FIARSE: Model-Heterogeneous Federated Learning via Importance-Aware Submodel Extraction
Authors: Feijie Wu
Xingchen Wang
Yaqing Wang
Tianci Liu
Lu Su
Jing Gao
Venue: NeurIPS 2024 poster (2024)
Keywords: Federated learning
Model heterogeneity
Primary area: optimization

Abstract: In federated learning (FL), accommodating clients' varied computational capacities poses a challenge, often limiting the participation of those with constrained resources in global model training.  To address this issue, the concept of model heterogeneity through submodel extraction has emerged, offering a tailored solution that aligns the model's complexity with each client's computational capacity. In this work, we propose Federated Importance-Aware Submodel Extraction (FIARSE), a novel approach that dynamically adjusts submodels based on the importance of model parameters, thereby overcoming the limitations of previous static and dynamic submodel extraction methods.  Compared to existing works, the proposed method offers a theoretical foundation for the submodel extraction and eliminates the need for additional information beyond the model parameters themselves to determine parameter importance, significantly reducing the overhead on clients. Extensive experiments are conducted on various datasets to showcase the superior performance of the proposed FIARSE.

FIARSE: Modee--etesogeneouss Federated Learning via Importance-Aware Submodel Extraction
Feijie Wu', Xingchen Wang', Yaqing Wang", Tianci Liu', Lu Su Jing Gaol
Pardue University *Googl DeepMind
[wu1977, wang2930, 1iu3351, lusu, jinggao)(puurdue edu yaqingwangogooglo. com
Abstract
In federated learning (FL), accommodating clients' varied computational capaci- ties poses challenge, often limiting the participation of those with constrained resources in global model training. To address this issue, the concept model het- erogeneity through submodel extraction has emerged, offering a tailored solution that aligns the model's complexity with each client's 's computational capacity. In this work, propose Federated Importance-Awar Submodel Extraction (FIARSE), a novel approach that dynamically adjusts submodels based on the importance of model parameters, thereby overcoming the limitations of previous static and dynamic submodel extraction methods. Compared to existing works, the proposed method offers theoretical foundation for the submodel extraction and eliminates the need for additional information beyond the model parameters themselves to determine parameter importance, significantly reducing the overhead clients. Extensive experiments are conducted on various datasets to showcase the superior performance of the proposed FIARSE.
1 Introduction
Federated learning (FL) 33 52 stands out as promising distributed training paradigm, in which the clients enjoy mutual information without jeopardizing data privacy. Specifically, the FL server requests the clients to train model with their local data and aggregates the models into global one. Such a paradigm, however, may fail real-world FL system, where the clients usually have varying computation capacities I3 42 46). likely preventing the clients with insufficient computation resources from being involved training a large global model 773.
To tackle the challenge, a practical solution is to enable model heterogeneity, ensuring that the model deployed on each individual client aligns with its local computation capacity. This can be done by extracting a submodel for each client from the global model, which encompasses a subset of the parameters of the global model. During the model training period, the parameters of each submodel are thereby retrieved from the counterpart of the global model. Importantly. each parameter of the global model is exclusively averaged among the submodels containing it
Depending on whether the submodels undergo reconstruction during the model training process,
existing works fall into two categories: static submodel extraction [13 25 33 35 dynamic submodel extraction
58
67 76 and
Static submodel extraction creates submodel for each client prior to the model training process. As illustrated in Figure Ta the submodel remains unchanged throughout the training process. However, static submodel extraction suffers from certain limitations that affect both local clients and global performance. Locally, the metrics or knowledge used to extract a submodel for each client are likely evolve during the training process. Since static submodels do not account for this evolution, they may fail to achieve optimal performance. Globally, the extractions of submodels from certain parts may incur client drift during the training, as pointed out by Alam et al. 2 and Liao al. 45 This
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

---

Global Model
Round
Round
Round
Round t
Round
Round
Static Submodel Extraction
Dynamic Submodel Extraction
[c] Importance-Awor Submodel Extraction
Figure 1: Three types of submodel extraction for model training, i.e. static, dynamic, and importance- aware (ours). The figure demonstrates the global model on the server and the local models of two consecutive rounds on a client. Note that solid lines represent the parameters preserved in the local model, while dash lines indicate the parameters excluded from the local model. In importance-awer submodel extraction, we present the importance of the parameters via the line thickness
phenomenon emerges when the clients update their submodels biased their local optima, thereby deviating from the global optimum. As result, it either degrades the training efficiency or leads to a surrogate convergence on global scale 34 64
Dynamic submodel extraction updates each submodel dynamically in each training round, and thus is able to capture the evolution of the global model. For example, FedRolex [2] employs rolling- based submodel extraction approach, addressing client drift by ensuring equal chances for training each parameter as shown in Figure Tb While the method demonstrates significant performance improvement over static submodel extraction in terms of the global model, it sacrifices the submodels' performance. This is because FedRolex treats every parameter equally, leading lack of clear guidance on submodel extraction.
To overcome the limitations of the above methods, in this paper, we propose Federated Importance- AwaRe Submodel Extraction, named FIARSE, for model-hhetrogenncuus FL. Specifically, the pro- posed FIARSE method extracts the submodels based on the importance levels of model parameters. Here important parameters are the edges of the neural network that can induce dramatic changes in the final outputs when removed.
Figure Tc visually illustrates the submodels extracted by FIARSE. demonstrated, FIARSE con- structs submodel by sequentially incorporating parameters in descending order of their importance levels (represented by the thickness of the edges in the model), from highest to lowest, until the client's maximum computation capacity is reached. In contrast to static submodel extraction, approach enables dynamic updates of the submodels, thereby effectively capturing the evolving nature of model parameters. When compared to rolling-based submodel extraction, FIARSE adaptively identifies important parameters, ensuring outstanding performance for both the global model and local submodels. Referring back to the model shown in Figure I the edges connecting the leftmost neuron at the second layer are indicative of important parameters. However, the bolling-based submodel extraction method would roll these parameters out of the submodel in round t + 1 (as shown in Figure Tb), resulting in inadequate training on these crucial parameters. In contrast, our proposed method can identify and retain these important parameters in the training process, illustrated in Figure Ic
Contributions. The contributions of this paper can be highlighted from the following perspectives:
Algorithmically, propose importance-ave -warre aware framework for modeel-heeroogeneuus federated learning. This framework can construct a client-specific submodel calibrated to each client's computation and storage capacity. It achieves this by representing the importance level of each model parameter with its magnitude, thereby avoiding additional storage or computational overhead needed to explicitly maintain the importance scores.
Theoretically, we prove that the proposed algorithm converges at a rate of O (1/VT). where T is the number of communication rounds. This convergence rate is consistent with that of the soite-of-the--ee art FL algorithms, indicating that the proposed submodel construction mechanism does not undermine the convergence properties. the best of our knowledge, this the first study to provide theoretical analysis for modee--ettrogeenityy FL. under partial-client participation.
Empirically, conduct extensive experiments image and text classification tasks, employing coaniing-fro--cratcche model ResNet, and a pretrained model RoBERTa. The results verify that FIARSE significantly outperforms existing approaches, particularly on the clients with limited capacity. The superior performance on resource-constrain devices demonstrates FIARSE's advantages in efficiently adapting submodels meet diverse capabilities.

---

2
Related Work
This section discusses the state-of-the-an works that are most relevant to our research. Appendix A provides a more comprehensive review.
Computation Heterogeneity in FL. Computation heterogeneity in FL refers to the varying com- putational capacities among clients, including differences hardware capabilities and resource availability.. One typical solution is to allow faster clients to perform more local updates, while slower ones update their local models fewer times [43] 50] 53 57 64 72]. However, these approaches require clients to train the full model, which becomes infeasible when some clients cannot load the full model due to limited computation resources. In our work, we extract a submodel for each client that fits within their computational capacity.
Model Customization in FI.. Model customization allows the clients to build their local models that align with their local computation resources [1] 28 46 66 80). To aggregate these heterogeneous models, the method often employs distillation for knowledge transfer, which requires a shared public dataset. However, this approach becomes infeasible when shared public dataset is unavailable 3 59 In our work, we eliminate the need for public dataset, broadening its applicability to wider range of scenarios.
Model Sparsification in FL. Model sparsification, also known as model pruning, removes the unimportant model parameters from a deep learning model, reducing computation overhead and tailoring model sizes to suit clients with varying computational resources g 45
For example, Flado 45] achieves model sparsification by requiring each client to maintain the importance levels of model parameters and extracting submodel that encompasses the most important model parameters. While effective, this method incurs considerable overhead on each client in terms of both storage and computation, posing significant challenges for resource-constrained devices. contrast, our work implicitly represents parameter importance through their values, eliminating the need to maintain separate importance scores for each parameter.
3 Preliminary: Model-HHetergeeneou Federated Learning
Problem Formulation. Consider there are N clients in an FL system. The computation capacity of each client E [NV] is metered by the maximum ratio of submodel extracted from the global model & E IRd and denoted by %/ E [0, 1]. and the values of % could vary among the clients. To enable submodel extraction, each client should assign binary mask ( E {0, 1 such that ||M@]],, S y.d. Let M be the collections of the clients' masks M i.e., M UseNN {0, 1 To
simultaneously optimize the model parameter and the clients' masks, the moneo--hetroggeneity FL
system is formulated
#ER CER (0, ax4 F(
min
A N
Σ KEIN]
Fr (+(oMM) A EadD l ( MO.M))
(I)
Let D, be the local dataset of client i E [N]. be the loss function which calculates the loss for model on a given data sample (including an input and target). Therefore, the local objective F-(-) in Equation (T) indicates the expected loss for client on the local dataset. For simplicity, we consider all N clients to carry equal weights (i.e., 1/N) Equation (1). and the proposed approach can be extended to the scenario where the clients are with different weights.
Partial Averaging. There are numerous submodel extraction approaches, which are categorized into static and dynamic submodel extractions. However, these methods adopt partial averaging to aggregate clients' models into global one, and the details are outlined as follows: At round e {0, ).
A Generic Solution:
The server randomly samples a subset of clients A C [N] and distributes the global model parameters i, to the selected clients.
Sampling:
Local Model Training: The clients E A performs K-times local updates via (.(()) oitk a 2 (i)
(6)
F. ( C M @ ! where k E (1...., and æ2.0 ã It is noted that M
represents a binary mask for client i 1-th round, which can be either predefined determined by the client [1 45 76).
13 33 or
3

---

Global Model Aggregation: The clients collect the model updates from the participants A and
perform the global model aggregation via Lt+1 = Te - Ag ("i ) Given a set of d-dimension vectors vo...., - R Ag is defined as: (i) For the j-th index, Ag = (Eien w5) ( # 0)): (ii) Ag = UsE(d ((9)
(i)
Limitations. The above solution adopts a consistent mask during local model training, which cannot obtain the optimal mask .M for various clients Equation ① expects. Some recent works (e.g., Flado [5) and PFedGate [8]) have proposed to capture the importance levels of each model parameter in achieving the objective of Equation ( where submodel consists of the most important parameters up to the maximum capacity of client. In these works, the clients hold the importance scores for each model parameter and extract a submodel accordingly. After the local training of the submodel, the clients take an additional step to optimize the importance scores. Despite the effectiveness of these approaches, their feasibility is compromised due to the massive costs related to storage and computation. These approaches entail minimum training memory and storage of (d)) and ((d) on client E [N], respectively, while HeteroFL [3] ensures the training memory within ((xd)) and does not require additional storage. Moreover, it is time-consuming to separate model parameters update and mask optimization into two steps. A work [8T] attempts to simplify the process by means of greedy pruning, where submodel consists of the parameters selected from the largest to the smallest absolute values. Apparently, this approach avoids mask optimization while evolving the submodel architectures since they are associated with model parameters. However, this work keeps the mask consistent during local model training. which does not make sense because an update of model parameters should lead to different mask.
FIARSE
Solution Overview. In this work, we explore the correlation between the value of model parameters and their importance levels, leveraging the insights from previous research (2] [4]. These studies reveal that the magnitude of model parameters can act as an indicator of their importance levels. This discovery offers an opportunity simplify Equation ( Given that our objective is extract important parameters for submodel construction, we can approximate this goal by selecting larger parameters to build the submodel, rather than explicitly maintaining an importance score for each parameter. Though simplified, the problem is still challenging since the model parameters themselves also variables to be optimized. To address this challenge, in Section 4.1 will present novel submodel construction method that can jointly select and optimize model parameters.
Finally, Section 4.2 introduces our proposed FL. algorithm FIARSE that seamlessly integrates the submodel construction method and optimizes the global model. In detail, the clients optimize the model parameters z by leveraging the submodel construction method. The server subsequently aggregates these optimized models from the clients and initiates a new training round. Given that the collected model parameters inherently reflect their importance levels, the aggregated global model parameters also effectively capture their importance from a global perspective. Algorithm concisely presents the pscudocode of FIARSE.
4.1 Submodel Construction
As highlighted in the overview, the insight that the values of model parameters are correlated with their importance allows us to reframe the problem of submodel construction. Intuitively, by controlling the number of parameters included in the submodel, we ensure the computation and/or storage costs of the submodel not exceed the budget of the clients. To achieve this, we establish a threshold for the model parameters based on each client's capacity. Only those parameters whose values exceed this threshold are included in the respective client's 's submodel. Thanks to the correlation between a parameter's 's value and its importance level, this approach ensures that the parameters included in the submodel are of greater importance than those that are excluded. This idea can be implemented by into a function of the parameter values:
converting the mask variable in Equation (I
min M(t) #ER"
A N
F. 2 ( KE|N]
Σ
where M (z)
1, 0,
0
(2)
0
where (-) represents the mask function of client i E [N] and incorporates the threshold 0, on given model such that [|M (i) || nd; and M(.) is the collections of all local mask
4

---

functions, As seen, the problem projects parameter importance to parameter values and thus can achieve parameter selection and model training through optimizing solely the parameter values.
Now the question is how to determine the threshold for Equation 2 In general, the threshold abides by the clients' local computation/storage capacity. Towards this end, we determine the value using TopK, (-) operation, which selects the top Y values of the given vector. For simplicity, we discuss model-wise threshold selection strategies in this section, where the threshold 0; is set for TopK... (|ã1).
Our proposed method is applicable for settings where different thresholds are assigned to different model parameters. Additional threshold selection strategies will be explored in Appendix D.
Conttolld Biased Gradient Descent (TCB-GD). We enhance Equation 2 by in- tegrating trriigh-tthoouhh estimation (STE)
49
where we assume the mask is labeled with
with probability determined by clip model parameter ă. Therefore, the gradient calculated in the backward propagation on client i E [N] process adheres to:
0
0.1). where Ø, means j-th element of a d-dimension
2/ 10 ( + 0.)
Val. F. @ O (a)) = -VF ④ ROMM M
(²) o (x) о
(3)
Threshold-comttollldd
Blased
A detailed derivation of the above equality is provided in Appendix There are two key differ- ences in comparison with the gradient computation used by local training of partial averaging. i.e., V.F (ā M() @ M First, the mask shifts with the model parameters changing. Second, the backward propagation considers the importance levels of model parameters and forms a biased gradient descent. This means the second term tries make a clear border between the important and non-important parameters.
Effectiveness. We analyze our proposed approach based on its two features, namely, threshold- controlled and biased gradient computations:
Thressooddconttrolldd::: By comparing Equation (3) with Equation we notice that the parameters no less than the designated threshold will be updated. In other words, this gradient descent method only updates the parameters that are greater or equal to the given threshold, and those parameters that are initially smaller than the threshold never get updated. Obviously, the computation cost each iteration remains constant or even smaller than the cost at the previous iterations.
Fl. clients usually update the model for multiple iterations. According to the description above, the trained submodel is shrinking because some parameters may drop behind the threshold, while no new parameters are introduced to the submodel. Therefore, the proposed gradient descent method keeps the computation cost constant or even smaller than our expectation.
Biased: Biasedness accelerates the update of the parameters near the threshold to distinguish their importance. In other words, less important parameters drop below the threshold and roll out, while the important ones continue to increase until stable. This feature guarantees the model parameters reflect their importance value by minimizing the existence of ambiguous parameters close to the threshold. In other words, the clients can easily identify the unimportant model parameters, facilitating the extraction of a submodel based on parameter values ranging from large to small until aligns with a client's maximum computation capacity.
We further integrate this submodel construction method into our proposed FL algorithm FIARSE and comprehensively discuss how threshold threshold-controlless biased gradient descent benefits the model- heterogeneity FL in the next section.
4.2 Algorithm Description
In FIARSE, global model is initialized with arbitrary parameters 2p E Rd (a pretrained model is allowed, which can be regarded as a special case of an arbitrary model).
Partial client participation is one of the features of FL algorithms because the server is unlikely to handle all the communications from clients, especially when the number of clients considerably
71 74). Therefore, we present our algorithm FIARSE in support of partial client participation: the beginning of each communication round E (0, 1,...., }. the server uniformly samples group of clients from [N] without replacement, denoted by A, which consists of A clients.
large [10 32
44
5

---

Subsequently, the server broadcasts the submodels to the selected clients and collects and merges their updates into the global model. In the rest of the section, we comprehensively discuss the details of these steps and exemplify them with t-th round.
Submodel Extraction on Server. Based on the set of participants A, the server learns their computation capac- ities (ni)iE, Then, the server fol- lows the threshold selection strategies described in Section (.. and extracts the submodel for all participants ac- cording to their computation capaci-
Algorithm FIARSE
Input: local learning rate 7)s global learning rate 7as local updates K, initial model To-
I: for 1 = 0, 2,..... do
2: Sample clients A S [N]
3: Send (Ø, @ MM (TE)) to clients i E A
4: for i E A in parallel do
ties. Take the model-wise threshold selection
example and select submodel for participant i E .A. The threshold is set for 82 TopK (|=)). Then, the server extracts a submodel encompassing the parameters | 2 O and sends it to the participant. This
5:
Initialize x7,0 = 21 3 M2 (a:)
6:
for
0, .,..,, K do
7:
91, V
(e)
(2) F, (t)
Fikk M,
(2)
(6)
(4)
(
8:
m1,4+1 Dikk
m 91,++1
9:
end for
procedure is equivalent the expres-
10:
Az, (1) = xt
x K
sion in Line 3 of Algorithm [ i.c.,
(0)
11:
Send Ar; to the server
3, M, (6) (.:.).
12:
end for
AggieA (Az (3)
Local Training on Clients E A. After receiving the submodel from the server, we thereby initialize the local
13: Φt-1 = ãt - 7/a-
14:
end for
masking function ! for training, which implicitly includes the threshold 0,. The threshold will remain constant during the local training. As outlined in Line 7 8, the client utilizes the TCB-GD to optimize the local model for K iterations. In each iteration & E (o..... K 1}, the client utilizes the masking function to sort out the parameters that drop behind the threshold. Then, the client computes
the gradient V (1) Fi "
(a(.)) using Equation (3) (Line 7) and updates the local model O M,
via i = x c mp V Van F3 (i @ M! (ii,)) (Line 8). As discussed in Section 4.1 the
training memory is bounded by O(yd), and there is no additional storage requirement. In contrast to other importance-awart works such as Flado, the proposed FIARSE is more feasible in practice.
Aggregation on Server. After the selected clients finish their local updates, the server aggregates the
updates from the clients (Line 10 11). Similar to the global model aggregation of partial averaging
described in Section 3 FIARSE updates the global model via 1t+1 z. n. Agg
(Ax/ (1)
(Line 13). A detailed description of the recursive function is placed in Appendix C.I
Given that the global model starts with randomly initialized parameters, this aggregation not only updates the global model parameters but also aligns their values with their importance levels. In the next training round f 1, the FIARSE will return to Line 3, regenerating submodel from the updated parameters, which is then sent back to the client. Since the values of the parameters represent better their importance levels than in the last training round, the newly generated submodel will contain more important parameters. The whole algorithm will then be repeated once again, resulting in a newly aggregated global model. This iterative process will progressively select important parameters and exclude unsignificant ones, steering the global model towards a state of convergence in which the importance of parameters is accurately represented. In the coming section, we theoretically analyze the convergence rate of the proposed FIARSE.
5 Convergence Analysis
Existing convergence analyses of FL algorithms predominantly rely on moodelhoooggeeeou settings [65]. However, the exploration of model headel--eerogeeetyy FL remains inadequately addressed. with some in this domain being recently introduced but relying on full client participation. This section aims to present thorough convergence analysis of the proposed FIARSE under non- convex objectives. Specially, our analysis is established under the scenarios of hetergeettr FL where not all clients actively participate in the round-by-round training process.
studies 588 69 76

---

Before showing the convergence result, we make the following three assumptions:
For all E [N], the local objectives F; are I.-Lipschitz smooth with differentiable mask function M For all w, R..
Assumption 5.1 -Maseed---smoothene
V w Pi
TwOMM M (w) Vol (o Mo (v) (i)) L
Assumption 5.2 (Bounded Global Variance). For all [NT. the variance between local gradient (.) and global gradient (-) is bounded under the same model parameters: For all w E Rd there exists constant of 2 for all j [n] such that
Σ VEN,
VFF há 115
VED. (w)- (w) soj.
(w)
(w)-VFb)
N
We further annotate o² Σド=
Assumption 5.3 (Masked Reduction). For all i E [N], the mask-incurred error is bounded with respect the model parameter Tt, 0.1..... There exists scalar 03 E [0, at round such that
v ( @ (a.) Va Fi
a @ M (ā:)
|| (
- 5 |
Lipschitz-smootf assumption has gained widespread acceptance in machine learning research, as evidenced by its incorporation in various studies such 11
74 75 81. Assumption [5 extends this assumption to a scenario where a binary mask is calculated based on the model parameters and subsequently applied to the model. The second assumption, widely made in the previous FL studies [74] 75), establishes bounds between the local objectives and the global objective due to the occurrence of non-i.i.d. data. Assumption 5.3 draws inspiration from [51 81 and characterizes the masking performance by comparing gradients with and without the application of the mask. Notably,
6 51
70
if M 1d (i.e., setting the threshold for 0 0), then 57 0.
With these three assumptions, we analyze the convergence rate of our proposed algorithm. Under non-convex objectives, our goal is to evaluate if the gradient norm can approach zero with respect to the model parameters ã when the communication round + co. Theorem 5.4 presents the convergence result of the proposed FIARSE, and a detailed proof is deferred to Appendix C
Theorem 5.4. Suppose that Assumption 5.1 5.2 and 5.3 hold. We define F(x) F (ār, Nxd), and
F()) 2 F. for all w E Rd. Let the local learning rate satisfy
Y
A 32K LTp
S min
2L ((K +1) 6LV(K + IJA 9L
12LVKN
Denote T as the total communication rounds. Therefore, the convergence rate of FIARSE for non-convex objectives should be
(F() - F.)N KATKAT
64N KL + T
32N
min E
VVF ( 21
1
(4)
EE(T]
The aforementioned theorem assesses the potential convergence of the global model towards stable solution when employing the proposed algorithm (FIARSE). This implies that the submodels utilized in the analysis may differ from those employed in updates at each iteration. Consequently, our analysis takes into account clients utilizing the complete model, with the difference relative to their local submodels being constrained by Assumption 5.3 This methodology aligns with the analytical framework advocated by [8I] Next, set the appropriate learning rates to achieve optimal convergence properties regarding the number of communication rounds, as outlined in corollary:
Corollary 5.5. Suppose that Assumption
5.2 and 5.3 hold. We define F(t) 2 F(E Nxd), and F()) 2 F, for all ã E Rd. Let the local learning rate m KVT and the global learning rate
5.1

---

7. 1, where T is the total communication rounds. Then, under non-convex objectives, FIARSE
converges to a small neighborhood of stationary point of standard FL as ' is large enough, i.e.
min VF (i)) S (
1000002 F(
N
F. + +
+
N T
Σ tE[T]
1
(5)
VT
where treat L constants.
Remark 5.6. Regarding the first term on the right-hand side (RHS) of Equation 5 it approaches zero as T tends infinity. However, an intriguing question arises concerning the potential for the second term to reach zero, given that the norm | cannot be zero. According to Assumption 5.3 straightforward case where ó; is always zero occurs when all clients use the full model - that is, when the threshold 0, in equation Equation (3) is set to zero in the proposed FIARSE. Therefore, under
federated learning (FL), our theorem aligns with state-of-the-art works in terms of the convergence rate, which focuses solely on the number of communication rounds T,, i.e., O (I/VT).
34 74
For model-heterogeneeuu FL, is noteworthy that 6, may tend toward zero oo, leading to T Ei= 5% I approaching zero. As explored by [51 69 can replicate the performance of the full model on all clients after a substantial number of communi- cation rounds T. Consequently, our proposed algorithm can achieve convergence rate of O as long as lim 8, 0.
1
this occurs because the submodels
Na²
AVT
Ignoring constant terms, the proposed FIARSE converges a rate of O (02) /vTT)
(02/v/T) under full-client
participation (i.e., A = N). Recently, some works have reported their convergence rates under model-heterogeeneuus FI. with full-client participation, such as pruning-greedy [81] with a rate of
O (Mo2/vZ /VT) and FedDSE 622 with O (Ko²/ /T). Evidently, our proposed method exhibits better theoretical performance.
Experiments
6.1 Setup
Datasets and Models. We evaluate the proposed methodology using a combination of two computer vision (CV) datasets and one natural language processing (NIP) dataset. Specifically, we employ CIFAR-10 10 and CIFAR- --0 datasets 337 for image classification, and the AGNews dataset [79] for text classification. For the first two datasets, we conduct training utilizing a ResNet- 18 architecture [17], with modifications made by substituting its batch normalization (BN) layers with static BN counterparts 113. For the AGNews dataset, we fine-tune a pre-trained RoBERTa-baat model 48
Data Heterogeneity. For CIFAR-10 and CIFAR-ION 100, we follow 22 30 and partition the datasets into 100 clients based on Dirichlet distribution setting 0.3. As for AGNews, we partition the datasets for 200 clients with Dirichlet distribution as well, but is with the parameter of a = 1.0. Note that the server or clients do not any public datasets during the training stage. In the testing phase, we refer to the superset of all clients' test datasets as "global test dataset."
System Heterogeneity. Specifically, the parameter y is defined as the ratio corresponding to the largest model that can be loaded onto a device. The experiments are conducted with four different model sizes represented by 7 {1/64, 1/16, 1/4, 1.0]. The allocation of clients to each level is balanced. It's important to note that our proposed method is flexible and can accommodate varying numbers of complexity levels client distributions.
Implementation. In this setting, we set the participation ratio 10% by default. We perform 800-round training on the CV tasks while running for 300 rounds on the NLP task. To avoid the randomness the results, we averaged the results from three different random seeds. In experiments, we report the results of all the baselines based on the best hyperparameter settings. Due to the space limitation, more experimental results and analysis are deferred Appendix D Our code is released at https: / http//gttttt /ggggtth....... com homm/Harliw.// FIASSE
8

---

Table 1: Test accuracy under four different submodel sizes. To be more specific, the columns from "Local" to "Model (1.0)" evaluate the test accuracy the local test datasets, while "Global" evaluates the average test accuracy of the global model of four different sizes (1/64, 1/16, 1/4, 1.0) on the global test dataset.
CIAAR-10
CIFAR-100
AGiNews
Method
Local
Model
(1/64)
Model
(1/16)
Midel
(1/4)
(1.0)
Global
Local
(1/64)
(1/16)
(1/4)
(1.0)
Global
Local
Glohal
HoteroFL
60.24
69.32
31.75
33.52
30.67
FedRolex
67.18
54,60
64.96
70.08
79.08
65.98
31.67
21.00
30.84
36.44
38.40
29.89
87.43
87.19
ScaleFI
72.10
69.04
71.64
70.08
77.64
67.37
39.69
36.16
42.56
39.56
37.56
87. 66.66
FIARSE
77.04
73.12
77.20
77.24
82.04
73.75
41.76
39.12
43.24
43.72
40.96
38.63
90.03
89.61
size=1
size=1/4
s/1e
size=1/64
Number of Cileent
20
1.5
15
15
15
10
10
10
10
5
0
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
0
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
Test Accuracy (9)
Test Accuracy 1%)
Test Accuracy (%)
Test Accuracy (%)
(a) HeteroFL Histogram
(b) FedRolex Histogram
(c) ScaleFL Histogram
(d) FIARSE Histogram
Figure 2: Histograms of various submodel extraction methods on CIFAR-10 10 under four submodel sizes. Each histogram shows the number of clients achieving different levels of test accuracy.
6.2 Submodel Performance on Local Dataset
In this setting, we evaluate the submodels' performance on each client's s test datasets. To be specific, the local models extracted from the global models. Figure comprehensively illustrates the number of clients across different test accuracies. Among the four figures presented, all exhibit a left-skewed distribution, with the exception of FedRolex. This outcome aligns with our expectations, as FedRolex employs rolling-based approach and is unable to concentrate on optimizing submodel performance on the local dataset, while the rest three approaches can spare efforts on specific (HeteroFL and ScaleFL) or important (FIARSE) part, effectively addressing performance on local datasets. Among these three approaches, we notice that FIARSE stands out with the best results, showcasing superior performance as more clients achieve higher accuracy compared to the other two methods. The averaged results are also reported by Table I under the column of CIFAR- 10 and "Local" to "Model (1.0)". Specifically, "Model (1/64)" to "Model (1.0)" shows the averaged local performances classified by the model sizes, and the "Local" shows the result by averaging across these four columns. Table also presents the test accuracy of CIFAR-100 and AGNews. The proposed FIARSE achieves at least 2% better than other baselines under these datasets.
6.3 Submodel Performance on Global Dataset
In this setting, we evaluate the performance of submodels with various sizes on the global test dataset to assess the generalizability of our proposed algorithm. Table [ presents the results of two CV datasets and one NLP dataset under the column "Global". In conjunction with Figure our proposed method FIARSE constantly outperforms other basclines in all submodels with different sizes by a substantial margin. Figure dives into the details of training and shows the test accuracy trend throughout the communication rounds. Consider the submodels are expected to surpass 70% test accuracy threshold. As previously discussed, FIARSE ultimately achieves superior test accuracy compared to other baselines. Across model sizes of { /1/44, 1/16, 1/4), our proposed method requires fewer rounds to reach the targeted accuracy compared to other baselines. While the performance disparity between FIARSE and FedRolex is less discernible under the full model (Model (1.0)), both methods significantly outpace static submodel extraction approaches in achieving 70% accuracy. In summary, the proposed method stands out by attaining the desired submodels with the fewest rounds among the approaches implemented in this section.
6.4 Unparticipated Clients Performance
The above evaluations are conducted on the clients who participated in the training process. However, more general scenario includes clients who skip the training phase but need models to process newly arrived data. In such cases, our algorithm can enable the server to customize models from the trained global model for them. Same as the expression in Line 3 of Algorithm [T the server extracts a submodel encompassing the parameters [ 2 0, and sends it to the client. Note that the unparticipated clients could have capacities different from that of any client involved in the training.

---

Hetero
FedRolex
ScaleFL
FIARSE
Test Accuracy (%)
60
60
60
60
50
50
50
50
40
800
40
200
600
40
400
800
40
600 Communication Rounds
Communication Rounds
Communication
Communication Rounds
(a) Model Size 1/64
(h) Model Size 1/16
(c) Model Size
(d) Model Size
HeterofL
FedRolex
ScalefL
FIARSE
Test Accuracy (%)
40
40
40
40
30
30
30
30
20
20
20
20
800
600
800
Communication Rounds
Communication Rounds
Communication Rounds
Communication Rounds
(c) Model Size 1/64
(f) Model Size 1/16
(g) Model Size 1/4
(h) Model Size 1.0
Figure 3: Comparison of test accuracy across communication rounds for different submodel extraction
strategies under four varying model sizes (1/64, 1/16, 1/4, 1.0) global test datasets of CIFAR-10 (upper, a - d) and CIFAR-100 (lower, e h).
we employ our algorithm as well as the baselines to extract submodels with different sizes and compare their performance on unparticipated clients. Generally, the performances of all methods increase as the size extracted submodels grows. Our algorithm consistently outperforms the baseline methods. In con- trast, alternative approaches, particularly static ones like HeteroFL and ScaleFL., suffer from more signifi- cant drops performance. For the case of extracting submodel that is much smaller than the minimum size involved in the training stage, our proposed method demonstrates remarkable superiority, outperforming existing works by at least 10%.
In Figure
80
Test Accuracy (9)
60
HeteroFL
40
FedRolex
ScaleFL
20
FIARSE
10-2
10-1
10
Model Size
Figure Comparison of test accuracy across different submodel sizes for different submodel extraction methods on global test dataset of CIFAR-10.
7 Conclusion
This work introduces an algorithm for model-heterogeneity FI., named FIARSE, that utilizes importance-avie aeootannce-aware operation to extract various sizes of submodels. In detail, we utilize TCB-GD that able to optimize the clients' local parameters reflect their importance levels. Subsequently, provide a theoretical analysis and highlight that the proposed work can converge to a neighborhood of a stationary point at the rate of O (I/VT) where T is the number of communication rounds.
Extensive experiments are conducted on ResNet- 18 and Roberta-base that demonstrate the significant superiority of our proposed method over the state-of-the-ard works.
The proposed approach relies on exploiting model sparsity, which is conditionally supported by some hardware. In light of this limitation, one of the future works is to investigate neuron-wise importance-aware submodel extraction, a method that calculates the importance level of neurons without depending on additional information.
Broader Impact
This work addresses model heterogeneity in federated learning due to varying computational capaci- ties among clients. The proposed method enhances the efficiency of on-device training and reduces computation and energy demands, which is particularly significant for resource-constrainel devices like smartphones in real-world applications. Moreover, the method facilitates the practical deploy- ment of federated learning systems heterogeneous environments, making them more accessible and scalable.
10

---

Acknowledgements
The authors would like to thank the anonymous reviewers for their constructive comments. This work supported part by the US National Science Foundation under grants NSF IIS-1747614, NSF IIS-2221108, and NSF CNS-2154059. Any opinions, findings, and conclusions or recommendations expressed this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
References
[1] Ahmad Ajalloeian and Sebastian U Stich. On the convergence of sgd with biased gradients. arXiv preprint arXiv:2008. 00000, 2020.
[2] Samiul Alam, Luyang Liu, Ming Yan, and Mi Zhang. Fedrolex: Model-heterogeneeus feder- ated learning with rolling sub-model extraction. Proc. of Advances in Neural Information Processing Systems (NeurIPS 22), pages 29677-29690, 2022.
[3] Norah Alballa and Marco Canini. A first look at the impact of distillation hyper-paramen parameters in federated knowledge distillation. In Proc. of the 3rd Workshop Machine Learning and Systems (MLSys'223) 23), pages 123-130, 2023.
[4] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv preprint arXiv: 1308.3432, 2013.
[5] Sameer Bibikar, Haris Vikalo, Zhangyang Wang, and Xiaohan Chen. Federated dynamic sparse training: Computing less, communicating less, yet learning better. In Proc. of the AAAI Conference on Artificial Intelligence (AAAI'22), pages 6080-6088, 2022.
[6] Léon Bottou, Frank E Curtis, and Jorge Nocedal. Optimization methods for large-scale machine learning. SIAM Review, 60(2):223-3 2018.
[7] Sebastian Caldas, Jakub Konečny, H Brendan McMahan, and Ameet Talwalkar. Expanding the reach of federated learning by reducing client resource requirements. arXiv preprint arXiv: 1812.072 2018.
[8] Daoyuan Chen, Liuyi Yao, Dawei Gao, Bolin Ding, and Yaliang Li. Efficient personalized federated learning via sparse model-adaptaatin. In Proc. of the International Conference Machine Learning (ICML 23), pages 5234-5256, 2023.
[9] Xuhao Chen. Escoin: preprint 18Xiv:1802.10220 2018
Efficient sparse convolutional neural network inference gpus. arXiv
[10] Yi-Chung Chen, Hsi- Wen Chen, Shun-Gui Wang, and Ming- Syan Chen. Space: Single-round participant amalgamation for contribution evaluation in federated learning. In Proc. of the Advances in Neural Information Processing Systems (NeurIPS 24), 2024.
[11] Yae Jee Cho, Andre Manoel, Gauri Joshi, Robert Sim, and Dimitrios Dimitriadis. Heterogeneous ensemble knowledge transfer for training large models in federated learning. In Proc. of the International Joint Conference on Artificial Intelligence (IJCAI'22, 2022.
[12] Rong Dai, Li Shen, Fengxiang He, Xinmei Tian, and Dacheng Tao. Dispfl: Towards communication-effiiie. personalized federated learning via decentralized sparse training. In Proc. of the International Conference on Machine Learning (ICML'22 '22), pages 4587-4604. PMLR, 2022.
[13] Enmao Diao, Jie Ding, and Vahid Tarokh. Heterofl: Computation and communication efficient federated learning for heterogeneous clients. In Proc. of International Conference on Learning Representations (ICLR (CC),)20), 2020.
[14] Wenzhi Fang, Ziyi Yu, Yuning Jiang, Yuanming Shi, Colin N Jones, and Yong Zhou. communication-effcciee stochastic zeroth-order optimization for federated learning. IEEE Transactions on Signal Processing, 70:5058-5073, 2022.

---

[15] Wenzhi Fang, Dong-Jun Han, Evan Chen, Shiqiang Wang, and Christopher G Brinton. Hierarchical federated learning with multi-timescale gradient correction. arXiv preprint arXiv:2409. 18448, 2024.
[16] Jonathan Frankle and Michael Carbin. The lottery ticket hypothesis: Finding sparse, trainable neural networks. arXiv preprini a8Xiv:/803. 03635, 2018.
[17] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proc. of the IEEE conference on computer vision and pattern recognition (CVPR'IO 16), pages 770-778, 2016.
[18] Shiqi He, Qifan Yan, Feijie Wu, Lanjun Wang. Mathias Lécuyer, and Ivan Beschastnikh. Gluefl: Reconciling client sampling and model masking for bandwidth-effiiient federated learning. In Proc. of the Conference on Machine Learning and Systems (MLSys 23). pages 695-707, 2023.
[19] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv: 1503.0253331111 2015.
[20] Torsten Hoefler, Dan Alistarh, Tal Ben-Nun, Nikoli Dryden, and Alexandra Peste. Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks. The Journal of Machine Learning Research, 22())10882-11005, 2021.
[21] Samuel Horvath, Stefanos Laskaridis, Mario Almeida, Ilias Leontiadis, Stylianos Venieris, and Nicholas Lane. Fjord: Fair and accurate federated learning under heterogeneous targets with ordered dropout. In Proc. of Advances in Neural Information Processing Systems 2Neu pages 12876-12889, 2021.
[22] Tzu-Ming Harry Hsu, Hang Qi, and Matthew Brown. Measuring the effects of non-identical data distribution for federated visual classification. arXiv preprint arXiv:1909.005 2019.
[23] Ming Hu, Zeke Xia, Zhihao Yue, Jun Xia, Yihao Huang, Yang Liu, and Mingsong Chen. Gitfl: Adaptive asynchronous federated learning using version control. arXiv preprint urXiv:2211.12444 2022.
[24] Ming Hu, Zhihao Yue, Xiaofei Xie, Cheng Chen, Yihao Huang, Xian Wei, Xiang Lian, Yang Liu. and Mingsong Chen. Is aggregation the only choice? federated learning via layer-wise model recombination. In Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '24, pages 110,,
[25] Fatih Ilhan, Gong Su, and Ling Liu. Scalefl: Resource-adaptive federated learning with hetcrogencous clients. In Proc. of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'2.) 233), pages 14532-24544 2023.
[26] Eugenia Iofinova, Alexandra Peste, Mark Kurtz, and Dan Alistarh. How well do sparse imagenet models transfer? In Proc. of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR'22), pages 12266-12276, 2022.
[27] Berivan Isik, Francesco Pase, Deniz Gunduz, Tsachy Weissman, and Zorzi Michele. Sparse random networks for communication-effiiaa federated learning. In Proc. of the International Conference on Learning Representations (ICLR 22), 2022.
[28] Sohei Itahara, Takayuki Nishio, Yusuke Koda, Masahiro Morikura, and Koji Yamamoto. Distillation-baser semi-supervised federated learning for communication-effiicee collabo- rative training with non-iid private data. IEEF Transactions on Mobile Computing, 22(1): 191-205, 2021.
(29) Siddhant Jayakumar, Razvan Pascanu, Jack Rae, Simon Osindero, and Erich Elsen. Top-kast: Top-k always sparse training. In Proc. of the Advances in Neural Information Processing Systems (NeurIPS" 20), pages 20744-20754, 2020.
[30] Divyansh Jhunjhunwala, Shiqiang Wang, and Gauri Joshi. Fedexp: Speeding up federated aver- aging via extrapolation. In Proc. of the International Conference on Learning Representations (ICLR 22), 2022.
12

---

[31] Yuang Jiang, Shiqiang Wang, Victor Valls, Bong Jun Ko, Wei-Han Lee, Kin K Leung, and Leandros Tassiulas. Model pruning enables efficient federated learning on edge devices. IEEE Transactions on Neural Networks and Learning Systems, 2022.
[32] Peter Kairouz, H Brendan McMahan, Brendan Avent, Aurélien Bellet, Mehdi Bennis, Ar- jun Nitin Bhagoji, Kallista Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, al. Advances and open problems in federated learning. Foundations and Trends in Machine Learning, 14( (4(1))): 1-20, 2021.
[33] Honggu Kang, Seohyeon Cha, Jinwoo Shin, Jongmyeong Lee, and Joonhyuk Kang. Nefl: Nested federated learning for heterogeneous clients. arXiv preprint urXiv:2308.07760 2023.
[34] Sai Praneeth Karimireddy, Satyen Kale, Mehryar Mohri, Sashank Reddi, Sebastian Stich, and Ananda Theertha Suresh. Scaffold: Stochastic controlled averaging for federated learning. In Proc. of the International Conference on Machine Learning (ICML 200), pages 5132-5143.
PMLR, 2020.
[35] Minjae Kim, Sangyoon Yu, Suhyun Kim, and Soo-Mook Moon. Depthfl: Depthwise federated learning for heterogeneous clients. In Proc. of the International Conference Learning Representations ((CLR'22), 2022.
[36] Jakub Konečný, H Brendan McMahan, Felix X Yu, Peter Richtárik, Ananda Theertha Suresh, and Dave Bacon. Federated learning: Strategies for improving communication efficiency. arXiv preprint arXiv:1610.05440 2016.
[37] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images, 2009.
[38] Eldar Kurtic, Denis Kuznedelev, Elias Frantar, Michael Goin, and Dan Alistarh. Sparse finetuning for inference acceleration of large language models, arXiv preprint arXiv:2310.06927, 2023.
[39] Mark Kurtz, Justin Kopinsky, Rati Gelashvili, Alexander Matveev, John Carr, Michael Goin, William Leiserson, Sage Moore, Nir Shavit, and Dan Alistarh. Inducing and exploiting activation sparsity for fast inference on deep neural networks. In Proc. of the International Conference on Machine Learning (ICML 20). pages
2020.
[40] Ang Li, Jingwei Sun, Binghui Wang. Lin Duan, Sicheng Li, Yiran Chen, and Hai Li. Lotteryfl: Personalized and communication-effieee non-iid datasets. arXiv preprint arXiv: 033711 2020.
federated learning with lottery ticket hypothesis on
[41] Ang Li, Jingwei Sun, Xiao Zeng, Mi Zhang, Hai Li, and Yiran Chen. Fedmask: Joint computa- tion and communication-efiin efficiien personalized federated learning via heterogeneous masking. In Proc. of the ACM Conference Embedded Networked Sensor Systems (SenSys 22), pages 42-55, 2021.
[42] Rui Li, Fenglong Ma, Wenjun Jiang, and Jing Gao. Online federated multitask learning. In Proc. of the IEEE International Conference on Big Data (BigData' (9)))aaa"9)),,,))) pages 215-220, 2019.
[43] Tian Li, Anit Kumar Sahu, Manzil Zaheer, Maziar Sanjabi, Ameet Talwalkar, and Virginia Smith. Federated optimization in heterogeneous networks. In Proc. of the Annual Conference on Machine learning and systems (MLSys 20), volume 2, pages 429-450, 2020.
[44] Xiang Li, Kaixuan Huang, Wenhao Yang, Shusen Wang, and Zhihua Zhang. On the convergence of fedavg on non-iid data, arXiv preprint 19Xiv:1907.02/89. 2019.
[45] Dongping Liao, Xitong Gao, Yiren Zhao, and Cheng-Zhong Xu. Adaptive channel sparsity for federated learning under system heterogeneity. In Proc. of the IEEF Conference on Computer Vision and Pattern Recognition (CVPR' 23), pages 20432-20441, 2023.
[46] Tao Lin, Lingjing Kong, Sebastian U Stich, and Martin Jaggi. Ensemble distillation for robust model fusion in federated learning. In Proc. of Advances in Neural Information Processing Systems (NeurIPS 200), pages 2351-2366 2020.
13

---

[47] Baoyuan Liu, Min Wang, Hassan Foroosh, Marshall Tappen, and Marianna Pensky. Sparse convolutional neural networks. In Proc. of the IEEE conference on computer vision and pattern recognition (CVPR'IS) pages 806-814, 2015.
[48] Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. Roberta: A robustly optimized bert pretraining approach. arXiv preprint arXiv: /907. 1692, 2019.
[49] Zechun Liu, Kwang-Ting Ting Cheng, Dong Huang, Eric P Xing. and Zhiqiang Shen. Nonuniform-te -o- uniform quantization: Towards accurate guantization via generalized straight-throus estimation. In Proc. of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR'22)) pages 4942 4952, 2022.
[50] Bing Luo, Xiang Li, Shiqiang Wang, Jianwei Huang, and Leandros Tassiulas. Cost-effective federated learning design. In Proc. of the IEEE Conference on Computer Communications 1NFOCOM'21), pages 1-10, 2021.
[51] Xiaolong Ma. Minghai Qin, Fei Sun, Zejiang Hou, Kun Yuan, Yi Xu, Yanzhi Wang. Yen-Kuang Chen, Rong Jin, and Yuan Xie. Effective model sparsification by scheduled grow-and methods. In Proc. of the International Conference on Learning Representations (ICLR (CL 2021.
[52] Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Aguera y Arcas. Communication-effiiiene learning of deep networks from decentralized data. In Proc. of the International Conference on Artificial intelligence and statistics (AISTATS' 17), pages 1273- 1282, 2017.
[53] Aritra Mitra, Rayana Jaafar, George J Pappas, and Hamed Hassani. Linear convergence in federated learning: Tackling client heterogeneity and sparse gradients. In Proc. of the Advances in Neural Information Processing Systems (NeurIPS pages 14606-14619, 2021.
[54] Hesham Mostafa and Xin Wang. Parameter efficient training of deep convolutional neural networks by dynamic sparse reparameterizztion. In Proc. of the International Conference on Machine Learning (ICML' '1),, pages 4646-4655. PMLR, 2019.
[55] Vaikkunth Mugunthan, Eric Lin, Vignesh Gokul, Christian Lau, Lalana Kagal, and Steve Pieper. Fedltn: Federated learning for sparse and personalized lottery ticket networks. In Proc. of the European Conference on Computer Vision (ECCV'22), pages 69-85, 2022.
[56] Sejin Seo, Seung- Woo Ko, Jihong Park, Seong-Lyun Kim, and Mehdi Bennis. Communication- efficient and personalized federated lottery ticket learning. In Proc. of the 2021 IEEE Inter- national Workshop on Signal Processing Advances in Wireless Communications (SPAWC'21), pages 581-585, 2021.
[57] Jaemin Shin, Yuanchun Li, Yunxin Liu, and Sung-Ju Lee. Fedbalancer: Data and pace control for efficient federated learning heterogeneous clients. In Proc. of the Annual International Conference on Mobile Systems, Applications and Services (MobiSys pages 436-449, 2022.
[58] Egor Shulgin and Peter Richtárik. Towards better theoretical understanding of independent subnetwork training. arXiv preprint arXiv:2306.16453 16484, 2023.
[59] Samuel Stanton, Pavel Izmailov, Polina Kirichenko, Alexander A Alemi, and Andrew G Wilson. Does knowledge distillation really work? In Proc. of the Advances in Neural Information Processing Systems (NeurIPS pages 6906-6919, 2021.
[60] Haoyu Wang, Handong Zhao, Yaqing Wang, Tong Yu, Jiuxiang Gu, and Jing Gao. Fedke: Federated knowledge composition for multilingual natural language understanding. In Proc. of the ACM Web Conference (WebConf'22 22), pages 1839-1850, 2022.
[61] Haozhao Wang, Yichen Li, Wenchao Xu, Ruixuan Li, Yufeng Zhan, and Zhigang Zeng. Dafkd: Domain-aware federated knowledge distillation. In Proc. of the IEEF/CVF conference on computer vision and pattern recognition (CVPR'23), pages 20412-20421, 2023..
14

---

[62] Haozhao Wang, Yabo Jia, Meng Zhang, Qinghao Hu, Hao Ren, Peng Sun, Yonggang Wen, and Tianwei Zhang. Feddse: Distribution-awen aware sub-moder extraction for federated learning over resource-constrainee devices. In Proc. of the ACM Web Conference (WebConf"244 pages 2902-2913, 2024.
[63] Haozhao Wang, Haoran Xu, Yichen Li, Yuan Xu, Ruixuan Li, and Tianwei Zhang. Fedoda: Federated learning with cross cross-rounds divergence-awant aggregation. In Proc. of the International Conference on Learning Representations (ICLR 2024.
[64] Jianyu Wang, Qinghua Liu, Hao Liang, Gauri Joshi, and H Vincent Poor. Tackling the objective inconsistency problem in heterogeneous federated optimization. In Proc. of the Advances in Neural Information Processing Systems (NeurIPS' 20), pages 7611-7622 2020.
[65] Jianyu Wang, Zachary Charles, Zheng Xu, Gauri Joshi, H Brendan McMahan, Maruan Al- Shedivat, Galen Andrew, Salman Avestimehr, Katharine Daly, Deepesh Data, et al. A field guide to federated optimization. arXiv preprint arXiv:2107.06911 2021.
[66] Jiaqi Wang, Xingyi Yang, Suhan Cui, Liwei Che, Lingjuan Lyu, Dongkuan Xu, and Fenglong Ma. Towards personalized federated learning via heterogeneous model reassembly. arXiv preprint arXiv:2308. 08643, 2023.
[67] Kaibin Wang, Qiang He, Feifei Chen, Chunyang Chen, Faliang Huang, Hai Jin, and Yun Yang. Flexifed: Personalized federated learning for edge clients with heterogeneous model architectures. In Proc. of the ACM Web Conference (WebConf" 23)), pages 2979-2990, 2023.
[68] Xingchen Wang, Haoyu Wang, Feijie Wu, Tianci Liu, Qiming Cao, and Lu Su. Towards efficient heterogeneous multi-modal federated learning with hierarchical knowledge disentanglement. In Proceedings of the ACM Conference on Embedded Networked Sensor Systems (SenSys '24) 2024.
[69] Yangyang Wang, Xiao Zhang, Mingyi Li, Tian Lan, Huashan Chen, Hui Xiong, Xiuzhen Cheng, and Dongxiao Yu. Theoretical convergence guaranteed resource-adapiiee federated learning with mixed heterogeneity. In Proc. of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD") 23), pages 1444-2455, 2023.
[70] Feijie Wu, Shiqi He, Song Guo, Zhihao Qu, Haozhao Wang. Weihua Zhuang, and Jie Zhang. Sign bit is enough: A learning synchronization framework for multi-hop all-reduce with ultimate compression. In Proc. of the ACM/IEEE Design Automation Conference (DAC'22), 22), pages 193- 198, 2022.
[71] Feijie Wu, Song Guo, Zhihao Qu, Shiqi He, Ziming Liu, and Jing Gao. Anchor sampling for federated learning with partial client participation. In Proc. of the International Conference on Machine Learning (CCML'23), pages 17379-374166 2023.
[72] Feijic Wu, Song Guo. Haozhao Wang. Haobo Zhang, Zhihao Qu, Jie Zhang, and Ziming Liu. From deterioration to acceleration: A calibration approach to rehabilitating step asynchronism in federated optimization. IEEE Transactions on Parallel and Distributed Systems, 34(5): 1548 1553,,15900000 2023.
[73] Feijie Wu, Zitao Li, Yaliang Li, Bolin Ding, and Jing Gao. Fedbiot: Llm local fine-tuning in federated learning without full model. In Proc. the ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD'24) 24), pages 3345-3355 2024.
the
[74] Haibo Yang, Minghong Fang, and Jia Liu. Achieving linear speedup with partial worker participation in non-iid federated learning. In Proc. of the International Conference on Learning Representations (ICLR 20), 2020.
[75] Haibo Yang, Xin Zhang, Prashant Khanduri, and Jia Liu. Anarchic federated learning. In Proc. of the International Conference on Machine Learning (ICML'22), pages 25331-25363, 2022.
[76] Kai Yi, Nidham Gazagnadou, Peter Richtárik, and Lingjuan Lyu. Fedp3: Federated personalized and friendyy network pruning under model heterogeneity. In Proc. of the Twelfth International Conference on Learning Representations (ICLR 2024.
15

---

[77] Jie Zhang, Song Guo, Xiaosong Ma, Haozhao Wang. Wenchao Xu, and Feijie Wu. Parameterized knowledge transfer for personalized federated learning. Proc. of the Advances in Neural Information Processing Systems (NeurIPS 2/), pages 10092-10104, 2021.
[78] Lin Zhang, Li Shen, Liang Ding, Dacheng Tao, and Ling-Yu Yu Duan. Fine-tuning global model via data-free knowledge distillation for non-iid federated learning. In Proc. of the IEEE/CVF conference computer vision and pattern recognition (CVPR 22), pages 10174-10183, 2022.
[79] Xiang Zhang, Junbo Zhao, and Yann LeCun. Character-level convolutional networks for text classification. In Proc. of the Advances in Neural Information Processing Systems (NeurIPS' 2015.
[80] Yuan Zhang, Wenlong Zhang, Lingjun Pu, Tao Lin, and Jinyao Yan. To distill or distill: Towards fast, accurate and communication efficient federated distillation learning. JEEE Internet of Things Journal, 2023.
[81] Hanhan Zhou, Tian Lan, Guru Venkataramani, and Wenbo Ding. Every parameter matters: Ensuring the convergence of federated learning with dynamic heterogencous models reduction. arXiv preprint 1rXiv:2310.08670, 2023.
[82] Maohua Zhu and Yuan Xie. Taming unstructured sparsity on gpus via latency-aware opti- mization. In Proc. of the ACM/IEEE Design Automation Conference (DAC'20), pages 1-6, 2020.
16

---

A Related Work
Computation Heterogeneity in FL. Computation heterogeneity in FL has become a critical area of research due to the varying computational capacities of participating clients. In traditional FL setups, each client is expected to perform the same volume of computation, such as training on local datasets for a fixed number of iterations, regardless of their hardware capabilities resource availability 68). This assumption leads to inefficiencies, particularly when slower devices Recent work has proposed adaptive aggregation strategies to handle computation heterogeneity by assigning different workloads or varying the number of local updates based on client resources, allowing faster clients to contribute
[4 15
18
24
63
cause stragglers that delay model aggregation 2
44
64
more to the global model while slower clients contribute less frequently [43] 50 53 57 64 72).
However, these works require the clients train the full model, so they are infeasible when some of the clients cannot load the full model due to limited computation resources. In contrast, our work extracts a submodel for each client that fits within their computational capacity.
Model Customization in FL. In addition to submodel extraction, another effective method for facilitating model heterogeneity is model customization [1]
28 46 66 77 80]. This approach
allows clients to construct local models that align with their local computation resources. Since the clients' local models could be very distinct, the existing works implement model aggregation through the technique of knowledge distillation [19 46 61 78.. In detail, each client first locally trains its model on a shared public dataset, and then sends the model's output (i.e., logits) to the server. The server gathers and aggregates clients' outputs into unified model output and broadcasts it to the clients [60]. Prior to the next round of local training, the clients thereby fine-tune the local models by incorporating the aggregated logits. Although the process effectively transfers knowledge across heterogeneous models, model customization requires a shared public dataset that should have a similar distribution with the clients' training data, which is unattainable in some cases [ [59]. In our work, we do not require public dataset, rendering it applicable to broader range of applications.
Model Sparsification in FL. Model sparsification, also known as model pruning, intrigues in- creasing research focuses with the introduction of lottery ticket hypothesis [16). This hypothesis addresses the existence of a sparse submodel within a large model, capable of direct training to yield improved performance. Early works [9 47 (22) have explored sparse models to mitigate the computation overhead. Notably, the industry has recently achieved remarkable advancements in the development of hardware that facilitates the training and inference of sparse models (20 26 38 39).
In the context of FI., two distinct strategies in search of an optimal sparse submodel: dense-to-sparse 27 31 41 and sparse-to-spee to-spe 5 12
55 56) These strategies are distinguished based on whether the global model starts dense. both approaches, clients initialize with a global model and iteratively train towards sparse model to mitigate over-parameterization Nonetheless, these methods face challenges when client computation capacities differ, particularly when loading the global model exceeds the maximum computation capacities of some clients. Consequently, there arises need for algorithms capable of tailoring submodels to accommodate various client computation capacities.
40
An existing work, Flado [45), realizes that the server tailors the submodels to align with various computation resources among clients. achieves the performance trade-off between the global model and the clients' submodels by differentiating model parameters based on their importance levels. However, this advantage comes at the cost of requiring clients to explicitly maintain the importance score of each model parameter. This requirement, consequently, introduces a considerable overhead on each client in terms of both storage and computation, which imposes great challenges on essoucce-onsttrained devices. Contrasting with Flado, our FIARSE explores the correlation between a model parameter's s importance level and its value. implicitly represents the importance level through the parameter's value, thereby eliminating the need to explicitly maintain separate importance scores for each model parameter.
17

---

B
Derivation of Equation (3)
Before deriving Equation
3
we should find formula for aM
d2
0M i
0g
12,1200
(6)
05
J5g
0,
j
0|āy1
0
[ 0,
12,1220.
0ny
[5g] + 0:
3
U 0|ū,|
20;
1 12,120
(8)
dn,
(10y) + 0:)2
As defined in the paper, M = 12,12,120, Therefore, we can obtain Equation 3 via
0F,(5 @ M
aF,( @ M
a O
(9)
0E @ M
OT
0F 3 M
dM
MM +20
(10)
07 の M
2/ M (1+ [ + 0,)3
VF の M()
(11)
where 3 is an element-wise product.
C Proof of Theorem 5.5
Prior to giving detailed proofs of the theorems, we cover some technical lemmas in this section, and all of them are valid in general cases.
C.1 Useful Lemmas
Comprehensive deseription for the aggregation on the server. Since FIARSE generates the submodel based on the parameter importance reflected by the magnitude of the model parameters, submodel is nested within other submodels that with larger size. Given set of model sizes {7s [M])),) we define a sorted set Y' Usg[N] (1i). where 0 < % < ... < Y S and n = h/l < N. Let us partition the global model &; into the disjoint submodels @1,10:11 Lt.166111 .... % Lti, No Nº
These models are separately held by set of clients
No._, 0. In round f, the server samples set of clients A to train
the model, and these models are therefore held by Ang 2 AA 2 ... 2 Ax, 2 Notably, the smallest submodel should be held by all clients, i.e., Nog [N], Ang = A. Let us define
AggieA (Ax Uf 1781. where
1
Eiedy
Aa "ng""
A #
An3s
(12)
0,
Ari =
Therefore, the global update follows Te41 = H. - 1aAg9iEA (wt have the following lemma:
(1))
Upon the description,
Lemma C.1. For vector E Rd, we partition it into sets, where we present it in Table 2 we select an A-client set out of a total of N clients [N]. Let us define that
Suppose
Aggie[M| (v)
U JE[N]
Σ NEN
Agg.eA (v) = U
Σ iEdns
(1) M
(13)
Nag
JEiN]
Anz
18

---

Table 2:
Vector Partition across Different Sizes. These notations are the same as the definition in
Equation T2
Submodel
"
1/
7/ 16-2
1/2-1=1 :1
Clients set
Na6
Nz
Nypa
Participation set
Anb
Arg.
Therefore, we have
N- (<-(x/s)
(*)
RAggiaA (v)
U jE(m)
( (3-
(14)
Naasl
NN
(M-(pxss)
Specially, Af N | we define
O.
Proof. For given submodel "[ng-1933 there are Nog clients holding the submodel. In other
clients do not hold any parameters of [[5]-;a] Ifa selected client e A holds words. [ ( [Na3] )
the submodel "ns]" it will divided by an integer & (1,..., A} (i.e., Ans k) with
probability of (12 >0(21111 aggregation:
Therefore, this part is expected to obtain the following result after (i)
Nug 11.l-1)-
(V-
EAggieA (Mbs m9r1
k-1
A-k
(15)
h iEN.s
1=1
Nass (
A-k
(i)
(16)
(7)
173s
k=1
Nag
KENN''
N-
1
2
(17)
N₂
iEN
By concatenating all j E [n], we can attain the desired results.
In addition to the above lemma, we provide bound for integer of [1....,N-AA)
and c (aa)
where c an
Lemma C.2. Given N and A are two integers where A S N, and e is an integer of (1,..., N- A}, the following two inequalities always Irue:
A N
A
<1;
(18)
N
Proof. For the first inequality, the lower bound holds when 1, while the upper bound constantly satisfies.
For the second inequality, we define f(c) cally decreasing.
and we aim to show that ((c is monotoni-
a (N)
19

---

Toward the goal, we reduce and prove the following inequality holds:
N- (1
1 (c-1) (A)
(19)
c.
N c - (c-1) 1).
[N (N-c) (N
A -
(20)
A
A
(N - c)!
N
(c(N - -c+ 1) - (c () c- 1))
(21)
(N c - 1)!
(N AYLA!
N
(N-c))
N c- A+ (N - c- 1)
(22)
(N-AM
(N-A-0)
cA
6-1
A
1+ N-C- $ II
1+
(23)
N
A-i
1=
Next, we show the establishment of Equation
23
by mathematical induction:
When c = 1, we have LHS = +
N-A while RHS = 1 + N-A
A
Apparently, the inequality
holds.
Let us assume that, when c= k, the conclusion holds, i.c., 1 1+ A+1
k4
II.E00 [1
When + have
II
( + N
k-1
II
1 1+
A
A
(24)
N - A
1=0
kA
1+ N - N-A-A A
(25)
N - k - A+1
(k: + 1)A
(26)
N A-A
This shows that the inequality (i.c., Equation decreasing. As c is an integer of {1...., N
23 still holds, indicating that f(c) is monotonically
AJ. we have
A
f()) s f(1)
(27)
N
Apparently, we can attain the desired results mentioned in Equation (18)
C.2 Preliminary
Lemma C.3. Suppose that Assumption 5.1
5.2 and 5.3 hold. Let the local learning rate satisfy
W S
With FIARSE, we have the following conclusion:
2L/K(K+4))
K-1
It 1
ΣE k=0
36K
(8/10112
IVF(()))1
(28)
N [E[N]
L.k
Proof. First, we establish a recursive relationship between
(n
01,4+1 #; and
(6)
E
1.k+1
(3)
D2
E
(4)
m
V
(2) F
M!
(6)
(z122) zz
2
(29)
2
+
K
1
E
t.k
(4)
Zt
12
2
+ (1
+
K mm
V
(n)
(1)
2 M (z
(3)
(30)
1
2
<
1
+
K
E
F.
Zt
2
(31)
20

---

+ +.(11 ([1+AM K)n E
V
Pi
Lish
(6)
o
M! (x/x) - Va @1 ( M (t:)
(
(
(32)
1 M (mx) V2, (a:) (#:) 1|
+ +4(1 + K)n E
Va. Pi
(33)
+ 4(1 + K)p E
V Fi
(Tt)
(ã:)
VF (ū (a:)
(34)
+ (1 + K)nj
E
VF
(355
where the second term in Equation
30 is expanded to four parts: Equation (32) Equation (33
Equation (4). and Equation (35). Furthermore, applying Assumption 5.1 to Equation (2 and
Assumption 5.3 Equation (33). along with the equalities Væ, (ãx) @ M (.x) = V 0mm
(itz)
and VF ( ④ M! (āx) = pl0m)) (ãt), we simplify the above inequality for
E
a 1,,41 2t 2
(i)
2
(36)
l|
$ 1 + K
- 4(1 + K)m L2 IE 1
(37)
+ 4(1 km 1|xx11 + EE VF Orreel (ãx) VF 00ml (3z) ||2 E VF (z))
(38)
Let Cb
C= of 11211 + E
VF!. 0:>1 (ax))
V (ã:) | +E +E| 0:nd (3x) 1/
(39)
2
As m 2L/K(K+4))
have
E
r,,+1 - 3c
(3)
2 S
1 +
K
2
2/th
(1)
- 8t | + 4(1 + KYni C
(40)
4(1 + K) (1+ 3 (1+2)
ni
(41)
K
$ 36(1 + K)ni C
(42)
Equation 42
holds because (1+ )²
k W 9 for all & E N4. Therefore, for all l E [K], we have
E
a
(8)
x
36(1 K)n? 0? |
(43)
2
+ 36(1 + K)yî
V 0:rdl (wx) V p((0m))
(a+) ||3
122 + E / [0mml (itz)
22
2
(44)
With this conclusion, we can bound the left-hand side of Equation
28
which is
K-1
K
Et
Σ
E
(6) t
x
||:
|
(45)
N
NE(N]
K=
NE(N
k=
1
36K²
|
2
+
E
V
[0:+:)
(wx)
V 10:ml (ax:)
2 + R
V [ (
(46)
N
NE[N]
Finally, by applying Assumption 5.2
to Equation
46 we achieve the desired conclusion.
Lemma C.4. Suppose that Assumption 5.7
5.2 and 3.3 hold. Let the local learning rate satisfy
For any t E [T] j E {o..... n), let v 1761 be
<
min 2L1/K(K+1) 6LT((+1)AA
| = V (ix) v,
(8) (i o M (a12) (47)
F
|as/ K KEN
0=
21

---

With FIARSE. we have the following conclusion:
E
1
1779
2
S
4A62
| 7 L? + (VV (48)
2
Proof.
In the beginning, let us define
9:
V
(it) V 11.11-1119 (0, 0 M,a (@+)).
(49)
9i.k
F
p Fiik M² (z
V Vz, -
To o OM (ai)
(50)
f.k
According to Equation
win 1775 equivalent to
K h6
g.
9..k
(51)
Nos
iEN,;
Nag K
iENgg
k=0
To find a bound for Equation Kauchy-Shward inequality:
48 we try to bound E ||l| [ using generalized mean inequality and
2
K
I
1
17)00
22
gr
+2E
91.k
2
Nog
NENg
Na1s
K
VEN,Y
1
(52)
$ 2
E
ge
100
2
+2
1
K
Σ
9i,
170)
Nog
K
iEN,3
km0
(53)
With the inequality above, the LHS of Equation 48) is bounded by
- N- (-(M%ss)
N
by
$2
E
91
(54)
j=0
W
N73
iEN.3
No
11
Σ
K
1755
1=
(x)
Nri
K
VEN
(55)
According to Lemma C.2
we have
N-
A
5
(56)
())
Nog
N
Therefore, we further bound Equation 55) for
N
|x
A
E
b2 2
1
1755
2
(57)
12
1=0
24
E
g.
2
+
24
Σ
K-1
Σ
E
0
17500
2
(58)
N
NK
0=
j= 0 NEN
22

---

24 N
Σ [E[N]
E
9:
(1)
+
2A NK
Σ KE[N]
K-1
9r.k
(c0)(())
2
(59)
k=
where the last equation holds because the second norm is non-zero when the client i [N] owns the part 1n/-1 : 3 E {O....,,11, ,,),, and different parts (i.e., bi-1:nn. 75] for different js) are independent with each other when calculating the second norm.
With Assumption 5.3 and Assumption 5.1 we separately bound two terms in Equation 55 for
g:
- 6 2 12:
(0:)](()) 9i.k
S
2 L.k
x
(60)
Therefore, With the inequality above, the LHS of Equation (88 is bounded by
N
No:
2
E
1
(61)
(*)
3m0
K
2A N
of
2A
Σ
1
3t ||
(62)
NK
E.k:
ic(N]
NE(N]
k=0
$2A63 @ 1 72K L?
68 2 12 0
+ VVF (a))11²
(63)
Since the learning rate meets the constraint of Lemma Equation 63 is obtained when Lemma C.3 applies. Furthermore, with the defined learning rate, we can attain the desired conclusion of Equation (48)
Lemma C.5. Suppose that Assumption
5.1
5.2 and 5.3 hold. Let the local learning rate satisfy
" S min 2L//K(++))) (LV((+1)A
With FIARSE, we have the following conclusion:
E [ 2.112 < 8 k2
(A6" | + |VF (..) (2.) 122++++0)
(64)
Proof. The recursive function of the global updates of FIARSE follows that
K Σ
o M (z(.))
L(41 x. 1)>
Agg
V
ca d,k
Fi
Li.k
(65)
h=0
I/ 11-561 to
Let us define g.,k
hn (n)0))
(1(1 t
+ M.. (z.²))
9i,k
(1)
(66)
Therefore,
K K-1
K 1
AggieA
Fi
2 M (a(22)
U jEin]
ge.k
175100
(67)
k==
mik
Axg
REA.3
k=0
The bound for | &; 112 formulated and simplified as follows:
K
ns71
100
E [1+11
-E
Pek
(68)
j=0
Anys
iEA,
0=0
2
<m
E
K
Σ
K-1
9
100
2
(69)
1=0
Ang
i
k=0
23

---

(M-(Mo3))
(N-
K-1 1
(*)
m
T K
IR
gih
(70)
1= 1
N3
Equation 66
is obtained based on Cauchy-Shwarz inequality, and Equation (70) holds according to
Lemma C.I
Let us define
9i (/ Va, P 1 (ir o M. (tt) - (ãx) o MMa (ãx);
(71)
b/- (/-m0)
VF by (zt) o M¹ (ã:) 4 (ã)).
9:
(72)
Since
91.k
9i,k
+ gt
(
+ +g. (
+ v-b--1n (a.),
(73)
(75((( defined Equation (50), we bound
2 by splitting it into four 2
where
91.k
9
terms:
bg 17 97.k
(74)
<4
9i,k
h4 $100
+
9:
100
||
+
+
4
||
2
+ 4 V (ā:))
(75)
2
2
Therefore, to bound Equation
(70).
should analyze the following inequality, i.e..
K-1
ΣΣ JEINNN
gek
(76)
Naj
(a)
2
h=
N-
(
<4 Σ
E
|0.b6
||
(77)
(X)
Nrg
1= EEN
k=U
(
+4K Σ
1
E
gi
1
2
(78)
N₂i
0= N
())
(N-
1
1 1-7(6))))))) gr
2
+4K
E
(79)
N₂i
3=0 SEN
N
+ 4K
E
V VE
(ãx 1
(80)
1=0
There are four terms in the above inequality, i.e., Equation (77). Equation Equation (0) Subsequently, analyze these four terms one by one.
78
Equation
79 and
For Equation we apply Lemma C.2 and obtain that
N-
N-
Σ
N
E
9rk
100
A N
Σ
B
Dek
1
J=OIEN
K=D
N₂3
f=
iEN.
k=0
(81)
24

---

In Lemma .4
we mention that
Σ
K-
9
K-
Dr,k
(00)(()
2
2
Pe,k
2
S 1.2
2,6
(1)
Zt
12
1=0 DE
k=
[E[N]
k=
(82)
Therefore, Equation
77 is further bounded by
N
No3
K ΣΣΣ j=
11
92.
2/
AT,
Σ
K-1 Σ
E
36
k=0
Noj
A
iE[N]
k=
(83)
Similarly, Equation
78 is bounded for
N
Σ
E
2
A
E
9:
0:
(84)
Nog
N
SE[N]
In view that the non-zero part of V and attain that
V U::7el
(.:) equivalent to M (æx). we apply Assumption 5.3
g
of
|
(85)
2
Therefore, the bound of Equation 78
N- (xsl)
1 - As?
Σ
E g.
(86)
Noi
IEN
10)(M-Mpan (risl) (x)
(2)-
For Equation (79), apply
I 1 and Assumption 5.2 and obtain
-M~ [M-ss)
(2)
Σ
E
9. 1o
17310
I 0²
(87)
(
With (2) -2)-(* (-11/s
< 1. Equation (80) is bounded and simplified for
())
N (irl))
1 (#x)
2
n
VF
(3x)
|IFF($)))
(88)
In conclusion, Equation
70
is bounded by
Nog
K-1
Σ
E
gi,k
In
(89)
5= DENN
of
0=0
N
A
4AL2
K -
E
x 2.4
1|2
+
4K
Ao?
1
4Ko² + +4K (a,)
(90)
N
[E[M]
A=
25

---

By applying Lemma
C3
we further simplify the inequality for
N-
K-
B 18100.
13 171100)
(91)
(*)
/=0 N3 k=0
N2
<4KA (L (1+ 36mj K
L) 83
|
2
4K (1 +1+ 36n/ AL) 0² + 4K (1 (1 (1+361
VF (it)11
(92)
By applying the above learning rate, we can attain the desired conclusion.
C.3
Main Proof of Theorem 5.4
As set F()) with the mask M 1 Nxd Assumption 5.1 is reduced to the statement that for all 0 E Rd
(F((v) VF((o)l2 2 L| 8||2, E [M].
Therefore, the global objective function F-)) is L-smooth function. As result, we have
T. "E | =
EF(241) F( S E (VF (1+1 3z)
(93)
2
The iteration function in FIARSE follows that:
Local updates:
M (z/.1)
F.++1 Lt,k m
Ve Fi
(94)
Global update:
K
(x)))
2 Mi (z.
Øe+1 C. Ag9
2if Lith
Pi
(95)
In1 1:7)((1)
Similar to Lemma C.5
we define 9t,k
to be
9,k
F.
L M (z())
(96)
Therefore,
AggieA
(1)
Fi
(2) (
Mn (a(22)
U jE[m]
9
bo 1100
(97)
Arys
REA.,
R=
In the proposed algorithm, the parameters are updated only when the submodels hold the counterpart. In this means, the definition for v1bs-and (ã+) is
phb--1n (ax))
Σ
V (r) (ax))
(98)
Noss
iEN..
Therefore, by applying Lemma C.I have
E E(F (wt) :e+1 ..))
E
pupli--o 1751 (fx.)
21441
178-19961
(99)
N No
n
E VFh(-1n)) (it)) -
(2)
Σ
K
Σ
gek
[n
1
(100)
NNag
(N)
1=0
i N
k=0
26

---

(N
K-1
1 K)
(*)
E
(ク(ク-113) (#t))
1
9
hg
m3))(0)
(101)
K
iEN
k=0
(x-1>1s))
(N-
(x)
|F
mi)
(.:)
(102)
2
(N)
i=0
N [
7
K
n
(A)
VF 115--199 (āx)
K
b m7)(6)
9 9t,k
2
1=0
Nass
K iEN.g
k=
(103)
where the last equation is built upon (a, b) = - ||a112 - 116112 + ||a
bl2
||a 12
al ||a
bll2- Lemma C.2 mentions that
N (
A N
1,
(104)
and we simplify Equation [103
with the conclusion from Lemma C.4
E (VF (it)
-;-1 - xb))
(105)
7 KA A
IVF ( 11
(4A6%
A2 L2
(IF+ (
(106)
2.V
2
By applying the above local learning rate, we can further simplify the equation for
E (VF F (w.) 5o+1 - 2x) S K A
(..) (1. 2n K A8 | 122 2 L'o²
4N
(107)
Plugging Equation (107) and Lemma C.5
back to Equation 93 we have
EF(2++1) - F(t,) S T) T K A
VF
L 2n K A | 1 + 36K2 36 L²
4N
n L
Ab
| + VF (a.) 2 +0²)
(108)
With the above learning rate, we reorder the formula of Equation 108 for
EF EF(#411 F(tt) < Mem KA
IFF (ã:)11² + K 1
8N
+ Am K (n. + 9KmL²) o²
(109)
By summing Equation (109 for all t {0..... T 1}. we have:
T
F. - F--F($t) S EF (1) F( = (BF( -
(110)
1=
KARKA A
T
T-1
VF 2 + 4n.mKA
82 | 12 4m K (n. (T. +9Km p²T
8N
(111)
By reorganizing the inequality above, we have:
(F - F.N
64N
32.V
T Σ
IVF (a:)33
T. KLo² +
Σ
10
(112)
n. KAT
EE(T]
Based on Theorem 5.4 when we apply local and global learning rates as described in Corollary 5.5
we can obtain the desired conclusion that the proposed FIARSE can converge to a stationary point at rate of O(IvVT).
27

---

Table 3: Hyperparameter Settings
CIFAR-I0 CIFAR- 100
AGNews
Local Epochs
2
Batch Size
20
20
20
Communication Rounds
800
800
300
Optimizer
SGD
SGD
Adam W
Learning rate (log10)
(-1
(-1,-2)
{-3, -4, -5}
Momentum
(0.0, 0.9)
(0.0, 0.9)
(00.9, 0.95))
Table 4: Test accuracy under four different submodel sizes on different datasets, and 20 out of 100 clients participate in the training at each round. To more specific, the columns from "Local" to "Model (1.0)" evaluate the test accuracy on the local test datasets, while "Global" evaluates the average test accuracy of the global model four different sizes (1/64, 1/16, 1/4, 1.0) on the global test dataset.
CIFAR-I0 10
CIFAR- 170
Method
Local
Model (1/64)
Model
Model
Model
Global
Local
Model
Model
Model
Model
Global
(1/16)
(1/4)
(1.0)
(1/64)
(1/16)
(1/4)
(1.0)
HeteroFl.
69.93
61.40
69.02
72.36
76.76
67.92
32.23
28.32
31.52
33.96
35.12
30.30
FedRolex
68.64
53.16
67.00
71.60
82.80
66.75
33.00
21.36
34.12
36.72
39.80
31.33
ScaleFL
72.05
68.44
71.12
70.36
78.28
67.27
39.57
37.92
39.60
41.84
38.92
37.63
FIARSE
79.65
73.84
80.00
80.40
84.36
76.61
42.27
40.32
43.28
43.52
41.96
38.97
D Additional Experiments
D.1 More Threshold Selection Strategies
Layer-wise threshold gives set of thresholds based on the computation cost of each layer E [L], where L the number of layers of the global model. Therefore, the threshold for each layer is 0,, TopK.,. (lã and 8, {8r))
Sharding-wis wise threshold is way in the middle that partitions the model into several shardings, and each sharding encompasses couple consecutive layers. This is designed for the case when the parameters have distinet distributions across the model. In this case, we partition the layers [L] into multiple group, iee, = {ll [s+1]}. Therefore, the threshold for each sharding is (1[(gsty))) TopK,, (1 .!l).
D.2 Hyper-parameter settings
Table 3 lists the hyperparameters that we use in the experiments. For CV datasets, we adopt vanilla SGD or momentum SGD (with the setting 0.9) as an optimizer. For the NLP dataset, we fine- tune the pretrained model with AdamW and set the parameters (81, (2) for (0.9, 0.95). In our experiments, we keep the learning rate constant. There is no weight decay during our training.
D.3 Experiments Compute Resources
We train the neural network and run the program on server with 8 NVIDIA A6000 GPUs, an Intel Xeon Gold 6254 CPU, and 256GB RAM. Our codes are running with Python 3.7 and Pytorch 1.8.1.
D.4 More Experimental Results
Participation rates of 20%. Table presents the test accuracy of CIFAR-10 10 and CIFAR- 100 for the case where the participation ratio 20%. Notably, upon increasing the participation ratio to 20%, FIARSE exhibits even more remarkable performance compared to the default setting, i.e., the participation ratio is 10%, surpassing baselines by least 7% and 3% for CIFAR-10 10 and CIFAR-100, respectively.
System heterogeneity with five different model sizes. The experiments are conducted with five different model sizes for 7/ (0.04, 0.16, 0.36, 0.64, 1.0). The allocation of clients to each level is balanced. It's important to note that our proposed method flexible and can accommodate varying numbers of complexity levels client distributions.
28

---

Table 5: Test accuracy under five different submodel sizes different datasets. To be specific, the columns from "Local" to "Model (1.0)" evaluate the test accuracy on the local test datasets, while "Global" evaluates the average test accuracy of the global model of five different sizes (0.04, 0.16, 0.36, 0.64, 1.0) on the global test dataset.
CIFAR-10
CIEAR-100
Method
Local
Model
(0.04)
(0.16)
Model
(0.36)
Mode:
(0.64)
Model
(1.00
Glkbal
Local
Mixel
(0.14)
Model
(0.16)
Model
(0.36)
Model
(0.64)
Ma321
(1.01)
Globsl
Local
Global
HetenFi
75.80
20:38
36.00
57.75
FedRoles
73.36
00:55
70.09
74.45
80125
51.45
71.07
38.51
28.40
37.75
41.10
42.10
43.19
36,19
89.27
$8.94
ScaleFL
74.32
71.95
73.24
73.90
74.00
73.50
68.94
42.43
42.90
46.75
42.49
42.05
39.95
40.21
99.67
59.51
FOODD
78.15
72.64
FIARSE
81,79
77.75
82,15
81,40
82,90
84.75
78.13
45.94
44.35
45.65
47.50
47.00
44.90
42.61
91.55
91,30
size=1
size-0.6 0.64
Sizem0.33
Size- 0.16
size=0.04
Number of Cilets
15
15
15
15
10
5
5
0.4
0.6
0.8
1.0
0.1
0.6
0.8
1.0
0.4
0.6
0.8
1.0
0.1
0.6
0.8
1.0
Test Accuracy (%)
Test Accuracy (%)
Test Accuracy (%)
Test Accuracy (%)
(a) HeteroFL. Histogram
(h) FedRolex Histogram
(c) ScaleFI. Histogram
(d) FIARSE Histogram
Figure 5: Histograms of various submodel extraction methods on CIFAR-10 under five submodel
sizes. Each histogram shows the number of clients achieving different levels of test accuracy.
Heteroff
FedRolex
ScalefL
FIARSE
80
80
80
80
80
Accuracy
70
70
70
70
70
50
50
400
600
800
600 Communication Rounds
200
200
400
800
260
400
600
800
200
400
600
800
Communication Rounds
Communication Rounds
Communication Rounds
Communication Rounds
(a) Model Size 0.04
(b) Model Size 0.16
(c) Model Size 0.36
(d) Model Size 0.64
(c) Model Size 1.0
HeteroFl
FadRolex
ScaleFL
RARSS
Test Accurasy (%)
40
40
40
40
30
30
20
20
20
20
20
200
600
400
800
600 Communication Rounds
200
400
800
600 Communication Rounds
200
Communication Rounds
Communication Rounds
Communication Rounds
(f) Model Size 0.04
(g) Model Size 0.16
(h) Model Size 0.36
(i) Model Size 0.64
(j) Model Size 1.0
Figure Comparison of test accuracy across communication rounds for different submodel extraction
strategies under five varying model sizes (0.04, 0,16, 0.36, 0.64, 1.0) on global test datasets of CIFAR- 10 (upper, e) and CIFAR-100 (lower, f f-j).
Table provides the results under CV and NLP tasks. The results are consistent with the case where four different model sizes were chosen. The proposed FIARSE outperforms all the baselines under both CIFAR-10 and CIFAR-I00 in terms of local performance and global performance. As for AGNews, the proposed method still achieves up to 2% improvement over the existing baselines.
Figure presents the model performance of various model sizes over the communication rounds. Similar to the analysis in Section 6.33 the proposed FIARSE significantly outperforms other baselines, especially under submodel with small sizes. The results demonstrate superiority of our proposed work in the scenario that we should apply the submodel to the global dataset.
Ablation study: Effectiveness of TCB-GD. Table T and presents the effectiveness by comparing our proposed work with pruning-greedy [8I] As mentioned before, gruiing-greedy is an approach that chooses the largest few values at the beginning of the local training and keeps the mask unchanged during local model training. Apparently, this method does not optimize the model parameters in terms of their importance. A main takeaway in experimental results is the necessity of optimizing
29

---

Table 6: Test aceuracy under four different submodel sizes CIFAR- 100 for ablation study. To be more specific, the columns within "Local" evaluate the test accuracy on the local test datasets, while "Global" evaluates the test accuracy of the global model on the global test dataset.
Local
Gobal
Method
Model
Model
Model
Model
Model
Model
Model
Model
Average
Average
(1/64)
(1/16)
(1/4)
(1.0)
(1/64)
(1/16)
(1/4)
(1.0)
FIARSE
39.12
43.24
43.72
40.96
41.76
35.04
39.53
41.22
38.71
38.63
Pruning-greedd
34.32
39.36
41.00
38.96
38.41
30.28
35.93
38.23
36,50
35,24
FIARSE (layerwise)
33.44
38,24
38.64
37,00
36.83
30.54
35.94
37.12
34,46
34.52
Table 7:
Test accuracy under five different submodel sizes on CIFAR- 100 for ablation study. To be more specific, the columns within "Local" evaluate the test accuracy on the local test datasets, while "Global" evaluates the test accuracy of the global model on the global test dataset.
Local
Gobal
Method
Model
Madel
Model
Model
Model
Average
Model
Model
Model
Model
Madel
Avemge
(0.04)
(0.16)
(0.36)
(0.64)
(1.0)
(0.04)
(0.16)
(0.36)
(0.64)
(1.0)
FIARSE
44.35
45.65
47,80
47.00
44.90
40.03
42.44
43,90
44.01
42.65
42.61
Pruning- Greedy
43.85
43.50
34.51
39.97
40.80
42.39
40.81
39.70
FIARSE (layerwise)
41.75
41.85
41.10
33.63
38.43
40.99
39.30
the model with respect the parameter's importance. In other words, only optimizing the model parameters cannot reflect their importance upon their absolute values.
Ablation study: Different Threshold Selection Strategies. Table compare work among various threshold selection strategies. For layerwise one, we can extract the model more balanced, where we preserve a fixed ratio of parameters for each layer. The results indicate that a balanced structure performs worse than the one without a balanced guarantee. For these results, we hypothesize that more parameters should be preserved for the first few layers, while the layers close to the output may have massive redundant parameters. Such conclusion can be verified by comparing ScaleFL 25 with HeteroFL [3]. This is because ScaleFL. preserves more model parameters the beginning of few layers while discarding the last few layers.
compare the proposed
Ablation study: Submodel Exploration. Figure and @iseparatlyy include two client heterogeneity settings, i.e., Figure is >' = [1/64, 1/16, 1/4, 1.0) with 25 clients each, and Figure 8 is 7 {0.04, 0.16 0.36, 0.64] with 25 clients each. Figure 7a and Sa show two phenomena: (i) all model sizes will gradually slow down their exploration speeds; (ii) even if the largest model size is smaller than the full model size, the number of untrained parameters will eventually go to zero, meaning that none of the parameters are ignored or deactivated, According Figure 76 and 8b] the extracted submodel for given size will gradually stabilize, indicating that suitable submodel architecture has been found. Moreover, submodel requiring a larger size makes it easier to obtain a stable architecture.
Exploratio Rate
2.0
Diferences
Mooi Dff cremze
2.20
1.64
205
20.
2:0
200
455
6:0
602
8.56
320
400
062
82c
232
403
20o
032
Communication Rounds
Communicatin Rounds
Communicatio Rounds
Communication Rounds
(a) Exploration Rates
(b) Model Differences
(a) Exploration Rates
(b) Model Differences
Figure 7: Exploration rates and model differ- ences against communication rounds for a client heterogeneity setting of (1/64, 1/16, 1/4, 1.0].
Figure 8: Exploration rates and model differ- ences against communication rounds for a client heterogeneity setting of (0.04, 0.16, 0.36, 0.64).
30

---

NeurIPS Paper Checklist
1. Claims
Do the main claims made in the abstract and introduction accurately reflect paper's contributions and scope?
Question:
Answer: [Yes]
Justification: We highlight our contributions in the Introduction (Section D and clearly present the idea of the proposed FIARSE.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine include aspirational goals as motivation as long is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: We mention our limitations and point out a future research direction in the Conclusion (Section)) 7).
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section their paper.
The paper should point any strong assumptions and how robust the results are violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). ). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairesss.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best
31

---

judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes]
Justification: We provide the theoretical conclusion in the Convergence Analysis (Section and the detailed proof provided in Appendix C
Guidelines:
The answer NA means that the paper does not include theoretical results.
All theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental Result Reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: We provide the experiment setup in Section 6.1 and Appendix D.2 Also, we release our code at htttts: http:////tttuuuu.mmaaaaaaaiiiiie
howp://w....ooaaaaaia/////ot wttp://aaaall//Faaa FARSE
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, No answer this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often good way to accomplish this, but reproducibility instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of model checkpoint, other means that appropriate to the research performed.
also be provided via detailed
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how reproduce that algorithm.
32

---

(b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is new model (c.g.. large language model), then there should either way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which authors are welcome to describe the particular way they provide for reproducibility. the case of closed-source models, may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers have some path reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, described in supplemental material?
Answer: [Yes]
The experiments of this work rely on three public datasets, namely, CIFAR-IN -1, CIFAR-100, and AGNews. Additionally, our experiment leverages a pretrained model named Roberta, which is available online.
Justification:
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://nips cc/ /wwuddeeeooeeuuuisseeeeeeeeeeeee
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https http://uuucccguu.deee//oodaaaaaa
for more details.
The authors should provide instructions on data access and preparation, including how access the raw data, preprocessed data, intermediate data, and generated data,
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental Setting/Details
Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Question:
Answer: [Yes]
Justification:
The experimental details are provided in Section 6.1 and Appendix D.2
Guidelines:
The answer NA means that the paper does not include experiments.
33

---

The experimental setting should be presented in the core of the paper to a level of detail that is necessary appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, or as supplemental material.
7. Experiment Statistical Significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: Figure and 6 display the results mean and standard deviation. Other experimental results are averaged with three random seeds for different hyperparameter settings. All results reported under the best hyperparameter setting.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results accompanied by enror bars, confi- dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
It should be clear whether the error bar is the standard deviation the standard error of the mean.
It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful to show in tables or figures symmetric error bars that would yield results that are out of range (c.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain the text how they were calculated and reference the corresponding figures tables in the text.
8. Experiments Compute Resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification:
The details of computation resources are provided in Appendix D.3
Guidelines:
The answer NA means that the paper does include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't 't make into the paper).
34

---

9. Code Of Ethics
Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of http://pppp..ppoooooooooooo//ooa
Question:
Answer: [Yes]
Justification:
We affirm that this work conform with the NeurlPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No. they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g.. if there is special consid- eration due to laws or regulations their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: We include section to discuss the broader impacts of our work, which is placed after the Conclusion (Section 7
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point that improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: Not applicable.
Guidelines: The paper poses such risks.
35

---

The answer NA means that the paper poses no such risks.
Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
Justification: We properly cite those open-source resources the paper. Specifically, the information is available in the experimental setup (Section(6.1)
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset used and, possible, include a URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g.. website). the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, pettasets.paperswiii paperswi thcode. com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should provided.
If this information is not available online, the authors encouraged to reach out to the asset's 's creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification: Not Applicable.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset is used.
36

---

At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification:
The paper does not involve crowdsourcing or research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification:
The paper does not involve crowdsourcing or research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
37


Reviews:
[{"review_id": "zrx0mU0GlB", "reviewer": "Reviewer_inPJ", "summary": "This paper tackles the problem of model heterogeneity in federated learning, where clients have different computational capabilities. The authors propose FIARSE, a method that extracts submodels of varying sizes from a global model based on the importance of parameters. The key idea is using a threshold-controlled biased gradient descent to jointly optimize model parameters and determine their importance. They provide theoretical convergence analysis and empirical results showing FIARSE outperforms existing methods.", "questions": "see Weaknesses", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Extensive experiments demonstrate consistent improvements over baselines across datasets and model architectures.\n- The theoretical analysis is solid.\n- The method is flexible and can accommodate different numbers of model sizes and client distributions.", "weaknesses": "- Because importance is determined by the size of model parameters, smaller parameters may never be selected, which is equivalent to them being 'deactivated.' This seems to have some impact on model performance.\n- Similarly, the paper doesn't explore how FIARSE might impact model fairness across different client groups. Could the importance-based extraction inadvertently amplify biases present in the data?\n- How sensitive is FIARSE to the choice of threshold? Some analysis on the impact of different thresholding strategies could be valuable.\n- Figure 3 seems to only show one set of experimental results. Due to the curves being quite close, they may be influenced by random factors. Can we conduct multiple experiments and display the results as mean + std?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to [W1].** Thanks for your question. Given an arbitrary neural network, it is impossible to state the optimal architectures for different sizes so that all these submodels can achieve their best performance after federated learning. Therefore, we should **explore different submodel combinations** to find out the best one where all submodels can perform as outstanding as possible. The proposed FIARSE achieves the exploration by means of importance-aware extraction, where we assume the magnitude of model parameters reflects their importance and extract a submodel for a given size with the largest parameters.\n\nIn our opinion, your concern focuses on how many parameters are explored by a small model. To elaborate on this, we conduct more experiments to demonstrate the number of parameters that different model sizes have explored at $t$-th round and the model differences between two models of $(t-50)$-th and $t$-th communication rounds, where $t \\in \\{50, 100, \\dots\\}$. In specific, we train ResNet-18 on CIFAR-10, which is partitioned across 100 clients using Dirichlet distribution with a parameter $\\alpha=0.3$, and ten clients are selected for training at each round. In the supplementary material, Figure 1 presents the numerical results, and the following paragraph will be added to Appendix D.4:\n\n**Ablation study: Submodel Exploration.** *Figure 1 includes two client heterogeneity settings, i.e., Figure 1(a)(b) is {1/64, 1/16, 1/4, 1.0} with 25 clients each, and Figure 1\\(c)(d) is {0.04, 0.16, 0.36, 0.64} with 25 clients each. Figure 1(a)\\(c) shows two phenomena: (i) all model sizes will gradually slow down their exploration speeds; (ii) even if the largest model size is smaller than the full model size, the number of untrained parameters will eventually go to zero, meaning that none of the parameters are ignored or deactivated. According to Figure 1(b)(d), the extracted submodel for a given size will gradually stabilize, indicating that a suitable submodel architecture has been found. Moreover, a submodel requiring a larger size makes it easier to obtain a stable architecture.*\n\n***\n\n**Response to [W2].** Thank you for raising an interesting aspect regarding fairness. In our work, model size is decided by client computation capacity. Hence, smaller models can be trained with more data, whereas some parameters in larger models may be trained on limited and biased data. Such limited and biased data could result in unfairness for clients with greater computational capacities, as the extract submodels may be unnecessarily large. However, these clients could extract smaller submodels to achieve a trade-off between model performance and fairness, which is an intriguing area for further investigation. We believe that **the importance-based extraction does not necessarily amplify biases** because the clients with large capacities opt not to use large but unfair models. Additionally, designing new local training approaches is another potential solution to address unfairness issues in our work. We will include this discussion in our paper and consider it for future study.\n\n***\n\n**Response to [W3].** In this work, we introduce three kinds of thresholding strategies, i.e., model-wise, layer-wise, and sharding-wise. We introduce the model-wise strategy in the main body (Line 156 -- 159), while another two are discussed in Appendix D.1 (Line 1019 -- 1026). In the appendix of the manuscript, Tables 6 and 7 show the empirical results under different client heterogeneity settings, and both tables train a ResNet-18 on the CIFAR-100 dataset:\n\n- Four different model sizes with 25 clients each:\n\n|Strategies|Model (1/64)|Model (1/16)|Model (1/4)|Model (1.0)|\n|--|--|--|--|--|\n|Model-wise|35.04%|39.53%|41.22%|38.71%|\n|Layer-wise|30.54%|35.94%|37.12%|34.46%|\n\n- Five different model sizes with 20 clients each: \n\n|Strategies|Model (0.04)|Model (0.16)|Model (0.36)|Model (0.64)|Model (1.0)|\n|--|--|--|--|--|--|\n|Model-wise|40.03%|42.44%|43.90%|44.01%|42.65%|\n|Layer-wise|33.63%|38.43%|40.29%|40.99%|39.10%|\n\nIt is noted that layer-wise strategy divides ResNet-18 into four parts in accordance with the predefined convolutional layers, where each convolutional layer includes two residual blocks. As a result, this strategy can also be regarded as a sharding-wise strategy. Based on the numerical results, we witness that model-wise strategy outperforms layer-wise strategy. More detailed analysis is provided in the Appendix D.4 (Line 1060 -- 1067).\n\n***\n\n**Response to [W4].** Thanks for your suggestions. We updated Figure 3, which is shown as Figure 2 in the supplementary materials. All these experiments were conducted under three different random seeds. We will update our experimental figures accordingly, including those in the appendix.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LPn5Lgq0Yj", "reviewer": "Reviewer_PQwa", "summary": "The authors proposed FIARSE, a model-heterogeneous federated learning framework that addresses the limitations of existing static and dynamic sub-model extraction methods. They introduced an importance aware sub-model extraction technique to extract heterogeneous sub-model from a shared global model. This approach has demonstrated significantly better performance compared to other model-heterogeneous federated learning methods, such as FedRolex and HeteroFL.", "questions": "1. Can the proposed technique generalize to various data heterogeneity scenarios? \n2. Is equal weighting used when aggregating local updates? \n3. What will be the impact of client model heterogeneity distribution on global model accuracy??", "limitations": "Refer to the weakness.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "Strengths:\n\n1. It addresses the important issue of model heterogeneity in federated learning, which is crucial for real-world federated learning applications. \n2. The proposed approach efficiently utilizes available resources of clients.\n3. The authors provide a theoretical convergence analysis of the proposed method.\n4. The paper is well-written and easy to follow.", "weaknesses": "Weakness:\n\n1. The performance comparison under different data heterogeneity settings is missing. \n2. The authors should discuss the communication cost and computation overhead to reach the target accuracy. \n3. The performance evaluation on different ratios of client model heterogeneity distribution is missing.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to [W1/Q1].** Thanks for your suggestion. We train ResNet-18 for 800 rounds using CIFAR-10, which is partitioned into 100 clients in a pathological scenario, where each client holds two classes. All these clients are equally distributed into four computation capacities {1/64, 1/16, 1/4, 1.0}. In each communication round, we sample 10 clients, and these clients locally train the model for four epochs with a batch size of 20. The following table presents the test accuracy of HeteroFL and the proposed FIARSE on both global and local datasets: (Note: The numerical cells are in the form of \"global/local\")\n\n|Method|Model (1/64)|Model (1/16)|Model (1/4)|Model (1.0)|Average|\n|-|-|-|-|-|-|\n|HeteroFL|73.96/75.24|79.04/79.64|81.85/82.24|80.83/81.96|78.92/79.77|\n|FIARSE|81.16/84.16|84.21/85.24|84.95/86.04|84.05/85.20|83.59/85.16|\n\n***\n\n**Response to [W2]** Thanks for your suggestion. Unlike the experimental setting described in the **Response to [W1/Q1]**, we partition CIFAR-10 into 100 clients using a Dirichlet distribution with a parameter of 0.3.\n\nAccording to the numerical results presented in Table 1 and Figure 3 in the manuscript, all baselines can achieve a global accuracy of 65% or higher, and various submodels can realize a global accuracy of 60%. Therefore, the table below presents the number of communication rounds, overall computation, and communication costs when **the average global accuracy reaches 65% and all submodels should achieve an accuracy higher than 60%**:\n\n|Method|Rounds|Total computation costs (TFLOPs)|Total communication costs (GB)|\n|-|-|-|-|\n|HeteroFL|560|4089.59|309.86|\n|FedRolex|NA(640)|4673.82|354.13|\n|ScaleFL|460|5144.41|274.57|\n|FIARSE|**380**|**3620.36**|**210.08**|\n\nNote to the table: (i) we evaluate the result every 20 rounds, so the value of rounds can be divided by 20. (ii) Model 1/64 of FedRolex never achieves an accuracy above 60%. So we present its result of the 640th round, where FedRolex achieves an average global accuracy of 65% for the first time.\n\n***\n\n**Response to [W3/Q3].** Thanks for your suggestion. Different from the experimental setting described in the **response to [W1]**, we partition CIFAR-10 into 100 clients using Dirichlet distribution with a parameter 0.3. Moreover, all these clients are divided into four computation capacities {1/64, 1/16, 1/4, 1.0} with the size of {40, 30, 20, 10}, respectively. The following table presents the test accuracy of HeteroFL and the proposed FIARSE on both global and local datasets: (Note: The numerical cells are in the form of \"global/local\")\n\n|Method|Model (1/64)|Model (1/16)|Model (1/4)|Model (1.0)|Avg|\n|-|-|-|-|-|-|\n|HeteroFL|67.50/69.70|70.81/70.17|68.83/70.85|60.70/69.00|66.96/70.00|\n|FIARSE|69.96/72.43|73.42/74.63|69.29/74.15|63.17/74.2|68.96/73.61|\n\n***\n\n**Response to [Q2].** Thanks for your question. The aggregation of a specific parameter depends on the number of clients training in that parameter. For example, if five clients train a parameter, it is updated with their average value. In this sense, equal weighting is used when aggregating local updates. Our method is applicable to the case where clients carry on different weights, and the aggregation rules can follow Pruning-Greedy [1].\n\n**Reference:**\n[1] Every Parameter Matters: Ensuring the Convergence of Federated Learning with Dynamic Heterogeneous Models Reduction, NeurIPS'23", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "fOcjBknOh1", "reviewer": "Reviewer_dCzP", "summary": "The authors address the low device capacities in federated learning. The authors notice that existing submodel extraction methods lack awareness of parameter importance when reducing the model, which may limit the model's performance. They propose an importance-aware dynamic submodel extraction method without the need for additional information beyond the model parameters. Both theoretical and empirical results confirm the effectiveness of the proposed method.", "questions": "Please see weakness", "limitations": "Please see weakness", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1) The topic of model heterogeneity in FL is interesting and meaningful.\n2) This work improves previous methods by considering parameter importance when extracting submodels, which is widely overlooked by existing methods.\n3) Comprehensive theoretical and empirical results confirm the advantage of the proposed method.", "weaknesses": "1) The authors directly masks unimportant parameters during model training, which may not be as efficient as structured-pruning methods (e.g., fedrolex, heterofl). It would be better to take a full comparison on capacity issues like model size, peak memory and FLOPs of different methods.\n\n2) Since only a fraction of model parameters will be assigned with large importance, I'm wondering whether the proposed method will degrade to static submodel extraction where fixed parameters may be always considered important and thus lead to limited model representability. It would be better to contain more analysis of the parameters' importance distributions.\n\n3) Fjord  [6] is an important baseline whose results should be empirically compared.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to [W1].** Thanks for your question. We train ResNet-18 using CIFAR-10, which is partitioned into 100 clients using a Dirichlet distribution with a parameter of 0.3. In each communication round, we sample 10 clients, and these clients locally train the model for four epochs with a batch size of 20.\n\nAccording to the numerical results in Table 1 and Figure 3 in the manuscript, all baselines can achieve a global accuracy of 65% or higher, and various submodels can realize a global accuracy of 60%. Therefore, the table below presents the number of communication rounds, overall computation, and communication costs when **the average global accuracy reaches 65% and all submodels should achieve an accuracy higher than 60%**:\n\n|Method|Rounds|Total computation costs (TFLOPs)|Total communication costs (GB)|\n|-|-|-|-|\n|HeteroFL|560|4089.59|309.86|\n|FedRolex|NA(640)|4673.82|354.13|\n|ScaleFL|460|5144.41|274.57|\n|FIARSE|**380**|**3620.36**|**210.08**|\n\nNotes to the table: (i) we evaluate the result every 20 rounds, so the value of rounds can be divided by 20. (ii) Model 1/64 of FedRolex never achieves an accuracy above 60%. So we present its result of the 640th round, where FedRolex achieves an average global accuracy of 65% for the first time.\n\nThe table demonstrates the superiority of the proposed FIARSE: it requires the fewest communication rounds, and the least communication and computation overhead among the selected methods. \n\n***\n\n**Response to [W2].** Thanks for your question. It is possible that our proposed method may eventually extract a constant submodel for a given size. Figure 1(b)(d) in supplementary material shows the differences gradually diminish between two models of $(t-50)$-th and $t$-th communication rounds, where $t \\in \\{50, 100, \\dots\\}$. However, it does not mean the performance is limited; instead, the proposed FIARSE finds **optimal model architectures** for various model sizes. This is because all model parameters are explored/trained, as shown in Figure 1(a)\\(c), demonstrating the number of parameters that different model sizes have explored. \n\nThe following tables present the test accuracy of HeteroFL and the proposed FIARSE on both global and local datasets after 1000 rounds of training: (Note: The numerical cells are in the form of \"global/local\")\n\n- Figure 1(a)(b): {1/64, 1/16, 1/4, 1.0} with 25 clients each\n\n|Method|Model (1/64)|Model (1/16)|Model (1/4)|Model (1.0)|Avg|\n|-|-|-|-|-|-|\n|HeteroFL|59.70/60.24|66.59/69.32|71.84/72.18|66.08/73.76|66.05/68.88|\n|FIARSE|69.57/73.12|74.93/77.20|76.55/77.24|73.94/82.04|73.75/77.40|\n\n- Figure 1\\(c)(d): {0.04, 0.16, 0.36, 0.64} with 25 clients each\n\n|Method|Model (0.04)|Model (0.16)|Model (0.36)|Model (0.64)|Avg|\n|-|-|-|-|-|-|\n|HeteroFL|68.57/70.24|75.91/78.00|78.36/79.32|75.87/83.68|74.68/77.81|\n|FIARSE|77.24/78.76|81.83/82.84|81.73/82.04|79.47/85.80|80.07/82.36|\n\n***\n\n**Response to [W3].** Thanks for your suggestion. We conducted empirical studies to train a ResNet with CIFAR-10 and CIFAR-100 using 100 clients, while other settings are consistent with those described in the response of **[W1]**. The tables below compare the proposed FIARSE and FjORD. \n\n- CIFAR-10:\n\n|Method|Model (1/64)|Model (1/16)|Model (1/4)|Model (1.0)|\n|-|-|-|-|-|\n|FjORD|71.36|71.48|70.04|77.40|\n|FIARSE|73.12|77.20|77.24|82.04|\n\n- CIFAR-100:\n\n|Method|Model (1/64)|Model (1/16)|Model (1/4)|Model (1.0)|\n|-|-|-|-|-|\n|FjORD|38.16|41.20|40.12|39.84|\n|FIARSE|39.12|43.24|43.72|40.96|\n\nIn Table 1 of the supplementary material, we compare FjORD and other baselines comprehensively. We also conduct one more client heterogeneity setting (i.e., {0.04, 0.16, 0.36, 0.64, 1.0} with 20 clients each) and present the numerical results in Table 2.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "m8JeBmnn9m", "reviewer": "Reviewer_hETm", "summary": "This works tackles the known problem of model heterogenity in FL, in which each client is allowed to use a different model according to its computational capabilities, while contributing to learn a global model. The proposed approach (FIARSE) samples submodels out of the global model by estimating the importance of its parameters, and pruning out least important components. The work also provides a theoretical foundation for submodel extraction, even if it is not clear how this analisis relates to the ones proposed in other works. The experiments are carried on CIFAR10/100 (CV task) and AGNews (NLP task).", "questions": "1. In the introduction, model-heterogeneous FL approaches are divided into static and dynamic submodel extraction, by looking at the costruction of submodels during the training. Why FjORD is regarded as static? In FjORD at each optimization step of portion of contiguous weights are sampled for training according to the client's computational capabilities, so this would make it dynamic based on the above distinction.\n2. What is the improvement and/or generalization on the theory part with respect to previous works?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The paper provides a convergence proof for the proposed submodel extraction procedure, matching state-of-art results in term of asymptotic convergence. The experimental setting is appropriate for substantiating the claims of the work, uses datasets and models commonly used in FL (CIFAR10/100 with ResNet-18-GN) and provides results under statistichal heterogeneity.", "weaknesses": "1. **FIARSE induces unstructured sparsity in the model.** This is relevant for claims of the paper, because it influences the efficiency of the proposed approach: not all the hardware supports sparse operations, and in general the performance are lower compared to dense models that are actually smaller by the same factor of the induced sparsity. This particularly outstanding given that previous works produce structural sparsity in the given model [1]. As such, this aspect needs to be more clearly stated and analyzed in support of the work's claims: for examples, it would be appropriate to discuss in more detail the computational performance of the proposed method with respect to the others, varying the submodel dimension.\n2. **Insufficient comparison with SOTAs.** The proposed approach misses comparison with recent approaches [1,2] which have the advantage of producing structured sparsity in the subsampled model. The works are correctly cited in the introduction, which raises some concers about the choice of excluding them from the evaluation. i believe that those FjORD and NeFL needs to be considered in the evaluation, and better described in the related work section (see next point).\n3. **Writing can be improved.** The works presents a discussion on approaches for model-heterogeneous FL in sections 1-2, that is essentially in the introduction and in one sections where the research problem is stated. I found that this structure makes the discussion of the related works not cohesive, resulting in not clear relationship with previous works. Ideally, one would like to understard which are the similar works and how the proposed approach differs from them. In its current form, it's difficult to have such clear idea.\nAlso on the theory, the work does not detail what is the improvement and/or generalization with respect to previous works [3].\n4. **Quality of images.** This is not really I take into account for assessing the paper, but please note that the figures are low-quality so they get grainy on the printed paper.\n\nPoints (1-2) are the most important for my evaluation, I believe this could be a good work but the empirical evaluation need to be more convincing in showing an advantage over existing approaches, not only in term of model quality (e.g. accuracy) but also in terms of resources.\n\n[1] Horvath et al., FjORD: Fair and Accurate Federated Learning under heterogeneous targets with Ordered Dropout, NeurIPS 2021\n\n[2] Kang et al., NeFL: Nested Federated Learning for Heterogeneous Clients\n\n[3] Shulgin et al., Towards a Better Theoretical Understanding of Independent Subnetwork Training, ICML 2024", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
**Figure 1:** We conduct the experiments to demonstrate the number of parameters that have been explored by different model sizes at $t$-th round and the model differences between two models of $(t-50)$-th and $t$-th communication rounds, where $t \in \{50, 100, \dots\}$. In specific, we train ResNet-18 on CIFAR-10, which is partitioned across 100 clients using Dirichlet distribution with a parameter $\alpha=0.3$, and 10 clients are selected for training at each round.

**Figure 2:** An updated version of Figure 3 in the submitted manuscript. 

**Table 1** and **Table 2:** An updated version of Table 1 and Table 5 in the submitted manuscript, where we add FjORD as one of our baselines.

Meta-review: The paper is well-written and supported by thorough theoretical analysis and strong experimental results. All reviewers have expressed positive feedback and recommend its acceptance.
Decision: Accept (poster)