Bayesian Evidence-Driven Prototype Evolution for Federated Domain Adaptation
Authors: Xiaoyang Yi
Li Peng
Yuru Bao
Jian Zhang
Venue: ICLR 2026 Poster (2026)
Keywords: Federated Learning
Domain Adaptation
Primary area: other topics in machine learning (i.e., none of the above)
TL;DR: We propose a prototype topology-based federated learning framework named FedPTE to alleviate feature distribution heterogeneity across domains.

Abstract: Federated learning (FL), as a privacy-preserving distributed machine learning paradigm, enables clients to collaboratively train a global model without sharing local data. However, in real-world scenarios, domain shift caused by different source clients leads to structural discrepancies in the feature space, resulting in performance degradation of the global model. Although existing prototype-based FL methods offer improvements in cross-domain feature alignment, they still struggle to adapt to dynamic semantic structures and fail to continuously respond to the changing semantic separability and variance structure during training. To address this, we propose FedPTE, an FL framework with prototype topology evolution. Specifically, FedPTE treats prototype clusters as variable topological units, employing Bayesian Gaussian Mixture Models and marginal likelihood ratios on the server to perform probabilistic inference, which enables adaptive structural adjustments. Meanwhile, FedPTE introduces a stability constraint mechanism to balance the adaptability of topological evolution and training stability. By conducting prototype topology-aware contrastive learning on clients, it enhances the discriminability and cross-domain consistency of features. Experimental results demonstrate that FedPTE achieves superior performance across multiple cross-domain datasets, showcasing its strong expressiveness and generalization capability in heterogeneous domains.

Published as a conference paper at ICLR 2026
BAYESIAN EVIDENCE-DRIVEN PROTOTYPE EVOLU- TION FOR FEDERATED DOMAIN ADAPTATION
Xiaoyang Y23.2,3, Li Peng Yuru Bao Jian Zhang!.23
College of Cryptology and Cyber Science, Nankai University
2 Tianjin Key Laboratory of Network and Data Security Technology
3 Key Laboratory of Data and Intelligent System Security, Ministry of Education (xiaoyangyi, peneyaanngy,nggglllll baoyuru @mamll 1lllll.. nankai edu. cn, zhang. jian@nankai. Jaannannaa.edu.crr enu.cn
ABSTRACT
Federated learning (FL., privacy-preserving distributed machine learning paradigm, enables clients to collaboratively train a global model without shar- ing local data. However, in real-world scenarios, domain shift caused by different source clients leads to structural discrepancies in the feature space, resulting performance degradation of the global model. Although existing prototype-baset FL methods offer improvements in cross-domain feature alignment, they still struggle adapt to dynamic semantic structures and fail to continuously respond to the changing semantic separability and variance structure during training. To address this, propose FedPTE, FL. framework with prototype topology evo- lution. Specifically, FedPTE treats prototype clusters as variable topological units, employing Bayesian Gaussian Mixture Models and marginal likelihood ratios on the server to perform probabilistic inference, which enables adaptive structural adjustments. Meanwhile, FedPTE introduces stability constraint mechanism balance the adaptability of topological evolution and training stability. By con- ducting prototype topology-aware contrastive learning on clients, enhances the discriminability and cross-domain consistency of features. Experimental results demonstrate that FedPTE achieves superior performance across multiple cross- domain datasets, showcasing its strong expressiveness and generalization capabil- ity in heterogeneous domains.
INTRODUCTION
Federated learning (FL), as privacy-preserving distributed machine learning paradigm, enables multiple clients to collaboratively train global model without sharing local data, demonstrating significant potential across various application fields (McMahan et al.] 2017: Ghari & Shen 2024] Liu et al.) 2025). However, conventional FL methods typically assume that data across clients is independently and identically distributed (IID), an assumption that often fails to hold in real-world scenarios (Gao et al. [0244] /Zhang et al. 2025b Gao et al. 2025). Particularly in healthcare, differ- ent hospitals may use varying imaging equipment, follow divergent diagnostic protocols, or serve geographically distinct patient populations, leading to substantial differences in feature distributions (Jia et al.] 2024b, Chen et al. 2024a),, which is a phenomenon known as domain shift (Le et al. 2024 Diang al. 2024). This shift is profoundly reflected in the structural discrepancies within the feature space, making it difficult for models trained on a single data source to generalize to other clients. Consequently, the global model struggles achieve optimal performance across all clients
(Jia et al. 2024a; Feng et al. 2025).
To mitigate domain shift, recent studies have introduced prototype-based FL methods (Wan al. 2024 Fu et al. 2025a b) to enhance cross-domain feature alignment. Some methods construct local and global prototypes simply by averaging features align representations, which often leads to information loss and inadequate representation of challenging domains (Zhang et al. 2025 Fu
et al. 2025b). Other methods cluster features on clients and upload more cluster centers to the server
"Corresponding author

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Published as a conference paper at ICLR 2026
for prototype clustering (Huang et al. 2023 Wang et al. 2024). However, clients participate more extensively in the FL process, the model progressively refines its estimation of feature distributions, resulting in noticeable in-domain variations within the same class. Relying static clustering and simple averaging prevents prototypes from accurately characterizing the evolution of features, making it difficult to continuously adapt to dynamic changes in semantic separability and variance structure during training (Wu et al. 2024 Qu et al. (2025).
A more desirable option is to view the server as a center that maintains a dynamic prototype topol- ogy (Liang et al. 2024] Li et al. 2025). using criteria to determine when to split a prototype cluster capture in-class structures or when merge similar prototype clusters to eliminate redundancy and noise based on statistical evidence (Huang et al. 2025). From this perspective, the server treats the number and structure of prototype clusters as an evidence-driven model state. When confronted with complex distributions within class or cross-domain neighbor conflicts, it automatically de- cides whether to refine certain prototype clusters to retain important information or merge approxi- mate prototype clusters to denoise and compress representations. However, if the server drastically alters the global prototype structure in a single round, which may severely mismatch the current client representations, leading convergence degradation. Overly conservative criteria may delay necessary refinements, while overly aggressive ones may frequently cause instability. Therefore, there is urgent need for a prototype learning framework capable of dynamically perceiving class granularity to achieve finer-grained modeling of cross-domain feature distributions.
Armed with these insights, propose Federated learning framework with Prototype Topology Evolution, FedPTE, which treats prototype clusters as variable topological units for probabilistic inference and topological maintenance to mitigate the heterogeneity of feature distributions across domains. Specifically, FedPTE employs Bayesian Gaussian Mixture Models (BGMM) and marginal likelihood ratios under a Normal-Inverse Inverse-Wishart (NIW) prior (Diebolt & Robert 1994; Zhao al. 2023) as statistical evidence on the server to determine whether to split global prototype clus- ter into finer sub-prototype clusters or merge several approximate prototype clusters into a more robust representation. This allows the global number and topology of prototype clusters to be adap- tively adjusted. To prevent training instability caused by abrupt topological changes on the server, FedPTE introduces split and merge penalty terms restrict drastic structural changes within a sin- gle round, thereby balancing adaptability and training stability. Finally, FedPTE performs prototype topology-awas contrastive learning on clients to effectively capture in-domain variance informa- tion and achieve cross cross-domain domain feature alignment, enhancing the model's generalization capability in heterogeneous domains.
Our contributions are as follows:
We propose a prototype topology-basee based FL framework, FedPTE, that treats prototype clusters as evidence-driven topological units, performing probabilistic inference and topological mainte- nance to alleviate feature distribution heterogeneity across domains.
We elaborately design splitting and merging criteria based on a probabilistic model with NIW prior and marginal likelihood ratios to refine aggregate prototype clusters, reducing reliance on empirical thresholds and static clustering.
We incorporate stability constraints on the server to limit abrupt topological changes, and conduct prototype topology-awe aware contrastive learning on clients, ensuring a balance between adaptive topological adjustment and training convergence.
Experimental results demonstrate that FedPTE achieves superior performance across multiple cross-domain datasets under various settings, indicating its expressiveness and generalization ca- pability in heterogeneous domains.
2 RELATED WORK
FL with domain shift refers to the issue of feature distribution heterogeneity in FL caused by data from different domains across clients. For addressing this, FPL (Huang et al., 2023) generates unbiased prototypes and combines consistency regularization align local features with unbiased prototypes, thereby enhancing the model's generalization capability under domain shift. FedHEAL (Chen al. 2024b) employs faimess aggregation strategy based distance variance reduce
2

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Preliminaries. In FL, each client & E K holds its private dataset Dj {xx;, " where x; an input sample and y: f1....,m, m... M) } is the corresponding class label. In FL with domain shift, different clients may belong to different domains. meaning there exists heterogeneity in the feature distributions of the same class of data across clients. Additionally, each client & contains Published as a conference paper at ICLR 2026
Reas
A
Rasp
IF SPLIT
... IF MERGE
A
A
4
Penatty
Penaly
Prototype Cluster
Prototype Clusters
Prototype Clusters
Prototype Cluster
Upload Cluster Centers (Prototypes)
Download Cluster Centers
A
Classifier
Kl
Feature Clusters
Feature Extractor
Feature Extractor
Feature Extractor
)
Local Training
Lee Cumen
Client
Client
Clients
Figure 1: The framework of FedPTE. Clients first upload local prototypes to the server. The server then adapts the global prototype topology through an evidence-bar based decision-making process that utilizes NIW prior and marginal likelihood ratios, regulated by penalty constraints. Finally, clients download the evolved cluster centers to guide their local training via a joint loss function.
the model's bias toward certain domains, thus improving the fairness of FL in the context of domain shift. AlignFed (Zhu et al., 2024) uses personalized feature extractors at each client to align features from different domains to set of predefined global target points, thereby reducing feature shift among clients. FedPLVM (Wang al.) (2024) utilizes dual-layer prototype clustering mechanism to capture variance information and introduces an a-sparse prototype loss function to balance in- class distances, thereby improving tross-domain model performance. FedLSA (Fu et al., 2025a) leverages a global semantic-awand classifier to enhance in-class separation and designs a contrastive loss based the Mises Fisher distribution to promote compactness and uniform distribution of in-class representations. FDSE (Wang et al.) 2025) decomposes each layer of the neural network into domain-agnostic feature extractor and domain-specifie shift eraser, iteratively extracting and climinating domain shifts in features. MPFT (Zhang et al. (2025a) generates Komain-spectio prototypes representing local data distributions clients and uses these prototypes centrally train global adapter on the server to mitigate feature distribution heterogeneity.
3 METHOD
a local model [(: w), which consists of a feature extractor ln wx) and a classifier g(: w wg), i.e.,
w Wh, wg). The local optimization objective of the model on client à is:
(w(w)=
1
Σ (x..))EDz
e(f(x, w),
No
where ((:--) is the loss function.
Prototype-based FL primarily focuses on the representations in the feature space. For a sample x;, its feature is z; = h(x;; wP) E Rdd The prototypes P = {pT m. ICmul in clustering methods are obtained by clustering the features and then calculating the mean of the cluster features:
Ji=1
Pk
D m.
Σ
h(x; w.)
(2)

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Published as a conference paper at ICLR 2026
where D is the subset of cluster samples through clustering algorithm such as FINCH (Sarfraz al. 2019), Cocal is the number of clusters of class m on client k. These prototypes can be uploaded from chents to the server during communication. After processing, the server sends them back to clients to mitigate the heterogeneity caused by domain shift.
The framework of FedPTE is illustrated in Figure [ It treats the global prototype set in FL as dynamically evolvable topological structure. The server adapts the global prototype topol- ogy through an evidence-based decision-making process that utilizes a NIW prior and marginal likelihood ratios, regulated by penalty constraints, thereby more precisely characterizing the cross- domain feature distributions of classes. Meanwhile, clients leverage the evolved global cluster cen- ters to constrain local training through a joint loss function, enhancing the discriminability and domain invariance of feature representations.
Overview.
3.1 BAYESIAN EVIDENCE FOR TOPOLOGY ADAPTATION
In each communication round, for each class m. clients upload their prototypes P The server collects all candidate points related to class m uploaded by all clients to form a prototype cluster, thereby maintaining the current global prototype topology g {g, | Specifically, the decision- making for server-side topology evolution relies on Bayesian hypothesis testing. It treats the current global prototype topology G as the component parameters of BGMM. Each prototype cluster g; corresponds to a Gaussian distribution component with mean f4y and covariance E, Then, a NIW conjugate prior is introduced for each component, as it simultaneously models both the mean and covariance of the Gaussian distribution. The prior is defined as:
p(u Σ₁) (IW(H) Σ, mo, Ko, 1/. So)
= =N(us 1 Σソ) W (Ejl So)
(3)
where W-1 is the Inverse- Wishart distribution, mg is the mean prior typically initialized to the current prototype cluster gj. Ko controls the strength of the mean prior, vn is the degrees of freedom which must be greater than the feature dimension d 1, and So is the scale matrix.
For each existing prototype cluster g; in the global prototype topology G, the corresponding data distribution may not be uni-modal but may contain undiscovered substructures. Therefore, we hy- pothesize that the feature corresponding to the current prototype cluster g, can be better represented by two finer-gue mner-grained components. Specifically, Gaussian distribution with unknown mean jt and covariance Σ. Then, we partition them closest to gy into sub-clusters and obtain the means 11,11 14 covariances Σ,,1, Σj and the number of prototypes in each sub-cluster NJ,1, N3.2 (N,,1 + N3,2 Nz).
assume all points in the set Set
from a single
We then compute the Bayes Factor between the split hypothesis (H₃: the feature is better represented by two components) and the non-split hypothesis (Ho: the feature is better represented by one component) by comparing the marginal likelihoods under the hypotheses. For hypothesis Ho:
N₂
/
p(S,) Ho)
II
(s Σ)
NIW(1, E mo, No: vo, So) du
For hypothesis Hi:
p(S,) = p(S,, (()) p(S,.2)
(5)
Through the NIW conjugate prior, the above marginal likelihood has an analytical solution. The log marginal likelihood under single component is:
N₂d
d log(2x)) + log( Ko KN;
MNJ ) log l'al " - log l'al
My
log ((S)(HH))
llgg'a
2
2
(6)
UD 2
UN; log |Ny 2
+ log [Sp
where Da is the multivariate Gamma function, KN; = 80 + NJ. UN, = u + Nj. and SN the posterior scale matrix calculated as:
No
SN = So + S +
(8 - mm) mo)
(7)
Ko + N₂
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Here, s is the mean of the points S,, and Sş is the scatter matrix Ex s)(s; =)"
We compute the statistical evidence for splitting, i.c., the marginal likelihood ratio:
Rapli- ( p(S).1Ho)) p(S,22HH)) H6,
(8)
Ho)
If Replic > 1, there is considered to be statistical evidence supporting the splitting of prototype cluster gy into new prototype clusters g₁,1 and 8,2-- The old prototype cluster g is removed from G, the new prototype clusters are added, and the global prototype cluster count [9] increases by 1.
Similarly, we need check whether two prototype clusters are too close and should be merged into one to eliminate redundancy and noise. For each pair of adjacent prototype clusters (gj Bi) in the topology G, we suspect they may represent the same semantic concept. Therefore, we compute the Bayes Factor between the merge hypothesis (H1: the feature corresponding to the two prototype clusters comes from the same component) and the non-merge hypothesis (Ho: the feature comes from two different components). For hypothesis Hi:
N
/
plS, (
π
N pc, Σ)
NIW(H, E mo. No. Vo. So) du dE
(9)
For hypothesis Ho:
p(Sy S Ho) p(S, Ho) ((()
(10)
The statistical evidence for merging is the marginal likelihood ratio:
S U HHHH) S(S U SH(Ho) p(S,)Ho)) p(S((H))
p(S, U
Rmerge
(11)
If Rmerge 1, there is considered to be strong evidence supporting the merging of prototype clusters gj and g: into a new prototype cluster gnew- The parameters of the new prototype cluster can be set the weighted average of the two subsets: gnew (N,g, + Nigi Nig:)/(NF N1). The old prototype clusters are removed, the new prototype cluster is added, and the global prototype cluster count [ decreases by 1.
3.2 STABILIZED EVOLUTION WITH GRADUAL CONSTRAINTS
During the evolution of the prototype topology, purely evidence-based split and merge operations may lead to unstable structures. For example, when a split operation produces two sub-clusters with significantly different sizes, or when two spatially close but semantically distinct prototype clusters are merged due to numerical coincidence, the stability of the global topology and semantic consistency can be negatively affected. address this issue, we introduce penalty mechanism to constrain the split decisions.
Specifically, for split operation, we define the balance ratio as:
B min(NN,1. J,, N222)
(12)
max 1, NV,2)
where N₁ + N2, = -Ny. A value of B closer to indicates a more balanced split, while one closer to indicates more imbalanced split. Based this, we define the split imbalance penalty
P Paplit Ssplit
B)
(13)
where Bypli is hyperparameter controlling the strength of the penalty. The penalized split decision criterion becomes:
In( P Paplit
(14)
split operation is executed only if the penalized evidence strength remains greater than 0, which effectively suppresses the generation of low-quality cluster structures caused by imbalanced splits.
For a merge operation, we focus on the semantic relevance between the two candidate prototype clusters g, and gi- Even if they spatially close, they should not be merged if their semantic
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Published as a conference paper at ICLR 2026
meanings differ significantly. To this end, introduce merge penalty based on feature distribu- tions corresponding to the two prototype clusters:
((p)(lp:) PKL (Pyll)))) (P
(15)
where m 1 (P, + Pt) and DxL is the Kullhack-Leible divergence. The merge penalty can then be defined as:
meerge =
Smeree D(pjllp:)
(16)
where Pmerree is hyperparameter controln the strength of the merge penalty. In the merge decision, we apply the penalty as:
In In(Rmerge) - merre 0
(17)
This criterion ensures that a merge operation executed only when both statistical evidence supports the merge and the semantic meanings of the two prototype clusters are sufficiently similar.
By introducing the imbalance penalties Pspiit and Pmerge. we impose necessary constraints on the topology evolution process. This ensures that the decision-making process relies not only on sta- tistical likelihood but also considers the quality the cluster structures and semantic consistency, providing clients with higher-qualite anchors in the feature space.
3.3
QUAL-OBJECTIVE Loss WITH TOPOLOGY CONTRAST
After the server updates the global prototype topology G, it distributes their cluster centers to clients, providing them with consensus-baad based anchors in the feature space. These anchors can be used to align and optimize the feature representations of clients' local models. Specifically, the local training objective for client & including a cross-entree cross-entropy loss and prototype topology-ane aware contrastive loss.
The cross-entropy loss ensures the model's basic classification capability by measuring the discrep- ancy between the model's predictions and the true labels:
Σ log exp(o, mily
Na
1
LCE
(18)
No
Σ/= exp(o!")
where og is the output logits of the model for sample x;, and [y:] indexes the ground-truth class.
The prototype topology-awan contrastive loss drives the alignment of local feature representations toward the global consensus, enhancing their discriminability and cross-domain invariance. The core idea that the feature space, a sample's 's feature should be close to the prototype cluster centers of its own class and far from prototype cluster centers of all other classes (van den Oord et al.) 2018). For sample (x,, 3/s) on client the positive prototype cluster centers g+ for feature z; consists of all prototype cluster centers in G with label ye. The negative prototype cluster centers G includes all prototype cluster centers in G whose labels are not y:. The prototype topology-aware contrastive loss is defined as:
1 NO
N
Eg exp(sim(zz; 2,, g 3/T))
Leontra
log
(19)
Egtegr e exp(sim g gt)/)))//) )/T) Ex -g- exp(sim(zi, ////
where sim(-.-) ) is a similarity function, typically cosine similarity. The temperature hyperparameter > 0 controls the sharpness of the distribution. This encourages the feature to exhibit high similarity with all positive centers and low similarity with all negative centers. Since the alignment targets are the high-quality global semantic centers optimized by the server, and the numerator sums over all positive centers, a sample is allowed to be close to any subclass center within its own class.
The overall training objective for client k is minimize the following joint loss function:
Liocal Lce A- Leontra
(20)
where À is hyperparameter that balances the importance of the supervised loss and the contrastive loss. By jointly optimizing these two objectives, the local model not only learns discriminative clas- sification boundaries but also aligns its feature representations with the globally consistent semantic topology, thereby significantly improving the model's generalization capability. After local train- ing, the client computes feature cluster centers for each class based on its local data to form local prototypes, which are then uploaded to the server to facilitate the next round of topology evolution.

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Published as a conference paper at ICLR 2026
Table 1: Main results of performance comparison on Digit with 5 clients where "Avg." means aver- age results among all clients. The best results are shown in bold.
Methods
Models
MNIST
SVHN
USPS
Synth
MNIST-M
Avg.
FedOPT
ResNet-10 10
88.75+0.07
26.00
82.58 .28
43.50=1.68
56.4220.69
59.45
FedDyn
ResNet-10
97.62+0.05
71.78=0.10 10
96.51=0.12
87.73+0.03
85.1640.34
87.76
Moon
ResNet-10
96,45+0.02
62.10=0.40
94.03+0.18
81.70=0.21
81.11+0.36
83.08
FedProto
ResNet-10
97. 97.65+0.04
72.02=0.50
96.20#0.22
87.36=0.16
84.36+0.05
87.52
FPL
ResNet-10
10+0.05
77.02+1.09
96.9940.08
90.50=0.34
87.8940.26
90.10
F
ResNet-10
97.8840.10
81.15+0.30
96.4920.08
92.08=0.09
90.1740.20
91.55
FedHEAL
ResNet-10
97. 97.8940.07
59. 19.80=0.61
96.29+0.15
83.60=0.45
85,56 46
84,63
FedPall
ResNet-50
97.99+0.38
73.70=1.21
91.88+0.77
96.37=0.19
77.48+0.05
87.48
MPFT
CLIP
91.66+0.08
41.92=0.43
84.00+0.13
75,48=0.15
68.31+0.14
72.27
FedPTE
CLIP
95.31+0.03
46.68#0.1
93.55.0..0
81.4220.06
71.13=0.02
77.62
FedPTE
ResNct-10
98.88+0.07
84.93=0.17
98.32+0.07
95.13=0.07
92.65+00.99
93.98
EXPERIMENTS
4.1 EXPERIMENT SETUP
We conduct experimental evaluations on Digit (Zhou et al.) 2020) and Office (Gong et al. 2012), where Digit includes 5 domains: MNIST (M), SVHN (SV), USPS (U), Synth (SY), MNIST-M (M- M), and Office includes four domains: Amazon, Caltech, DSLR, Webcam. Following the settings of existing methods, we use ResNet-10 (He et al. 2016)) as the local model for clients and compare with FedOPT (Reddi et al. 20221). FedDyn (Acar et al. 2021). Moon (Li et al. 2021). FedProto Tan et al. 2022). FPL (Huang et al. 2023), FedPLVM (Wang et al. 2024). FedHEAL (Chen et al.) 2024b). FedPall Zhang al. (202cc). which uses ResNet-50 and three-layer layer multilayer percep- tron. Meanwhile, we use CLIP VIT-B-32 (Radford et al. (021)) as the local model for comparison with MPFT (Zhang al., 2025a). Convergence analysis is Appendices/A A additional experiments on different domain distributions and medical datasets are presented in Appendices B Supplemen- tary experimental details can be found in Appendices Further analysis of the method and the
disclosure of LLM use are provided in Appendices D and respectively.
Specifically, unless otherwise stated, each client possesses the entire dataset of one domain, with local training conducted for 2 epochs and batch size of 512. For Digit, clients undergo 50 com- munication rounds, while for Office, they undergo 80 communication rounds. For methods using ResNet, we adopt a learning rate of le-2, whereas for methods using CLIP-ViT-B-32 we use learning rate of 1e-3, In FedPTE, we set A 100, 0.06, Sypli 1.0, and 8merge 1.5. All experiments are repeated three times with different random seeds on single Tesla 40G A100 GPU.
4.2 MAIN RESULTS
Domain Shift Results. Tables I and 2 present the performance comparison between FedPTE and baselines on Digit and Office, respectively. Among them, FedOPT is prone being dominated by gradients from a single domain under strong domain shift scenarios, leading to significant perfor- mance degradation on domains that exhibit substantial distributional discrepancies from the main- stream, such as SVHN, Synth, and Amazon. In contrast, methods incorporating dynamic regulariza- tion or prototype clustering, such as FedDyn, FedProto, and FedPLVM, demonstrate better stability in representation learning and overall outperform simple aggregation approaches.
Additionally, the alignment between the pre-trained model and the target domain significantly influ- ences the results. CLIP-based methods achieve remarkable performance on Office, which closely resembles CLIP's pre-training distribution, but perform considerably worse on Digit, a dataset com- prising oow-resolution and stylistically diverse digit images. This indicates that when pre-trained representations mismatch the distribution of the downstream domain, fine-tuning is susceptible to performance degradation due to noise in the uploaded prototypes.
In comparison, FedPTE achieves consistent improvements, which lies in its evidence driven mainte- nance of prototype topology and topology-awand client optimization, collectively enhancing in-class
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Published as a conference paper at ICLR 2026
Table 2: Main results of performance comparison on Office with clients where "Avg." means average results among all clients. The best results are shown in bold.
Methods
Models
Amazon
Caltech
DSLR
Webcam
Avg.
FedOPT
ResNet-10
23.26=1.07
13.19#0.21
33.33+
41.81
27.90
FedDyn
ResNet-10
63.54+2.55
46.37=0.55
42.71+2.95
63.28+1 .60
53.97
Moon
ResNet-10
55.90=0.89
36.59=0.42
13,54+1.47
78.53+0.80
58.64
FedProto
ResNet-10
50.17=3.54
38.37=0.21
61,46+1.47
75.1440.80
56.29
FPL.
Re
60.59=5.35
45.93=1.79
40.62+4.42
61.02=00.03
52.04
FedPLVM
ResNet-10
75.12+1.13
52.22+2.21
65.75+4.42
78.36+2.77
67.86
FedHEAL
ResNet-10
68.85=1.88
46.97+4.03
43.33+4.78
76.33+2.85
58.87
FedPall
ResNet-50
76.21=1.59
41.41+4.20
66.67
67.82+1.99 .99
65.53
MPFT
CLIP
91.30#0.11
91.67+0.23
96.88+0.07
96.47=0.11
94.08
FedPTE
CLIP
97.92+0.05
96,44+0.12
100.00=0.02
100.00=:0.04
98.59
FedPTE
ResNet-10 10
80.21=0.43
57.38+0.91
71.79:3.90
82.66+1.38
73.01
M
M
M-M
SV
M-M
SV
M-M
SY
ST
SY
(4) a = 1.0
(b) a 0.1
(c) a = 0.01
FodDyn
Moon
FedProto
FPL
FedPLVM
FedHEAL
FodPTE
Figure 2: Main results on Digit with 5 clients under different Dirichlet partitions a.
separability the representation space and reducing cross-domain representation variance. As a re- sult, FedPTE demonstrates robust performance advantages, proving the effectiveness of dynamic evidence-basee based prototype topology and topology-aware alignment mitigating domain shift.
Domain Shift Results with Non-III Data. We explore the impact of Non-IID data model performance under domain shift, as shown in Figure 2 Here, a smaller a indicates higher data heterogeneity. As heterogeneity increases, baselines exhibit significant performance degradation on complex domains such as SVHN and USPS, indicating their difficulty in simultancously ad- dressing the dual challenges of domain shift and data heterogeneity. In contrast, FedPTE outper- forms all comparative methods across all domains. Through its evidence driven prototype topol- ogy maintenance mechanism, it maintains stable in-class separability even under highly heteroge- neous data distributions, demonstrating its effectiveness and cross-domain generalization capability.
Table 3: Ablation results on Digit with clients.
4.3 ABLATION RESULTS
Rypli
Papli
Rmengee
P
Pmeerg
Lecatra
Avg.
Component Ablation. We explore the im-
83.67
pact of different components on the per- formance of FedPTE, as shown in Table
85.72
86.31
3 When only splitting Ryplit used, The model's average accuracy increases by 2.05%, demonstrating the necessity dy- namically adjusting the number of prototype clusters. After introducing the penalty term for splitting P Popin the performance further improves to 86.31%. When merging Rmerge and its
88. 14
89.43
93.98
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100
100
Accuracy (%)
95
93.11
93:60
93.98
93:60
93,66
Accuracy (%)
95
93.57
93.98
93.58
93,84
90,41
80
80
0.02
0.04
0.06
0.08
0.10
50
100
150
200
(a) The value of
(b) The value of A
Figure 3: paypee-r ablation results on Digit with clients.
responding penalty term meerge are incorporated, the accuracy reaches 14% and 89.43%, respec- tively, indicating that a reasonable merging mechanism effectively optimizes the prototype topol- ogy. Finally, with the introduction of prototype topology-awan achieves its best performance, highlighting the critical role of contrastive learning enhancing fea- ture separability and cross-domain generalization capability. These results validate the effectiveness and necessity of each component in FedPTE.
contrastive loss Ccontr, the model
Hyper-parameter Ablation. Figure 3 shows the impact of temperature coefficient т and loss weighting factor À on the performance of FedPTE. When т increases from 0.02 to 0.06, the av- erage accuracy improves steadily from 93.1 15.11% % to 93.98%, %, with the best performance and the lowest standard deviation achieved at = 0.06, indicating the most stable model performance under this configuration. As further increases to 0010, the accuracy slightly decreases to 93.60%. Overall, FedPTE exhibits relatively low sensitivity to changes in the temperature coefficient.
Additionally, when À 1, the model performance is the lowest, suggesting insufficient strength of contrastive learning. As À increases to 100, the accuracy significantly improves to 93.98%, confirm- ing the importance of contrastive learning in the training process. When À is further increased to 200, the accuracy slightly decreases to 93.84% with an increased standard deviation. These results demonstrate that FedPTE achieves its optimal configuration model effectively leverages contrastive learning to enhance feature separability while maintaining training stability, thereby delivering the best performance.
0.06 and X 100, where the
Table 4: Multi-domain results of performance comparison Office with various number of clients.
Mixed Ratio= 0.3
Mixed Ratio= 0.5
Mixed Ratio= 0.7
Methods
Model
10
16
10
16
4
10
16
FedOPT
ResNet-10
26.21
29.90
27.44
29.43
29.98
26.63
29.60
29.82
21.94
FedDyn
1e
55.09
60.25
58.72
58.73
62.41
63.21
56.43
61.70
54.64
Moon
Re
56.59
58.06
59.65
57.95
60.03
58.89
59.82
59.84
52.73
FedProto
ResNet-10
51.22
55.80
55.46
52.48
56.61
$7.82
55.01
51.10
50.87
FPL
ResNet-10
57.67
63.63
61.58
58.84
64.33
63.34
58.86
66.66
54.76
FedPLVM
ResNet-10
69.68
62.51
63.36
66.61
61.19
62.52
68.02
66.01
58.20
FedHEAL
Re
71.82
68.85
60.89
66.94
62.97
67.82
59.73
FedPTE
ResNet-10
72.64
75.62
74.72
73.28
72.48
70.23
73.20
73.15
72.48
4.4 MULTI-DOMAIN RESULTS
Inspired by more complex FL scenarios, we explore the case where client's data is mixed with data from other domains, as well as the case where multiple clients share the same domain, as shown in Table 4 Here, the mixed ratio controls the proportion of data from other domains that client possesses, and each domain is assigned to at least one client randomly. As the mixed ratio increases from 0.3 to 0.7, the performance of all baselines exhibits varying degrees of fluctuation

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Published as a conference paper at ICLR 2026
degradation. This indicates that high degree of inter-domain data mixing intensifies the chal- lenges of local model training and global aggregation. In contrast, FedPTE demonstrates minimal performance fluctuation, highlighting the ability of its prototype topology evolution mechanism to effectively adapt to the complex multi-modal data distributions within clients.
Furthermore, the number of clients increases from 4 to 16, the heterogeneity is further amplified. Most baselines show a declining performance trend with the growth in client number, particularly under mixed ratio of 0.7 with 16 clients, where FedOPT's performance drops 21. 11.9%. In com- parison, FedPTE maintains stability as the client scale expands, validating the strong scalability of its dynamic topology maintenance mechanism across different system sizes. effectively captures local sub-class structures under multi-domain mixing while leveraging topology-awe aware contrastive learning to enhance in-class consistency and inter-class discriminability of features, thereby achiev- ing robust feature alignment and model generalization.
Table 5: Unseen domain results of performance comparison on Digit with clients.
Self-training
None
Methods
M
SV
U
SY
M-M
M
SV
U
SY
M-M
FedOPT
80.61
29.03
70.38
31.99
45.46
80.05
22.32
53.01
33.89
48.07
FedDyn
96.26
58.09
89.95
75.02
62.79
95.53
50.91
84.73
72.43
59.11
Moon
94.74
51.53
86.61
70.03
62.21
93.63
43.17
81.51
66.48
57.76
FedProto
96.69
57.76
90.48
76.11
63.82
95.69
51.99
86.67
73.34
59.38
FPL
97.43
61.33
89.77
79.47
64.84
96.63
58.50
87.10
77.31
60.31
FedPLVM
96.11
65.03
90.06
80.40
68.74
96.09
60.27
88.11
80.20
65.64
FedHEAL
96.44
54.14
90.11
66.85
62.64
96.30
45.95
85.32
62.26
58.49
FedPTE
98.32
68.69
90.54
83.21
70.98
98.30
64.37
90.22
84.98
69.94
4.5
UNSEEN DOMAIN RESULTS
Table 5 presents the adaptation evaluation results of FedPTE and comparative methods on unseen domains. Following the setting in FDSE (Wang et al.) 2025), we adopt a leave-one-domain-ou evaluation protocol where each time one domain is held out as the target test domain while the remaining four domains participate in training. The model is evaluated on the target domain under two settings, including direct evaluation (None) and evaluation after self-training. For the self- training setup, we first use the model trained on the source clients to predict data in the target domain and generate pseudo-labels We then select the top 20% of samples with the highest pseudo- label confidence to form cogf-coonidence subset and perform 2 rounds of adaptive training on the model using this subset.
The experimental results demonstrate that FedPTE significantly outperforms all baselines under both evaluation settings, exhibiting superior domain generalization capability. In the direct evaluation, FedPTE achieves leading average performance across all five unseen domains, indicating that the learned feature representations possess stronger cross-domain invariance. After self-training, the performance of all methods improves, but FedPTE shows the most stable and robust enhancement. Notably, the performance fluctuation of FedPTE before and after self gelf-training minimal, suggesting that the initial model already provides a stable feature foundation, requiring only a small number of target domain samples for effective adaptation.
CONCLUSION
This paper addresses the issue of domain shift in FL by proposing a prototype topology evolution- based framework named FedPTE. It adaptively adjusts the global prototype topology through Bayesian inference and marginal likelihood ratios, effectively capturing multi-modal distribution characteristics within classes while reducing redundancy and noise. The stability constraint mech- anism the server effectively prevents training oscillations caused by abrupt topological changes, while the contrastive learning loss on clients further promotes the alignment of features with global semantic centers, enhancing the model's 's discriminability and generalization capability. Experiments validate the superior performance of FedPTE across multiple cross cross-domain tasks, demonstrating its ability to better model feature distributions in heterogeneous domains.
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Published as a conference paper at ICLR 2026
ACKNOWLEDGMENTS
This work was supported by the National Key R&D Program China (2022YFB3105202) and the National Science and Technology Major Project of China (2025Z
ETHICS STATEMENT
This work adheres the ICLR Code of Ethics. All authors have read and committed to upholding the code throughout the submission and review process. Our research presents FL framework de- signed to improve model performance under domain shift without centralizing private client data. All experiments are conducted on publicly available benchmark datasets and curated medical imag- ing datasets that are de-identified and intended for research use. No new data involving human subjects is collected for this study.
Like all machine learning models, the performance of FedPTE is dependent on the training data. While we demonstrate its effectiveness across diverse domains, the model could potentially inherit or amplify biases present in the source datasets. We have evaluated FedPTE on datasets with inherent domain shifts mitigate biases related specific data sources and promote fairness. We believe the benefits of FedPTE, which aims to make FL more robust and applicable to real-world heterogencous environments, outweigh the potential risks, which we consider to be minimal and manageable.
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A CONVERGENCE ANALYSIS
R Let F(w)= = [ E
(w( be the global objective function, where Lx(W) is the local objective
for client k, defined as:
Cx(w) = LCE(w) + A Leontra g)
(21)
We make the following assumptions:
Assumption 1. Lipschitz Smoothness: The local objective (w, 9) is L-smooth:
(W, - VLx(v, &
- - vll, Vw, v, Vk
(22)
Assumption 2. Bounded Variance: The stochastic gradient on each client has bounded variance:
E [IVLLx(W,:E] (w, [w, S o²
(23)
Assumption 3. Bounded Gradient: The expected squared norm of stochastic gradients is bounded:
E [I {) < G
(24)
Assumption 4. Prototype Stability: The global prototype topology evolves gradually such that:
g - 6
(25)
where 5 is a small constant, ensured by the penalty constraints in FedPTE.
Assumption 5. Lipschitz Contrastive Loss: The contrastive loss is Le-Lscccitzz with respect to prototype positions:
Coontra W, 9) Leonrr (w, g')l L
G'll G'
(26)
Proof. Let ((() denote the global model at communication round t, and We ((+1) is the local model of client l after local updates.
For each client k, after 7 steps of local SGD with learning rate n, by the T-smoothness of La and the bounded variance assumption, we have:
r/ (1 (1- Lip I (w g(0)]2++
Labr o² (27)
[WCC(W (++1) g())) S LA
Lu (w g(t) -17
The contrastive loss Lecutra depends on the global prototype set G. Under Assumptions 4 and 5 the change the contrastive loss component between rounds is bounded:
(Econt(W ((++)) Leontra (womtr(w,,rr (()) S ALoo
(28)
After local updates, the global model is aggregated as:
W (++1)
(++1)
(29)
K k=
Due to the L-smoothness of the global objective F and the bounded prototype evolution, we can derive:
E[F(((++)) g((+)))) F(w"), np (1- (1- LnTT)
Lafr
AL
2
(30)
Summing over T' rounds and rearranging, we obtain:
(I. g())) ((F(w("),gl) - F*)
Lno²
2AL.8
(31)
1T' - LITT)
Lijt
12 - LITT)
where F is the minimum value of F.
By choosing 7 OLIvVT) and assuming O(IVVT) (ensured by FedPTE's penalty mecha-
nisms), we have:
T Σ
(32)
VT
This shows that FedPTE converges to a stationary point at an average rate of O(1VVT). The penalty mechanisms in FedPTE ensure 8 is sufficiently small, thereby guaranteeing stable convergence. n1
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B ADDITIONAL EXPERIMENTS
B.1 MULTI-CLIENT RESULTS
Homain-balancedd Figure 4a shows the performance FedPTE and baselines under domain- balanced settings with varying numbers of clients. As the number of clients increases, the aceu- racy FedPTE slightly decreases from 93.98% to 91.92%, yet it consistently and significantly outperforms all baselines. This trend indicates that in domain-balanced environments with rela- tively uniform data distribution, FedPTE can effectively capture the feature diversity introduced by multiple client participations through its Bayesian evidence-driven prototype topology evolution mechanism, thereby maintaining high performance. Although an increased number of clients may introduce greater data heterogeneity, FedPTE's dynamic prototype adjustment and stability con- straints ensure the robustness of the training process, preventing severe performance fluctuations. This trend demonstrates that FedPTE can effectively leverage the data diversity from multiple client participations, thereby achieving robust generalization in heterogeneous data environments.
Domain-imballnced. We also explore the performance of FedPTE and baselines under domain- imbalanced settings, shown in Figure 4b Specifically, we configure at least half of the clients to be in the same domain, with the remaining clients proportionally distributed across the other do- mains. When at least half of the clients reside in the same domain, the data distribution exhibits significant skewness. FedPTE's accuracy decreases from 88.66% to 84.37%, but the decline is rel- atively small, and its performance remains significantly superior to other methods. For instance, with 25 clients, FedPTE achieves an accuracy of 84.37%, while FedPLVM, FPL, and FedProto only achieve 79.37%, 64.84%, and 52.70%. respectively. This highlights FedPTE's strong adaptability under severe distribution shift. Its prototype topology-aware contrastive learning mechanism effec- tively aligns local features with global semantic centers. Concurrently, Bayesian inference automat- ically identifies redundant prototypes for merging and refines semantic substructures for splitting, thereby preserving semantic discriminability amidst inter-domain conflicts.
100
100
FailPrto
FalPLVM FedPTE
FailProia
FaiPLVM
PaiPTS
80
80
Accuracy
Accuracy
60
50
50
10
20
15
20
(a) Domain-bane mamain- results
(b) Domain-iimbalanced results
Figure 4: Multi-client results Digit with various numbers of clients.
B.2 REAL-WORLD DOMAIN RESULTT
Following the setup of FEAL (Chen et al, 2024a), we evaluate the performance of FedPTE on four real-world medical imaging datasets, including two classification datasets Fed- Bed-Camelyon, Fed-ISIC and two segmentation datasets Fed-Polyp. Fed-Prostate. Specifically, Fed-Camelyon is breast cancer histology dataset comprising different domains, Fed-ISIC is a skin lesion dataset with domains, Fed-Polyp is an endoscopic polyp dataset with domains, and Fed-Prostate is prostate MRI dataset with 6 domains. Further details are provided in Table and Figure S For the image classification task, use ResNet-10 10 with 50 communication rounds. For the image segmentation task, we employ U-Net (Ronneberger et al. 2013) and change the cross-entropy loss into the Dice loss Millettri al. 2016) with 60 communicttion rounds.
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Table 6: Details of real-world medical imaging datasets.
Datasets
Train Size
Test Size
Source
47548
11888
Camelyon 17
Bándi et al.
2019
27923
6981
Camelyon17
Bändi et al.
2019
Fed-Camelyon
68043
17011
Camelyon Bándi et al.
2019
103870
25968
Camelyon 17
Bändi et al.
2019
117377
29345
Camelyon (Bándi et al.
2019
9930
2483
BCN (du Terrail et al. 2022)
3163
791
HAM_vidir.moolloooo..o .mfliimmoomxxx (du Terrall et al.
2022)
Fed-ISIC
2691
672
HAM LAM__idir.nme widdi__moder (du Terrail al.
2022)
1807
452
HAM L.M_ndsendahl (du Terrail al.
2022)
800
200
Kvasir (Jha et 2020)
157
39
ETIS Siila 2014)
Fed-Polyp
304
75
ColonDB Tajbakhsh al.
2016
490
122
ClinicDB (Bernal et al.
2015
225
36
BIDMC Litjens al. 2014
306
78
BMC Bloch et al. 2015
134
24
HK Litjens et al. 2014
Fed-Prostate
387
81
I2CVB Lemaitre et al. 2015
337
84
RUNMO
Bloch et al 2015
152
23
UCL (Litjens et al.
2014
Table Real-world domain results performance comparison on Fed-Polyp and Fed-Prostate The best results shown in bold.
Fed-Polyp
Ped-Prostate
Methods
Kvasir
ETIS
ColonDB ClinieDB
BIDMC
BMC
HK
I2CVB
RUNMC
UCL
FedOPT
51.62
58.21
55.81
59.25
50.04
50.31
50.90
50.86
50.53
50.43
FedDyn
77.54
62.46
73.11
63.30
83.01
83.86
86.90
80.24
80.49
79.72
Moon
49.87
56.35
58,94
54.63
85,82
78.51
86.16
81.44
78.34
77.31
FedProto
78.25
63.40
71.93
66.63
85.18
88.48
87.40
81.65
86.60
85.31
FPL.
80.88
65.63
73.14
68.77
88.99
88.50
88.82
83.50
87.64
86.09
F
76.05
64.08
66.44
68.77
88.24
89.28
87.99
87.49
86.75
83,50
FedHEAL
71.33
64.14
63.87
66.21
88.62
86.30
88.85
87.17
82.48
83.07
FedPTE
84.17
68.08
76.05
69.80
89.61
90.20
89.60
90.98
89.51
89.40
Specifically, Figure Figure&ppeeentss presents the performance of FedPTE and baselines on medical image classifi- cation. The experimental results demonstrate that FedPTE achieves the best performance across all domains, showcasing strong generalization capability in heterogeneous medical data scenarios. Its evidence-driven prototype topology evolution mechanism adaptively adjusts the global proto- type structure to align with the data distribution characteristics of different medical centers, thereby enabling more effective cross-domain knowledge fusion.
In addition, Table shows the performance FedPTE and baselines on medical image segmen- tation, evaluated using the Dice coefficient (%), where higher values indicate better segmentation quality. The results indicate that FedPTE achieves the best performance across all ten test domains, demonstrating excellent domain generalization capability in pixel-level tasks. Notably, traditional FL methods perform significantly worse across all domains, further highlighting the necessity of explicitly handling domain shift in medical image segmentation.
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Fed-C Ped-Camelyon
Domain
Domain
Domain
Domain
Domain 5
Fed-ISIC
Domain
Domain
Domain
Domain
Fed-Polyp
Domain
Domain
Domain
Domnin 4
Fed Ped-Prostate
Domain
Domain
Domain
Domain
Domain $
Domain 6
Figure 5: Examples from real-world medical imaging datasets.
100
100
FPL
FPL VM
90
PuPEVM
FoEFTE
FeiPTE
Accuracy (%)
Accuracy (%)
Domian
Domian
Domian 3 Domian
Domian
Domian
Domia
Domian
Domian
(a) Camelyon
(b) Fed-ISIC
Figure 6: Real-world domain results of performance comparison on Fed-Camelyon and Fed-ISIC.
B.3 NIW PRIOR STUDY
Prior Hyper-parameter Ablation. FedPTE employs fixed priors make computations indepen- dent of each other and avoid maintaining complex states across communication rounds. Specifically, we set the strength of the mean prior Kg to 0.1, indicating weak confidence in the initial prior mean and allowing the posterior distribution to be more readily dominated by the client prototype data up- loaded in the current round. For the degrees of freedom Ph. adhering to the theoretical requirements of the NIW distribution, we set it to Pn = d + 5, where d is the feature dimension. This is one of the minimum values that satisfies the distribution's 's definition while providing weak informativeness, again serving to avoid overly strong prior assumptions. For the scale matrix Sp. initialize it as So = (n) d - 1) I, where is the identity matrix. This represents unit-scaled covariance prior, which is common and robust default choice.
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Table NIW Prior hyper-parameter ablation results on Digit with clients.
Kg
P/
0.01
0.05
0.1
0.5
d d+2 2
d d+3
d
10
d+ 20
MNIST
98.94
98.94
98.88
98.96
98.96
98.93
98.88
99.04
98.91
SVHN
84.41
84.46
84.93
84.52
84.65
83.93
84.93
84.66
84.20
USPS
98.28
98.49
98.32
98.44
98.28
98.33
98.32
98.55
98.55
Synth
94.97
95.11
95.13
95.22
95.05
95.04
95.13
95.12
95.12
MNIST-M
91.92
91.43
92.65
91.86
92.25
91.94
92.65
92.10
92.16
Avg.
93.71
93.69
93.98
93.80
93.84
93.63
93.98
93.89
93.79
Table [ shows the impact of different prior hyperparameter values on model performance. The results indicate that long these parameters set within reasonable ranges, which maintaining the nature of weakly informative priors, their variation has minimal impact on the final topology evolution decisions and model performance.
Prior Component Ablation. To explore the effectiveness of the NIW prior, we compared FedPTE's performance against variants ing random evolution and a sim- ple heuristic, as shown in Table Specifically, the random evo- lution variant simulates undirected topological changes by performing splitting and merging operations at fixed probabilities. The simple heuristic variant removes the Bayesian estimation process for each cluster's covariance and discards the Bayesian posterior mean update mechanism. It replaces the log marginal likelihood used for split-merge decisions with the negative value of the cluster's sum of squared errors (SSE): log P(Dx) - SSE(DD) = Σ 1x-
Table 9: Prior component ablation results on Office with 4 clients. The best results are in bold.
Amazon
Caltech
DSLR
Webcam
Avg.
Random Simple
67.19
53.78
46.88
54.24
55.52
75.00
54.22
56.25
66.10
62.89
NIW 80.21
57.38
71.79
82.66
73.01
(33)
XED=
Consequently, the decision criterion shifts from selecting the operation that maximizes Bayesian evidence to the one that minimizes the total within-cluster SSE.
The experimental results demonstrate that the NIW prior is crucial for FedPTE's robust perfor- mance. Specifically, the random evolution strategy performs the worst since random operations frequently introduce semantically inconsistent or noisy topological changes. These arbitrary modifi- cations disrupt the semantic structure of the prototype topology, failing to provide clients with stable and meaningful anchors in the feature space, ultimately leading to severe performance degradation. The simple heuristic variant lacks the comprehensive probabilistic perspective of Bayesian model comparison. which inherently balances goodness-of with model complexity. Consequently, the SSE-based approach is more prone getting stuck in local optima, which limits its ability dis- cover the globally optimal prototype topology.
In contrast, using the full NIW prior mechanism yields the best results, achieving an average ac- curacy of 73.01% and outperforming the other variants across all domains. This significant per- formance gap confirms that the Bayesian evidence-driven approach provides more reliable and principled foundation for prototype topology evolution compared to alternatives lacking probabilis- tic grounding.
B.4 PENALTY STUDY
Penalty Ablation. Figure illustrates the impact of different penalty coefficient combinations the performance of FedPTE. If the split penalty is too small, the model tends to over-split proto- type clusters, generating large number of redundant subclasses, which leads to fragmented in-class
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2.0
92.53
93.52
93.29
92.01
2.0 69.83
71.16
70.55
68.63
1.5
93.71
93.98
93.64
92.72
71.64
73.01
69.35
69.97
Merge
Merge
1.0
92.68
92.90
93.33
70.87
70.39
71.88
0.5
91.79
92.65
92.85
67.54
68.02
68.64
69.35
0.5
1.0
1.5
2.0
0.5
1.0
1.5
2.0
Split
Split
(a) Results on Digit
(h) Results on Office
Figure 7: Penalty ablation results on Digit with 5 clients and on Office with clients.
structures and introduces noise. Conversely, the model fails to capture fine mme-grained semantic struc- tures. Similarly, if the merge penalty is too small, the model excessively merges prototype clusters that are semantically similar but slightly different in distribution, while an excessively large merge penalty prevents necessary prototype aggregation, causing the topological structure to retain numer- ous similar yet unstable prototypes, thereby increasing the risk of training oscillations. Despite this, FedPTE exhibits certain degree of robustness the selection of penalty coefficients, maintaining relatively stable performance within the ranges of 3ppla E [0.5, 1.5] and meerge E [1.0, 2.0]. This en- ables effectively balance structural refinement and noise suppression most scenarios, thereby enhancing the model's generalization capability and convergence stability.
Table 10: Adaptive weight results on Digit with 5 clients and on Office with clients.
Digit USPS
Office
MNIST
SVHN
Synth
MNIST-M
Amazon
Caltech
DSLR
Webcam
Adaptive Fixed
98.89
85.25
98.55
95.57
93.47
81.77
60.89
65.62
77.97
98.88
84.93
98.32
95.13
92.65
80.21
57.38
71.79
82.66
Adaptive Weight Strategy. We explore strategy for adaptively adjusting the penalty coefficients Sxplit and Smerge. as shown in Table 10] Specifically, use the Sucore to determine whether to adaptively increase or decrease the coefficients:
Sscore = 11 tanh Sintr
(34)
Smntrr
where Sintra represents the intra-cluster distance, i.e., the average distance from all points within cluster to their center, and Symer denotes the inter-cluster distance, i.e., the average distance between all different cluster centers.
can be observed that the adaptive penalty mechanism demonstrates more adaptable performance in most cases. When the intra-cluster distance is relatively small, Sxcare approaches 1, and FedPTE appropriately relaxes the penalty constraints, allowing for more structural optimization. Conversely, when the intra-cluster structure is loose, it strengthens the penalty to avoid unstable topological changes. is worth noting that on Office, the adaptive strategy performs better on the Amazon and Caltech domains, while the fixed parameter method still maintains advantage the DSLR and Webcam domains. This discrepancy may stem from the data distribution characteristics of different domains. When the data distribution is relatively compact, fixed penalty parameters provide more stable constraints, whereas when the data distribution is more complex and variable, the adaptive penalty strategy can better handle such heterogeneity.
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Overall, the adaptive penalty strategy shows promising potential. By dynamically balancing the flexibility of topological evolution and training stability, this mechanism can automatically adjust decision thresholds based actual cluster structure characteristies, reducing the reliance empir- ical hyperparameter tuning.
Table 11: Privacy protection results of various values of perturbation on Digit with 5 clients.
Perturbation
MNIST
SVHN
USPS
Synth
MNIST-M
Avg.
0.1
98.91
84.63
98.23
95.05
92.17
93.80
1.0
98.60
81.55
98.06
94.42
90.29
92.59
5.0
95.46
73.18
95.59
87.93
78.55
86.14 14
50.0
88.40
61.29
92.80
81.47
68.25
78.44
Table 12: Privacy protection results of various values of scale on Digit with clients.
Scale
MNIST
SVHN
USPS
Synth
MNIST-M
Avg.
0.1
98.96
84.49
98.39
95.00
92.19
93.80
1.0
98.60
81.55
98.06
94.42
90.29
92.59
5.0
96.11
74.56
96.13
90.90
84.60
88.46
10.0
97.29
81.07
94.89
90.15
80.19
88.72
B.5 PRIVACY PROTECTION
We explore the impact of incorporating differential privacy into prototypes on FedPTE, specifically examining the effects of different perturbation values and scale parameters, shown in Tables [ and 12, Following existing methods (Canonne et al. 2020 Wang et al., 2024), we set the privacy budget and the delta parameter 4.0 and Ie-5, respectively. When the perturbation value 0.1, the model maintains high performance, indicating that FedPTE can effectively preserve its feature representation capability under mild privacy protection. As the perturbation value increases to 5.0 and 50.0, the performance degrades significantly, with average accuracy dropping to 86. 14% and 78.44%, respectively. This demonstrates that strong noise substantially interferes with the model's ability to learn features from complex domains.
Additionally, when the scale parameter is 0.1, the performance is similar to that with a perturbation value of 0.1. When the scale parameter increases to 5.0, the performance degradation is smaller compared to the case with a perturbation value of 5.0, suggesting that the scale parameter may provide gentler noise control mechanism. The performance with scale parameter of 10.0 is similar to that with 5.0, indicating that within this range, the model is relatively insensitive to changes in the scale parameter.
is noteworthy that even when using privacy protection techniques, FedPTE achieves performance comparable to advanced baselines. As result, FedPTE can maintain over 90% of its original performance under moderate privacy protection, effectively balancing the requirements of privacy preservation and model utility.
C EXPERIMENTAL DETAILS
C.1 PROTOTYPE TREND
Figure iillustrates the dynamic evolution trend of the prototype topology on the server across com- munication rounds. The results reveal that the number of prototypes per class fluctuates continuously between rounds, reflecting how the cedence-drrven prototype evolution mechanism in FedPTE con- tinuously optimizes the global feature representation. Further analysis shows strong correlation between the variation in prototype count and the model's performance across different domains.
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comparing with the main experimental results in Figure 2 it can be observed that domains with larger number of prototypes (such as MNIST and MNIST-M generally correspond to higher clas- sification accuracy. Moreover, the dynamic fluctuation in prototype count remains relatively stable, which attributed to FedPTE's penalty mechanism that prevents excessive splitring or merging, thereby ensuring balance between topological changes and semantic consistency.
3.5
SVII
AENIST
Avg. Number of Prototypes
USPS
3.0
Sinch
NNIISM
2.5
2.0
1.5
1.0
0.5
10
20
30
40
50
Communication Rounds
Figure 8: Prototype trend of FedPTE on Digit with clients.
Accuracy (%)
50
25
0
20
40
60
80
20
40
60
80
20
40
60
80
Communication Rounds
Communication Rounds
Communication Rounds
(a) Mixed Ratio 0.3
(b) Mixed Ratio
0.5
(c) Mixed Ratio
0.7
Clients=4
Clients=10
Clients=16
Figure 9: Convergence performance of FedPTE on Office with multi-domain.
C.2 CONVERGENCE PERFORMANCE
Figure demonstrates the convergence behavior of FedPTE in multi-domain mixed client scenarios, comparing performance curves under configurations of 4, 10, and 16 clients. FedPTE exhibits fa- vorable convergence and stability across all settings. Specifically, when the communication rounds reach approximately 40, the model performance under all three client configurations stabilizes, with accuracy maintained at around 70%. Notably, even as the number of clients increases from 16, FedPTE maintains similar convergence speeds and final performance levels, indicating that its pro- totype topology evolution mechanism exhibits strong adaptability to system scale. During the early training phase (first 20 rounds), all configurations show rapid performance improvement, reflecting FedPTE's ability to effectively utilize initial communication rounds to quickly establish discrimina- tive feature representations.
C.3 DATA DISTRIBUTION
Figure Iilllustrates the data distribution across clients in a FL scenario on Digit, which simultane- ously faces challenges of data heterogeneity and domain shift. Here, each client belongs distinct
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Donsin
Numbers
Numbers
Numbers
510
150
200
500
100)
450
400
500
Clier
2003
Client
900
Client
1200
(a) 1.0
(b) 0.1
0.01
Figure 10: Examples of data distribution on Digit with 5 clients under different Dirichlet partitions
a.
(a) 10 Rounds
(b) 20 Rounds
(c) 30 Rounds
(d) 40 Rounds
(e) 50 Rounds
(f) 10 Rounds
(g) 20 Rounds
(h) 30 Rounds
(i) 40 Rounds
(i) 50 Rounds
Figure 11: T-SNE Visualization of different communication rounds on Digit with clients under data size ratio 0.1 (a e) and data size ratio 1.0 (f-
domain, and the local data distribution follows Dirichlet distribution controlled by the parameter a. When a = 1.0, the label distribution within each client is relatively uniform, approaching IID. In this case, the primary challenge for FL stems from the feature distribution differences caused by varying domains. In contrast, when a = 0.1 or = 0.01, significant label heterogeneity arises among clients, where each client holds different categories and quantities of data. Under these conditions, FL must contend with the dual challenges of domain shift and label distribution skew.
C.4 T-SNE VISUALIZATION
We explore the feature extraction performance of FedPTE across different sample ratios and com- munication rounds. Figure I1 shows the t-SNE (Maaten & Hinton 2008) visualization of client data features. When clients are trained and tested on only 10% of Digit, the model fails effectively separate features of different categories within the first 30 rounds. As training progresses to 30-50 rounds, the class boundaries the feature space gradually become clearer, indicating that the model requires longer training cycles learn effective representations with limited data.
In contrast, when trained with 100% of the data, the model achieves distinct in-class separation within just 10-20 rounds, with significantly improved compactness and discriminability of feature clusters. This demonstrates that sufficient data provides richer gradient signals, accelerating the formation of discriminative feature structures. In low-data scenarios, FedPTE ultimately achieves
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stable feature alignment through progressive prototype topology evolution, highlighting its adapt- ability to data-scarce environments.
D METHOD ANALYSIS
D.I NUMERICAL COINCIDENCE
Semantic separability and variance structure changes from the continuous evolution of clients' local feature ex- tractors during the federated training process. In the early stages of training, the model's feature representation capa- bility is weak, and features of the same class may be entan- gled, forming broad, high-variance unimodal distribution. As training progresses, the feature extractors are continu- ously optimized on their respective domain data, and their discriminative power gradually strengthens. This causes the previously entangled class features to begin developing clear substructures, manifesting as a refinement in seman- tic separability and an evolution in the variance structure. If prototypes remain static, they cannot capture this evolution. Global prototypes would become blurred average of dif- ferent sub-mode features, unable to provide precise anchors for any specific sub-mode. This leads to misalignment in feature alignment, where client models are pulled towards an inaccurate consensus point, thereby limiting further im- provements in model performance.
0.9905
sim
0.9778
5 X
0.9873
sim
Figure 12: An example of the numer- ical coincidence.
The numerical coincidence refers to the scenario where two vectors are close in terms Fuclidean distance or cosine similarity in the feature space, yet their corresponding deep semantic information differs. This proximity is typically not due to genuine semantic similarity but instead caused by irrelevant domain-specife features training noise. As shown in Figure 12 in the feature space, the feature vector of a digit '5' might, due to a blue texture, unexpectedly hie close to the feature vector of digit '8'. In such case, if the prototype clusters representing '5' and '8' are merged based solely on spatial distance, different semantic categories will be confused, severely impairing the model's discriminative ability.
D.2 COMMUNICATION OVERHEAD
The communication cost FedPTE primarily consists of model parameter and prototype parameter transmission, which similar to FPL. and FedPLVM. Instead of upload-
Table 13: Wall-clock results Of- fice with 4 clients.
ing M prototypes per client, each client uploads most
M x Clocal cluster centers, each being d-dimensional vec- tor. Thus, the complexity of uploading prototypes is O(M Clocal d). Since ResNet has millions of parameters while feature dimension d 512 and M 10, the condition M Clocal d & dmodel holds, indicating that the additional communication overhead is relatively small and acceptable.
Methods
Wall-clock
FedOPT FedDyn
9,094s
11.936s
Moon
13.256s
FedProto
12.154s
FPL
15.973s
D.3 COMPUTATIONAL COMPLEXITY
FedPLVM
23.008s
FedHEAL
18.547s
The main computational overhead on the server lies in topol- ogy evolution. For each prototype, clustering and marginal likelihood calculations are required. The marginal likelihood calculation involves the determinant and inverse of covariance matrix, with complexity (dd).
FedPall
17.340s
FedPTE
17.798s
The primary computational overhead clients involves calculating the contrastive loss and per-
forming clustering. The contrastive loss requires computing the similarity between samples and
all global prototype cluster centers, with complexity of O |G] d). We additionally test the
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time required for FedPTE and baselines to complete local training and communication round on a single A100 GPU, with results shown in Table 13 It can be observed that FedPTE maintains acceptable computational time while delivering expressive results.
Table 14: Comparison results on DomainNet with 6 clients. The best results in bold.
Methods
Clipart
Infograph
Painting
Quickdraw
Real
Sketch
Avg.
FedProto
12.77
18.03
29.31
13.00
30.86
16.67
20.11
FPL
35.71
22.80
33.52
17.00
41.15
22.31
28.75
FedPLVM
55.19
33.16
45.05
22.67
52.70
42.56
41.89
FedPTE
58.85
33.44
53.25
31.40
59.22
46.19
47.06
D.4 LARGE-SCALE PERFORMENCE
We compare the performance of prototype-hasee methods with FedPTE on the large-scale DomainNet (Peng et al.) 2019). which comprises domains, 345 classes per domain, and approximately 600000 images in total, shown in Ta- ble [4 Specifically, all models undergo 200 communica- tion rounds, with FedPTE's contrastive loss weight À set to 1. The results demonstrate that FedPTE achieves the best performance across all six domains, showcasing its signifi- cant advantages in handling complex cross-domain FL tasks. Traditional prototype-baat baset methods rely on static cluster- ing, making it difficult to capture potential multiple visual modes within class. In contrast, FedPTE can adaptively split or merge prototype clusters based on statistical evidence, distribu-
Table 15: Wall-clock results on Do- mainNet with clients.
Methods FedOPT
Wall-clock
514.4366
FedDyn
499.409s
Moon
731.948s
FedProto
499 227s
FPL
524.476s
FedPLVM
808.268s
FedHEAL
944,433s
thereby more accurately modeling the tions within classes, which is particularly crucial in classifi- cation tasks with large number of classes.
FedPall
745.655s
FedPTE
726.9838
Furthermore, on large-scale datasets, FedPTE's Bayesian evidence computation is parallelized. On a server with sufficient computational resources, the time required for topology evolution in each communication round depends not the total number of prototype clusters, but on the time needed to process the single largest cluster. This enables FedPTE to efficiently handle complex seman- tic topologies containing large number of prototype clusters. We supplement the computational times of FedPTE and the baselines on DomainNet in Table 15 showing that FedPTE's per-round computation time remains within reasonable range.
E THE USE OF LARGE LANGUAGE MODELS (LLMS)
During the preparation of this work, the authors LLMs to improve the clarity and fluency of the writing. This assistance was limited to polishing grammar, rephrasing sentences, and enhancing readability.
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Reviews:
[{"review_id": "arZ6FD5X1s", "reviewer": "Reviewer_Pn6w", "summary": "This paper introduces FedPTE, a Bayesian prototype-topology–based federated learning (FL) framework designed to tackle domain shift and data heterogeneity in cross-domain FL. Traditional prototype-based FL methods rely on static clustering or averaging and fail to adapt to evolving class structures.\nFedPTE models prototypes as dynamic topological units whose number and structure evolve via Bayesian Gaussian Mixture Models (BGMM) and marginal likelihood ratio tests under a Normal–Inverse–Wishart (NIW) prior. The server decides whether to split or merge prototype clusters based on evidence strength, guided by penalty constraints to maintain stability. Clients perform prototype topology–aware contrastive learning, aligning local representations with global prototypes.\n\nExperiments on Digit (MNIST/SVHN/USPS/Synth/MNIST-M), Office (Amazon/Caltech/DSLR/Webcam), and multiple medical imaging datasets (Camelyon, ISIC, Polyp, Prostate) show that FedPTE outperforms baselines such as FedProto, FedPLVM, FedHEAL, and FPL. The paper also reports ablation studies, non-IID analysis, privacy perturbation effects, and multi-domain scalability. Overall, FedPTE claims better adaptability, robustness, and generalization across heterogeneous domains.", "questions": "1 How sensitive is FedPTE to NIW hyperparameters (κ₀, ν₀, S₀)? Are priors fixed or updated adaptively across rounds?\n\n2 Could the split/merge evidence thresholds be learned dynamically rather than hard-coded?\n\n3 Does the BGMM assumption hold when feature distributions are highly non-Gaussian (e.g., with ReLU activation skew)?\n\n4 How does FedPTE behave when one domain is highly dominant (client imbalance)?\n\n5 Is the Bayesian evidence computation parallelized, and what is its runtime complexity per round in large-scale FL?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1 Original idea: Introduces Bayesian evidence to dynamically evolve prototype topology—bridging probabilistic inference with federated representation learning.\n\n2 Comprehensive experiments: Covers IID/Non-IID, unseen domain, medical imaging, and privacy scenarios.\n\n3 Strong empirical performance: Consistent gains over FedProto, FedPLVM, FPL across all datasets.\n\n4 Well-designed ablations: Component and hyperparameter studies are clear (Figure 3–4, Table 3).", "weaknesses": "1 Limited novelty beyond existing prototype frameworks.\nWhile Bayesian modeling adds rigor, the overall structure (prototype aggregation + contrastive alignment) resembles prior works like FedPLVM and FPL. The innovation lies mainly in the split/merge inference.\n\n2 Assumption of Gaussian prototypes.\nReal FL data distributions (e.g., in medical or digit datasets) may be non-Gaussian; the NIW assumption can oversimplify multi-modal or skewed clusters.\n\n3 Hyperparameter sensitivity.\nPenalty coefficients (β_split, β_merge) and evidence thresholds are empirically set; no adaptive rule or theoretical guidance is provided.\n\n4 Computational overhead.\nMarginal likelihood evaluation (O(d³)) and frequent topology updates could become expensive for large models or high-dimensional features, though claimed “acceptable” (Table 10) without quantitative scaling analysis.\n\n5 No theoretical convergence guarantee.\nThe stability of prototype evolution across rounds is discussed qualitatively but lacks formal proof or bound.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "s7D0jFypcC", "reviewer": "Reviewer_y5F7", "summary": "FedPTE frames federated domain adaptation as evidence-driven prototype topology evolution. The server uses BGMM with NIW prior and marginal likelihood ratio to split/merge global prototypes, adding a stability penalty; the client uses topology-aware contrastive loss for training. This has achieved performance improvements on other feature shift datasets such as Digit/Office.", "questions": "1. More ablation experiments are needed to verify whether the reference of the stability constraint mechanism will affect the specific performance.\n2. What specific weaknesses are addressed relative to FedPLVM/MPFT? And what are the advantages of NIW proofs compared to previous heuristics?\n3. \"Numerical coincidence\": Give an example where spatial proximity hides a semantic mismatch or provide insight into why this happens and how to prevent it through penalties.\n4. Reports communication and runtime comparisons to prototype baselines.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The article mainly focuses on the fact that static clustering methods are difficult to solve the semantic separability and variance structure changes between prototype clusters in feature offset scenarios, and from the experimental results, it has excellent performance, and the experiment is complete.\n2. The ablation experiment verified the effectiveness of the effects of each component, which solved my confusion to a certain extent.", "weaknesses": "1. The causes and impacts of semantic separability and variance structure changes under feature transfer have not been fully explained. In addition, how should I understand the concept of “numerical coincidence” mentioned in Section 3.2? Why does this lead to situations where spatial proximity but different semantics occur?\n2. The ablation experiments were not performed on the same experimental dataset, which makes me speculate about the method's effectiveness. For example, based on Table 3 and Figure 4, I cannot judge the effect of the stability component without adding $P_{split}$ and $P_{merge}$ and adjusting their corresponding parameters.\n3. In Formula 2, the calculation of local prototypes is done by generating different feature centers through FINCH clustering, while the left side is the local prototypes of samples of the same type, which are not equal in number.\n4. Though the authors have extended experiments on mixed data from more clients in the appendix, the main results are conducted in a small-scale environment (5 clients), limiting the reliability of the results and raising potential scalability concerns of the proposed method. \n5. Comparison with some latest SOTA methods on federated domain shift is not included, for example: \n[1]  \"FedPall: Prototype-based Adversarial and Collaborative Learning for Federated Learning with Feature Drift.\" ICCV, 2025.\n6. The distinction between related work and other work should be further clarified.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TNV2ByXeqV", "reviewer": "Reviewer_P4u6", "summary": "This paper addresses domain shift in federated learning by proposing FedPTE, a framework that dynamically evolves prototype topology through Bayesian inference. The key innovation is treating prototype clusters as variable topological units that can split or merge based on statistical evidence from Bayesian Gaussian Mixture Models with Normal-Inverse-Wishart priors. The framework includes penalty mechanisms to ensure stability and uses prototype topology-aware contrastive learning on clients to enhance feature alignment across domains.", "questions": "Please find in the above weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The use of Bayesian inference with NIW priors for prototype topology evolution is mathematically principled and moves beyond simple averaging or static clustering approaches.\n2. FedPTE consistently outperforms baselines, achieving 93.98% on Digit and 73.01% on Office, with particularly notable improvements on challenging domains.\n3. The penalty terms for split/merge operations effectively balance adaptability with training stability, addressing a key challenge in dynamic prototype methods.\n4.  The paper addresses important aspects like communication overhead, computational complexity, and privacy protection with differential privacy experiments.", "weaknesses": "1. The method introduces several hyperparameters (βsplit, βmerge, κ0, ν0, S0)\n2.  The O(d³) complexity for marginal likelihood calculations could become prohibitive for high-dimensional features, though this isn't thoroughly discussed.\n3. While the Bayesian framework is principled, the paper lacks convergence guarantees or theoretical analysis of when/why the topology evolution helps with domain shift.\n4. Some of deign choices needs to be further clarified, e.g., Why use FINCH clustering initially? How sensitive is performance to the NIW prior initialization?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KevH8w6rR1", "reviewer": "Reviewer_pRNn", "summary": "This paper proposes FedPTE, a framework designed to address domain shift among clients. FedPTE dynamically adjusts the structure of global prototype clusters using Bayesian Gaussian Mixture Models (BGMM) and marginal likelihood ratios, determining when to split or merge prototypes based on statistical evidence. A stability constraint mechanism is introduced on the server to prevent unstable topology changes, while topology-aware contrastive learning on clients enhances feature discriminability and cross-domain consistency. Experiments demonstrate that FedPTE achieves generalization and stability.", "questions": "Please see the weaknesses.", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The work targets a critical pain point in FL——domain shift under heterogeneous data, making the motivation both practical and research-relevant.\n2. FedPTE maintains good performance under moderate privacy noise, suggesting potential for deployment in privacy-sensitive fields.", "weaknesses": "1. Relies on Gaussian mixture assumptions: performance may drop if data significantly deviates from this distribution.\n2. Server-side Bayesian inference and covariance inversion have $O(d^3)$ complexity, which can be expensive in high-dimensional spaces.\n3. Although probabilistic evidence is used, the paper lacks a deeper theoretical analysis of convergence guarantees or probabilistic bounds.\n4. Lack of large-scale or real-world deployments where communication and noise issues are more severe.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)