Collaborative and privacy-preserving cross-vendor united diagnostic imaging via server-rotating federated machine learning

To assess the effectiveness and efficiency of the SRFLM, we conduct extensive experiments on both a classification task and a multi-vendor CT image reconstruction task using publicly available datasets. The classification experiments indicate that our SRFLM has the potential to learn robust representations from heterogeneous data, while the CT image reconstruction results demonstrate its capacity to generate high-quality diagnostic images across different vendors. Our evaluation metrics encompass both convergence behavior and reconstruction accuracy, showing the advantages of the rotational server-communication mechanism and the dynamic server-election strategy. These mechanisms can mitigate the adverse effects of non-independent identically distribution (non-IID) data and enhance overall model generalization. Detailed quantitative analyses and qualitative visual comparisons are provided in the following subsections, which collectively demonstrate that SRFLM not only accelerates convergence but also delivers superior performance compared to traditional FL methods.

Overview of SRFLM

Next, we briefly introduce the overall framework of SRFLM for cross-vendor united diagnostic imaging. Unlike traditional FL frameworks that rely on a fixed server and uniform aggregation of all model parameters, SRFLM introduces a rotational server-communication mechanism and a dynamic server-election strategy. This design facilitates effective use of local knowledge from decentralized datasets and enhances convergence by adaptively selecting the most suitable provisional server. As illustrated in Fig. 1, each vendor keeps its private dataset locally without sharing raw data or relying on a fixed server. Instead, each vendor can serve as a provisional server while the remaining vendors act as clients, similar to the conventional FL framework.

In SRFLM, each vendor trains a local model using its vendor-specific private data and then shares either all model parameters or selected critical parameters to enable task-specific adaptation. Specifically, for the classification task, all model parameters are shared between the provisional server and the vendors. Meanwhile, for the multi-vendor CT reconstruction task, only the parameters of the image-domain sub-network are exchanged to enable latent image feature sharing and allow flexible adaptation to diverse sampling conditions and protocols. In the provisional server, the local model parameters are updated through federated fine-tuning using its internal data. In this way, the server incorporates its own data to further optimize the global model²². In the rotational server-communication mechanism, each vendor can flexibly act as the provisional server, enabling every participant to contribute to the global model using its own local data. Additionally, the dynamic server-election strategy selects a provisional server based on the performance of the previous round to accelerate model convergence. With the SRFLM, the possibly unconverged aggregated model can be fine-tuned using data from the provisional server, which is dynamically selected to be the most representative of global knowledge. Therefore, SRFLM effectively mitigates vendor-specific data heterogeneity and promotes model generalization across diverse clinical imaging scenarios.

Peripheral blood cell classification

Datasets and settings

To evaluate the classification performance of SRFLM under non-IID settings, we conducted experiments on a medical pathological dataset. Pathological microscopic images typically contain abundant cellular and tissue information that is crucial for disease diagnosis, treatment, and prognosis analysis. The Peripheral Blood Cell (PBC) dataset²³ comprises 17,092 microscopic images of normal peripheral blood cells, which can be categorized into 8 classes: neutrophils, eosinophils, basophils, lymphocytes, monocytes, immature granulocytes, erythrocytes, and platelets. These images were acquired using the CellaVision DM96 analyzer and annotated by expert clinical pathologists at the Hospital Clinic of Barcelona. All images were partitioned into training, validation, and testing sets with a ratio of 7:1:2²⁴.

We performed comparative experiments under three common real-world scenarios of data distribution, including the regular non-IID data distribution, class non-IID data distribution, and size non-IID data distribution. To test robustness on non-IID data, vendors were given a skewed private data distribution. First, we used the Dirichlet distribution on label ratios to simulate the regular non-IID data distribution across vendors, with the Dirichlet parameter set to 0.5 to ensure high data heterogeneity. For the class non-IID data distribution, we adopted a class ratio of 4:2:1:1 such that each vendor possessed completely distinct classes, while maintaining an equal quantity of 1,600 images per vendor. For the size non-IID data distribution, we set the Dirichlet parameter to 1.0 to ensure that the classes among vendors were similar, but the number of images was distributed in a ratio of 4:3:2:1.

Baselines

In the experiments, we compared several representative FL methods, including FedSGD (federated stochastic gradient descent)⁸, FedAvg (federated averaging)⁸, FedAdam (federated Adam optimizer)²⁵, and HarmoFL (harmonizing local and global drifts in federated learning on heterogeneous medical images)²⁶. Additionally, the performance of single-vendor training (denoted as SinTrain) was included as a benchmark for comparison.

Implementation details

Four vendors were involved in the experiments, with each vendor assigned a model weight of 1/3. Each vendor deployed a convolutional neural network (CNN) consisting of two convolutional units as its local model. The training employed the Stochastic Gradient Descent (SGD) optimizer with a base learning rate of 0.01. Furthermore, a learning rate decay was applied at each communication round, where the learning rate was multiplied by a factor of 0.5 to achieve gradual decay. During the communication round (i.e., rotations), the local training comprised 10 epochs for each vendor, and the server epoch (i.e., fine-tuning round) was set to 20. The total number of communication rounds was set to 20 for the PBC dataset. Classification accuracy was selected as the primary evaluation metric to assess the performance of the proposed SRFLM framework relative to the baselines. Fig. 2 illustrates the SRFLM framework and the corresponding validation workflow for PBC classification.

Classification results

The average test accuracy of vendors on the PBC pathology classification task is shown in Fig. 3. Under the regular non-IID setting, SRFLM outperforms all the competing methods. For example, our SRFLM achieves 95.2% accuracy on Vendor 1 compared to HarmoFL’s 94.1%. SRFLM consistently maintains this advantage across vendors, indicating its superior ability to adapt to local data variations while preserving global model consistency. Meanwhile, under the other two severe non-IID settings, our SRFLM also obtains robust classification performance and surpasses all baselines. In the data class non-IID scenario, SRFLM outperforms HarmoFL with improvements of 6.49%, 6.77%, 8.68%, and 6.42% across four vendors, respectively. For data size non-IID, SRFLM further improves accuracy by 7.40%, 9.81%, 8.05%, and 9.51% compared to HarmoFL. Notably, SRFLM demonstrates stronger generalization than HarmoFL in severe non-IID cases, with smaller variance (0.35-0.65 vs. 0.59-0.88 in data class non-IID) across vendors. Specifically, in the data class non-IID scenario, SRFLM achieves absolute accuracy gains of 1.98% (FedSGD), 21.82% (FedAvg), 35.91% (FedAdam), and 6.49% (HarmoFL) at Vendor 1. Similar improvements are observed for other vendors. In the data size non-IID scenario, SRFLM increases accuracy by 0.34% (SinTrain), 56.16% (FedSGD), 56.20% (FedAvg), 63.85% (FedAdam), and 7.40% (HarmoFL) at Vendor 1. The developed rotational server-communication mechanism in SRFLM can fully consider the heterogeneous characteristics of local data to build the global model, thereby achieving state-of-the-art performance.

Generalization to unseen vendors

To further assess the generalization capability of the SRFLM, we perform a generalization evaluation under the setting of class non-IID data distribution in the PBC classification task. Specifically, the first stage pretrains the SRFLM framework on three vendors (Vendor 1–3) using the classification loss \({{{{\mathcal{L}}}}}_{class}\). In the second stage, an unseen vendor (Vendor 4) is incorporated into the pre-trained SRFLM framework. During this stage, the model continues to optimize \({{{{\mathcal{L}}}}}_{class}\) for Vendor 1–3, and then for the added Vendor 4, an unseen classification loss \({{{{\mathcal{L}}}}}_{class-un}\) is employed. The four-vendor SRFLM framework uses dynamic server election to facilitate adaptive generalization for the unseen vendor. For a fair comparison, the standard FL framework (FedAvg) and FedOSS (federated open set synthesis)²⁷ are also evaluated using the same setting. For FedAvg and SRFLM, the number of training rounds in the pretraining and generalization stages is set to a 1:1 ratio (10 rounds each).

Table 1 presents the per-vendor classification accuracies under the class non-IID setting. FedAvg exhibits degraded performance due to the introduction of new-class data and fails to generalize effectively to Vendor 4. By employing open set recognition, FedOSS accurately classifies samples from the unseen vendor. Through dynamic server election, SRFLM adaptively integrates new-class data from the unseen vendor into the pre-trained framework, enabling better adaptation to novel data distributions. Specifically, SRFLM outperforms FedAvg by absolute margins of 21.16%, 19.17%, 14.13%, and 22.20% on Vendors 1–4, respectively. Compared to FedOSS, SRFLM achieves higher accuracy on Vendor 1 (93.50% vs. 90.21%), Vendor 2 (92.64% vs. 91.34%), and Vendor 3 (90.86% vs. 89.65%), and improved accuracy on the unseen Vendor 4 (88.89% vs. 86.62%). Across all four vendors, SRFLM obtains an average accuracy of 91.47%, outperforming both FedOSS (89.92%) and FedAvg (72.31%). These results demonstrate that SRFLM not only generalizes effectively to unseen vendors but also delivers robust overall performance under class non-IID distributions, compared to the traditional FL methods.

Sensitivity analysis on the optimal fine-tuning round

In this work, we conduct a sensitivity analysis to determine the optimal number of federated fine-tuning rounds. Specifically, in the PBC classification experiments under the three non-IID settings, the provisional server undergoes additional fine-tuning to better adapt to local data distributions while attempting to preserve the accumulated global knowledge. To assess this trade-off, we construct the SRFLM framework using varying fine-tuning rounds, denoted as epoch_server, with values ranging from 5 to 50 in increments of 5. This analysis aims to identify the optimal epoch_server that minimizes the global knowledge forgetting while effectively adapting to local variations.

As shown in Supplementary Fig. 1, SRFLM’s classification accuracy increases steadily with incremental fine-tuning epochs across all three non-IID scenarios. It reaches statistically significant peaks at intermediate values of epoch_server, followed by gradual performance decay. Specifically, regular and class non-IID scenarios respectively demonstrate peak performance at 25 and 20 epochs (95.73% ± 1.61%, 98.13% ± 0.96%), followed by observable decay (Δ = 4.56% for regular non-IID, from 95.73% to 91.17% at 35 epochs, and Δ = 5.36% for class non-IID, from 98.13% to 92.77% at 35 epochs) due to deteriorated local-global knowledge balance. Meanwhile, size non-IID scenarios show minimal performance fluctuation (< 1.58% standard deviation), with epoch sensitivity reduced to 0.21 Cohen’s d effect size. This differential response demonstrates that the value of epoch_server can be used to balance the trade-off between global knowledge and local variations. The optimal 20–25 epoch window achieves 97.43% ± 1.12% local accuracy. For PBC classification experiments, we selected epoch_server = 20 to prevent performance decay (Δ = 5.36%) while preserving global knowledge conservation.

Multi-vendor CT reconstruction

Datasets and settings

We used four publicly available datasets and one local private dataset to evaluate the performance of the proposed SRFLM method in a medical CT image reconstruction task. A total of 10,000 chest and abdominal CT images are collected from 4 publicly available datasets including: (1) Vendor 1 from 2016 NIH-AAPM-Mayo Clinic Low Dose CT Grand Challenge containing reconstructed CT images from 10 patients (SIEMENS SOMATOM Definition Flash/AS+)²⁸, (2) Vendor 2 from Low-dose CT image and projection dataset containing a publicly available dataset comprising CT projection data from patient exams (GE Discovery CT 750 HD)²⁹, (3) Vendor 3 from AbdomenCT-1K acquired at multi levels of kVp and effective mAs by PHILIPS CT scanners³⁰, (4) Vendor 4 from CTSpine1K containing spinal CT images at multi levels of kVp and effective mAs from by TOSHIBA CT scanners³¹, and (5) Vendor 5 from the local private dataset includes 2200 chest-to-abdomen CT image pairs from 20 patients, covering both routine dose and simulated quarter-dose scenarios. Vendors 1, 2, 3, and 4 are used for model construction, and Vendor 5 is used for an external validation study of unseen data to demonstrate the generalization ability of SRFLM.

All the CT images were treated as normal-dose scans and used to simulate low-dose sinograms under different imaging geometries and sampling protocols³². Specifically, Vendor 1 data were simulated with geometry G1 and dose level D1, Vendor 2 with G2 and D2, Vendor 3 with G3 and D3, Vendor 4 with G4 and D4, and Vendor 5 with G5 and D5. In total, 2,006 sinograms were generated for (G1, D1), 2,300 for (G2, D2), 1,200 for (G3, D3), 1,606 for (G4, D4), and 2,200 for (G5, D5). For each vendor, 90% of the simulated data were used for training and the remaining 10% for testing. The imaging geometry and scanning protocol parameters (G) along with the corresponding dose levels (D) for all client datasets are provided in Supplementary Table 1.

Baselines

We select the standard ResNet as the backbone network and conduct the experiments using the PyTorch³³ platform. To evaluate the performance of our SRFLM, three competing FL-based reconstruction algorithms, including FedAvg⁸, FedProx⁹, and CIIL (cyclic institutional incremental learning)¹¹, are included for comparison. We also compare SRFLM with the SinTrain model and the CenTrain model. For the SinTrain model, each institution uses its own local data to train a local model. The CenTrain model is obtained by uniformly training on data from all four vendors, with an additional image post-processing step. Peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) are used to quantify reconstruction performance. Due to gradient dependency issues in the privacy guarantee analysis of differentially private stochastic gradient descent (DP-SGD) training, we replaced all BatchNorm layers with GroupNorm layers across models to ensure consistency.

Implementation details

In the experiment, four vendors are trained in a collaborative manner, and the model weights of each vendor are set to 1/3. During the training process, the number of server rotations is set to 8. The learning rate is 2.0 × 10⁻⁴, batch size is 1, batch number is 20, and the number of training epochs is 100 with weight decay at each 10 epochs by multiplying 0.9. After executing four rotations in a fixed order, a new server is adaptively selected to continue training via the dynamic server-election strategy.

To assess the generalization ability of SRFLM when meeting dataset from unseen vendor, we conducted a generalization experiment where a new vendor was introduced during training procedure. For example, with well-trained SRFLM on the four selective vendors, another unseen vendor was introduced and trained with the pre-trained SRFLM in an unsupervised manner. We compared the SRFLM generalization results on the new vendor with the SinTrain model and CenTrain model.

We also utilize DP-SGD strategy to enhance the privacy protection performance of the proposed SRFLM model. Then, we compare the reconstruction performance among all the competing methods with DP-SGD. In addition, we conducted an ablation study on the rotational server and dynamic server-election strategy to further demonstrate the efficiency of SRFLM.

All the models are optimized using the Adam algorithm with a momentum of 0.9 and weight decay of 1 × 10⁻⁴. The forward and back projections were performed with the ASTRA toolbox³⁴. All deep learning models trained on two NVIDIA RTX A6000 graphics processing units with 48 GB of memory. Fig. 4 shows the proposed SRFLM framework and validation workflows in multi-vendor CT reconstruction.

Reconstruction results

Figure 5 illustrates the reconstruction results, corresponding regions-of-interest (ROIs) of different methods from the four vendors. It can be observed that FBP introduces serious noise-induced artifacts. SinTrain model suppresses noise-induced artifacts to some extent, but fails to reconstruct tissue details effectively, especially at Vendor 3. The CenTrain model demonstrates better performance than the SinTrain model, while some residual noise-induced artifacts still exist in the CenTrain results. For the FedAvg, FedProx, and CIIL, they can reconstruct cross-vendor CT images simultaneously within the FL framework. However, they still suffer from increased noise and undesired artifacts in the reconstructed images due to the severe data heterogeneity among the four vendors. Meanwhile, the proposed SRFLM outperforms all other competing methods at all the cases with more tissue details recovery and more clear edges generation, as shown in the positions highlighted by the red arrow. It is seen that our SRFLM can provide the closest results to the ground truth in all comparison methods. Furthermore, the quantitative measurements provided in Supplementary Table 2 indicate that our SRFLM achieves superior reconstruction performance in cross-vendor united diagnostic imaging. SinTrain achieved remarkable improvements over traditional FBP methods across various metrics, but its enhancement of image quality remains somewhat limited. CenTrain encountered challenges in cross-institutional imaging scenarios. Federated learning methods such as FedAvg, FedProx, and CIIL demonstrated advantages in handling data heterogeneity and improving reconstruction quality; our proposed SRFLM, however, outperformed all others. Compared to the second-best method, SRFLM yields the highest PSNR gain (an average increase of 1.812 dB) and the highest SSIM gain (an average increase of 0.049).

Generalization to unseen vendors

To evaluate the generalization ability of our SRFLM, we compare the reconstruction performance of the SRFLM with the SinTrain model and CenTrain model on Vendor 5. The SinTrain model refers to the iRadonMAP model independently trained within each vendor, using an unsupervised training method. The CenTrain model, on the other hand, involves training with data from all five vendors combined. Our SRFLM method first utilizes data from four vendors to train a dynamic cyclic FL model. Subsequently, a fifth vendor is added, which employs unsupervised training, meaning it has no paired data. We then use the dynamic cyclic FL model, already trained with data from the four vendors, to conduct generalization experiments, treating the fifth vendor as a vendor of the other four. Representative reconstruction results are shown in Fig. 6a. The results show that our SRFLM produces images of Vendor 4 with the clearest fine structures, the fewest visual artifacts, and the highest structural fidelity compared to the other two competing methods, as visually verified in the representative reconstruction results. This demonstrates that the utility and generalization ability of our SRFLM for use in cross-vendor united CT reconstruction, compared to the traditional FL methods.

Performance evaluation under privacy protection

In this study, we set privacy budget of ε = 8 in the cross-vendor united CT reconstruction. Fig. 6b shows the results of SRFLM with the addition of DP-SGD, along with the results of the comparison methods. From the results, it can be seen that all the methods with DP-SGD produce worse results than those without DP-SGD, especially in the structure details recovery. The main reason is that noise is introduced to protect privacy. This noise interferes with the model’s training process, reducing its ability to learn detailed features, especially in complex imaging tasks like medical imaging. Furthermore, FedAvg with DP-SGD exhibits over-smoothing results in the final images, and FedProx with DP-SGD loses some fine details and results in CT value shifts. In contrast, SRFLM with DP-SGD maintains better reconstruction results in cross-vendor united CT reconstruction task, allowing for better balance between privacy protection and image quality.

Ablation study

We conduct an ablation study to demonstrate the efficiency of the rotational server-communication mechanism and the dynamic server-election strategy. In particular, our SRFLM performs 4 fixed-order rotational server cycles, and then trains another 4 cycles by selecting the server from the dynamic server-election strategy. SRFLM (w/o D) is the SRFLM method that executes eight fixed-order rotational server cycles without the dynamic server-election strategy. SRFLM (w/o R&D) is the FL method that removes the rotational server-communication mechanism and the dynamic server-election strategy. The corresponding reconstruction results and error maps from four different vendors are shown in Supplementary Fig. 2. It can be observed that SRFLM (w/o D) fails to suppress noise-induced artifacts successfully, and SRFLM (w/o R&D) can not reconstruct structure details effectively. In contrast, our SRFLM achieves the best reconstruction results with minimal noise and artifacts. The experiments demonstrate that by employing the rotational server-communication mechanism and the dynamic server-election strategy, SRFLM more effectively accounts for data characteristics from each vendor and achieves better model convergence in the cross-vendor united CT reconstruction task.

Privacy analysis

In this section, we conduct a comprehensive privacy analysis by incorporating differential privacy (DP-SGD) into the FL process. Our objective is to assess the impact of DP-SGD on classification performance while preserving sensitive information in a privacy-preserving manner.

Datasets and settings

We validate the performance of the SRFLM trained models using the publicly available MNIST dataset³⁵, which is a classic benchmark for handwritten digit classification. The MNIST dataset consists of 70,000 images of size 28 × 28; 60,000 images are used for training and 10,000 for testing. In our federated setup, each vendor is assigned a portion of the training dataset, and the data available at different vendors may originate from distinct distributions in practice. To mimic these realistic scenarios, we employ a Dirichlet distribution with a parameter of 0.5 to simulate severe non-independent and identically distributed (non-IID) label distribution skew among vendors.

Similar to the PBC classification task, the experimental settings for MNIST are kept consistent with one exception: the integration of DP. In addition to the three common non-IID scenarios (regular non-IID data distribution, non-IID data distribution with imbalanced classes, and non-IID data distribution with imbalanced data sizes), we also integrate DP-SGD mechanism into the FL framework to evaluate the trade-off between privacy protection and model performance. Fig. 7 depicts the overall SRFLM framework and the validation workflow for MNIST image classification.

Baselines

For comparison, we selected three representative FL methods: FedSGD⁸, FedAvg⁸, and FedAdam²⁵. All methods are evaluated both with and without differential privacy to examine their robustness under privacy constraints. Additionally, a model trained on data from a single vendor (defined as SinTrain) is included as a baseline.

Implementation details

Four vendors are employed in the experiments, each assigned a model weight of 1/3. The private model for each vendor is implemented as a CNN with two convolutional units. We utilize the SGD optimizer with a base learning rate of 0.01, and the learning rate is decayed by a factor of 0.5 at each communication round. Furthermore, for the DP setting, we apply gradient clipping with a threshold C of 0.5 and introduce Gaussian noise with a noise level σ of 2.0 to the exchanged local parameters. During the communication round, the local training comprised 10 epochs for each vendor, and the server epoch was set to 10. The total number of communication rounds was set to 10 for the MNIST dataset. Classification accuracy is reported as the primary evaluation metric.

Classification results

Each experiment was independently repeated five times, and the average performance with standard deviations is reported in Fig. 8. The results without DP indicate that all FL methods outperform the SinTrain baseline under various non-IID settings, with SRFLM achieving superior classification performance compared to FedSGD, FedAvg, and FedAdam. For instance, FedAdam exhibited sensitivity to different non-IID configurations and struggled to deliver promising results under unbalanced data class and size distributions. Notably, under the non-IID data distribution with imbalanced data size, SRFLM maintained performance levels similar to those observed under regular non-IID conditions, whereas the competing methods experienced a marked performance decline.

Subsequently, we evaluated the privacy preservation performance by applying differential privacy with a fixed privacy budget (ε = 3) across all methods, as shown in Fig. 8. The introduction of DP noise considerably degraded the classification accuracy of the competing methods, particularly under the non-IID settings with imbalanced class and size distributions. Both FedSGD and FedAvg were unable to effectively mitigate the severe perturbations induced by the DP noise, while FedAdam’s momentum and learning rate adjustments proved to be highly sensitive to the DP settings. In contrast, SRFLM with DP achieved performance comparable to its non-DP counterpart, demonstrating a robust optimization mechanism that effectively counteracts the adverse effects of DP noise through its server-rotating framework. These findings underscore SRFLM’s ability to balance the trade-off between privacy protection and model performance, outperforming existing FL methods under stringent privacy constraints.

Theoretical analysis

A convergence analysis of FedAvg in centralized FL³⁶ demonstrates that, under a constant learning rate, the difference between the solution obtained by FedAvg and the optimal solution w^* is on the order of Ω((E_k−1)σ) ⋅ ∥w^*∥². E_k denotes the number of local computation steps performed on each device, σ is an upper bound on the variance of the stochastic gradients, and w^* represents the optimal solution, Ω represents the lower bound of the difference in terms of asymptotic notation. This finding indicates that there is always a non-negligible gap between the FedAvg solution and the optimal solution, and the distance between them cannot fall below this lower bound during iterations. Convergence to the optimal solution can only be achieved when the learning rate decays with t, which is consistent with the theoretical analysis presented in the Methods section. By employing appropriate learning rate adjustments and dynamic server election, our SRFLM can achieve optimal model performance under varying degrees of data heterogeneity.

Datasets and settings

We employ the Cancer Instance Segmentation and Classification dataset, also known as PanNuke³⁷, to conduct classification experiments under different levels of heterogeneity. PanNuke is a dataset for nuclei instance segmentation and classification, semi-automatically generated with comprehensive annotations of cell nuclei across 19 tissue types and 5 distinct cell categories. The dataset comprises a total of 189,744 labeled nuclei, each with an accompanying instance segmentation mask, distributed over 7901 images of size 256 × 256 pixels. These images were captured at  ×40 magnification with a resolution of 0.25 μm/pixel. To simulate varying levels of heterogeneity, we utilize Dirichlet distributions with parameters of 0.3, 0.5, 0.7, and 1.0 to model the non-IID label distribution biases among vendors. Four vendors are configured, and ResNet-18³⁸ is adopted as the backbone network. All the models are implemented using the PyTorch library. During the communication round, the local training comprised 10 epochs for each vendor, and the server epoch was set to 10. The total number of communication rounds was set to 10 for the PanNuke dataset. All other experimental settings are kept consistent with those in the PBC classification experiments.

Experimental results

The average loss convergence curves in Fig. 9 indicate that our SRFLM obtains stable convergence rates under progressive data distribution shifts, indicating SRFLM’s robustness across heterogeneous datasets. For near-IID settings (α = 1.0) shown in Fig. 9a, both FL algorithms demonstrate comparable initial convergence rates, and then SRFLM establishes better performance through its rotational server mechanism. This architecture enables sequential integration of vendor-specific data priors during model fine-tuning, achieving a considerable reduction in steady-state error rate (0.32 vs. FedAvg’s 0.38). As heterogeneity intensifies (α = 0.7, 0.5, 0.3), the convergence process of FedAvg becomes progressively unstable, showing considerable instability in its loss curve. When α is set to 0.3, we observe large swings in loss values (reaching up to 0.15 difference between peak and trough values). This instability arises because different devices generate conflicting gradient updates with their divergent local model adaptations. Moreover, this instability stems from FedAvg’s static aggregation strategy, where directly averaging parameters from mismatched sources increases the difference between optimal solutions, i.e., Ω((E_k−1)σ) ⋅ ∥w^*∥^2 36. Meanwhile, SRFLM dynamically selects vendors with minimal \(\Delta {{{{\mathcal{L}}}}}_{k}\) (Eq. 4), stabilizing erratic model updates through server rotations to integrate vendor-specific gradient contributions, i.e., \(\nabla {{{{\mathcal{L}}}}}_{g}\) (Eq. 2). The rotational server-communication mechanism and dynamic server-election strategy reduce parameter divergence \({\mathbb{E}}\parallel {\bar{w}}_{t}-{w}_{t}^{k}{\parallel }^{2}\) by \({\sigma }^{2}{({E}_{k}-1)}^{2}{G}^{2}\) (Lemma 3 in Supplementary Note 1), enabling SRFLM to maintain a near-linear convergence rate (slope ≈ −0.15/round) even under extreme heterogeneity (α = 0.3), whereas FedAvg’s convergence rate degrades quadratically (slope drops to  −0.04/round). The rotational fine-tuning (20 server epochs) further balances vendor-specific adaptation and global generalization, as evidenced by SRFLM’s stable residual error (Q₁ + Q₂ ≈ 0.12) versus FedAvg’s escalating residuals (up to 0.28 for α = 0.3). This allows SRFLM to achieve 2.3 × faster optimal convergence compared to FedAvg in non-IID scenarios.