end cloud collaborative visual computing and other key industry scenes, and has broad market prospects and social value. Under the double constraints of severe non-IID (β=0.02) and extreme communication budget (10 rounds), the present application can obtain a precision improvement of 13.37% compared with the strongest baseline.

Description

Technical Field

[0001] This invention belongs to the field of data processing technology, specifically relating to a geometric topology-aware federated learning method and system for strongly heterogeneous data. Background Technology

[0002] In an era where the need for data privacy protection and cross-institutional collaborative modeling is increasingly urgent, Federated Learning (FL) has become a core technological paradigm supporting privacy-sensitive scenarios such as medical image analysis, multimedia content understanding, and intelligent visual computing. Federated Learning is a distributed paradigm that allows multiple clients to collaboratively train a global model without sharing the original data. Its classic implementation, FedAvg, involves the server distributing the global model to each client in each round. After performing several steps of stochastic gradient descent on their local data, each client uploads its model parameters (or gradients) to the server for weighted average aggregation.

[0003] Although data privacy-preserving collaborative modeling techniques based on federated learning have been widely applied in fields such as medical imaging, multimedia analysis, and intelligent visual computing in recent years, in actual deployment, the data distributed across different clients generally exhibits severe non-independent and identically distributed (Non-IID) characteristics. Coupled with the dual constraints of limited communication bandwidth and the risk of privacy leakage, existing federated learning methods face enormous pressure in core metrics such as accuracy, robustness, and communication efficiency. Therefore, existing federated learning methods still face the following technical problems when confronted with the dual challenges of severe non-IID and limited communication budgets:

[0004] (1) Client drift and global model performance degradation in severely non-independent and identically distributed scenarios: Traditional federated learning algorithms (such as FedAvg and its improved variants) assume that the data of each client approximately follows the same distribution. However, in multimodal scenarios such as medical images (PathMNIST, OrganCMNIST, etc.) and natural images (CIFAR-10, STL-10, etc.), there are significant class imbalances and statistical biases in the data distribution among clients. When using the Dirichlet distribution with extremely small concentration parameters (such as β=0.05 or β=0.02) to simulate extreme non-IID scenarios, the local optimization directions of each client diverge severely, causing the global model to drift continuously after aggregation, and ultimately resulting in a significant decrease in accuracy.

[0005] Existing model-centric federated learning methods (such as FedProx, SCAFFOLD, and MOON) primarily improve upon the original FedAvg at the optimization algorithm level. For example, FedProx introduces a proximal regularization term in the local target to constrain the deviation between local updates and the global model, while MOON reduces cross-client feature space inconsistencies through model-level contrastive learning. While these methods can alleviate client drift to some extent, they mostly employ a "parameter-level correction" approach based on local proximal terms or model contrast. When simulating extreme non-IID scenarios using Dirichlet distributions with minimal parameters (e.g., β=0.05 or β=0.02), these methods can only indirectly constrain model parameters after client drift has already occurred, failing to fundamentally compensate for the missing class distribution information of each client. Essentially, they remain "post-hoc parameter-level corrections" performed after data distribution differences have already caused model deviations, without addressing the root cause of data distribution heterogeneity. As the heterogeneity of data among clients further intensifies, relying solely on indirect parameter-level corrections often fails to achieve sustained and significant performance improvements.

[0006] (2) Synthesis quality bottleneck and cross-round redundancy overhead of agglomerative data sharing methods: Dataset condensation (DC) aims to compress the knowledge contained in large-scale real datasets into a small-scale, learnable synthetic dataset S, so that downstream models trained on the synthetic dataset S can achieve performance close to that trained on the complete real dataset. The distribution matching method based on maximum mean discrepancy (MMD) is one of the most widely used technical routes. Its basic idea is to make the feature distribution of the synthetic dataset S approximate the distribution of the real data T as closely as possible in a certain latent feature space.

[0007] Existing model-centered federated learning methods (such as FedDM and FedVCK) communicate by distilling small-scale synthetic datasets locally on each client. While this agglomerative data-sharing method alleviates model-level drift to some extent by sharing small-scale synthetic datasets, its agglomerative loss uses uniformly weighted MMD cross terms and fails to differentiate the geometric correlation between real and synthetic samples. This causes synthetic samples to tend to degenerate into "class mean centers," losing important intra-class diversity and making it difficult to guarantee the quality of synthetic data. Furthermore, existing model-centered federated learning methods typically select samples in each distillation round based on uniform sampling or the current model loss. This easily leads to highly homogeneous agglomerative knowledge across rounds, causing valuable upload bandwidth to be consumed by redundant updates. Under extreme communication budgets (e.g., 10 rounds), this redundancy is further amplified, causing the marginal information gain of the agglomerative data transmitted in each round to decrease sharply.

[0008] (3) Weakening of global discriminative boundaries and persistent drift of low-mastery regions under severe data heterogeneity: Existing model-centered federated learning methods only use ordinary cross-entropy or fixed-weight supervised comparison targets when aggregating on the server side, without considering the "confusion class topology" in the global prototype space. Under severe data heterogeneity, since each client cannot observe samples of all classes, the inter-class discriminative boundaries of global aggregation are easily blurred on those confusion class pairs (hard-negative classes) shared across clients. This makes the global model remain in a low-mastery state on those easily confusion class pairs shared across clients for a long time, which is difficult to improve through a limited number of communication rounds. In addition, existing model-centered federated learning methods lack an adaptive boundary adjustment mechanism based on prototype geometry, which makes it impossible to apply the same separation intensity to all negative classes and to focus on strengthening the real confusion class pairs, further reducing the robust discriminative ability of the system in complex heterogeneous scenarios. Summary of the Invention

[0009] The purpose of this invention is to provide a geometric topology-aware federated learning method and system for highly heterogeneous data. It aims to address the core technical pain points of model drift and agglomeration redundancy caused by severely non-IID client data, limited communication bandwidth, and blurred global discrimination boundaries in federated learning scenarios, as well as the technical shortcomings of existing technologies such as inefficient agglomeration, insufficient discrimination, and expensive communication in severely non-IID environments. Through a systematic approach, it achieves efficient, robust, and privacy-friendly support for federated collaborative modeling tasks.

[0010] This invention systematically solves three major problems in federated learning—low cohesive quality, high cross-round redundancy, and weak discriminative boundaries—through three core innovations: geometrically perceptual distillation based on optimal transmission, sample selection based on error-novelty coupling, and prototype alignment based on adaptive topological boundaries. It provides a new paradigm and engineering practice guidance for building a robust, efficient, and privacy-preserving federated collaborative modeling system.

[0011] The technical solution adopted by this invention to solve the technical problem is as follows:

[0012] The first objective of this invention is to provide a geometric topology-aware federated learning method for strongly heterogeneous data.

[0013] This invention provides a geometric topology-aware federated learning method for strongly heterogeneous data, which mainly includes the following steps:

[0014] Step 1: The client performs geometry-aware distillation based on optimal transmission;

[0015] S101: On the client side, construct a multi-scale Gaussian kernel similarity matrix between real samples and synthetic samples for each category;

[0016] S102: Construct the transport cost matrix from real samples to synthetic samples based on the multi-scale Gaussian kernel similarity matrix; solve the optimal contribution allocation matrix through Sinkhorn iteration to replace the unified weight cross term in the standard MMD cohesive loss;

[0017] S103: Rewrite the unified weighted cross term in the MMD cohesive loss using the optimal contribution allocation matrix as the weighting matrix to obtain the geometrically sensed cohesive loss;

[0018] Step 2: The client performs sample selection based on error-novelty coupling;

[0019] S201: Utilize the self-integration output of the current round global model and the previous round global model to smoothly estimate the lack of knowledge of the samples; define the importance weight of the error based on the self-integration prediction error;

[0020] S202: Novelty score is defined based on the maximum similarity between samples and historical knowledge in the latent space;

[0021] S203: Construct a co-importance score by multiplicatively amplifying the error importance weight and the novelty score, and finally normalize it to obtain the knowledge selection distribution;

[0022] Step 3: The server performs prototype alignment based on adaptive topology boundaries;

[0023] S301: The server aggregates all logical prototypes uploaded by clients by weighting the number of samples to obtain a global logical prototype;

[0024] S302: Select the Top-K obfuscation classes from the global logical prototype in descending order to form the Top-K obfuscation class set;

[0025] The learnable global prototype is initialized using feature prototype priors for each category;

[0026] S303: Define adaptive topological boundaries for each category and its confusion class, and construct an adaptive topological prototype to calibrate the loss. The server uses the joint loss to update the global model parameters and the learnable global prototype simultaneously.

[0027] Furthermore, in step S101, the multi-scale Gaussian kernel similarity matrix between the real sample and the synthetic sample is:

[0028] ;

[0029] in, For a predefined set of kernel scale parameters, To share the embedding function, K is the number of kernel scale parameters in the predefined set of kernel scale parameters. For category Real samples, For category The synthetic sample; the transportation cost matrix is: , It is a matrix of all ones. It is a multi-scale Gaussian kernel similarity matrix. Small batches of real samples The number of samples in For synthesizing knowledge sets The number of samples in the sample;

[0030] In step S102, the optimal contribution allocation matrix is: , , For the set of edge constraints, For the reason OK, The space of real number matrices composed of columns Let be the Frobenius inner product, and ε > 0 be the entropy regularization coefficient. For entropy, For category;

[0031] In step S103, the geometrically sensed cohesion loss is:

[0032] ;

[0033] in, Small batches of real samples Average multi-scale Gaussian kernel similarity between real samples For synthesizing knowledge sets Average multi-scale Gaussian kernel similarity between intra-synthetic samples The cross term is the weighted average of the optimal transmission terms; summing over all categories yields the overall client cohesion objective: .

[0034] Furthermore, in step S201, the self-integration prediction error is:

[0035] ;

[0036] in, The cross-entropy loss is given by α ∈ [0, 1], where α is the self-integration coefficient. For the current round of the global model, For the previous round of global model, For local samples, For local samples Tags;

[0037] The error importance weights are:

[0038] ;

[0039] in, A constant is used to control the numerical scale; the larger the self-integrated prediction error, the lower the degree of knowledge the current global model has of the local sample, and the corresponding smoothed error importance weights. The closer it is to 1, the higher its weight will be in subsequent sampling.

[0040] Furthermore, in step S202, the novelty score is:

[0041] ;

[0042] Where sim(·, ·) is the feature similarity measure. Indicates category In the After the round ends, the server aggregates a historical knowledge set. To share embedded functions, For local samples, s is the category. In the After the round ends, the server aggregates the historical knowledge set. The samples in;

[0043] If the current sample is highly similar to historical condensed knowledge in the latent space, its novelty is close to 0; otherwise, it is close to 1. That is, during the first round of communication, Take 1;

[0044] Furthermore, in step S203, the collaborative importance score is:

[0045] ;

[0046] Where β ≥ 0 is the novelty balance coefficient. For the importance weight of the error, Score for novelty;

[0047] The knowledge selection distribution is as follows: , and All samples are local samples. For client-local categories The sample set, For the previous round of global model, Indicates category In the After the round ends, the server aggregates a historical knowledge set. For local samples The score for the synergistic importance.

[0048] Furthermore, in step S301, each category The logical prototype is:

[0049] ;

[0050] in, For the client Previous category Local samples, For the client Previous category The local sample set, For the client Previous category The number of local samples, To remove the global model output of the last softmax layer;

[0051] The global logic prototype is: , For category Total number of samples across all clients For category In the client The number of samples on the platform.

[0052] Furthermore, in step S302, the Top-K confusion class set is:

[0053] ;

[0054] in, This is the global logical prototype. To be most easily associated with categories at the prediction level Confusion Each class index.

[0055] Furthermore, in step S303, the adaptive topology boundary is:

[0056] ;

[0057] in, Let cos(·, ·) be the basic boundary constant, and cos(·, ·) be the cosine similarity; if the categories Learnable global prototype Learnable global prototype with category h The closer they are in the prototype space, the more easily they are confused, and thus their topological boundaries... The larger the value, the larger the margin will be subtracted from the logit of the corresponding negative samples, thus pushing them further away; conversely, the smaller the value, the further away the topological boundary. Smaller, avoiding excessive and forced separation of already far apart class pairs;

[0058] The joint loss is: , The classification cross-entropy loss is the sum of the knowledge gathered in the current round, where λ is the weighting coefficient. Calibrate the loss for the adaptive topology prototype.

[0059] The second objective of this invention is to provide a geometric topology-aware federated learning system for strongly heterogeneous data.

[0060] This invention provides a geometric topology-aware federated learning system for strongly heterogeneous data, mainly comprising: a client-side geometric perceptual distillation module based on optimal transmission, a client-side sample selection module based on error-novelty coupling, a server-side prototype alignment module based on adaptive topological boundaries, and a client-server integrated training and aggregation module for federated collaborative modeling; in each round of communication (t = 1, 2, …, T), the server first transmits the current global model... Distributed to all participants Each client has local data. Knowledge is gathered from history First, the ECKS module is used to perform sample selection based on error-novelty coupling: for each category Construct a non-uniform sampling distribution that balances knowledge and novelty. Based on this, small batches of real data were sampled. Subsequently, the OGCA module is used to perform geometry-aware distillation based on optimal transmission, i.e., for this category... Synthetic knowledge set Perform geometry-aware distillation updates guided by optimal transport; after all local distillation iterations for all categories are complete, the client computes the logical prototype for each category. And will update the knowledge aggregation With logical prototype All uploaded data is then sent to the server. The server aggregates the condensed knowledge uploaded by all clients into... and the logical prototype Weighted aggregation based on sample size to form a global logical prototype Then, the ATPA module is used to perform prototype alignment based on adaptive topological boundaries: a learnable global prototype set is initialized based on historical condensed knowledge. Use adaptive topological boundaries for the global model With Learnable Global Prototype Set Conduct joint training.

[0061] A third objective of this invention is to provide an electronic device.

[0062] The present invention provides an electronic device, which mainly includes: a processor, a communication interface, a memory, and a communication bus;

[0063] Memory, used to store computer programs and local data uploaded by users;

[0064] A processor for executing a computer program stored in a memory to implement the steps of the geometric topology-aware federated learning method for strongly heterogeneous data as described in any one of claims 1-8;

[0065] A communication interface for communication between an electronic device of the present invention and other devices;

[0066] The communication bus is used to enable communication between the processor, communication interface, and memory.

[0067] The beneficial effects of this invention are:

[0068] This invention combines geometrically perceptual distillation based on optimal transmission, sample selection based on error-novelty coupling, and prototype alignment based on adaptive topological boundaries to systematically address the technical challenges of federated learning under conditions of severely non-independent and identically distributed data and extreme communication budgets, such as low agglomeration quality, high cross-round redundancy, and weak discriminative boundaries. The advantages of this invention can be summarized as follows:

[0069] (1) In view of the problems of client drift and global model performance degradation in the severe non-independent and identically distributed scenarios in the existing technology, this invention proposes a geometric perception distillation mechanism based on optimal transmission and a prototype alignment mechanism based on adaptive topological boundaries, in an effort to build high-quality condensed knowledge that preserves local geometric structure at the client level, so as to fundamentally alleviate the model degradation problem caused by distribution drift.

[0070] Specifically, this invention significantly improves the discriminative ability of the global model under severe data heterogeneity through a dual mechanism of geometrically perceptual distillation based on optimal transmission and prototype alignment based on adaptive topological boundaries. Under a severely non-IID setting with a Dirichlet concentration coefficient β=0.05, FedGAT achieves improvements of 9.60, 1.95, 10.13, and 8.02 percentage points compared to the strongest baseline FedVCK on four medical image datasets: PathMNIST, OrganSMNIST, OrganCMNIST, and PneumoniaMNIST, respectively. Further improvements of 7.74, 5.96, 8.75, and 8.06 percentage points are achieved under the more challenging β=0.02 setting. On the three natural image datasets CIFAR-10, STL-10, and ImageNette, this invention improves performance by 11.80, 10.55, and 13.20 percentage points respectively compared to FedVCK at β=0.05, and maintains a stable lead of 13.04, 6.73, and 5.60 percentage points at β=0.02. It truly achieves a paradigm shift from passively adapting to heterogeneity to actively reshaping the discrimination boundary, and realizes a strategic improvement in accuracy in severely non-IID scenarios.

[0071] (2) To address the bottlenecks in synthesis quality and cross-round redundancy overhead in existing agglomerative data sharing methods, this invention proposes a sample selection mechanism based on error-novelty coupling. This mechanism aims to explicitly prioritize the selection of real samples that the current model has not yet mastered and that are most complementary to historical agglomerative knowledge for distillation, thereby ensuring that each round of communication injects truly valuable new information into the global model. Specifically, through efficient agglomeration guided by geometrically perceptual distillation based on optimal transmission and a sample selection mechanism based on error-novelty coupling, this invention successfully solves the engineering bottleneck of communication efficiency in existing data-centric federated learning methods. On the Path, OrganS, and Pneumonia datasets, the communication volume per round of this invention is only 1.78 MB, 0.47 MB, and 6.24 MB, respectively, which is 6.8 times, 26.0 times, and 68.3 times lower than typical model-centered methods (FedAvg, FedProx, MOON, etc., 12.13 MB, 12.20 MB, and 426.15 MB), respectively; and further reduced by 12.7%, 9.6%, and 47.0% compared to the closest baseline FedVCK. Even in the extreme scenario where the communication budget is limited to 10 rounds, FedGAT still maintains an accuracy of 87.13%, 74.60%, 88.06%, and 93.11% on Path, OrganS, OrganC, and Pneumonia, respectively, which is 8.64, 1.95, 16.48, and 9.90 percentage points higher than FedVCK, respectively, demonstrating strong deployment adaptability in edge federated learning scenarios, balancing communication efficiency and edge deployment friendliness.

[0072] (3) To address the weakening of the global discriminative boundary and the continuous drift of low-mastery regions under severe data heterogeneity in existing technologies, this invention constructs a prototype alignment mechanism based on adaptive topological boundaries. By identifying the Top-K confusion classes for each category and defining a topological boundary that dynamically changes with the prototype's geometric relationship, the inter-class discriminative ability of the global model is enhanced. Specifically, this invention achieves active focusing on "difficult samples + new samples" through a sample selection mechanism based on error-novelty coupling. Simultaneously, in conjunction with the topological boundary enhancement of the Top-K confusion classes on the server side, each round of communication can inject maximum marginal information gain into the weakest inter-class discriminative region of the current model. Compared to the traditional round-by-round uniform distillation mode, this mechanism significantly enhances the ability to correct long-term low-mastery regions, strengthens the active elimination of low-mastery regions and cross-round knowledge redundancy, and ensures the robust convergence level of the system under severe data heterogeneity.

[0073] (4) This invention provides privacy-friendly synthetic knowledge sharing with broad industry adaptability. Specifically, this invention uses random Gaussian noise as the initial distribution for synthetic knowledge, ensuring that the synthesized image differs significantly from the original real data at the visual level, while still transmitting effective discriminative signals at the distribution level. This invention achieves near-complete training accuracy within a limited communication budget (10 rounds), significantly reducing the privacy attack surface caused by gradient exposure across rounds. Membership inference attack (MIA) experiments on the OrganS dataset show that this invention achieves excellent defense metrics (maximum AUC 0.539 and average AUC 0.509, close to 0.5 for random guessing), with a defense rate of 60%, significantly better than FedAvg (10%) and FedVCK (50%). Given its robust generalization capabilities on both medical image and natural image datasets, this invention can effectively adapt to various key industry scenarios such as joint diagnosis of medical images, cross-bank financial modeling, multi-factory industrial quality inspection, and multi-terminal cloud collaborative visual computing, demonstrating broad market prospects and social value.

[0074] (5) The overall system's efficient collaboration and practical value;

[0075] This invention achieves a complete closed loop in federated learning, moving from high-bandwidth, model-layer correction to low-bandwidth, data-layer reconstruction, through a systematic design based on geometrically perceptual distillation of optimal transmission, sample selection based on error-novelty coupling, and prototype alignment based on adaptive topological boundaries. The client is responsible for generating geometrically rich, cross-round complementary condensed knowledge, while the server is responsible for accurately enhancing the ability to distinguish confused class pairs under heterogeneous data conditions. This systematic technical paradigm not only provides an average accuracy improvement of up to 13.37% for severely non-IID tasks on eight datasets, including medical imaging and natural images, but also achieves low-bandwidth, high-precision, and privacy-strengthening multi-objective collaboration with a single-round upload volume as low as 1.78 MB (6.8 times lower than the model-centered method), providing forward-looking technical support for intelligent cross-institutional modeling in privacy-sensitive industries. Attached Figure Description

[0076] Figure 1 This invention provides a schematic diagram of the overall workflow of a geometric topology-aware federated learning system for strongly heterogeneous data.

[0077] Figure 2 This is a schematic diagram of the workflow of the client performing geometry-aware distillation based on optimal transmission in this invention.

[0078] Figure 3 This is a schematic diagram illustrating the client-side workflow for sample selection based on error-novelty coupling in this invention.

[0079] Figure 4This is a schematic diagram illustrating the workflow of server-side prototype alignment based on adaptive topology boundaries in this invention. Detailed Implementation

[0080] The present invention will be further described in detail below with reference to the accompanying drawings.

[0081] In a first aspect, the present invention provides a geometric topology-aware federated learning system for strongly heterogeneous data.

[0082] This invention provides a geometry-topology-aware federated learning system for strongly heterogeneous data. By constructing a federated learning framework based on geometry awareness and topological distillation, named FedGAT (Federated Geometry-Awareand Topological Condensation), a complete closed loop is formed, from the aggregation of high-quality knowledge on the client side to the topological awareness alignment on the server side.

[0083] This federated learning framework based on geometry perception and topological distillation mainly includes the following modules:

[0084] The client-side module is based on the Geometric Aware Distillation (OGCA) module for optimal transmission, the client-side module is based on the Error-Novelty Coupling (ECKS) module for sample selection, the server-side module is based on the Adaptive Topological Boundary Prototype Alignment (ATPA) module, and the client-server integrated training and aggregation module is oriented towards federated collaborative modeling.

[0085] like Figure 1 As shown, the specific workflow of this federated learning framework based on geometry perception and topological distillation is as follows:

[0086] In each round of communication (t = 1, 2, …, T), the server first sends the current global model. Distributed to all participants Each client has local data. Knowledge is gathered from history First, the ECKS module is used to perform sample selection based on error-novelty coupling: for each category Construct a non-uniform sampling distribution that balances knowledge and novelty. Based on this, small batches of real data were sampled. Subsequently, the OGCA module is used to perform geometry-aware distillation based on optimal transmission, i.e., for this category... Synthetic knowledge set Perform geometry-aware distillation updates guided by optimal transport; after all local distillation iterations for all categories are complete, the client computes the logical prototype for each category. And will update the knowledge aggregation With logical prototype All uploaded data is then sent to the server. The server aggregates the condensed knowledge uploaded by all clients into... and the logical prototype Weighted aggregation based on sample size to form a global logical prototype Then, the ATPA module is used to perform prototype alignment based on adaptive topological boundaries: a learnable global prototype set is initialized based on historical condensed knowledge. Use adaptive topological boundaries for the global model With Learnable Global Prototype Set Conduct joint training.

[0087] Secondly, this invention provides a geometric topology-aware federated learning method for strongly heterogeneous data.

[0088] like Figure 1 As shown, the present invention provides a geometric topology-aware federated learning method for strongly heterogeneous data, and its specific implementation process is as follows:

[0089] Step S1: The client performs geometry-aware distillation based on optimal transmission;

[0090] In each round of communication on the client side, the knowledge contained in the local real data is compressed into a small-scale synthetic knowledge set S with high quality. Its core feature is embedding an instance-level optimal transmission mechanism into the classic MMD agglomerative loss, so that the absorption weight of synthetic samples to real samples is no longer determined by a uniform distribution, but rather adaptively allocated by the degree of geometric fit. Through multi-scale kernel similarity and entropy regularization optimal transmission, instance-level matching weights between real and synthetic samples are differentially allocated, thereby overcoming the inherent defect of the traditional MMD agglomerative loss where synthetic samples collapse towards the class mean due to the "uniform weight cross term". Figure 2 As shown, the specific implementation process is as follows:

[0091] S101: Construction of multi-scale Gaussian kernel similarity matrix;

[0092] Suppose the client targets the category in the current round. Real data in small batches The corresponding condensed knowledge set is ,in, Small batches of real data The Middle A real sample, To consolidate knowledge The Middle A synthetic sample. In the shared embedding function. Under the influence of this method, the present invention first constructs a multi-scale Gaussian kernel similarity matrix between real samples and synthetic samples:

[0093] ;

[0094] in, The set of kernel scale parameters is a predefined set (preferably {0.5, 1.0, 2.0, 4.0, 8.0} times the median distance between real and synthetic samples), and K is the number of kernel scale parameters in the predefined set, preferably 5. Specifically, an adaptive kernel bandwidth mechanism can be used to calculate the set of kernel scale parameters, i.e., first calculate the median distance between each pair of real and synthetic samples in the embedding space. Then, based on the set of multiples {0.5, 1.0, 2.0, 4.0, 8.0}, we obtain... , For the first The bandwidth multiple per core.

[0095] This multi-scale Gaussian kernel similarity can simultaneously capture both the coarse-grained distribution structure and fine-grained local variations in the Reproducing Kernel Hilbert Space (RKHS), thus providing a more accurate characterization of the geometric relationship between real and synthetic samples.

[0096] S102: Solving for optimal transport using entropy regularization and the optimal contribution allocation matrix;

[0097] In a multi-scale Gaussian kernel similarity matrix Based on this, the transportation cost matrix from real samples to synthetic samples is defined as:

[0098] ;

[0099] in, It is a matrix of all ones. Small batches of real data The number of real samples in the middle, To consolidate knowledge The number of synthetic samples. The higher the similarity of a synthetic sample to a real sample, the lower its transportation cost, and the higher its matching weight should be in subsequent contribution allocation. Based on this, an entropy-regularized optimal transport problem is constructed to learn categories. Optimal contribution allocation matrix :

[0100] ;

[0101] in, , For the reason OK, The space of real number matrices composed of columns Let be the Frobenius inner product, and ε > 0 be the entropy regularization coefficient. Entropy term. Set of boundary constraints. Defined as:

[0102] ;

[0103] in, For length is A column vector of all 1s. For length is A column vector of all 1s. The above marginal constraints ensure that the total contribution provided by real samples and the total supervision received by synthetic samples are globally conserved, making the contribution allocation process have a clear probabilistic interpretation.

[0104] Since directly solving for the optimal contribution allocation matrix is ​​computationally expensive, this invention employs the Sinkhorn iterative algorithm for efficient approximation. Let:

[0105] ;

[0106] Then alternately update the scaling vector:

[0107] ;

[0108] After T iterations (preferably T = 20), an approximate optimal contribution allocation matrix is ​​obtained:

[0109] ;

[0110] in, For the first The scaling vector on the real sample side in the next Sinkhorn iteration. For the first The scaling vector for the synthesized sample in the next Sinkhorn iteration. For the first The synthetic sample scaling vector obtained after the Sinkhorn iteration. and For the process The final scaling vector obtained after iteration.

[0111] S103: Geometrically Aware Convergent Loss and Gradient Update;

[0112] This invention utilizes categories Optimal contribution allocation matrix Replace the uniform weighted cross term in the standard MMD cohesion loss This mechanism meticulously characterizes the geometric correspondence between synthetic and real samples using instance-level weights, enabling each synthetic sample to preferentially absorb knowledge from the geometrically most relevant real samples. This completely resolves the pain points of agglomeration results collapsing towards class mean and losing intra-class diversity, significantly improving the discriminative value of synthetic data. The optimal transport-weighted cross term is defined as:

[0113] ;

[0114] in, Assign matrix to the optimal contribution The Middle Line number The elements of the column represent real samples. To synthetic samples The optimal contribution weights to be assigned. It is a multi-scale Gaussian kernel. Based on this, the category can be obtained. The geometric perception condensation loss is:

[0115] ;

[0116] in, Small batches of real data Average multi-scale Gaussian kernel similarity between real samples To consolidate knowledge Average multiscale Gaussian kernel similarity between intra-synthetic samples.

[0117] Summing over all categories yields the overall client cohesion objective:

[0118] ;

[0119] This cohesion objective uses SGD (learning rate 1.0, momentum 0.5, no weight decay) to cohesively aggregate the knowledge set. Gradient descent updates are performed, while gradient clipping with a maximum norm of 30 is enabled to ensure training stability. Compared to the standard uniform-weighted MMD cohesive loss, the above formula uses category... Optimal contribution allocation matrix By assigning differentiated weights to different synthetic samples, each synthetic sample can preferentially absorb knowledge from the geometrically most relevant real samples. The agglomeration process no longer merely approximates the class mean but better preserves intra-class diversity and local geometric structure. This design enables the agglomeration results to cover multiple subclusters in the real data rather than a single mean center, thereby significantly improving the discriminative value of the synthetic data for the global model.

[0120] This invention, while drawing on the formal modeling of client drift in model-centered federated learning methods, further shifts the focus from the parameter space to the data level: by performing high-quality geometric perception agglomeration on the client, it can fundamentally provide the global model with more balanced and complete training materials, which is a perspective lacking in existing model-centered federated learning methods.

[0121] Furthermore, this invention introduces an entropy-regularized optimal transport (OT) mechanism on the client side, adaptively allocating instance-level matching weights between synthetic and real samples based on multi-scale Gaussian kernel similarity. This preserves richer intra-class diversity and local geometric structure, enabling the agglomeration results to cover multiple subclusters in the original real data, thereby significantly improving the discriminative value of the synthetic data. This invention overcomes the fundamental limitation of traditional MMD-type federated distillation methods that rely solely on uniform weighted cross terms and are prone to class mean collapse in synthetic samples. It specifically addresses the key problems of existing MMD-type agglomeration methods that lead to class mean collapse and loss of intra-class diversity due to the use of uniform weighted cross terms.

[0122] Step S2: The client performs sample selection based on error-novelty coupling;

[0123] Before each round of distillation begins on the client side, a non-uniform real sample distribution is constructed for each category. This ensures that the sampled samples possess both characteristics of being "not yet mastered by the current model" and "complementary to historical condensed knowledge," thereby significantly enhancing the marginal value of condensed knowledge transmitted in each round of communication. For example... Figure 2 As shown, the specific implementation process is as follows:

[0124] S201: Modeling the degree of unknowingness based on self-integrated prediction error;

[0125] This invention utilizes the global model of the current round. Compared to the previous global model The self-integrated output provides a smooth estimate of the "unknown" of the samples, avoiding bias caused by the instantaneous fluctuations of a single model on heterogeneous data. For local samples... and its labels The self-integrated prediction error is defined as:

[0126] ;

[0127] in, The cross-entropy loss is used, where α ∈ [0, 1] is the self-integration coefficient, preferably α = 0.5. Based on this, the importance weights of the smoothed errors are defined as follows:

[0128] ;

[0129] in, This is a constant used to control the numerical scale. A larger self-ensemble prediction error indicates a lower level of knowledge the current global model possesses regarding the local sample; the corresponding smoothed error importance weights are adjusted accordingly. The closer it is to 1, the higher its weight will be in subsequent sampling.

[0130] S202: Novelty modeling based on historically condensed knowledge;

[0131] To further reduce the risk of repetitive and homogeneous sampling of knowledge across rounds, this invention introduces a novelty term to characterize the difference between the current sample and historical aggregated knowledge. Specifically, let Indicates category In the The server aggregates the historical knowledge set after each round. For any local sample , For client-local categories The novelty of a sample set is defined as:

[0132] ;

[0133] Where sim(·, ·) is the feature similarity measure (preferably cosine similarity), and s is the class. In the After the round ends, the server aggregates the historical knowledge set. The novelty of a sample is close to 0 if it is highly similar to historical condensed knowledge in the latent space, and close to 1 otherwise. (i.e., the first round of communication) Take 1.

[0134] S203: Collaborative Importance Score and Knowledge Selection Distribution;

[0135] The above two smoothed error importance weights and local samples are combined. The novelty coupling is scored as the co-importance score:

[0136] ;

[0137] Where β ≥ 0 is the novelty balance coefficient, preferably β = 1.0.

[0138] This synergistic importance score considers both the difficulty of local samples on the current model and their novelty relative to historical knowledge; these two factors work together through a multiplicative structure to create a synergistic amplification effect. After normalization, the categories are obtained. The corresponding knowledge selection distribution is as follows:

[0139] ;

[0140] Where x is the category Local sample variables, For local samples The score of collaborative importance, and All samples were local samples.

[0141] Finally, at the beginning of each distillation round, For client-local categories The sample set, the client is based on a non-uniform sampling distribution from Weighted sampling yields small batches of real data. It is then fed into the Optimal Transfer-Based Geometric Sensing Distillation (OGCA) module for geometric sensing condensation.

[0142] Existing methods typically employ uniform sampling or rely solely on the current model's loss for sample selection in each distillation round, easily leading to highly homogeneous condensed knowledge across rounds. This invention explicitly couples two dimensions—those not yet mastered by the current model and those complementary to historical condensed knowledge—to the sample selection distribution. This ensures that the real samples focused on in each distillation round are both difficult samples for the current local model and the most novel samples relative to historical condensed knowledge. This mechanism enables FedGAT to maintain near-100-round accuracy on datasets such as Path, OrganC, and Pneumonia with only 10 rounds of communication budget, effectively eliminating homogeneous redundancy across rounds. It ensures that the condensed knowledge uploaded in each round, even under extreme communication budgets, injects maximum marginal information gain into the global model, achieving a paradigm shift in federated distillation from uniform sampling to information gain-driven sampling.

[0143] Step S3: The server performs prototype alignment based on adaptive topology boundaries;

[0144] After aggregating the condensed knowledge and logical prototypes uploaded by each client on the server side, the inter-class discrimination boundaries are adaptively calibrated based on the global inter-class geometric relationships, and the global model and learnable global prototypes are jointly updated. The aim is to solve the problem of ambiguous discrimination boundaries caused by the neglect of confusing class topological relationships in traditional server-side aggregation methods. Figure 3 As shown, the specific implementation process is as follows:

[0145] S301: Aggregation of client-uploaded knowledge and server-side logical prototypes;

[0146] In the In round-robin communication, each client In addition to uploading the updated cohesive knowledge In addition, based on the current global model Calculate each category Logical prototype:

[0147] ;

[0148] in, For the client Previous category Local samples, For the client Previous category The local sample set, For the client Previous category The number of local samples, To remove the global model output of the last softmax layer, the server performs a weighted aggregation of all client-uploaded logical prototypes based on the number of samples to obtain the global logical prototype:

[0149] ;

[0150] in, For category Total number of samples across all clients For category In the client The number of samples on the platform.

[0151] S302: Top-K Confusion Class Identification and Learnable Global Prototype Initialization;

[0152] Based on global logical prototype vector This can further identify categories. The Top-K confusion class set is as follows:

[0153] ;

[0154] This Top-K confusion class set includes those most easily confused with categories at the prediction level. Confusion Class Index The preferred value is K = 3. To obtain stable semantic initialization, the server utilizes the values ​​up to the [previous value]. The accumulated history of the wheel embodies knowledge Calculate each category Feature prototype priors:

[0155] ;

[0156] in, This represents the encoder of the global model at the start of this round. The set of learnable global prototypes is further defined as:

[0157] ;

[0158] Use each category Feature Prototype Prior Learnable global prototypes in the set of learnable global prototypes Initialize the parameters and then use them as trainable parameters for joint optimization with the server-side model.

[0159] S303: Adaptive topology boundary and prototype alignment loss;

[0160] To avoid applying the same separation strength to all negative classes, this invention applies different separation strengths to different classes. and its confusion class Define adaptive topology boundaries:

[0161] ;

[0162] in, Basic boundary constants (preferred) = 0.2), cos(·, ·) is the cosine similarity. The geometric meaning of this boundary is: if the categories Learnable global prototype Learnable global prototype with category h The closer they are in the prototype space (i.e., the more easily they are confused), the higher their topological boundaries. The larger the value, the larger the margin will be subtracted from the logit of the corresponding negative samples, thus pushing them further away; conversely, the smaller the value, the further away the topological boundary. Smaller, avoiding excessive and forced separation of already far apart class pairs.

[0163] Based on the condensed knowledge uploaded in the current round For each sample First through the projection head get Therefore, the normalized denominator is constructed as follows:

[0164] ;

[0165] Wherein, τ is the temperature coefficient, preferably τ = 0.07; For the first The set of learnable global prototypes of wheels. For a set of learnable global prototypes In and sample Category The corresponding learnable global prototype. Based on this, the adaptive topology prototype calibration loss is constructed as follows:

[0166] ;

[0167] Finally, the server uses the following joint loss to update both the global model parameters and the learnable global prototype simultaneously:

[0168] ;

[0169] in, The cross-entropy loss is the classification loss based on the knowledge aggregated in the current round, and λ is the weighting coefficient.

[0170] Existing methods typically employ ordinary cross-entropy or SupCon comparison targets on the server side, without considering the confusion class topology in the global prototype geometry. This invention identifies the Top-K confusion classes for each category based on the global logical prototype, and assigns dynamic topological boundaries to different class pairs during prototype alignment, which vary with their prototype cosine similarity, thereby significantly strengthening the inter-class discrimination boundaries under severe data heterogeneity.

[0171] This invention addresses the issue of adaptive topology prototype calibration loss. In this model, an adaptive topological boundary is embedded as a soft-margin constraint in the similarity comparison of positive / negative samples, and jointly optimized with the classification cross-entropy loss of agglomerated data. Through this mechanism, the global model can impose stronger discriminative constraints on truly confusing class pairs, improving the average test accuracy to near the level of the full communication budget (100 rounds) under the extreme communication budget. This achieves a strategic leap from "low bandwidth to high discriminative power" and realizes adaptive discriminative enhancement from "geometric proximity to wider boundary," which is one of the keys to FedGAT's significant accuracy improvement under severe data heterogeneity.

[0172] Step S4: Client-server integrated training and aggregation for federated collaborative modeling;

[0173] The server uses SGD (learning rate 0.01, momentum 0.9, no weight decay) to optimize the global model. With Learnable Global Prototype Set Perform joint training and apply a StepLR decay policy to the learning rate (decay by 0.1x at the midpoint of the training rounds).

[0174] Thirdly, the present invention provides an electronic device.

[0175] The present invention provides an electronic device, which mainly includes: a processor, a communication interface, a memory, and a communication bus;

[0176] Memory, used to store computer programs and local data uploaded by users;

[0177] A processor is used to execute a computer program stored in memory to implement the steps of a geometric topology-aware federated learning method for strongly heterogeneous data provided in the second aspect.

[0178] A communication interface for communication between an electronic device of the present invention and other devices;

[0179] The communication bus is used to enable communication between the processor, communication interface, and memory.

[0180] Fourthly, the present invention provides a computer-readable storage medium.

[0181] The present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of a geometric topology-aware federated learning method for strongly heterogeneous data provided in the second aspect.

[0182] Fifthly, the present invention provides a computer program product containing instructions.

[0183] The present invention provides a computer program product containing instructions that, when run on a computer, cause the computer to perform the steps of a geometric topology-aware federated learning method for strongly heterogeneous data provided in the second aspect.

[0184] To verify the effectiveness of the present invention, the following experiments were conducted.

[0185] 1. Experimental environment and hyperparameter details;

[0186] (1) Experimental environment: All experiments were performed on an NVIDIA RTX 4090 GPU, and the code implementation was based on PyTorch 2.1.2 and MedMNIST 3.0.1. In terms of model architecture, for the 28×28 and 32×32 resolution datasets (PathMNIST, OCTMNIST, OrganSMNIST, CIFAR-10, STL-10, ImageNette), a three-layer ConvNet (128 channels per layer, ReLU activation, instance normalization, average pooling) was used; for the 224×224 resolution datasets (OrganCMNIST, PneumoniaMNIST), ResNet18 (with instance normalization) was used.

[0187] (2) Data partitioning: The training data is partitioned into 10 clients using the Dirichlet distribution Dir(β). This invention is evaluated under two severe non-IID settings: β=0.05 and β=0.02. The random seed is fixed at 2026.

[0188] (3) Agglomeration budget: The agglomeration knowledge scale for each client is determined by the compression rate p% associated with the dataset. For PathMNIST, p = 1%, and for OrganSMNIST and PneumoniaMNIST, p = 5%. All agglomeration images are initialized with random Gaussian noise.

[0189] (4) Client-side hyperparameters: Agglomerative samples are optimized using SGD (learning rate 1.0, momentum 0.5, no weight decay applied), and the maximum norm of gradient clipping is 30. In OGCA, the entropy regularization coefficient ε = 0.05, and the Sinkhorn iteration... = 20, adaptive kernel bandwidth multiples {0.5, 1.0, 2.0, 4.0, 8.0}; self-integration coefficient α = 0.5 and novelty balance coefficient β = 1.0 in ECKS.

[0190] (5) Server-side hyperparameters: The global model uses SGD optimization (learning rate 0.01, momentum 0.9, no weight decay) combined with StepLR scheduling (decay by 0.1 at the midpoint of the training rounds). The projection head in ATPA is a two-layer MLP (128+ hidden dimensions, batch normalization), temperature = 0.07, basic boundary = 0.2, Top-K confusion class K = 3.

[0191] (6) Communication settings: The total number of rounds T = 100 under the full communication budget and T = 10 under the limited communication budget; all 10 clients participate in each round.

[0192] 2. Key experimental results;

[0193] (1) Under full communication budget: FedGAT achieved 89.93%, 75.27%, 89.47%, and 94.71% respectively on Path, OrganS, OrganC, and Pneumonia with β = 0.05; and 88.87%, 78.83%, 87.96%, and 92.79% respectively with β = 0.02. Overall, it outperformed the strongest baseline FedVCK by up to 13.37%.

[0194] (2) Under the limited communication budget (10 rounds): FedGAT achieved 87.13%, 74.60%, 88.06%, and 93.11% accuracy on Path, OrganS, OrganC, and Pneumonia, respectively, with a lead of 8.64, 1.95, 16.48, and 9.90 percentage points over FedVCK, respectively, with a β=0.05 setting. It maintained an accuracy of 86.69%, 74.40%, 86.38%, and 91.19% accuracy, further leading FedVCK by 8.31, 2.72, 14.57, and 8.66 percentage points, respectively.

[0195] (3) Natural image dataset: FedGAT achieved 74.56%, 68.03%, and 76.13% (β= 0.05) on CIFAR-10, STL-10, and ImageNette, respectively, and 73.81%, 63.49%, and 67.01% (β= 0.02) on ImageNette, respectively, leading FedVCK by up to 13.20 percentage points.

[0196] (4) Communication efficiency: FedGAT's upload volume per round on Path, OrganS and Pneumonia is only 1.78 MB, 0.47 MB ​​and 6.24 MB respectively, which is 6.8 times, 26.0 times and 68.3 times lower than the model-centered baseline.

[0197] (5) Privacy: The maximum AUC of LiRA-based MIA attack against FedGAT on OrganS is 0.539, the average AUC is 0.509, and the defense rate is 60%, which is significantly better than FedAvg (10%) and FedVCK (50%).

[0198] 3. Ablation test results;

[0199] Ablation experiments on Path and OrganS showed that:

[0200] (1) When OGCA (that is, the OT weighted cross term is degenerated into the uniform weight of Mean or MMD) is removed, the accuracy drops most significantly, to 79.74% / 80.50% (Path) and 71.04% / 71.17% (OrganS), respectively, thus demonstrating that instance-level geometric perception contribution allocation is crucial for preserving local structure.

[0201] (2) When ECKS is removed, the accuracy of Path and OrganS drops to 86.70% and 72.82% respectively (under limited communication budget), proving that prioritizing highly novel samples can effectively reduce cross-round redundancy.

[0202] (3) When ATPA is replaced with server-side SupCon or only cross-entropy is used, the accuracy decreases, which verifies the necessity of adaptive topology boundary.

[0203] (4) A slight but consistent decrease also occurred when the adaptive kernel bandwidth was replaced with the fixed RBF bandwidth, which verifies the benefits of multi-scale similarity modeling.

[0204] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A geometric topology-aware federated learning method for strongly heterogeneous data, characterized in that: Includes the following steps: Step 1: The client performs geometry-aware distillation based on optimal transmission; S101: On the client side, construct a multi-scale Gaussian kernel similarity matrix between real samples and synthetic samples for each category; S102: Construct the transport cost matrix from real samples to synthetic samples based on the multi-scale Gaussian kernel similarity matrix; solve the optimal contribution allocation matrix through Sinkhorn iteration to replace the unified weight cross term in the standard MMD cohesive loss; S103: Rewrite the unified weighted cross term in the MMD cohesive loss using the optimal contribution allocation matrix as the weighting matrix to obtain the geometrically sensed cohesive loss; Step 2: The client performs sample selection based on error-novelty coupling; S201: Utilize the self-integration output of the current round global model and the previous round global model to smoothly estimate the lack of knowledge of the samples; define the importance weight of the error based on the self-integration prediction error; S202: Novelty score is defined based on the maximum similarity between samples and historical knowledge in the latent space; S203: Construct a co-importance score by multiplicatively amplifying the error importance weight and the novelty score, and finally normalize it to obtain the knowledge selection distribution; Step 3: The server performs prototype alignment based on adaptive topology boundaries; S301: The server aggregates all logical prototypes uploaded by clients by weighting the number of samples to obtain a global logical prototype; S302: Select the Top-K obfuscation classes from the global logical prototype in descending order to form the Top-K obfuscation class set; The learnable global prototype is initialized using feature prototype priors for each category; S303: Define adaptive topological boundaries for each category and its confusion class, and construct an adaptive topological prototype to calibrate the loss. The server uses the joint loss to update the global model parameters and the learnable global prototype simultaneously.

2. The geometric topology-aware federated learning method for strongly heterogeneous data according to claim 1, characterized in that, In step S101, the multi-scale Gaussian kernel similarity matrix between the real sample and the synthetic sample is: ； in, For a predefined set of kernel scale parameters, To share the embedding function, K is the number of kernel scale parameters in the predefined set of kernel scale parameters. For category Real samples, For category The synthetic sample; the transportation cost matrix is: , It is a matrix of all ones. It is a multi-scale Gaussian kernel similarity matrix. Small batches of real samples The number of samples in For synthesizing knowledge sets The number of samples in the sample; In step S102, the optimal contribution allocation matrix is: , , For the set of edge constraints, For the reason OK, The space of real number matrices composed of columns Let be the Frobenius inner product, and ε > 0 be the entropy regularization coefficient. For entropy, For category; In step S103, the geometrically sensed cohesion loss is: ； in, Small batches of real samples Average multi-scale Gaussian kernel similarity between real samples For synthesizing knowledge sets Average multi-scale Gaussian kernel similarity between intra-synthetic samples The cross term is the weighted average of the optimal transmission terms; summing over all categories yields the overall client cohesion objective: .

3. The geometric topology-aware federated learning method for strongly heterogeneous data according to claim 1, characterized in that, In step S201, the self-integration prediction error is: ； in, The cross-entropy loss is given by α ∈ [0, 1], where α is the self-integration coefficient. For the current round of the global model, For the previous round of global model, For local samples, For local samples Tags; The error importance weights are: ； in, A constant is used to control the numerical scale; the larger the self-integrated prediction error, the lower the degree of knowledge the current global model has of the local sample, and the corresponding smoothed error importance weights. The closer it is to 1, the higher its weight will be in subsequent sampling.

4. The geometric topology-aware federated learning method for strongly heterogeneous data according to claim 1, characterized in that, In step S202, the novelty score is: ； Where sim(·, ·) is the feature similarity measure. Indicates category In the After the round ends, the server aggregates a historical knowledge set. To share embedded functions, For local samples, s is the category. In the After the round ends, the server aggregates the historical knowledge set. The samples in; If the current sample is highly similar to historical condensed knowledge in the latent space, its novelty is close to 0; otherwise, it is close to 1. That is, during the first round of communication, Take 1.

5. The geometric topology-aware federated learning method for strongly heterogeneous data according to claim 1, characterized in that, In step S203, the collaborative importance score is: ； Where β ≥ 0 is the novelty balance coefficient. For the importance weight of the error, Score for novelty; The knowledge selection distribution is as follows: , and All samples are local samples. For client-local categories The sample set, For the previous round of global model, Indicates category In the After the round ends, the server aggregates a historical knowledge set. For local samples The score for the synergistic importance.

6. The geometric topology-aware federated learning method for strongly heterogeneous data according to claim 1, characterized in that, In step S301, each category The logical prototype is: ； in, For the client Previous category Local samples, For the client Previous category The local sample set, For the client Previous category The number of local samples, To remove the global model output of the last softmax layer; The global logic prototype is: , For category Total number of samples across all clients For category In the client The number of samples on the platform.

7. The geometric topology-aware federated learning method for strongly heterogeneous data according to claim 1, characterized in that, In step S302, the Top-K obfuscation class set is: ； in, This is the global logical prototype. To be most easily associated with categories at the prediction level Confusion Each class index.

8. The geometric topology-aware federated learning method for strongly heterogeneous data according to claim 1, characterized in that, In step S303, the adaptive topology boundary is: ； in, Let cos(·, ·) be the basic boundary constant, and cos(·, ·) be the cosine similarity; if the categories Learnable global prototype Learnable global prototype with category h The closer they are in the prototype space, the more easily they are confused, and thus their topological boundaries... The larger the value, the larger the margin will be subtracted from the logit of the corresponding negative samples, thus pushing them further away; conversely, the smaller the value, the further away the topological boundary. Smaller, avoiding excessive and forced separation of already far apart class pairs; The joint loss is: , The classification cross-entropy loss is the sum of the knowledge gathered in the current round, where λ is the weighting coefficient. Calibrate the loss for the adaptive topology prototype.

9. A geometric topology-aware federated learning system for strongly heterogeneous data, applied to the geometric topology-aware federated learning method for strongly heterogeneous data as described in any one of claims 1-8, characterized in that, include: The client-side module is based on a geometrically perceptive distillation module with optimal transmission; the client-side module is based on error-novelty coupling for sample selection; the server-side module is based on adaptive topological boundary prototyping; and the client-server integrated training and aggregation module is oriented towards federated collaborative modeling. In each round of communication (t = 1, 2, …, T), the server first sends the current global model. Distributed to all participants Each client has local data. Knowledge is gathered from history First, the ECKS module is used to perform sample selection based on error-novelty coupling: for each category Construct a non-uniform sampling distribution that balances knowledge and novelty. Based on this, small batches of real data were sampled. ; Subsequently, the OGCA module is used to perform geometry-aware distillation based on optimal transmission, i.e., for this category Synthetic knowledge set Perform geometry-aware distillation updates guided by optimal transport; after all local distillation iterations for all categories are complete, the client computes the logical prototype for each category. And will update the knowledge aggregation With logical prototype All uploaded data is then sent to the server. The server aggregates the condensed knowledge uploaded by all clients into... and the logical prototype Weighted aggregation based on sample size to form a global logical prototype Then, the ATPA module is used to perform prototype alignment based on adaptive topological boundaries: a learnable global prototype set is initialized based on historical condensed knowledge. Use adaptive topological boundaries for the global model With Learnable Global Prototype Set Conduct joint training.

10. An electronic device, characterized in that, include: Processor, communication interface, memory, and communication bus; Memory, used to store computer programs and local data uploaded by users; A processor for executing a computer program stored in a memory to implement the steps of the geometric topology-aware federated learning method for strongly heterogeneous data as described in any one of claims 1-8; A communication interface for communication between an electronic device of the present invention and other devices; The communication bus is used to enable communication between the processor, communication interface, and memory.

Images