Gains: Fine-grained Federated Domain Adaptation in Open Set
Authors: Zhengyi Zhong
Wenzheng Jiang
Weidong Bao
Ji Wang
Cheems Wang
Guanbo Wang
Yongheng Deng
Ju Ren
Venue: NeurIPS 2025 poster ()
Keywords: federated learning
domain adaptation
federated domain adaptation
Primary area: deep_learning

Abstract: Conventional federated learning (FL) assumes a closed world with a fixed total number of clients. In contrast, new clients continuously join the FL process in real-world scenarios, introducing new knowledge. This raises two critical demands: detecting new knowledge, i.e., knowledge discovery, and integrating it into the global model, i.e., knowledge adaptation. Existing research focuses on coarse-grained knowledge discovery, and often sacrifices source domain performance and adaptation efficiency. To this end, we propose a fine-grained federated domain adaptation approach in open set (Gains). Gains splits the model into an encoder and a classifier, empirically revealing features extracted by the encoder are sensitive to domain shifts while classifier parameters are sensitive to class increments. Based on this, we develop fine-grained knowledge discovery and contribution-driven aggregation techniques to identify and incorporate new knowledge. Additionally, an anti-forgetting mechanism is designed to preserve source domain performance, ensuring balanced adaptation. Experimental results on multi-domain datasets across three typical data-shift scenarios demonstrate that Gains significantly outperforms other baselines in performance for both source-domain and target-domain clients. Code is available at: https://github.com/Zhong-Zhengyi/Gains.

Gains: Fine-grained Federated Domain Adaptation in Open Set
Zhengyi Zhong Wenzheng Jiang'; Weidong Bao', Ji Wang", Qi Wang", Guanbo Wang', Yongheng Deng', Ju Ren" I Laboratory for Big Data and Decision, National University of Defense Technology College of Science, National University of Defense Technology *Department of Computer Science and Technology, Tsinghua University
Abstract
Conventional federated learning (FL. assumes a closed world with a fixed total number of clients. In contrast, new clients continuously join the FI. process in real-world scenarios, introducing new knowledge. This raises two critical demands: detecting new knowledge, i.e., knowledge discovery, and integrating it into the global model, i.e., knowledge adaptation. Existing research focuses on coarse- grained knowledge discovery, and often sacrifices source domain performance and adaptation efficiency. To this end, we propose a fine- ainegrained federated domain adaptation approach in open set (Gains). Gains splits the model into encoder and a classifier, empirically revealing features extracted by the encoder are sensitive domain shifts while classifier parameters are sensitive class increments. Based on this, we develop fine-grained knowledge discovery and contribution-driven aggregation techniques to identify and incorporate new knowledge. Additionally, an anti- forgettngg mechanism is designed to preserve source domain performance, ensuring balanced adaptation. Experimental results on multi-domain datasets across three typical data-shift scenarios demonstrate that Gains significantly outperforms other baselines in performance for both source-domain and larget-domain clients. Code is available at: https//gitubb.com/Zorrg httpghhbbb...mo/ooooooiooiiiaiia Zhengyi/Gains.
Introduction
As typical distributed intelligent model training paradigm, federated learning (FL)
33
36
67
has garnered significant attention from researchers in recent years [5] 32 39 35
45
12
66
59
19
48]. Conventional FI. is often studied in a setup with a fixed number of clients 33 its applicability in a more realistic scenario when new clients, i.e., target domain, are allowed to join the learning process. To scale FL effectively in such scenarios, we have to deal with heterogeneous or evolving client data distributions, e.g., IoT networks, cross-device applications. This prompts researchers to prioritize the study of two critical techniques in the field: (i) assessing whether the new client contributes previously unseen knowledge (37), referred to as knowledge discovery; (ii) devising strategies to integrate it into the global model for improving generalization under the updated domain setting [18 7) which call knowledge adaptation.
3D
which limits
Though the practical demands and corresponding techniques are well specified, bottlenecks still remain in achieving the deployment purpose (Fig. [T.. Regarding knowledge discovery, is rarely investigated in FL., and existing strategies hardly process complicated scenarios. Take example; it facilitates the discovery of new classes, i.e., class
Existing challenges:
the latest work, FOSDA 37
Equal Contribution (zhongzhengyi20ee mudd.cdu.ccm jiangwenzheng@nult..e 2f Corresponding Author (wangji eud...du.cn.e
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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increment. in the presence of an open set. However, when faced with domain increment, which is more universal in life. FOSDA encounters the failure of dealing with new domain knowledge. Hence, more sine-grained knowledge discovery approach is required to discriminate class increment or domain increment. As for knowledge adaptation, current methods primarily attempt to improve the performance of the newly trained model on target domains. Technically, they often suffer from performance degradation on the source domain while easily overlooking the efficiency of knowledge adaptation [8]. Consequently, we need to introduce a mechanism for rapid and balanced knowledge adaptation, securing seamless integration of new knowledge while consolidating original capabilities.
Proposed solution: To this end, this paper presents a fine- Grained federated domain adaptation method in open set (Gains), which aims at achieving fine- grained knowledge discovery and rapid adaptation without sacrificing the perfor- mance the source domain. Specifically, we discover new knowledge and identify its type (domain increment or class incre- ment) from the changes in model parame- ters and extracted features. Then, the feder- ated aggregation process is optimized with the guidance of the quantified parameter and feature's contributions to the target domain, thereby accelerating the integration of new knowledge into the global model. Meanwhile, an anti-forgetting mechanism (AFM) is designed and used in the training process of the source-domain clients to circumvent source source-domain performance degradation, achieving a balance between the target and source domains. To sum up, this work's contribution is three-fold:
FL system
Upiced Distrbate
Adapttation
Server Agueattion
Clenk1
Clent
Navu
New
Global
New Doraai
New Class
Avoid Performence Oegrodición
Domais Fine-grained Knowladge Discovery
Doraie
Source Clenns
Rapid/ Balance Knowledge Adaptation
Figure I: Challenge discription.
Adaptation pipeline. We propose novel training pipeline within FL that supports fine-grained discovery and discrimination of new knowledge from client updates and efficient integration of incremental knowledge into the global model.
Practical solution. We present efficient federated optimization method that enables contribution evaluation of diverse components during knowledge adaptation and suppresses performance decline the source domain.
Experimental validation. We conduct extensive experiments on typical multi-domain datasets under various levels of knowledge shifts. Empirically, Gains achieves superior performance on both target and source domain clients over other state-of-the-art methods.
2 Related work
Domain adaptation. Domain adaptation (DA) can be categorized based on the labeling status of the target domain into unsupervised DA, suneviuper DA, and supervised DA [47]. They can also be divided based on whether the source domain data is involved into source-dependent DA and source-free DA 24 The distribution shift a lasting challenge [22. and typical DA approaches include adversarial learning-base methods and alignment based methods. Adversarial learning- based methods introduce adversarial networks (such as GANs) to align the feature distributions between the source and target domains 88 20 64
13 49 Alignment-based methods achieve alignment between the source and target domains by minimizing the differences feature or data distributions [23 10
54 (9] Common alignment metrics include KI. divergence [34], Maximum Mean Discrepancy (MDD (25). and Wasserstein distance [34]. In addition, other methods such as self-training [3 46 and meta-learning [2] 44 50 51 have also been applied in DA. Unlike most DA work that considers adapting the source model to the new domain and continual learning that considers catastrophic forgetting (29 55 56 68 65 63 we focus solving the problem of better adaptation to the new domain while avoiding performance degradation in the source domain.
Federated domain adaptation. The FDA methods primarily include domain alignment-based data-based, learning-based, and aggregation optimization-
approaches (31]. Among them, domain alignment consists of feature [53 7 and gradient alignment [58] 17 Besides, mixed training
approaches are also adopted. For instance, [60] uploads prototypes from different domains to the
server for fine-tuning. In data adjustment methods, data augmentation 44 3 22 and data generation

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14 27 57] are commonly used. Chen et al. B generated data with other domain styles on single client through style transfer between clients. In carming-based approaches. common strategies include adding alignment regularization terms [6.. representation learning [ 61, and transfer learning 2 For example, Craighero et al. 7 proposed SemiFDA, which trains local feature extractors on clients to align them with the server. In aggregation optimization-bu based methods, the primary focus is on optimizing aggregation weights [62], gradients [43], and aggregation strategies 41 For example, FedHEAL [5] removes some less important updates from client models and determines aggregation weights based on the distance between the global model and each local model. AutoFedGP [18] calculates the distance between the source and target domains to derive new automatic weighting scheme. The aforementioned FDA works are primarily based on the assumption of closed environment. Currently, there is limited research on FDA in open environments. Even exists, e.g., FOSDA [37], it is only applicable to class-incremental scenarios and does not consider the impact the source domain.
3 Methodology
This section starts with motivation example and outlines the pipeline of our developed feder- ated domain adaptation scheme, Gains. Subsequently, we elaborate on fine-grained knowledge discrimination and contribution-driven knowledge adaptation two key components in Gains.
Motivation. Without loss of generality, we use the LeNet model and MNIST dataset as an example, considering scenario where the first three new clients' data is from the source domain, the fourth introduces 1-4 new classes, and the fifth brings new domain data (details are shown in Appendix. A When new clients participate in training. the variations of the encoder, classifier, and extracted feature are measured by the distance (e.g., Euclidean distance) before and after training in the target domain. From Fig. 2 we have the following findings: (i) the variation of the encoder (i.e., f f does not show a clear fluctuation trend no matter in class or domain incremental scenarios; (ii) the changes in the classifier parameters (i.e., Difse) are more pronounced in the daas-inncemmena. scenario: (iii) while both new classes and domain will bring obvious changes to the feature values (i.e., Dif f²), it is more significant in the domain-incremental scenario. Therefore, it is reasonable to consider combined evaluation of D and Diff to determine whether the new client introduces new knowledge and whether such knowledge class- or domain-related.
5.30
0.30
3000
(oer clacios
0.20
0.15
2000
6.10
150
500
Erooder
New Gleet
Clazalerr
New carli
New clied
Figure 2: Differences in the encoder (left), classifier (middle), and extracted feature values (right) when the new client carries different types of knowledge.
Framework. Inspired by the above empirical discoveries, we propose fine-grained federated domain adaptation framework in open set, Gains (shown in Fig. 3 Specifically, it consists of two main components: knowledge discovery and knowledge adaptation. In the knowledge discovery stage, the target domain performs local training based on the source model and uploads the updated version back to the server. Then, the server uses public dataset calculate the variations of Di f and Diff determining whether the new client introduces new knowledge and further discriminating its type in fine grains. Based on the results of this differentiation, in the knowledge adaptation stage, the contribution of different model components in each source model is calculated. After that, the server executes contribution-driven aggregation to accelerate the speed of target domain adaptation. Considering it may lead to overemphasis on the target domain, potentially resulting in the performance degradation of the source domain, an anti-forgetting mechanism is included in the local training of the source client to balance the knowledge of the target and source domains.
3

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Knowledge Discovery Global model
New client training
Fine-grained discrimination
Server
Datributee
Uprod
Chunderchi
model
mode
Encoder feature Classifier
New data
Source Intrder C Coeeter
Sourse
Turast CooderrCoodee
Torast
Nacoddrr
Knowledge Adaptation
Frender
Domaan shift (CX (CX 10/1 (CC.0C0) Server
afacune
Class shift sifooeey
Aggreadier
++ft
CX XOC
XOL
Balanced local training
Contribution aggregation
Contribution calculation
Global Aggregated Model
Source Domain Model
Target Damain Model
Workflow
Figure 3: Gains consists of two phases: knowledge discovery (upper) and knowledge adaptation (lower). The former works identifying the type of new knowledge, while the latter attempts to achieve rapid integration new knowledge and strike a balance between new and old knowledge.
Notations. We denote the N client source domain dataset by D = (25 /
P J.n
| J. The server's public data is DP = {(x²)1))) y))). The target domain dataset is DJ = (xr, Wyy j-0
The original pre- pre-trained source domain model is W comprising an encoder E and a classifier C'S Similarly, we write the target domain trained model as WT, which includes ET and C the total federated iteration and R is the local training epoch.
3.1 Fine-grained knowledge discrimination
When new client enters, the server first distributes original source global model WS to the target domain for local training Q times. The optimization process is as follows:
W (q + 1) W (q) 1/V (q), D²). ). 0,.... ., .Q.,
where 7 is learning rate, L(W" (4), D²) is the loss the q-th local training epoch, and the final target model is W = (T((}) Once the target client finished the local training, WT will be uploaded to the server. Then, DP' is input into ES and ET to obtain the feature values FS
ES (x*) and FT = (x*), respectively. According to the finding (iii) in the motivation, we first judge whether the new client brings new knowledge based on the variation of DiffE f. If Di o is big enough, we believe that the data distribution from the target domain is different from that of the source domain, which means new knowledge is coming. Furthermore, according finding (ii), we can determine whether this new knowledge is related to new class by calculating Diff Specifically, we use the Manhattan distance and the Euclidean distance to calculate Di and Di f respectively.
We set Ty and To as thresholds for discovering new knowledge and determining the type of new knowledge, respectively. When Di Tr. conclude that the target domain has introduced new knowledge. If Dif f > Tc simultaneously. it indicates that the new knowledge corresponds to new class; otherwise, considered new domain knowledge.
3.2
Contribution-driven knowledge adaptation
In the knowledge adaptation phase, two key issues need to be addressed: first, the rapid knowledge adaptation to the target domain; and second, the balance between new and old knowledge. To achieve the former one, propose the contribution-drive aggregation strategy, which means assigning greater weights to clients with higher contributions. As for the latter balance problem, an anti-forgetting mechanism is presented.
Domain-increment contriuutionddivee aggregation. In this paper, we believe that the more similar the source domain client is to the target domain, the more beneficial it is for the fusion of new

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knowledge. Then the greater the contribution is. In the and the classifier adopt the feature-based and warameter-basee contribution calculation methods, respectively. In the feature-based calculation, the encoder contribution CD (1) of the n-th source client to the target domain during the i-th iteration is calculated as follows:
scenario, the encoder
D
CD (1- (1- E M(L+DiSSE
(2)
D
N
DE
n=
where DifSE (i) is measured by the distance between (1) = (x)) and F (1) (0)
E (i) is the encoder uploaded by the target domain in i-th iteration, while E (i) is from the n-th
source client. Similarly, in parameter-basee aggregation, the classifier contribution of n-th source
client CD (i) calculated follows:
N
DA
(D) DiSfE(()) Ex (Y/2 (((++D)ff())
2n
(i)
|D
IDA
where DifSR (1) is measured by the distance between C (1) and C Ultimately, we obtain
the contribution lists (CDf (i), (D), (i).... (i)) and (CDY (i), CDL (1).
(i) of the source encoder and source classifier during the i-th iteration in the domain inniuinnnnremettall scenario. The aggregation processes follows:
D
E(i) = m= (D.())E)0))
N
x E (1),
(4)
I Σ
[D
D
0(1) = Σ m=1 CD (D [ +
C² (1).
(5)
Σn=
D
The aforementioned aggregation process facilitate the rapid adaptation of knowledge by dynamically improving the contribution-baser weights in each iteration.
innremnnlrmettlll contribution-driven aggregation. Similarly, in the ctassinnrremenal scenario, for the encoder aggregation process, adopt the same Stature-based method calculate the contri- bution. The Encoder contribution of the n-th source client in i-th iteration is CC (1). Then, the contri- bution list of the encoder in class-incremental scenarios is obtained {CCP (i), CCf (i), ,CC% (1)). The aggregation process is as follows:
D
E(i) >." (I) +
X E (t).
(6)
DD
DE
The aggregation of the classifier employs a channel-wise supplementation method. First, the classifiers from the source domain are aggregated based on the amount of data from each client, resulting in (i)
D
DSS (t). Suppose there are KS classes in the source domain and TT new classes added in the target domain. Consequently, the classifier has KS + KT channels. The parameters of the classifier aggregated from the source domain are denoted (i) = [Channels; , Channels ks. Channel' K$ Chanmels K +KT]. and the parameters of the target domain classifier are denoted [Chamnell ... Channelf Channelf K* Channell k In the final aggregated classifier, the channels corresponding to the source domain classes directly adopt the parameters from C (i), while the channels for the target domain classes retain the parameters from C² (i). That is,
CT
C(i) Channeti ... Channet
Channel +1 Channelfs4+0
(7)
SouraeDomain
Domain
theoretical convergence analysis of Gains is provided in the Appendix.
Anti-forgetting mechanism. The above aggregation may lead to a bias towards the target domain knowledge in the aggregated model, potentially causing a decline performance on the source domain tasks. To mitigate this, we introduce anti-forgetting mechanism for the source domain clients during each round of local training. Specifically, we control the distance between the current model W (i, r) and the memory model W (0, 0) in the local training to prevent the local model
5

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from excessively deviating from the historical model. Here, W (0. 0) represents the local model in the source domain before the new client enters. (i, is the n-th client model during the i-th global iteration and r-th local training epoch. The local loss function for the source clients is defined as follows:
K KT
CO (1, r), D.)
Vie log( + X (ME W (0. (0.00/
(8)
D
where À is a balance coefficient. Through the above training process, we can achieve rapid federated domain adaptation while avoiding forgetting the source domain knowledge, thereby maintaining a balance between new and old knowledge.
3.3 Algorithm
As shown in Alg. 1 when a new client joins, the server distributes the source global model W the target domain for local training, getting W Subsequently, the server decomposes W and W into an encoder and classifier and derives the feature using the public dataset. Based on the differences in the feature extracted by E and ET, as well as the parameter differences between C and CT,, the algorithm discriminates the type of new knowledge and confirms its type. Then, we calculate the contributions of the source clients to the target client in both encoders and classifiers. According to knowledge types and model components, specific aggregation strategies are used to accelerate knowledge adaptation. Furthermore, to prevent the aggregation process from overly favouring the target client, the anti-forgetting mechanism is incorporated into the local update process of the source clients. After all clients complete local training, they upload their models to the server for aggregation based on their contributions. This process repeats until convergence. If no new knowledge is detected at the outset, the original model is deployed directly the newly joined clients for inference without any further training.
4 Experimental verification
This section first explores the threshold for knowledge discovery and validates Gains under three data shift scenarios. Then, to verify its scalability, we conduct experiments in more target domains and a sequential FDA scenario. Finally, ablation studies reveal the necessity of the AFM component.
4.1 Experiment setting
Our experiments are conducted on a single NVIDIA RTX 4090 GPU. We construct a federated learning framework that includes one server and 50 clients for validation. Following (7], we evaluate Gains in three scenarios of target data shifts: mild, medium, and strong shifts. Specifically, under the mild shift scenario, clients in both the source and target domains are drawn from the same sub-dataset but contain different classes. Under the medium shift scenario, all clients in the source domain are from one sub-dataset, while clients in the target domain are from another sub-dataset. Under the strong shift scenario, different clients in the source domain contain different sub-datasets, and clients in the target domain are from other sub-datasets. The main results are shown in Table
Dataset. The datasets include the DigitFive (i.e., DF) for the digit classification and the Amazon Review (i.e., AR) for the product review. DF comprises five sub-datasets: MNIST, MNIST-M, SVHN, USPS, and SynthDigits. Each one contains 10 classes of digits from 0 to 9. The AR dataset records user reviews of products on the Amazon website and includes four subdatasets: Books, DVDs, Electronics, and Kitchen housewares. Each sub-dataset contains two classes
Baselines. We include two categories of basclines. The first is to address the domain adaptation problem, including FOSDA [37]. SemiFDA 77), AutoFedGP [8] and FedHEAL (5). The second focuses the heterogeneous problem, including FedAVG [3 FedProx (26) and FedProto [4].
Evaluations. (i) the accuracy of the target client (T-Ace); (ii) the average accuracy of the source clients (S-Acc); (iii) the global accuracy (G-Ace).
4.2
New knowledge discovery
The key to discovering new knowledge lies in setting an appropriate threshold, i.e., Tp and Te. In Fig. we observe that when new clients introduce unseen class domain knowledge, the fifff

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Algorithm 1: Gains
Input: Number of source clients N; original source global model W and client model
(Wi (0, 0), W (0, 0),-. W (0, 0)); number of iteration 7; number of local training R: public
data D ({))
Output: Global model
Distribute original source model W to target client
W +
Target client performs local updating based on W
Target client Uploads W to server
//Knowledge Discovery
Split W into encoder E and classifier C split the W into E" and CT
gs t E (x"), H8T E [x"((")) (x²)
Calculating Diff and Diff"
if Diff >Tę then
Target client brings new knowledge if (Dfff>Il' >I' then
11
L Class Increment=True
12
else
Domain Increment=True
14
I/Knowledge Adaptation for iteration i = 0..... do
15
if Domain dicrement=True then
17
Calculating encoder contributions (CDF, CD.
,CD
based on Eq.
Calculating classifier contributions {CDf. CD CD based on Eq.
19
Aggregating all clients' parameters using Eq and Eq.
if Class Increment=Thue then Calculating encoder contributions {CCF, CC CCN
21
based on Eq.
22
Aggregating all clients' parameters using Eq. and Eq.
23
Server distributes the aggregated model all clients for client n = 1, do
24
25
Locally update model R rounds using Eq. 8
26
Upload W (i, .t') to the server
Target client locally update model R rounds and upload to the server
28
else
Apply the original model newly joined clients for inference tasks without training
increases significantly, with all values exceeding 1000. Furthermore, in the case of class increment, the Diff f undergoes substantial changes. Even when only new class is added to the target client, the parameter change of the classifier is still greater than 0.25, which is significantly higher than that of domain increment clients. Therefore, for the DigitFive dataset, consider setting the threshold Tp to 1000 and the threshold TV to 0.25. For the Amazon Review dataset, given the limited number of classes, only conduct validation in the domain increment scenario. Taking DVDs the source domain data and Kitchen Hardware as the target domain data as an example, when the new client does introduce
data, the Dif f fluctuates between 50 and 150. However, when the new nodes bring in new domain data, the change value increases to 534.76. Therefore, we consider setting the threshold TF for the Amazon Review dataset 400.
4.3 Knowledge adaptation
Mild data shift. Under the mild data shift scenario, we experiment using the MNIST data from the DigitFive dataset, assuming that the target domain contains data labeled as [1, 5), while the source domain consists of [0, 2, 3, 4, 6, 8, 9). Gainy achieves 99.34% new client accuracy (T-Acc) while maintaining 93.21% source client accuracy (S-Acc) and 94.44% global accuracy (G- Acc). This demonstrates Gains's 's effectiveness in class-incremental scenarios. The feature-based contribution calculation and channel- wise classifier aggregation allow seamless integration of new

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Table 1: Main results. The bold font represents the optimal result.
Federated Domain Adaptation
Heter-FL
Scenario
Metric
SemiFDA [ICDM224]
AutoFedGP
FedHEAL ICVPR
FedAVG IAISTATS' 17]
FedProx
Ours
[ICLR224]
[MLSys
[AAAI22]
DigitFive
F-Ace
99.34
0.00
0.00
68.11
22.60
55.73
72.35
77.61
S-Ace
93.21
12.72
13.53
0.00
99.29
0.36
99.53
0.16
Mild
G-Ace
94.44
10.18
10.83
13.62
83.95
11.44
94.09
62.12
7-Ace
7.91
93.68
94,88
45.66
S-Ace
90.09
19.46
19.44
6.22
88.71
76,20
86.50
33.56
Medium
G-Ace
91.65
17.82
17.14
6,93
89.70
79.12
88.18
43.23
T.Ace
98.98
31.14
96.98
85.29
S-Ace
93.18
13,60
14.21
11.60
83.32
43,90
43.32
62.23
Strong
G-Ace
94,34
13.13
17.60
11.35
86.05
52.28
$1.72
37.47
Amazon Review
T-Ace
84.60
49.55
51,.45
50.50
50.56
66.74
74.55
50.11
S-Ace
82.81
49.55
49.33
50,50
50.56
67.19
74.44
50.11
Medium
G.Acc
83.09
49.82
50.58
50.48
74.12
50.01
7-Ace
80.54
50.48
55.41
50,03
83.34
51.20
53.73
50.10
S-Ace
84,95
50.27
59.25
50.02
86.54
51.36
53.95
50.11
Strong
G-Ace
83.85
50.33
58,29
50.02
85.74
51.32
53.89
50.10
classes. Meanwhile, the anti-forgetting mechanism further ensures stable source performance by constraining parameter drift during local updates.
Medium data shift. For a more complex scenario, medium data shift, we conduct validation using DigitFive and Amazon Review datasets. As for DigitFive, the source domain data derived from SVHN, while the target domain's data is from MNIST. For Amazon Review, the corresponding data DVDs and Books, respectively. In Table IT. Gains achieves 97.91% T-Ace and 90.09% S-Ace in DigitFive, outperforming all baselines. Notably, FedHEAL achieves competitive T-Acc (93.68%) but exhibits unstable source performance (S-Acc=88.7I ().. similar phenomenon can be observed scenarios:
in the Amazon Review dataset. This validates the effect of Gains in leveraging feature gap in the encoder and parameter variation in the classifier dynamically prioritize source clients with higher contributions.
Strong data shift. In extreme cases, each client in source and target domains may come from different domains, which refer to as strong data shift. For DigitFive, we assume that the target domain client data is from MNIST, and the source domain consists of four clients, each holding MNIST-M, SVHN, USPS, and SynthDigits datasets, respectively. For the Amazon Review, the target domain is Books, and source-domain clients are from the DVDs, Electronics, and Kitchen Housewares datasets. In Table Gains achieves 98 98.98% T-Acc and 93.18% S-Acc in DigitFive, demonstrating robustness extreme heterogeneity. Similarly. Gains achieves 80.54% T-Acc, 84.95% S-Ace and 83,85% G-Acc in Amonzon Review, showing significant advantages over other methods.
Adaptation speed. The above content illustrates that the Gains method can improve learning performance in the source and target domains. To further demonstrate its advantage in domain adaptation speed, we visualize the training process of DigitFive under different methods in Fig. 4 where the vertical axis represents the global accuracy and the horizontal axis represents the number of epochs. It can be that method not only achieves the highest accuracy but also has the fastest convergence speed, enabling it to reach better results more quickly. This is because we optimize the aggregation process of the encoder and classifier based on their respective contributions, which allows for more efficient adaptation of new knowledge on the basis of the source domain model. The convergence process diagram for the Amazon Review dataset provided in the Appendix. C
Generalization verification. In Table I we only validate some cases under the mild (Mi), medium (Me), and strong (St) data shift scenarios. To further verify the generalization ability of Gains, change the source/target domain datasets and test the DF and AR datasets under above three scenarios, and the results shown in Table Here, (1,5) indicates that the target domain data labels are and 5. "SV-MT" represents the scenario where the source domain is SVHN and the target domain is MNIST under the Me data shift. MTM, BK, DD,, and KC are the abbreviations for the MNISTM, Book, DVDs, and Kitchen datasets, respectively. As shown in Table under the same multi-domain dataset, our method still maintains comparable level when the target domain is different, indicating strong generalization capabilities of Gains. Please refer to Appendix. D for more validations on the generalization.
8

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Compared with traditional federated learning, Gains Thee ACC Accuarey
Heeeaag Text Accurncy
Oupd
CuRS
CURS
FOSDA
Iuer Test
Cockipoo
30
40
326
20
40
320
40
100
Communc Spoch
Communcation tpoch
Communicatio Epech
(a) mild data shift.
(b) medium data shift.
(c) strong data shift.
Figure Training process DigitFive under different data shift scenarios.
Table 2: Generalization verification.
Sequential FDA. In the previous experiments, we primarily focus on the scenario where only single new client joins in FL. In this part, we take DigitFive as an example to verify the performance when contin- uous new clients arrival (i.e,, sequential FDA). In the inssemnncreettal scenario, we assume that the source domain classes are {0.1,2.3), and subsequently, three clients carrying [4.5], (6,7), and (8.9) join the FL process. In the domain-incremente source domain the SVHN, and the target domains include MNIST, MNIST-M. and SynthDigits, respec- tively. Table 3 shows the results after incorporating different target domain data into the training process. can be observed that Gains still exhibits strong robustness in sequential FDA.
[1.5]
6.9
[0,1.5)
99.34
94.42
99.39
Mi-DF
SA
93.21
96.03
87.16
GA
94.44
95.71
89. 99.64
SV-MT
MT-MTM
SYN-MTM
97.91
94.46
90.49
Mc-DF
SA
90.09
99.56
98.57
GA
91.65
98.54
96.95
MTM
98.98
91.67
93.94
scenario, the
St-DF
SA
93.18
97.58
96.20
GA
94.34
96.40
95.75
DD-BK
BK-DD
ET-KC
84.60
82.01
86.39
Mc-AR
SA
82.81
86.85
89.93
GA
83.09
85.88
89.26
DD
KC
80.54
78.22
85,38
St-AR
SA
84.95
88.90
87.73
83.85
86.23
17
Ablation study. This part examine the role of the Anti-forgetting Mechanism in Gains using DigitFive dataset. shown in Table the absence of the AFM indeed causes significant performance degradation for the source clients across all scenarios, illuminat- ing the effectiveness of this component. Moreover, the performance drop is most pronounced the class- incremental scenario (i.e., mild data shift). This is consistent with our observations in the motivation, the changes to the model parameters nificant during class increment. Without AFM, in the mild data shift scenario, the client model deviates most severely from its original parameters, resulting in the greatest performance decline.
Table 3: The performance of sequential FDA.
[4.5]
(6.7)
(8,9)
TA
99.88
91.35
96.89
Mi
SA
93.53
99,43
99.35
GA
96.82
98.08
99.00
MNIST
MNISTM
SYN
TA
95.27
83.53
93.53
Me
SA
87.91
90.05
89.66
most sig-
GA
89.38
88.96
90.21
Table Ablation study of AFM.
Mild
Medium
Strong
AFM w/o AFM
99.05
90.09 84.35
94.77
9.24
92.46
4.4 Computing complexity analysis.
mainly increases the computational load during the server-side contribution calculation. Its complexity O(N P. ..dd d). where N' is the number of source domain clients, P is the size the public dataset, and d is the number of model parameters. Inevitably, extra computational costs occur during the above process. However, by calculating the weights based on contribution, more efficient aggregation be achieved, thereby significantly redueing the number of federated iterations and reducing the overall training time. Taking the DigitFive dataset in the mild shift scenario as an example, the consumed computing resources and the number of iterations as shown in Table 5
4.5 Sensitivity analysis of the thresholds
Although the thresholds are manually set, the model exhibits strong robustness to threshold variations. As can be seen from Figure 2, the changes in Diff f and Dif are very significant, which means

---

that the thresholds can take values over wide range, with Diff ranging from 700 to 3400 and DiffC from 0.05 0.27. We also conduct experiment tests on various thresholds using the mild shift scenario in the DigitFive dataset as example. Assuming the source domain data is MNIST-M and the target domain data MNIST, with TF E 800, 1000, 1200 and Tc E 0.20, 0.25, 0.27. The experimental results obtained are shown in Table and Table...rrom the above two tables, it can be seen that the model performance remains stable when parameters fluctuate within reasonable ranges (performance variation 1%).
Conclusion and discussion
Conclusion. This paper presents a novel fine- aeee-rraned fed- erated domain adaptation framework in open set (Gains) that addresses the challenges of fine- aue-grained knowledge discovery and rapid and balanced knowledge adaptation.
Table 5: Convergence Comparison of
Different Methods.
Method Converge Round
Time
By splitting the model into an encoder and a classifier, Gains effectively identifies the type new knowledge based on the variations in extracted features and model param- eters, enabling more precise knowledge adaptation. The proposed contribution-driven aggregation strategy accel- erates the integration of new knowledge into the global model, while the anti-forgetting mechanism ensures the preservation of source domain performance. Extensive experiments on multiple datasets demonstrate that Gains can achieve balanced adaptation and rapid convergence under various data shift scenarios.
Gains
5
807.45
FedHEAL
40
1368.4
FedAVG
20
1977.20
FedProx
40
6880.80
FedProto
32
9519.68
Table 6: Accuracy Results for Different Tp Values.
TF
T-Acc
S-Acc
G-Acc
800
99.62
92.01
93.15
1000
99.34
93.21
94.44
1200
99.24
93.06
93.91
Discussion. This paper proposes a fine-grained do- main adaptation framework in FL. Although the pipeline achieves satisfactory results, some limitations still exist. First, in the knowledge discovery phase, it still relies on manually set thresholds, and achieving automatic knowl- edge discovery remains a significant challenge. Second, in the knowledge identification phase, we consider do- main increment and class increment. However, for more complex scenarios, such as task increment or scenarios involving both class increment and domain increment, further exploration is needed. In addition, it's worth noting Gains significantly different from traditional federated continual learning. First, settings are different. FCL primarily focuses scenarios where existing clients encounter new data, while FDA focuses on cases where new clients join and bring unseen data. Second, the objectives are different. FCL primarily addresses the catastrophic forgetting caused by new data in existing clients. In contrast, Gains focuses on rapidly adapting to the new domain while preventing performance degradation of the source domain clients, achieving efficient and balanced domain adaptation.
Table 7: Accuracy values for different To settings.
Tc
T-Acc
S-Acc
G-Acc
0.20
99.75
92.34
93.29
0.25
99.34
93.21
94.44
0.27
99.86
92.71
93.01
Acknowledgment. This work is supported by National Natural Science Foundation of China under Grant 62273352 and 72501290.
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A Motivation experiment settings
In the motivation experiments, treat the last layer of LeNet as the classifier and the remaining layers as the encoder. In the class-incremental scenario, the source domain data contains classes (3, 6, 7, 8, 9). After source-domain training is completed, the first three are from the source domain, the fourth contains new classes, and the fifth is from a new domain. Under the class-incremental setting, consider the target client data classes be (5), (1, 5), [0, 1, 5), and (0, 1, 2, 5), corresponding to the addition of 1, 2, 3, and classes, respectively. In the domain-incremente scenario, the target domain the SVHN dataset.
sequentially introduce new clients, where
B Experimental details
During the experiment, the model used for the DigitFive deattFe is a CNN model, while the model used for the Amazon Review dataset an LSTM. The corresponding hyperparameters for the two datasets are follows:
Table 8: Hyperparameter setting.
Learning Rate
Optimizer
Batch Size
DigitFive Amazon Review
0.005
SGD
128
0.5
SGD
64
The public dataset used by the server for new knowledge discovery is collected from open sources and typically includes various types of globally known data. Under the scenarios of mild data shift and medium data shift, after determining the data classes contained the source domain clients, we split the data using the Dirichlet distribution with hyperparameter of 0.1.
C Adaptation speed of Amazon Review
presents the training process of Gains and other baselines on the Amazon Review dataset under the medium data shift and strong data shift scenarios. As shown in the figure, Gains achieves convergence in global performance with only small number of epochs. This further indicates that Gainy can accelerate the target domain adaptation process and more rapidly integrate target domain knowledge into the global model.
Fig. 5
0.85
Average Accuracy
0.80
0.80
0.75
0.70
FOSOA
FOSDA
0.70
SeminuA
0.65
AutoFeaGP
0.65
AutofedGP
FedHEAL
0.60
FedAVG
0.60
0.55
FedFrox
FadProto
0.55
Fed
FeaProx
0.50
20
40
60
100
20
40
80
100
Communication Epoch
Communication Epoch
(a) Amazon Review, medium data shift.
(b) Amazon Review, strong data shift.
Figure 5: Training process of Amazon Review under different data shift scenarios.
hhtps://ai..uu.cdu/MMS..
https:/mijjiamooo wwt.wn/.ww...ttt.o.eoe wwt.tb.iio/mmaazo/nndaaaooeoeedo
22

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D More validations on generalization
In the main manuscript, validated the effectiveness of Gains part of the cases under three data shift scenarios, In this part, we will verify all the cases under medium data shift and strong data shift, further supporting the generalization capability of Gains. Table 9 and Table show the results under different data shift scenarios for the DigitFive dataset, while Table and for the Amazon Review dataset under similar conditions. It can be observed that for the DigitFive dataset, the T-Acc, S-Ace, and G-Acc all exceed 90% across all scenarios. Similarly, for the Amazon Review dataset, the T-Ace, S-Acc, and G-Ace are mostly above 80%.
and Table 12 present the results
Table 9: DigitFive, medium data shift.
Source domain
Target domain
T-Acc
S-Ace
G-Acc
MNIST-M
USPS
93.39
96.48
95.86
MNIST
USPS
92.10
99.50
98.02
SynthDigits
USPS
98.55
98.30
98.35
SVHN
USPS
90.16
90.78
90.65
USPS
MNIST-M
93.42
99.25
98.08
MNIST
MNIST-M
94.46
99.56
98.54
SynthDigits
MNIST-M
90.49
98.57
96.95
SVHN
MNIST-M
90.97
92.38
91.30
USPS
MNIST
98.99
99,41
99.33
MNIST-M
MNIST
99.07
97.89
98.12
SynthDigits
MNIST
98.89
98.59
98.65
SVHN
MNIST
97.91
90.09
91.65
USPS
SynthDigits
94.16
99.30
98.27
MNIST-M
SynthDigits
92.76
97.38
96.45
MNIST
SynthDigits
92.23
99.53
98.07
SVHN
SynthDigits
92.69
91.10
91.42
USPS
SVHN
92.19
99.20
95.79
MNIST-M
SVHN
92.52
96.94
94.06
MNIST
SVHN
93.25
99.30
95.68
SynthDigits
SVHN
91.69
98.79
97.37
Table 10: Amazon Review, medium data shift.
Source domain
Target domain
T-Ace
S-Ace
G-Acc
Books
Kitchen
82.22
86.43
85.59
DVDs
Kitchen
83.16
86.36
85.72
Electronics
Kitchen
86.59
89.93
89.26
Kitchen
Books
77.54
88.97
86.68
DVDs
Books
80.13
83.83
83.09
Electronics
Books
76.37
88.36
85.97
Kitchen
DVDs
77.36
89.94
87.42
Books
DVDs
82.01
86.85
85.88
Electronics
DVDs
77.50
88.65
86.42
Kitchen
Electronics
85.55
89.67
88.85
Books
Electronics
77.66
87.95
85.89
DVDs
Electronics
82.75
87.40
86.47
Table 11: DigitFive, strong data shift.
Source domain
Target domain
T-Ace
S-Ace
G-Ace
MNIST-M. MNIST, SynthDigits, SVHN USPS, MNIST, SynthDigits, SVHN USPS. MNIST-M, SynthDigits. SVHN USPS, MNIST-M, MNIST,SVHN SVHN USPS, MNIST-M, MNIST, SynthDigits
USPS
98.49
95.56
96.14
MNIST-M
93.94
96.20
95.75
MNIST
98.98
93.18
94.34
SynthDigits
97.02
95.96
96.17
SVHN
91.67
97.58
96.40
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Table 12: Amazon Review, strong data shift.
Source domain
Target domain
T-Ace
S-Ace
G-Acc
Books, DVDs. Electronics
Kitchen
85.38
87.73
87.14
Kitchen, DVDs, Electronics
Books
80.54
84.95
83.85
Kitchen, Books, Electronics
DVDs
78.22
88.90
86.23
Kitchen, Books, DVDs
Electronics
86.32
85.61
85.79
E Broader impact
This paper is the first propose fine-grained knowledge discovery and integration pipeline in the FDA. It can significantly enhance the autonomous evolution capabilities of distributed nodes in open environments without human intervention. Additionally, have open-soureed our code for reference in future work.
Theoretical analysis
In this subsection, will analyze the convergence of Gains using domain- example. The following assumptions are made:
Assumption (Smoothness and Strong Convexity). The local loss function convex and M-smooth.
Then, we have:
M-smoothness: YW 1), (i,
L(W (i,r 1)) ((W) - (VL(WS W. ((, (1,r) (
Assumption 2 (Smoothness and Strong Convexity). As the number of iterations increases, the contributions of each source domain client the target domain gradually become stable.
The other assumptions are the same as those in Reference [28]. We first analyze the convergence of the Encoder. During each round of global update, the global parameters are:
N
W = - CD (1) ( R)) B()VL (W)
Under the smoothness assumption, the local loss functions of the clients are convex and M-smooth, then the global loss function is also convex and M-smooth, yielding the following result:
M
L(W(i + 1)) L(W()) (VEWO))
w(i) < |W(i)) W(i + 1)
N VL (1 R)) + 2 (M Ri)) = =-NZ<(W()) where
Let W(1) = -1
Σ
E
A=/
|
3(1) 1D_ +> [D
we can get:
C(W(i+ + 1)) L(W()) + +7 vL((()) < Mn² [VC(()))
For simplicity,
L(W(i 1)) - L(V()) < Mr²
IVCOW(N -
From the above equation, it can be derived that to ensure the total loss value decreases with each Mn"
iteration, 17 must be satisfied. Therefore, after times of iterations, we get:
IVLWON ((W(O)) L(W())
My -
2

---

Since L(W(T) > O, the following conclusion is obtained:
VCOOO) - 22()(0))
I (M 27)
Then when / - 00.
- (C((())) =0 O. 1-300
lim T
This indicates that as the number of iterations increases, the global gradient norm tends towards zero, thereby ensuring the convergence of the algorithm. The convergence analysis of the Classifier is similar that the Encoder and will not reiterated here.
25


Reviews:
[{"review_id": "5mJU8widXA", "reviewer": "Reviewer_va2g", "summary": "This paper introduces a novel fine-grained federated domain adaptation framework in open set, named Gains, which aims to tackle the critical challenges of fine-grained knowledge discovery and rapid, balanced knowledge adaptation in federated learning. Specifically, Gains develops fine-grained knowledge discovery techniques to identify whether the new client introduces new knowledge and further discriminate its type (domain increment or class increment). Based on this, the model employs a contribution-driven aggregation strategy to prioritize source clients with higher contributions during the knowledge adaptation phase, accelerating the integration of new knowledge into the global model. Additionally, an anti-forgetting mechanism is incorporated to prevent performance degradation on the source domain, ensuring a balanced adaptation between the target and source domains. Extensive experiments conducted on multi-domain datasets across various data shift scenarios demonstrate that Gains significantly outperforms other methods in terms of performance for both source-domain and target-domain clients.", "questions": "-In Figure 2, it seems that the Encoder has the greatest Diff change in the new class. Why is it said that “the variation of the encoder does not show a clear fluctuation trend no matter what...”?\n-In line 22, does \"new clients, i.e., target domain\" refer to new clients in the target domain or new clients from the target domain?", "limitations": "-Equations (2) and (3) are somewhat perplexing and require additional descriptions of the formulas.\n-According to the paper's description, Gains can reduce the number of federated iterations, thereby achieving rapid adaptation. However, this point is insufficiently emphasized in the method section of the paper.\n-The discussion is not thorough enough. Future improvement directions should be provided in the discussion part.\n-More experimental validations on larger-scale clients are expected.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "strengths and weaknesses\nThe writing of this paper is clear and the topic is interesting. I will summarize the merits and flaws of this work based on my understanding. In terms of merits, I think this work is advantageous in three points:\n\n(1) Innovative Research Approach. The paper proposes a fine-grained federated domain adaptation framework (Gains). It leverages the sensitivity of the encoder to domain shifts and the classifier to class increments, enabling fine-grained knowledge discovery and classification of knowledge types (domain increment or class increment). This approach is innovative and provides a new perspective for knowledge discovery and adaptation in federated learning.\n\n(2) The experiments are extensive and convincing. The paper conducts extensive experiments to verify the effectiveness of Gains. In scenarios involving class increment and domain increment, Gains significantly outperforms other methods in target domain accuracy, source domain accuracy, and global accuracy. The paper also evaluates adaptation speed, generalization ability, and sequential federated domain adaptation scenarios.\n\n(3) The code and data are open-sourced, providing a reference for future research and enabling other researchers to reproduce and build upon the work.\n\nThough there exist no major concerns, I have a few comments as well as suggestions to improve this manuscript. These include:\n\n(1) Lack of experimental validation in large-scale client scenarios. The current experiments only validated the effectiveness of Gains in a scenario with 50 clients (Section 4.1), but did not test scenarios with a larger scale of clients (e.g. 100+).It is recommended to supplement the experiments in two aspects: one is to expand the source-domain client number to 100; the other is to increase the number of clients carrying new knowledge in each batch during the sequential domain adaptation process from 1 to 10.\n\n(2) Some formulas in the paper remain perplexing. For instance, it's hard to comprehend the physical meanings of formula (2) and formula (3).I believe the expressions of these formulas need to be simplified, or an explanation should be provided for each part of them.\n\n(3) The discussion part is somewhat weak. In view of the problems existing in the current manuscript, what potential solutions could be explored in the future? To be specific, what paths for automated knowledge discovery could be investigated? And what are the scenarios of task - increment?\n\n(4) The description of the effectiveness of the Gains method is somewhat vague. The paper repeatedly claims that Gains can enable the global model to quickly achieve federated domain adaptation. According to the experimental validation results presented later on (Line 273-281), this rapid adaptation stems from a reduction in the number of federated iterations, rather than the generally assumed computational cost. Therefore, I think it is necessary to clarify this in the methods section, or otherwise, it might lead to misunderstandings.\n\n(5) Some typos can be found in the manuscript. For example, it seems that some of the separating lines in Table 2 and Table 3 have disappeared.\n\nI would further update my score if my concerns are well addressed during the rebuttal.", "was_revised": true, "final_justification": "The authors' rebuttal has thoroughly addressed all my initial concerns, especially regarding large-scale experiments, formula clarity, and discussions. I'm convinced by their detailed clarifications and additional validations, significantly strengthening the paper's merit. I think it is a good work. Hence, as promised, I am delighted to upgrade the score to 5 accordingly.", "rebuttal": "Thank you sincerely for your thoughtful comments and valuable insights on our manuscript. We have carefully addressed each of your concerns, dedicating significant effort to revise and clarify the points you raised. The following is our response:\n\n## W1. Large-scale experiments\n\nTaking the medium shift in the DigitFive dataset (source: SVHN; target: MNIST) as an example, we respectively increase the number of source domain clients from 50 to 100, and increase the number of newly joined clients each time from 1 to 10, obtaining the following experimental results:\n\n| Method | T-Acc| S-Acc| G-Acc|\n| ------ | ---- | ---- | ---- |\n| Gains-100clients-1newclient | 93.09 | 92.99 | 93.02 |\n| Gains-50clients-1newclient | 97.91 | 90.09 | 91.65 |\n| Gains-50clients-10newclient | 95.67 | 87.29 | 90.35 |\n\nFrom the above table, it can be seen that when the number of source domain and target domain clients increases, the method proposed in the paper still maintains a good performance. This part will be included in the final version.\n\n\n## W2. Explanations of formulas\n\nFormulas (2) and (3) are the foundation of our contribution-driven aggregation mechanism, designed to adaptively weigh each source client’s encoder and classifier during aggregation, depending on both their similarity to the target domain and their sample size.\n\nFormula (2) is as follows:\n\n$CD^E_n(i) = \\frac{1}{(1 + \\mathrm{Diff}^F_n(i)) \\times \\sum_{n=1}^{N} \\left( \\frac{1}{1 + \\mathrm{Diff}^F_n(i)} \\right)} \\times \\frac{\\sum_{n=1}^{N} |\\mathcal{D}^S_n|}{|\\mathcal{D}^T| + \\sum_{n=1}^{N} |\\mathcal{D}^S_n|}$,\n\nwhere $\\frac{1}{1 + Diff^F_{n}(i)}$ assigns a higher contribution to source clients whose encoder features are more similar to the target domain (i.e., with a smaller $Diff^F_n(i)$); the normalization $\\frac{1}{\\sum_{n=1}^{N} \\frac{1}{1 + Diff^F_{n}(i)} }$ ensures fairness among all clients; the sample proportion component $\\frac{\\sum_{n=1}^{N} |\\mathcal{D}^S_n|}{|\\mathcal{D}^T| + \\sum_{n=1}^{N} |\\mathcal{D}^S_n|}$ ensures that source clients with more data have an appropriate level of influence. Formula (3) follows a similar logic but focuses on the classifier parameters ($Diff^C_n(i)$). A lower distance indicates a better fit to the target domain; thus, a higher contribution weight is assigned. We apologize for the inconvenience and will include explanations in the final version.\n\n## W3. Concerns about the discussion\n### (1) Solutions to automated knowledge discovery\n\nTo automate the selection of thresholds, we can use a statistics-based approach. In the pre-experiment, we repeatedly introduce clients that carry new knowledge into the federated-learning system and, each time, record the resulting $Diff^F$ and $Diff^C$ values. After collecting many such samples, we compute the means ($\\mu_F$, $\\mu_C$) and standard deviations ($\\sigma_F$, $\\sigma_C$) of the two metrics. We then set the thresholds as:\n\n- $T_F = \\mu_F + \\alpha\\sigma_F$,  \n- $T_C = \\mu_C + \\beta\\sigma_C$,\n\nwhere $\\alpha$ and $\\beta$ are tunable coefficients that control how strict the thresholds should be.\n\n### (2) Solutions to complex increment scenarios\n\nWhen both domain shift and class shift occur simultaneously in the target domain, our method still works. We can combine Domain-incremental and Class-incremental contribution-driven aggregation strategies. The aggregation strategy is as follows:\n- **Encoder**: Contribution calculated by Eq. (2), aggregated by Eq. (4).\n- **Classifier**:\n  - Old-class channels aggregated via Eq. (3) and Eq. (5),\n  - New-class channels are directly adopted from the target domain model, as described in Line 176 of the manuscript.\n\nTo this end, we validated the scenario where both class increment and domain increment occur simultaneously. Specifically, using the DigitFive dataset medium shift as an example, the source domain client data is MNIST with classes {0,2,3,4,6,7,8,9}; the target client includes two types of data: one is MNIST classes {1,5}, and the other is SVHN dataset classes {0,2,3,4,6,7,8,9}. The experimental results obtained are as follows:\n\n| Method | T-Acc| S-Acc| G-Acc|\n|--------|------|------|------|\n| Gains-domain+class increment | 97.53 | 91.88 | 92.91 |\n| Gains-only domain increment | 97.91 | 90.09 | 91.65 |\n| Gains-only class increment | 99.34 | 93.21 | 94.44 |\n\nThese results indicate that under the mixed incremental scenario, the performance achieved by Gains is comparable to scenarios with only domain or class increments, without significant degradation. For more complex task-increment scenarios, such as extending from image classification tasks to object detection tasks, adaptive architectures can be designed by incorporating meta-learning techniques. This allows the model to autonomously identify and handle task space expansion, automatically differentiate parameters, and adapt independently, thereby ensuring continual knowledge growth and effective control of unlearning.\n\nWe will include the above experimental validation and discussion in the final version.\n\n## W4. Concerns about method effect\nIn fact, rapid adaptation is reflected not only in fewer iterations but also in shorter computation time. Inevitably, extra computational costs occur when calculating the contributions on the server. However, by calculating the weights based on contribution, more efficient aggregation can be achieved, thereby significantly reducing the number of federated iterations and reducing the overall training time. Taking the DigitFive dataset in the mild shift scenario as an example, the consumed computing resources and the number of iterations are as shown in the table below:\n\n| Method           |  Rounds to converge | Convergence time |\n| ---------------- | ------------------  | ---------------- |\n| **Gains**       |  **5**               | **807.45**                    |\n| FedHEAL          | 40                    | 1368.4                    |\n| FedAVG           | 20                    | 1977.20                   |\n| FedProx          | 40                    | 6880.80                   |\n| FedProto         | 32                    | 9519.68                   |\n\nAlthough Gains consumes more computational resources per round, it reduces the number of communication rounds by approximately 84.8%, resulting in lower overall training time. We will further emphasize this point in the paper.\n\n## W5. Missing table lines\nThank you for your correction. We will revise the formats of Table 2 and Table 3 in the final version.\n\n## Q1. Doubts about Figure 2\n\nAs shown in Figure 2, in the class-incremental scenario, when the number of new classes is 1, the change in the encoder parameters is significantly lower than in the case where the new client does not experience a shift; when the number of new classes is 4, the amount of change is comparable to that when the new client does not experience a shift. This change increases as the number of new classes increases. This indicates that the amount of change in the encoder is closely related to the number of new classes, but not obviously related to whether new class knowledge is introduced. In addition, in the domain-incremental scenario, the change in the encoder is also comparable to that without increment. Therefore, the variation of the encoder does not show a clear fluctuation trend.\n\n## Q2. Doubts about Line 22\n\n“new clients, i.e., target domain” refers to new clients from the target domain. We usually consider the data carried by newly joined clients as belonging to the target domain, and the target domain may or may not be the same as the source domain."}, {"review_id": "kNgJFAQuAf", "reviewer": "Reviewer_JgVT", "summary": "This paper proposes a fine-grained federated domain adaptation (FDA) method for open-set scenarios where new clients dynamically join federated learning. It addresses two core challenges: Identifying whether new clients introduce new classes or new domains, i.e., Knowledge discovery; and integrating new knowledge while preserving source-domain performance, i.e., Knowledge adaptation. Experiments on DigitFive and Amazon Review datasets show superior accuracy and faster convergence over baselines under mild/medium/strong data shifts.", "questions": "(1) In line 135, \"local training \\hat{I} times\", isn't the I defined in the previous text the total number of federated training rounds? Why is it the number of local training rounds here?\n\n(2) In line 130, the superscript of encoder E should be capital S.\n\n(3) Please explain how public datasets are constructed and add a discussion on alternatives to public datasets in the discussion section.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "(1) Strengths: \n\nThe paper presents a methodologically contribution to federated domain adaptation, distinguished by its novel fine-grained knowledge discovery framework that effectively discriminates between class and domain increments. \n\nThe work flows logically from empirical motivation to algorithmic design, with exceptionally thorough experimental validation across various data-shift scenarios and datasets, demonstrating SOTA results. \n\nThe inclusion of scalability tests, generalization analyses (20+ domain pairs), and ablation studies further solidifies its credibility, while public code release enhances reproducibility. Overall, I think it is well-organized and written.\n\n(2) Weaknesses: \n\nSome notations are confusing, such as the definition of \"local training \\hat{I} times\" in Line 135, which may lead readers to misunderstand the relationship between local training rounds and federated training rounds. \n\nAdditionally, the superscript of encoder E in Line 130 should be capital S. The method for constructing public datasets and alternative approaches to public datasets are not adequately explained. \n\nFurther discussion on these aspects is needed in the discussion section. The computing complexity analysis is expected, especially when more clients participate.\n\nFigure 3 is not cited in the text. In Figure 3, defined symbols such as E^S, C^S, E^T, and C^T can be used for abbreviation. There are too many font types and too many font size gradations, making it somewhat difficult to read.", "was_revised": true, "final_justification": "The authors have responded thoughtfully to my concerns. In particular, their clarification on computational complexity, which is critical in the context of federated learning, was appreciated. Based on these improvements, I have decided to increase my score.", "rebuttal": "Greatly thank the reviewer for your time and valuable feedback. We have made every effort to solve your problem and sincerely hope to meet your requirements. The responses are as follows:\n\n## W1 & Q1. Notations\n\nIn the paper, $\\hat{I}$ refers to the number of local training iterations performed on the new client after joining the federated learning. The updated model is then uploaded to the server for fine-grained identification of new knowledge types. If new knowledge is detected, global federated training is conducted for $I$ rounds. To avoid confusion, we will denote this local training epoch as $Q$ in the final version.\n\n## W2 & Q2 & Q3. Superscript error \\& Concerns about the public dataset\n\n(1) Superscript error\n\nYes, the superscript of encoder E should be capital S. Thank you for your careful reading. We will correct the superscript of Encoder E in line 130 in the final version.\n\n(2) Public dataset\n\nIn our experiments, the public data is sampled from the DigitFive and Amazon Review datasets, which are strictly disjoint from client data and only stored on the server. Generally speaking, it can be accessed from other datasets that are totally different from clients' data, such as Office-Home, thereby avoiding direct privacy leakage.\n\nTo address scenarios without public datasets, a lightweight client-encoder distillation mechanism can be adopted. Specifically, the server can collect statistical summaries (e.g., encoder outputs’ mean and covariance) from clients instead of raw data, ensuring privacy. By comparing these anonymized feature statistics, the server can approximate $Diff^F$ and $Diff^C$ for knowledge discovery.\n\n## W3. Computing complexity analysis\n\nCompared with traditional federated learning, Gains mainly increases the computational load during the server-side contribution calculation. Its complexity is 𝑂(N⋅P⋅d), where N is the number of source domain clients, P is the size of the public dataset, and d is the number of model parameters. Inevitably, extra computational costs occur during the above process. However, by calculating the weights based on contribution, more efficient aggregation can be achieved, thereby significantly reducing the number of federated iterations and reducing the overall training time. Taking the DigitFive dataset in the mild shift scenario as an example, the consumed computing resources and the number of iterations are as shown in the table below:\n\n| Method           | Rounds to converge    | Convergence time |\n| ---------------- | --------------------- | ---------------- |\n| **Gains (Ours)**     | **5**            | **807.45**           |\n| FedHEAL          | 40                    | 1368.4           |\n| FedAVG           | 20                    | 1977.20          |\n| FedProx          | 40                    | 6880.80          |\n| FedProto         | 32                    | 9519.68          |\n\nAmong the methods with comparable learning effects, although Gains consumes more computing resources in each round, it reduces the number of iterations by 84.8%, thereby reducing the overall training time. We will show this result in the experiment section.\n\n## W4. Concerns about Fig.3\nSorry, it is a mistake. Figure 3 should be cited in line 117:\n\n\"Framework. Inspired by the above empirical discoveries, we propose a fine-grained federated domain adaptation framework in open set, Gains (as shown in Fig. 3). Specifically, it consists of two main components: knowledge discovery and knowledge adaptation.\"\n\nIn the final version, we will simplify the characters in Figure 3 to make them clearer and easier to understand."}, {"review_id": "XWBWXkQK4b", "reviewer": "Reviewer_7wkT", "summary": "This work proposes a fine-grained federated domain adaptation method named Gains, designed to address the challenges of knowledge discovery and knowledge adaptation in open-set scenarios. By splitting the model into an encoder and a classifier, Gains is able to separately handle domain and class increments, and it utilizes a contribution-driven aggregation mechanism to achieve more efficient knowledge integration. Additionally, the paper introduces an anti-forgetting mechanism that prevents the degradation of source domain performance.", "questions": "1. The primary step of this work is detecting the type of increment. The manual setting of thresholds may lead to subjectivity in the results. The sensitivity of the DiffF and DiffC thresholds to model performance should be further explored. \n2. In the experiments, are class increments and domain increments tested separately? Has the paper considered the case where both class and domain increments occur simultaneously in the target client? How would the aggregation process work in such a scenario? \n3. The algorithm 1 overlooks one scenario: if the target client does not introduce new knowledge, the current framework will skip aggregating client's parameters, which is clearly thoughtless.\n4. The experimental results in Table 1 lack explanations for two crucial observations: (1) Why do FOSDA and SemiFDA achieve T-Acc of 0.00 under Mild conditions but perform better in Medium and Strong cases? (2) Why do AutoFedGP and FedAVG exhibit S-ACC close to 0.00 in Mild scenarios?\n5. The current study lacks sensitivity experiments on the balance coefficient $\\lambda$, and an in-depth analysis is required.\n6. It would be valuable to present baseline results under no domain shift conditions to more convincingly demonstrate the performance degradation phenomenon on the source domain as described in lines 37-38.\n7. Gains requires computing multiple contributions and distance metrics. Does this increase model complexity? How does its training time compare with other methods?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n1. The fine-grained knowledge discovery method (distinguishing between domain and class increments) offers a novel solution to domain adaptation problems in federated learning. Compared to existing methods, Gains provides a more detailed handling of knowledge increments in open-set environments. \n2. The anti-forgetting mechanism ensures that the integration of new knowledge does not degrade the performance of the source domain, thus maintaining stability throughout the adaptation process. \n3. The experiments cover various levels of data shifts (mild, medium, and strong), validating the effectiveness of Gains across different scenarios. \n\nWeaknesses\n\n1. The work relies on manually set thresholds (such as DiffF and DiffC). While this approach works effectively in the experiments, it remains a challenge to automatically adjust these thresholds in response to continuously changing data in practical applications. \n2. The current method seems to design separate aggregation strategies for class and domain increments. However, in real-world scenarios, class and domain increments may occur simultaneously. The paper does not fully address how to handle such mixed scenarios in practice. \n3. The experimental section does not sufficiently support the paper's arguments, and more analysis of experimental results is needed. For example, there is a lack of hyperparameter experiments on the balance coefficient $\\lambda$ in the Anti-forgetting mechanism.", "was_revised": true, "final_justification": "The authors have responded thoughtfully to my concerns. In particular, their explanation on the sensitivity analysis of important hyper-parameters and experimental results on mixed incremental scenarios, were appreciated. Based on these improvements, I have decided to increase my score.", "rebuttal": "Thank you sincerely for your valuable comments. We have made every effort to respond to each point individually, addressing your concerns to the best of our ability. We hope these revisions adequately address all the issues you raised. Your input is greatly appreciated.\n\n## Q1 & W1. Sensitivity analysis of the $Diff^F$ and $Diff^C$ thresholds\n\nAlthough the thresholds are manually set, the model exhibits strong robustness to threshold variations. As can be seen from Figure 2, the changes in $Diff^F$ and $Diff^C$ are very significant, which means that the thresholds can take values over a wide range, with $Diff^F$ ranging from 700 to 3400 and $Diff^C$ from 0.05 to 0.27. We also conduct experiment tests on various thresholds using the mild shift scenario in the DigitFive dataset as an example. Assuming the source domain data is MNIST-M and the target domain data is MNIST, with $T_F \\in {800, 1000, 1200}$ and $T_C \\in {0.20, 0.25, 0.27}$. The experimental results obtained are shown in the following table:\n\n| $Diff^F$ | T-Acc | S-Acc | G-Acc |\n|------|--------|--------|--------|\n| 800  | 99.62  | 92.01  | 93.15  |\n| 1000 | 99.34  | 93.21  | 94.44  |\n| 1200 | 99.24  | 93.06  | 93.91  |\n\n| $Diff^C$ | T-Acc | S-Acc | G-Acc |\n|-------|-------|-------|-------|\n| 0.20  | 99.75 | 92.34 | 93.29 |\n| 0.25  | 99.34 | 93.21 | 94.44 |\n| 0.27  | 99.86 | 92.71 | 93.01 |\n\nFrom the above two tables, it can be seen that the model performance remains stable when parameters fluctuate within reasonable ranges (performance variation < 1%).\n\n## Q2 & W2. Mixed incremental scenarios\n\nWhen both domain shift and class shift occur simultaneously in the target domain, we can combine Domain-incremental and Class-incremental contribution-driven aggregation strategies. The aggregation strategy is as follows:\n- **Encoder**: Contribution calculated by Eq. (2), aggregated by Eq. (4).\n- **Classifier**:\n  - Old-class channels aggregated via Eq. (3) and Eq. (5),\n  - New-class channels are directly adopted from the target domain model, as described in Line 176 of the manuscript.\n\nTo this end, we validated the scenario where both class increment and domain increment occur simultaneously. Specifically, using the DigitFive dataset medium shift as an example, the source domain client data is MNIST with classes {0,2,3,4,6,7,8,9}; the target client includes two types of data: one is MNIST classes {1,5}, and the other is SVHN dataset classes {0,2,3,4,6,7,8,9}. The experimental results obtained are as follows:\n\n| Method | T-Acc| S-Acc| G-Acc|\n|--------|------|------|------|\n| Gains-domain+class increment | 97.53 | 91.88 | 92.91 |\n| Gains-only domain increment | 97.91 | 90.09 | 91.65 |\n| Gains-only class increment | 99.34 | 93.21 | 94.44 |\n\nThese results indicate that under the mixed incremental scenario, the performance achieved by Gains is comparable to scenarios with only domain or class increments, without significant degradation. We will include this new experiment and clarify the support for mixed-increment scenarios in the final version.\n\n## Q3. Algorithm 1\n\nWhen no new knowledge is introduced, the original model can be directly applied to newly joined clients for inference tasks without requiring training. We will complete this explanation in the final version of the algorithm.\n\n## Q4. Explanations of Table 1\n\n### (1) The T-Acc of FOSDA and SemiFDA\n\nFOSDA is designed for open-set scenarios by leveraging an uncertainty-aware mechanism to distinguish known from unknown classes. Under a mild domain shift, the inter-domain discrepancy is too small to activate the unknown class detector properly, causing a large number of target samples to be incorrectly rejected, which leads to T-Acc approaching zero. As the domain shift increases (Medium/Strong), the feature distribution discrepancy becomes more pronounced, enabling FOSDA to perform effective domain separation.\n\nSemiFDA employs an unsupervised feature alignment strategy (based on CORAL) with a frozen classification head. In the Mild setting, the target distribution is extremely close to the source, resulting in insufficient feature updates and poor adaptation of the classifier—hence a T-Acc of 0.00. As the domain gap widens, stronger distributional shifts provide more adaptation signals, improving alignment and classification performance.\n\n### (2) The S-Acc of AutoFedGP and FedAVG\n\nIn the Mild scenario, AutoFedGP suffers from scarce and noisy target data. Its auto-weighting mechanism overemphasizes the limited target gradients and suppresses source gradient contributions, leading to severe source forgetting.\n\nFedAVG assumes fully IID data and lacks any domain adaptation mechanism. Under Mild conditions, the introduction of new target-domain classes exacerbates data distribution skew across clients, resulting in unstable training dynamics (as shown in Fig. 4(a)). Consequently, FedAVG fails to balance performance between source and target domains. The reported results reflect only the final training round.\n\n## Q5 & W3. Sensitivity analysis of $\\lambda$\n\nWe test the performance on the DigitFive dataset under the medium shift scenario (task: USPS → MNIST) with $\\lambda$ ∈ {0.0, 0.1, 0.3, 0.5, 0.7, 1.0}. Each $\\lambda$ is tested with three repeated training runs, taking the average. The results are as follows:\n| λ   | T-Acc  | S-Acc  | G-Acc  |\n|-----|---------|---------|---------|\n| 0.0 | 99.20   | 83.35   | 85.87   |\n| 0.3 | 99.14   | 93.87   | 95.41   |\n| 0.5 | 98.99   | 99.41   | 99.34   |\n| 0.7 | 93.76   | 99.35   | 97.59   |\n| 1.0 | 85.55   | 99.43   | 93.47   |\n\nFrom the above experimental results, it can be seen that when $\\lambda$ approaches 0, new knowledge dominates aggregation, leading to old knowledge forgetting (S-Acc decreases). When $\\lambda$ is too large, target domain performance is limited (T-Acc decreases). Overall, $\\lambda=0.5$ achieves optimal balance, and subsequent experiments are set accordingly.\n\n## Q6. Results under no domain shift conditions.\n\nIn the table below, we present the accuracy of the source domain clients without the entry of new clients. Compare with Table 1 of the paper, it can be seen that almost all baselines show a decline in performance on the source domain, while Gains has the smallest decline. We will include these results in Table 1 in the final version.\n\n| Scenario |DigitFive| Amazon Review|\n|----------|--------|------|\n|  Mild    |99.46 |-|\n|  Medium  |89.23 |81.70 |\n|  Strong  |94.32 |85.65 |\n\n## Q7. Concerns about the training time.\n\nInevitably, extra computational costs occur when calculating the contributions on the server. However, by calculating the weights based on contribution, more efficient aggregation can be achieved, thereby significantly reducing the number of federated iterations. Taking the DigitFive dataset in the mild shift scenario as an example, the consumed computing resources and the number of iterations are as shown in the table below:\n\n| Method           |  Rounds to converge | Convergence time |\n| ---------------- | ------------------ | ------------------------- |\n| **Gains (Ours)**     |  **5**                 | **807.45**                   |\n| FedHEAL          | 40                | 1368.4                    |\n| FedAVG           | 20                | 1977.20                   |\n| FedProx          | 40               | 6880.80                   |\n| FedProto         | 32                | 9519.68                   |\n\nAlthough Gains consumes more computational resources per round, it reduces the number of communication rounds by approximately 84.8%, resulting in lower overall computation costs. Moreover, since the contribution calculation is performed on the server, it does not impose an additional computational burden on the clients. On the contrary, the significantly reduced number of rounds substantially lowers the communication overhead for clients. The above results will be shown in the final version.\n\nThank you for your time and efforts. We hope this has addressed your concerns and answered your questions.\nPlease don’t hesitate to reach out if you have any further questions."}, {"review_id": "Bsp5Ef56Iv", "reviewer": "Reviewer_AsDt", "summary": "The paper proposes Gains, a framework for fine-grained federated domain adaptation in open-set settings. It detects and distinguishes between domain and class shifts by analyzing changes in feature representations and classifier parameters. Gains then adapts the global model using contribution-based aggregation while preserving source performance with an anti-forgetting mechanism. Experiments on benchmark datasets are conducted to show the effectiveness of the proposed method under various data shift scenarios.", "questions": "1. The proposed fine-grained knowledge discovery relies on manually set thresholds (TF and TC) for DiffF and DiffC. How sensitive is the method to these thresholds? Could the authors propose a principled or automated way to set them, possibly based on validation metrics or adaptive criteria?\n2. The server uses a public dataset to measure feature and classifier differences. In many federated settings, such datasets may not be available or may violate privacy assumptions. Can the authors clarify what constitutes the “public dataset,” and how the method would perform or adapt without it?\n3. While the empirical trends for DiffF and DiffC are shown, there is no theoretical reasoning for why these metrics reliably distinguish class vs. domain increments. Can the authors provide a formal justification or deeper empirical analysis (e.g., statistical separability) to support this design choice?\n4. Since the problem setting overlaps with FCL (e.g., handling class increments), why weren’t established FCL baselines like FedWeIT, FedCIL, or FedFCL included in the comparison?\n5. The evaluations are based on small models (CNN, LSTM). How does Gains scale to modern architectures like ResNet, ViT, or BERT, especially in terms of DiffF/DiffC computation and aggregation overhead?", "limitations": "The authors acknowledge key limitations, such as reliance on manually set thresholds and the focus on only domain/class increments, omitting more complex scenarios (e.g., simultaneous or task increments).", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. The paper addresses federated domain adaptation (FDA) in open-set settings with fine-grained knowledge discovery (distinguishing class vs. domain increments), which is underexplored.\n\nWeaknesses: \n1. Lack of theoretical justification for the discrimination mechanism: While convergence of the adaptation strategy is analyzed, there is no theoretical backing for why DiffF and DiffC reliably differentiate domain vs. class shifts. The method might fail in high-dimensional or complex domains (e.g., vision transformers, NLP models) where parameter variation is harder to interpret.\n2. Unfair comparisons:  FOSDA and SemiFDA are not inherently designed for class+domain incremental scenarios, so benchmarking them directly without adaptation may not be valid. No strong baselines from federated continual learning (FCL) or class-incremental learning (CIL) are included (e.g., FedWeIT, FedCIL, FedFCL, etc.).", "was_revised": true, "final_justification": "The authors addressed my concerns. Therefore, I raise my score.", "rebuttal": "We'd like to express our sincere gratitude to the reviewer for your careful reading and highly valuable feedback, which has been extremely beneficial to us. We have made every effort to address your concerns, and some of them will be included in the final version. The following is the the details:\n\n## Q1. Analysis of the $Diff$ thresholds\n### (1) Sensitivity analysis\nAlthough the thresholds are manually set, the model exhibits strong robustness to threshold variations. As shown in Fig. 2, the changes in $Diff^F$ and $Diff^C$ are very significant, which means that the thresholds can take values over a wide range, with $Diff^F$ ranging from 700 to 3400 and $Diff^C$ from 0.05 to 0.27. We also conduct experiments on various thresholds under the mild shift scenario of DigitFive (source: MNIST-M; target: MNIST) as an example, with $T_F \\in {800, 1000, 1200}$ and $T_C \\in {0.20, 0.25, 0.27}$. The results are as follows:\n\n|$T_F$|T-Acc|S-Acc|G-Acc|\n|-|-|-|-|\n|800|99.62|92.01|93.15|\n|1000|99.34|93.21|94.44|\n|1200|99.24|93.06| 93.91|\n\n|$T_C$|T-Acc|S-Acc|G-Acc|\n|-|-|-|-|\n|0.20|99.75|92.34|93.29|\n|0.25|99.34|93.21|94.44|\n|0.27|99.86|92.71|93.01|\n\nIt can be seen that the model performance remains stable when parameters fluctuate within reasonable ranges (performance variation < 1%).\n\n### (2) Alternative solutions\nTo automate the selection of thresholds, we can use a statistics-based approach. In the pre-experiment, we repeatedly introduce clients that carry new knowledge into the federated-learning system and, each time, record the resulting $Diff^F$ and $Diff^C$ values. After collecting many such samples, we compute the means ($\\mu_F$, $\\mu_C$) and standard deviations ($\\sigma_F$, $\\sigma_C$) of the two metrics. We then set the thresholds as:\n- $T_F = \\mu_F + \\alpha\\sigma_F$,  \n- $T_C = \\mu_C + \\beta\\sigma_C$,\n\nwhere $\\alpha$ and $\\beta$ are tunable coefficients that control how strict the thresholds should be.\n\n## Q2. Concerns about the public dataset\nPublic datasets are commonly utilized in FL to simulate shared server knowledge and enable cross-domain evaluations—e.g., FCCL[1] and SacFL[2] both rely on such resources to facilitate client model alignment. Our use aligns with this widespread and pragmatic practice.\n\nIn our experiments, the public data is sampled from the DigitFive and Amazon Review datasets, which are strictly disjoint from client data and only stored on the server. Generally speaking, it can be accessed from other datasets that are totally different from clients' data, such as Office-Home, thereby avoiding privacy leakage.\n\nTo address scenarios without public datasets, a lightweight client-encoder distillation mechanism can be adopted. Specifically, the server can collect statistical summaries (e.g., encoder outputs’ mean and covariance) from clients instead of raw data, ensuring privacy. By comparing these anonymized feature statistics, the server can approximate $Diff^F$ and $Diff^C$ for knowledge discovery. This part will be shown in the experimental setting and discussion.\n\n- [1] Huang W, et al. Learn from others and be yourself in heterogeneous federated learning[C]//CVPR. 2022: 10143-10153.\n\n- [2] Zhong Z, et al. SacFL: Self-Adaptive Federated Continual Learning for Resource-Constrained End Devices[J]. TNNLS, 2025.\n\n## Q3 & W1. Concerns about new knowledge discovery mechanism\n### (1) Empirical analysis\nWe conducted a detailed analysis of the DigitFive dataset. In the class increment scenario, the source domain data is MNIST with classes {0,1,2,3}, and we sequentially add data from {0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, where the first four cases correspond to no increment and the latter six cases correspond to class increment. In the domain increment scenario, the source domain is SVHN, and we sequentially add MNIST, MNIST-M, and SynthDigits data. We obtained the mean and variance of $Diff^F$ and $Diff^C$ under different conditions, as shown in the table below:\n\n|Type|Avg. $Diff^F$|Avg. $Diff^C$|\n|-|-|-|\n|No Increment|143.28|0.08|\n|Domain Increment|2897.64|0.11|\n|Class Increment|1832.53|0.29|\n\nAs shown above, $Diff^F$ increases dramatically during domain and class increments, while $Diff^C$ exhibits clear peaks during class increments. Using a simple decision boundary (e.g., $Diff^F$ > 1000 → new knowledge, $Diff^C$ > 0.25 → new class), we can easily distinguish these two knowledge increment scenarios.\n### (2) Theoretical supports \nThis work is based on experimental findings that the Decoder (especially the classification head) is more sensitive to changes in classes, while the features extracted by the Encoder are sensitive to changes in knowledge. Therefore, we detect new knowledge by observing changes in the features extracted by the Encoder and the parameters of the Decoder. This approach is well supported by previous studies. For example, Rebuffi et al. [1] found that an increase in the number of classes leads to changes in the structure and parameters of the classifier, indicating that the classifier is sensitive to class changes. Zhong et al. [2] proposed that when new knowledge is introduced, the features extracted by the Encoder undergo significant changes. Therefore, the findings of previous research provide strong theoretical support for the knowledge discovery method proposed in this paper.\n\n- [1] Rebuffi S A, Kolesnikov A, Sperl G, et al. icarl: Incremental classifier and representation learning[C]//CVPR. 2017: 2001-2010.\n\n- [2] Zhong Z, Bao W, Wang J, et al. SacFL: Self-Adaptive Federated Continual Learning for Resource-Constrained End Devices[J]. TNNLS, 2025.\n## Q4 & W2. Concerns about baselines\n### (1) FOSDA and SemiFDA\nAlthough FOSDA and SemiFDA are not specifically designed for class+domain shift scenarios, in our experiments, our method has been compared with them in both individual class increment and domain increment scenarios (Table 1), demonstrating excellent superiority. This further illustrates that Gains possesses good adaptation capabilities.\n### (2) FCL baselines\nWhile our work is primarily situated in the open-set federated domain adaptation (FDA) setting, which differs in several key aspects from FCL (illustrated in the discussion), we agree that including FCL baselines addressing class-incremental scenarios would enrich our evaluation. To address this, we conducted additional experiments incorporating FedWeIT and FedCIL as baselines in the class-incremental scenario under mild data shift (DigitFive dataset, target client introduces new classes {1,5}). \n\n|Method|T-Acc|S-Acc|G-Acc|\n|-|-|-|-|\n|Gains (Ours)|99.34|93.21|94.44|\n|FedWeIT|76.22|86.03|84.14|\n|FedCIL|69.85|88.14|83.39|\n\nGains achieves significantly higher T-Acc while maintaining S-Acc, demonstrating both effective new class integration and source knowledge retention. These baselines will be included in the final version.\n\n## Q5 & W1. More complex models\nWe test the ResNet18 model in the DigitFive dataset under the medium data shift scenario (source: SVHN, target: MNIST). All baselines are reimplemented with ResNet18 as backbone for fair comparison.\n\n|Method|T-Acc|S-Acc|G-Acc|Convergence time|\n|-|-|-|-|-|\n|Gains (Ours)|98.50|93.47|94.47|3528.98|\n|FOSDA|11.29|19.46|17.82|-|\n|SemiFDA|12.31|9.76|10.27|-|\n|AutoFedGP|9.78|6.22|6.93|-|\n|FedHEAL|97.52|92.21|93.27|3113|\n|FedAVG|56.92|69.20|65.23|12568|\n|FedProx|52.63|71.41|66.52|20101.80|\n|FedProto|9.76|6.93|7.50|14890|\n\nWe can see that Gains maintains strong generalization on both source and target domains. It outperforms all baselines across all metrics, confirming robustness across architecture types. Meanwhile, under the condition of equivalent learning effectiveness, the computational resources consumed by Gains are lower than those of most other methods (comparable to FedHEAL). Although the calculation of server-side contribution degree will consume more computing resources during the aggregation compared to traditional FL, this process will accelerate the model convergence, thereby reducing the training time. Therefore, it will not result in significant computational resource overhead. This part will be included in the final version.\n\n## L1. Experiments in complex scenarios\nWhen both domain shift and class shift occur simultaneously in the target domain, our method still works. We can combine Domain-incremental and Class-incremental contribution-driven aggregation strategies. The aggregation strategy is as follows:\n- Encoder: Contribution calculated by Eq. (2), aggregated by Eq. (4).\n- Classifier:\n  - Old-class channels aggregated via Eq. (3) and Eq. (5),\n  - New-class channels are directly adopted from the target domain model, as described in Line 176 of the manuscript.\n\nTo this end, we validated the scenario where both class increment and domain increment occur simultaneously. Specifically, using the DigitFive dataset medium shift as an example, the source domain client data is MNIST with classes {0,2,3,4,6,7,8,9}; the target client includes two types of data: one is MNIST classes {1,5}, and the other is SVHN dataset classes {0,2,3,4,6,7,8,9}. The experimental results obtained are as follows:\n\n|Method|T-Acc|S-Acc|G-Acc|\n|-|-|-|-|\n|Gains-domain+class shift|97.53|91.88|92.91|\n|Gains-domain shift|97.91|90.09|91.65|\n|Gains-class shift|99.34|93.21|94.44|\n\nThe results indicate that under the mixed incremental scenario, the performance achieved by Gains is comparable to scenarios with only domain or class increments, without significant degradation. For more complex task-increment scenarios, such as extending from image classification tasks to object detection tasks, adaptive architectures can be designed by incorporating meta-learning techniques. This allows the model to autonomously identify and handle task space expansion, automatically differentiate parameters, and adapt independently, thereby ensuring continual knowledge growth and effective control of unlearning. We will include the above experimental validation and discussion in the final version."}]

Author rebuttal:

Meta-review: This paper considers federated domain adaptation (FDA) in open-set settings with fine-grained knowledge discovery (distinguishing class vs. domain increments), which is acknowledged as a novel problem setting by all reviewers. The proposed algorithm employs a contribution-driven aggregation strategy to prioritize source clients with higher contributions during the knowledge adaptation phase, and an anti-forgetting mechanism is incorporated to prevent performance degradation on the source domain.

The reviewers have some common concerns regarding 1) Validations under more complex scenarios, 2) Computational complexity, 3) Choice of hyperparameters, 4) Lack of theoretical justification for the discrimination mechanism. During the rebuttal and author-reviewer discussion phases, the authors have supplement additional empirical results to address most concerns of Reviewers va2g, JgVT, 7wkT.

The remaining concerns are mainly around lack of theoretical backing to the algorithm design. I agree with Reviewer AsDt that the proposed algorithm lacks of theoretical justification or derivation. Both contribution-driven aggregation and anti-forgetting mechanism seem based on weighted combination of models, where the weighting schemes are manually designed. Is it possible to learn the weights or derive the weighting scheme theoretically? In addition, the authors adopt the normalized $\frac{1}{1+Diff_n}$ as the weight for client $n$, considering the Gibbs distribution (where $ Diff_n $ is viewed as the energy) might be a better way.
Decision: Accept (poster)