FedFree: Breaking Knowledge-sharing Barriers through Layer-wise Alignment in Heterogeneous Federated Learning
Authors: Haizhou Du
Yiran Xiang
Yiwen Cai
Xiufeng Liu
Zonghan Wu
Huan Huo
Guodong Long
Venue: NeurIPS 2025 poster ()
Keywords: Heterogeneous Federated Learning
Public-Data-Free
Knowledge Gain Entropy
Primary area: general_machine_learning

Abstract: Heterogeneous Federated Learning (HtFL) enables collaborative learning across clients with diverse model architectures and non-IID data distributions, which are prevalent in real-world edge computing applications. Existing HtFL approaches typically employ proxy datasets to facilitate knowledge sharing or implement coarse-grained model-level knowledge transfer. However, such approaches not only elevate risks of user privacy leakage but also lead to the loss of fine-grained model-specific knowledge, ultimately creating barriers to effective knowledge sharing. To address these challenges, we propose FedFree, a novel data-free and model-free HtFL framework featuring two key innovations. First, FedFree introduces a reverse layer-wise knowledge transfer mechanism that aggregates heterogeneous client models into a global model solely using Gaussian-based pseudo data, eliminating reliance on proxy datasets. Second, it leverages Knowledge Gain Entropy (KGE) to guide targeted layer-wise knowledge alignment, ensuring that each client receives the most relevant global updates tailored to its specific architecture. We provide rigorous theoretical convergence guarantees for FedFree and conduct extensive experiments on CIFAR-10 and CIFAR-100. Results demonstrate that FedFree achieves substantial performance gains, with relative accuracy improving up to 46.3% over state-of-the-art baselines. The framework consistently excels under highly heterogeneous model/data distributions and in large scale settings.

FedFree: Breaking Knowledge-sharing Barriers through Layer-wise Alignment in Heterogeneous
Federated Learning
Haizhou Du
Yiran Xiang*
Yiwen Cai*
Xiufeng Liu"
Zonghan Wut
Huan Huo
Guodong Long'
Shhagghai University of Electric Power, Shanghai, China
Technical University of Denmark, Kongens Lyngby, Denmark
East China Normal University, Shanghai, China
University of Technology Sydney, Sydney, Australia
Abstract
Heterogeneous Federated Learning (HtFL) enables collaborative learning across clients with diverse model architectures and non-lID data distributions, which are prevalent in real-world edge computing applications. Existing HiFL approaches typically employ proxy datasets to facilitate knowledge sharing or implement coarse-gran gourse-graind movel-level knowledge transfer. However, such approaches not only elevate risks of user privacy leakage but also lead to the loss of fine one-ggaieed model-specific knowledge, ultimately creating barriers effective knowledge sharing. To address these challenges, we propose FedFrre, novel proxy-data- free and model-free HtFL. framework featuring two key innovations. First, Fed- Free introduces a reverse layer-wise knowledge transfer mechanism that aggre- gates heterogeneous client models into a global model solely using Gaussian- based pseudo-data, eliminating reliance proxy datasets. Second, it leverages Knowledge Gain Entropy (KGE) to guide targeted layer-wise knowledge align- ment, ensuring that each client receives the most relevant global updates tailored to its specific architecture. We provide rigorous theoretical convergence guaran- tees for FedFree and conduct extensive experiments CIFAR-10 10 and CIFAR- 100. Results demonstrate that FedFree achieves substantial performance gains, with relative accuracy improving up 46.3% stateoo-thhe-ad baselines. The framework consistently excels under highly heterogeneous model/data distribu- tions and in large-scale settings.
Introduction
Heterogeneous Federated Learning (HtFL. represents a significant advancement in federated learn- ing (FI.), addressing the prevalent challenges of statistical and model heterogeneity encountered in real-world edge computing scenarios [1]. In these settings, participating clients often possess de- vices that have limited resources with varying computational capabilities, necessitating the use of diverse local model architectures tailored specific needs [2. 3]. This inherent heterogeneity, how- ever, introduces significant knowledge-sharing barriers. as knowledge encoded within disparate model structures difficult to effectively aggregate and disseminate across the federation.
Existing HtFL methodologies often attempt to bridge this knowledge-sharing gap using tech- niques like knowledge distillation [4. 5. 6, 7, 8, 9, 10, 11, 12], representation and prototype shar-
EEail: haizhou.du @ shiep.edu.cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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ing [13, 14, 15, 16, 17] and architectural adaptation and matching [18, 19, 20, 21, 22, 23]. These methods have overcome the bottlenecks imposed by client resource limitations, enabling more ef- ficient model collaboration and training across devices in heterogeneous federated learning. How- ever, knowledge distillation transfers knowledge across models via proxy data but risks privacy leakage. prtreseenaatoo/protoyye sharing exchanges intermediate features or class prototypes lacks fine-grained layer-wise adaptation. Architectural adaptation directly aligns heterogeneous structures through matching compression, yet faces suboptimal knowledge retention problems.
These limitations reveal two fundamental and persistent challenges in HtFL. The key challenge is how to share personalized knowledge without the proxy dataset, causes local-to-globe knowledge- sharing barrier. Traditional knowledge reanfer-based methods fail to obtain learned knowledge without the proxy dataset. Eventually, it leads to the failure of collaborative training among cross- clients. The other important challenge is how to decide that the corresponding knowledge dis- tributed to well- clients, causes global-to-loca knowledge-sharing barrier. Conventional meth- ods always directly distribute the transferred global model to heterogeneous local models using sim- ple strategies.
To overcome these challenges, we propose FedFree (Federated Proxy-Data- and Model-free), a novel HtFL framework that operates entirely without proxy data. FedFFree introduces two core innovations: First, employs a reverse layer-wise knowledge transfer mechanism. Rather than the server dictating knowledge to clients, FedFree identifies critical layers (defined in 3.3) from local models as the source of knowledge, transferring layer-wise local knowledge the global model layers. This local-to-global flow is facilitated by Gaussian-based pseudo-data generated on the server, aiming to elicit functional responses for local and global layer matching, thereby circumventing the need for proxy data. Second, for the global-to-local knowledge distribution, FedFree introduces Knowledge Gain Entropy (KGE), a novel metric designed to quantify the knowledge density difference between corresponding global and local layers. By comparing layers of the same type (e.g., global layers offering the high-density knowledge to each client, enabling targeted and efficient knowledge alignment.
using KGE, the server identifies and transmits
The main contributions of this paper are summarized as follows:
We propose FedFree, a novel HtFL. framework that addresses the knowledge-sharing chal- lenges between heterogeneous clients and the global model, by enabling proxy- proxy-data-free and model-free solutions for fine granular knowledge alignment.
We introduce reverse layer-wise knowledge transfer mechanism, utilizing critical local layers as the knowledge source and server-generated pseudo-data for grivacy-presenve local-to-globi knowledge sharing.
We design Knowledge Gain Entropy, a novel metric to quantify knowledge density of global layers relative to local critical layers. KGE guides global-to-local knowledge align- ment, enabling personalized knowledge upgrades only for clients with verifiable global gains.
We provide the rigorous theoretical analysis of FedFree's convergence on both non-convex and strongly convex. Extensive experiments on CIFAR-10 and CIFAR- 100 demonstrate that FedFree consistently outperforms eight state-of-thh-ar homogeneous and heteroge- neous FL baselines, achieving significant accuracy improvements across diverse settings.
2 Related Work
Existing approaches attempt to enable knowledge sharing across heterogeneous clients primarily through knowledge distillation, representation sharing, and architectural adaptation techniques.
Knowledge Distillation in HtFL. Knowledge Distillation (KD) is a widely adopted technique where knowledge from one model (teacher) is transferred to another (student), often via soft labels or intermediate features. Several HtFL methods leverage KD, but they frequently rely on auxiliary data. For instance, FedMD [24] requires shared proxy dataset for clients to compute and exchange soft predictions. FedDF [25) uses logits averaged over client models on a proxy dataset to create global ensemble teacher for distillation. FedKD [26) distills knowledge from diverse client models

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into a global server model, typically assuming access to server-side proxy data for the distilla- tion process. FedGKD [5] focuses on mitigating client drift in FL using KD from historical global models, but primarily targets statistically heterogeneous settings with homogeneous models.
While effective in some contexts, the reliance of many KD-based HtFL. methods on proxy datasets raises privacy concerns and practical hurdles related to data accessibility and relevance, motivating the need for proxy-data- alternatives.
Representation and Prototype Sharing. Another line of work avoids direct weight aggregation by sharing intermediate representations prototypes. FedProto [13] has clients upload learned class prototypes instead of model parameters, which the server aggregates. FedTGP [14] extends this by introducing trainable global prototypes and contrastive learning to handle heterogeneity better. FCCL [15] learns generalized representations using a cross-correlation matrix derived from unla- beled proxy data and employs KI) to prevent forgetting. These methods reduce communication costs and handle architectural differences to some extent. However, they often focus on aligning output representations (logits or prototypes) rather than enabling fine-grained, layer-wise knowl- edge exchange, and some still depend on proxy data (e.g., FCCL).
Architectural Adaptation and Matching. Techniques also exist to handle differing architec- tures directly. Model transformation methods convert models into a common format; for example, FedMA [27] uses Bayesian matching to align and average layers across heterogeneous neural net- works. Model compression and pruming approaches like HeteroFL [28] train a global super-model on the server and deploy dynamically pruned sub- models clients based on their resources. Oth- ers generate personalized models, like pFedHR [29]. While these methods directly tackle model heterogeneity, layer matching be complex and computationally expensive, pruning may discard potentially useful knowledge, and personalized model generation might not fully leverage collab- orative insights from other clients' structures. Furthermore, ensuring optimal knowledge transfer specifically tailored to each client's needs remains challenge.
Positioning FedFree. While notable progress has been made in HtFL, critical challenges remain. Many existing methods still rely on proxy datasets, raising privacy concerns and limiting gener- alization. Furthermore, even proxy-data-free approaches often lack mechanisms for fine-graing -raiirane,,, targeted knowledge exchange: effectively aggregating knowledge (ooall)o-gloobl)) and distributing it optimally gglobal-to-loca) across structurally diverse clients remains an open problem. These gaps highlight the need for frameworks that operate without proxy data while enabling precise, layer-aware knowledge transfer.
Methodology
3.1 Problem Statement
We consider a heterogeneous federated learning setting with N clients. Each client i E (1...., ......,NT N) possesses a private dataset D; and trains a local model M, characterized by parameters 0.. Crucially, both the datasets D; (non-IID) and the model architectures M, are allowed to be heterogencous across clients. This heterogeneity reflects real-world constraints where clients may have different hardware capabilities, data distributions, and task requirements, leading to variations in layer types, layer counts, node counts, etc. The collaborative goal to optimize the performance of these per- sonalized models by minimizing global objective function, typically formulated as weighted average of local losses:
Σ P. (;; HO
min
(1)
where F, is the local loss function for client i on its data D,, n, |D is the size of the local dataset, and p; = n En= nj the weighting factor for client The primary challenge lies in enabling effective knowledge sharing among the heterogeneous parameters (0.) without violating privacy or requiring shared proxy dataset.
3

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Client
Knowledge Extraction Module
Server
Kmwleegy-hharnn
Crikel SYP
Ganvias-luae
Pezdd
Selectio
Kamntadte darine
Previns Liusna
Client 2
Knswlldgg Extraction Mudule
Layers
Ericcal
COO
Decorepontio
Client
Knowledge Extraction Module
Knowledge Gata Estrope Estiation
Cllkel
Krowlolge
Selecuun
Kauwlldgge Alignment Masiule
Figure 1: The overview of FedFree architecture. Both fi,0- O1,6r O. O2 pp 0% represent the parameters of the corresponding layers (a, b, m,n,p,9 uploaded by the matching clients (1, i) during the f-th round of training.
3.2 The FedFree Framework Overview
FedFree addresses the challenges breaking the knowledge-sharing barriers HtFL. through three specialized modules, (1) Knowledge Extraction Module, (2) Knowledge-Sharing Module, and (3) Knowledge Alignment Module, as depicted in Figure 1. The Knowledge Extraction Module operates the client side, where each client conducts local updates and selectively uploads the most critical layers based on parameter change magnitudes. Subsequently, Knowledge-Sharing Module aggregates this knowledge in reverse layer-wiss manner the server side: it generates Gaussian pseudo-date and updates global model layers by minimizing the output differences with the received eritical client layers, thereby avoiding the need for real proxy datasets. Moreover, the Knowledge Alignment Module computes the Knowledge Gain Entropy (KGE) for targeted knowledge distribu- tion between the updated global layers and client layers. Finally, it distributes only those global lay- ers offering the richest knowledge improvement back to the respective clients. This targeted distribu- tion ensures architecture-awar personalization without enforcing homogeneous models. Through this design, FedFree enables generalized, scalable, privacy-preserve knowledge transfer across diverse and heterogeneous clients.
3.3 Knowledge Extraction Module
This module includes local update and critical layer selection steps on each participating client. Local Update. In round i, client i performs standard local training using its private data D, for E epochs (or steps). updating its local model parameters from 0 to f Let 0r, denote the parameters of the /-th layer of client i's model at the end the local training in round
Critical Layer Selection. To efficiently capture the most significant learning, FedFree identifies critical layers. Client i calculates the magnitude of change for each layer using the L2-norm:
|0 1,1 0 112
A0
(2)
110 112
This A0,, reflects the extent of parameter updates for layer l. The client then selects set L containing the parameters (0%,) of the top-k layers exhibiting the largest A In our experiments, we typically use 2. These selected critical layer parameters L are then uploaded to the server.
This selective upload reduces communication overhead compared to uploading the entire model.
3.4 Knowledge-sharing Module (Lorallto-Global)
After critical local knowledge is extracted, the next step is to integrate these insights at the server side without compromising privacy. This server-side module aggregates the knowledge received from clients' critical layers into global model, crucially, without using any proxy data.

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Global Model and Pseudo-data. The server maintains global model G". For the heterogeneous settings evaluated in this work (HtFL), this global model utilizes specific architecture (detailed in Appendix D.I, Table A1) designed to serve as an effective intermediary for knowledge aggregation and distribution across diverse client models of varying complexities. While its architecture may not be larger than all individual heterogeneous client models, its role is to capture and fuse essential functional knowledge from corresponding client layers via the reverse knowledge transfer mecha- nism described subsequently. Let 9j denote the parameters of the j-th layer of this global model at round t. Since no real client data is available at the server, and to avoid the complexity of training a separate data generator, we employ simple yet effective strategy for generating synthetic pseudo- data X probe layer responses. We initialize X from standard multivariate Gaussian distribution, i.e., X (N, I). This choice provides diverse set of input signals capable of eliciting varied functional responses from neural network layers without relying on any prior knowledge of the true data distribution or introducing data- data-dependent privacy risks. The dimensions of X are dynamically adjusted based on the input structure of layers. We emphasize that this server- generraed X contains no client-specific information, thereby preserving privacy.
The core idea is to update the global model layers Go such that their outputs pseudo-data mimic the outputs of the corresponding critical client layers L U, L4- For each uploaded critical layer 02 E L', the server identifies a corresponding layer g in the previous global model G (typically based on layer type and potentially approximate depth). Note: Sending the parameters 0f necessary because they are the knowledge we transfer to the global model using X. The server feeds the same pseudo-date X to both layers to obtain their outputs: Yr, = , and 1 - The knowledge-sharing process aims to minimize the discrepancy between these outputs using distillation like loss, effectively transferring the functional knowledge of " into gj. The loss for updating global layer 9j is computed by averaging over all client layers ) mapped to it:
Reverse Knowledge Transfer.
Lo (10,))
1 K0 H
-
07 x
(3)
The global layer of (weights w/ and bias b3) are updated using gradient descent on this loss:
w² s w/ aV w LD. bj - 1/-1 a LLD
(4)
(5)
where a is the server-side learning rate. This update is performed for all global layers that corre- spond to received critical client layers, resulting in the updated global model G
3.5 Knowledge Alignment Module (Global-to-Looal)
After aggregating knowledge into the global model G³, this module determines how to best distribute this potentially richer knowledge back to enhance the personalized local models.
Knowledge Gain Entropy (KGE) Estimation. To guide the targeted distribution of global knowl- edge, we introduce the Knowledge Gain Entropy (KGE). KGE is designed as a heuristic metric to assess whether global model layer of may offer richer set of learned patterns compared client's local layer 0- Our central hypothesis is that a global layer, having been updated using knowledge aggregated from multiple diverse clients, is likely develop weight distribution that encodes a broader range of features. We propose that this increased diversity can be reflected in the Shannon entropy (-) of its quantized weight distribution. Thus, KGE is defined as the difference in entropy:
(6) In practice, H(-) is estimated from the flattened weight tensor after quantization into set number of bins (e.g., 256 bins) [30]. A higher entropy H (gg)) is interpreted as suggesting potentially more diverse learned patterns within the global layer.
KGE 05) H(g)) H(O.)). if type = type(g)).
We acknowledge that relating higher entropy directly to knowledge gain or improved generalization is guiding principle in FedFree, and that high entropy could, in some isolated instances, indicate
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Targeted Knowledge Distribution. For each client i that uploaded critical layers Li the server identifies the global layer 9). which maximizes the positive Knowledge Gain Entropy (KGE) with respect to any of its uploaded critical layers 0 E 1. That is, 9j. arg max 9f [ [KG (3) > 0 f D If such gj.- exists (i.e., least one global layer offers potential knowledge gain), its parameters are sent back to client The client then replaces its corresponding local layer 0f with the received global layer gf.. This ensures that clients receive targeted updates expected to be most beneficial, rather than simple average. If global layer yiclds positive KGE for client's less converged or noisier parameters. However, within our framework, where global layers aggre- gate diverse information and clients subsequently perform local training, KGE serves as a computa- tionally efficient proxy to identify global layers that are promising candidates for enhancing client models. The intuition is that layers with positive KGE have assimilated a wider variety of infor- mation than the client's s current local layer, offering potential for beneficial updates. The empirical success of KGE, as demonstrated Section 4, supports its utility for targeted knowledge transfer.
critical layers, no layer is sent back to that client for that communication round.
Handling Dimensional Mismatches. Dimensional discrepancies between global layer 9 and local layer 0f are resolved through partial parameter space projection. Let dg and di denote the flattened weight dimensions of global and local layers, respectively, with minimum projection dimension dmin min(dg: di). The first dmin elements of global parameters are projected to corresponding positions in the local layer, while exceeding dimensions are zero-initialized to preserve structural consistency:
[r) 0,
15 dmin:
otherwise.
This projection maximizes retention of global knowledge in shared parameter space through direct element-wise correspondence (0 < S dminn) while unprojected dimensions (r 2 dmin) retain local initialization to ensure stable model evolution.
3.6 Convergence Analysis
We provide a theoretical analysis of the convergence behavior of FedFree under standard assump- tions commonly adopted in federated optimization literature, including L-smoothness, fu-strong vexity, bounded variance, and bounded gradients. These assumptions, along with complete proof details, presented in Appendix B.
We establish the convergence of FedFree on both the strongly convex and the non-convex settings.
Theorem 1 (Strongly Convex Case). Suppose Assumptions 1-4 (Appendix B.l) hold, with μ > O, and let the server and client learning rates as and be appropriately chosen. Then, after T communication rounds, the iterates generated by FedFree (Algorithm 1) satisfy:
E [[((0T]] - O )
where 0t denotes the final global model, and F* is the optimal value the objective function. Theorem -onveConvex Case). Under Assumptions 1, 3, and (Appendix B. and appropriately chosen learning rates, FedFree achieves the following convergence result in the non-convex setting:
E [[IFFO>) = O }
min
tE (O.....TTI
The proofs leverage standard techniques from federated optimization theory, adapted to account for the pseudo-data-basee knowledge aggregation and KGF-guided alignment mechanisms unique to FedFree. The complete derivations are provided in Appendix B.

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Algorithm FedFree
1: Server initializes global model parameters G
2: for each communication round 1,2..... . do
3: Select subset of clients St (or all clients by default).
4: for each client E St in parallel do
5: Perform local training: o +- LocalUpdate(@!" D2).
6: Compute layer updates A0 (Equation 2), select top-k critical layers LA
7: Send 1. to the server.
8:
end for
9: Server aggregates knowledge:
10: Generate pseudo-data X (O.
11:
for each global layer 9f corresponding to L' do
12:
Compute distillation loss LD (Equation 3) and update of (Equations 4, 5).
end for
14: Server distributes knowledge:
for each client E S, do
16:
Find global layer 9/. maximizing positive KGE (Equation 6).
17:
if gj. cxists then
18:
Send 9j.- to client i for targeted layer replacement.
19: Insert adapter if dimensions mismatch (Equation 7).
20: end if
21:
end for
22:
end for
Evaluations
4.1 Experimental Setup
Datasets. We use two standard benchmark datasets for image classification: CIFAR-10 [31] and CIFAR-100 [31]. These datasets provide diverse class structures suitable for evaluating FL algo- rithms under different levels of task complexity.
Statistical Heterogeneity. To simulate real-world non-llI data distributions across clients, partition the datasets using a method similar to [32]. Specifically, for non-IIDI, in CIFAR-IO, we distribute data from out of 10 categories to each client (non-IlI: 1/10). In CIFAR- 100, we divide the data from 10 out of 100 categories for each client (non-IID: 10/100). For the data distribution bias study (Section 4.3), we also evaluate IID and other non-IID partitioning strategies based on label skew as follows. Details are provided with the specific experiment.
Model Heterogeneity. To evaluate performance under model heterogeneity (HtFL settings), define eight distinct architectures with varying depths and layer widths, randomly assigning one ar- chitecture to each client. The specific configurations of these eight distinct CNN architectures, along with the architecture of the server's s global model, are detailed in Appendix D. (Table Al). For ho- mogeneous FL (HmFL settings) comparisons, all clients use the same standard CNN architecture (also detailed in Appendix D.1).
Baselines. We compare FedFree against eight representative FL methods, categorized by their han- dling of heterogeneity:
Homogeneous Baselines (HmFL): FedAwg [33], Per-FedAvg [34] (personalization via meta-learning). FedProx [35] (handles statistical heterogeneity via regularization), and PFedLA [36] (personalization via layer-wise aggregation). These are evaluated in settings where clients have identical model architectures but non-IID data.
Heterogeneous Baselines (HtFL): FedProto [13] (prototype). FedKD [26] (KD, adapted for comparison), FedGH [37] (shared global head), and FedTGG [14] (trainable global prototypes). These are evaluated in settings where both data and models are heterogencous.

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Table 1: Comparison of final average test accuracy (%). HmFL denotes Homogeneous Models (non-IIDI), HtFL denotes Heterogeneous Models (non-IIDI). t indicates FedFree's percentage point improvement over the best-performing baseline in that category (HmFL HtFL).
Setting
Algoritim
Cliints
Clients
100
CIFAR-10
CIFAR-100
CIFAR-10
CIFAR-100
CIFAR-10
CIFAR-100
FedAvg [33]
$4.44
25.39
52.20
23.93
29.21
16.87
Per-FedAvg [34]
HmFL
FodProx [35]
73.54
42,70
73.94
40.68
73.64
35,59
PFedLA
90.94
16.63
FedFree
91.45 (15911)
89.34 (u97R))
90.85
(1829)1)
52.91 (308991)
86.08
50.16
FedProto [13]
81.68
32.88
67,
22.90
28.03
18.98
FedKD [26]
85,18
39.52
88.31
39.16
76.43
33,63
HtFL
FodGH [37]
94,24
66.28
91.85
63.60
74.14
29.93
FedTGP [14]
82.08
37.63
38.04
34,99
71.18
18,70
FedFFree
95.81 (1.77%
76.83 (189291)
95.35 (Ma19-T)
70.08 (1LIN9511
(7.03-033775111
49,20 (4L385
We select these baselines cover diverse strategies, including averaging, personalization, regu- larization, prototype sharing, and knowledge distillation approaches applicable to homogeneous or heterogeneous settings.
Implementation Details. All experiments were implemented using Python 3.1 and Py PyTorch 1.11, executed cluster with Intel Xeon Gold 6126 CPUs and NVIDIA GTX 2080Ti / Tesla T4 GPUs. For local training, we use the SGD optimizer with a learning rate of r 0.01 and a batch size of 10 for E = 5 local epochs per round. For FedFree, set the critical layer selection parameter (based on the sensitivity analysis in Appendix D.3, Figure A 1) and the server-side learning rate a = 0.01 unless otherwise specified. Total communication rounds specific hyperparameters for baselines (tuned for fair comparison where possible), are provided in Appendix D.2. Unless otherwise specified, results are averaged over runs with different random seeds in different settings. Accuracy reported is the average test accuracy across all participating clients on their local test sets after the final communication round.
2
200. Further details, including
4.2 Evaluation Results and Analysis
Table shows FedFree consistently outperforms all homogeneous and heterogeneous baselines across both datasets and varying clients' numbers. Notably, the performance gains are particularly substantial on the more complex CIFAR-100 dataset, where FedFree achieves improvements of up to 38.97% (over FedProx, 10 clients, HmFL.) and 46.3% (over FedKD, 100 clients, HtFL.). This suggests that FedFree's ' layer-wise knowledge sharing and alignment mechanisms are particularly effective when dealing with finer-grained class distinctions and higher model/data diversity.
The superiority over HmFL baselines like PFedLA highlights the benefit FedFree's KGE-based when models are homogeneous. The significant gains over HtFL baselines like FedGH and FedProto underscore the effectiveness of operating directly layer parameters (via reverse transfer) combined with targeted aligmment, compared to sharing only prototypes or classifier heads, especially without relying on proxy data like many KD methods typically do.
alignment compared to simpler layer aggregation strategies,
Furthermore, observing the detailed learning curves presented in Appendix D.7 (see Figures A3-A6), FedFree generally exhibits stable convergence. The stability, particularly noticeable in the 100-client HiFL setting (e.g., Figure A6(c)), can be attributed to the selective nature of updates (only critical layers uploaded, only high-KGE layers received) and the supervised knowledge-sharing mechanism using pseudo-das -ata, which likely provides a more consistent aggregation signal compared to direct parameter averaging or prototype matching in highly heterogeneous environments.
4.3 Impact of Data Skew on Performance
To assess robustness to varying statistical heterogeneity, we evaluate FedFree on CIFAR-100 with 100 clients under three data distribution settings: IID, non-llI with partitioning ratio of 8:1:1 (non- IIDI) and 6:2:2 (non-IIDD2) respectively [32]. Figure 2 shows the results. As expected, performance is highest under IID settings. While accuracy decreases under non-Ill settings, FedFree maintains

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50-
Accuracy (%)
40
Accuracy(%)
60-
30
Fedfree with non- IIDI
Foderee
50
160
150
200
10
Round
Clients
Figure 2: Accuracy on CIFAR- --0 with 100
Figure 3: Scalability analysis on the HtFL
clients across non-IID1 and non-IID2.
setting (non-IID1).
Accuracy(5)
Accuracy
20.
30
10
Averaag Appneg stion
130
150
Round
Round
(a) Critical vs. Random Layer Selection
(b) FedFree Sharing vs. Layer Averaging
Figure 4: Ablation analysis CIFAR-I00 with 100 clients (HtFL, non-IID1), Comparing (a) crit- ical layer selection using Equation 2 vs. random layer selection, and (b) FedFree's pseudo-data knowledge sharing vs. simple averaging uploaded layers.
strong performance even under significant data skew (non-IIDI). The performance gap between different levels of non-III) is relatively contained, indicating robustness. This resilience stems from the personalization inherent in the framework: clients primarily update based local data, and the global model serves to inject useful generalized knowledge identified via KGE, rather than enforcing strict conformity, mitigating the negative impact of conflicting data distributions during aggregation.
4.4 Scalability Analysis
We examine how FedFree scales with an increasing number clients (10, and 100) the HiFL setting. Figure plots the final accuracy on CIFAR-10 and CIFAR-100, 100. Accuracy moderately de- creases as the number of clients grows, particularly from to 100 clients. This trend is common in FL due to the increasing statistical heterogeneity and the potential for more diverse local models as the client pool expands. However, compared with Table 1, FedFree maintains significant perfor- mance advantage over baselines mechanism plays a core role here by selectively incorporating knowledge, potentially preventing aggregation of conflicting updates from large, diverse client pool. We observe similar scalability trends under homogeneous model settings as detailed in Figure A2) Appendix D.5.
100 clients, demonstrating scalability. The KGE alignment
4.5 Ablation Studies
To validate the contribution of FedFree's core components, we conduct ablation studies on CIFAR- 100 with 100 clients in the HtFL setting (non-IIDI), shown in Figure 4.
compare selecting the top-k layers with highest change rate (Equation 2, used in FedFree) against randomly selecting k layers to upload (Figure 4(a)). Selecting critical layers based on change rate significantly outperforms random selection. This con- firms that the parameter change magnitude effectively identifies layers undergoing significant learn
Critical Layer Selection Strategy.

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ing that are valuable for knowledge sharing. Randomly sharing layers fails to capture the richest updates, leading poor performance.
Knowledge-sharing Mechanism. We compare FedFree's knowledge-sharing aggregation (updat- ing global layers based minimizing output difference pseudo-data, Equation 3) against directly averaging the parameters of uploaded critical layers of the same type (ignoring incompatible types). Figure 4(b) shows that FedFree's pseudo-data-based knowledge-sharing significantly outperforms simple layer averaging. This highlights the benefit of using functional knowledge distillation via pseudo-data outputs for aggregation, which more robust architectural differences than direct parameter averaging.
These ablations confirm the effectiveness of both the critical layer selection strategy and the pseudo- data-driven knowledge-sharing mechanism within FedFree.
Conclusion
This paper tackles the challenge of breaking knowledge-sharing barriers heterogeneous feder- ated learning. We introduced FedFree, a novel framework breaking knowledge-shande barriers via reverse layer-wise knowledge transfer (using pscudo-data for proxy-data-free aggregation) and Knowledge Gain Entropy (for targeted, layer-specific knowledge alignment). Supported by theo- retical convergence guarantees and extensive experiments, FedFree significantly enhances personal- ized model performance, consistently outperforming state-of-the-art HtFL baselines on benchmark datasets. Moreover, FedFree offers a practical and privacy-preservie the potential of collaborative learning across diverse devices and data distributions. But practical deployment on physical devices and environments with extremely large models remains untested. In future work, we will evaluate FedFrree in real-works deployment scenarios with enhanced hetero- geneity, including more diverse model architectures and non-IID data distributions.
pathway towards realizing
Acknowledgement
We thank the reviewers for their helpful comments. This work was partially supported by Shanghai Municipal Education Commission Artificial Intelligence Plan (22024-119).
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13

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Appendix
A
Notation
Table Al summarizes the main notations used throughout the paper.
Table A1: Notations
Symbol
Description
N
Total number of clients.
Total number of communication rounds.
E
Number of local training epochs/steps per round.
i
Index for clients (1....,N) .....,N..... .N.
t
Index for communication rounds (0, .O,..., 1). Index for layers within a model. Parameters of the entire local model for client at the start of round 4. Parameters of the [-th layer for client at the start of round t. Change in parameters for layer of client i during round t (Equation 2).
I
0
1,
L
Set critical layer parameters uploaded by client in round Number of critical layers selected by each client. Global model parameters at the start of round t. Parameters of the j-th layer of the global model G Flattened weight dimension of the local layer 0f,- Flattened weight dimension of the global layer g)- Minimum projection dimension, dmin min (dg. di).
k
G
gf
dg
dmin
g
Represents aggregated state, e.g., g' Ei= VFF.F. (used in proofs). Local loss function for client i. Global loss function F(0) (()==>= Pt (.)). Optimal value of the global loss function. Local dataset of client i.
FO
F()
D,
n
Size of dataset D;- Weight of client p: n./ E;
p
X
Server-generated pseudo-data based on (0,0 I).
CD
Knowledge-sharing loss on the server (Equation 3). Entropy of layer's weight distribution (Equation 6). Knowledge Gain Entropy (Equation 6).
HO)
KGB
Adapter layer inserted for client after layer in round (Equation 7).
W,b
Parameters of the adapter layer Σ
n
Learning rate for client-side local training.
Learning rate for server-side global model updates (Fquations 4, 5).
Lipschitz constant
smoothness (Assumption 1).
Strong convexity constant (Assumption 2).
Variance bound for local stochastic gradients (Assumption 3).
G
Bound for expected squared norm of local stochastic gradients (Assumption 4).
T
Measure of objective function heterogeneity (F EP:F.)
3
Angle between of and of (used in proof).
Constant relating of and of (used in proof).
B Proof of Convergence Analysis
We present the convergence proof of FedFree under standard assumptions federated optimization literature. The proof consists of two parts: convergence under strongly convex objectives and non- convex objectives. All necessary assumptions, intermediate lemmas, and detailed derivations are provided below.
14

---

B.1 Assumptions
We first introduce standard assumptions that are used throughout the convergence analysis. Assumption (L-smoothness). Each local objective F, is L-smooth, meaning that for all v, w,
(((e)= s Fi(w) + (c w. VF((w) - 2110 w|l
(A1)
where (.-)) denotes the standard inner product. Equivalently,
[VV VF:(w)]l S Llle wwll
(A2)
and
F F(()) 2L [F
(A3)
where FT = min, Fi(w)).
Assumption (Strong Convexity). Each local objective F; is p-strongly convex, i.e.. for all v, w,
F((v) 2 ((ww)) + (v - w, VF((w))
2 l| w|l?.
(A4)
Assumption 3 (Bounded Variance). For any client i, the variance of the stochastic gradients is bounded:
(V. VF,(0.)) so²
(A5)
where & a random sample from client i's local dataset.
Assumption (Bounded Stochastic Gradients). The second moment of stochastic gradients is uni- formly bounded:
E BII S G
(A6)
B.2 Key Lemmas
We establish several lemmas to facilitate the convergence proofs. Lemma (One-Step SGD Progress). Under Assumptions and 2, for suitable learning rates satis- fying The + ca2, cos B1 S z. we have;
E [10 1- s (1- + ca2 cos 3:)) 110 1 BBB
(A7)
where = D.o?
1 6L7 + 8(F - G) and = F - Σ P
Lemma 2 (Bounding the Variance). Under Assumption 3, the variance between stochastic and expected gradients is bounded as:
E
Σ
(A8)
Lemma (Bounding Client-Server Divergence). Under Assumption 4 and non-increasing learning rates, the expected divergence between local models and the averaged model is bounded as:
0 0
(E
(A9)
Lemma 4 (Gradient Consistency). Under Assumption 3, the averaged stochastic gradient approxi- mates the true gradient:
N
VF(O) (VV))(())) = gi-
Σ
(A10)
Lemma (Bounded Global Gradient Norm). Under Assumption 4, we have:
N
< Σ G
(AI1)
1=1
15

---

B.3
Proof of Convergence for Strongly Convex Objectives
We first establish convergence in the strongly convex case.
Proof of Theorem I. The update rule in FedFree is:
0++ = fj -n acoi.
(A12)
where of aligns with of via of = cgi cos Bt.
Since the directions of F(Of) and V.n are related, so let of cofcost, where is the angle of of and gt-
Let A, E100 17113. From Lemma 1, Lemma 2, Lemma 3, it follows that
A+11 S (1 - a(n + co;cos3:))4: + B
(A13)
where
B
Σ
No 6LT + - 12
(A14)
i=1
For diminishing step size, Ne + c0,00881 A S 7+3 where e = max
B for some 1 and 7 0. We will prove I+y
B 8p-T (7 + } We prove it by induction. Firstly, the definition of # ensures that it holds for
Assume the conclusion holds for some it follows that
A - (1 - u(nt + co,cos8:)) + (n + ca,cos3:)
B²B
<
t t+?
t tt7
7)
++
B²B
81
(A15)
+
(1+))²
(1 (1+
(1+ 7)2
< v
++
Then by the L-smoothness of F(-)
L A, S B[F(0)) F <
L v
(A16)
2 2
Specially, if we choose 3
2 7 m // E} land denote k then T) + ca2cos8 =
Then, we have 7+t
BB
BBB
4B
U = max
Bp - 1 (7 (7+1)4
3p - + +
S
+
(A17)
E[F( F* < 2 +t < K 2B
p(7 +1)
A1
+ p
2
Applying Lemmas 1, 2, and 3, and using standard induction argument on diminishing step size 8 Ni + co2, cos 31 F+7 for appropriate 7, we derive:
E [F())] F FF (
(A18)
where constants depend on L,, n1, G, E.
Detailed derivations provided in the subsequent calculations.
16

---

B.3.1 Proof of Lemma!
Proof. Note that 0++1 0 n aqt..
|10 0:1|² 110 (n carcos gf - 87 (n carcos3i) + (n ca.cos gg/l
= 0 of - (m + co,cos 2
+ 2n + carcos}i) (0)- 0r (n + ca,cos gi)
A
+ (n + ca,cos8i)2
gf efll"
(A19)
Note that EA2 We next focus on bounding A1. Again we split A into three terms:
100 0g - (n + 3))
= 110 -011 -2(m + ca,cosBi) (0) 0,, gg)
(A20)
+ (n + carcos31)
|
Ba
From the the T-smoothness of F.()), follows that
VV (0t) s 2L (Pr (0t,) PP).
(A21)
By the convexity of || 2 and Equation A21, we have
B₂ (n. + ca,cos
||'||
N
< (n + c0.c0833)
pi Σ
VF: (0%, 12
(A22)
i=1
N
< 2L(1 cancos31)
2
Σ
pi (F((())) - -F)).
Note that
B1 = 2(m) + co. (8)
8 .()
2(m + co,
(0) 07, (.()))))
iml
(A23)
-(1, ca;c0331)
Σ
Pc (0)
8y v..((()))
N
2(( + co.cos
Σ
ps (0). 0f. (F
By Cauchy-Schware inequality and AM-GM inequality, we have
(0) 8 V. (0%,) S (n) + ca)cos3)) 10 02,11 (n ca.cos3) |/V (O.)))
(A24)
By the μ-strong convexity F.(:), have
{8) 0;, VF, (0W)) < - -(F, (Bh,) F((01))
11 110 0:11
(A25)
17

---

By combining the equations above, it follows that
A1 |10 - 0i (n + co,c)))/))'11
N
< ||0| - 0/11² + 2T. + cancos
Σ (Fi(0%,)) - -F()
1=1
100 - 10,11 + (m + concosBi) || (0W))1))
+ (n + c0,,co8,))
Pi
(1i + co)cosBi)
==1
N
2(n - co.
Pi
[F' (01,))
F:(00) 1
2 1100 0f 0111))
N
= (1 -m(n + co.cos8:))
||0f 0/ + Σ
Ps 00 -6
i=1
N
4L(m + 30,
Σ (F((O).)) - Ft) 2(n + co.c0881) Σ
ps (Pr (0%,) R.(OF))
(A26)
We next aim bound C. We define 7t 2(n + co,cos3)) 2 + co,cos8i)). Since
(n + c: S 4z. (n + carcos8i) S S 2(m + ca1cos3)). Then we split C' into two terms:
C= 22) + ca,cos3i) - 22 carcos81)) Σ
Ps (P.(OL.) - FF?)
N Σ
+ 2(1 + ca:cos;))
Pi (F:(0)) - FT)
N
N
(A27)
%
Pi (F)(0) - F*) + (2(n= + ca:cos -11) Σ
Σ 1=1
Ps (F* - -F?)
i=1
Σ Pi (F:(O1.)) F*) +4I(mp ca,cos3:)
7
where in the last equation, we use the notation r EN DePP -F;) = F - -
To bound D, we have
N
N
pe (F((0))) - Fr) = Σ Pi (E((O)))) - E((O))
Σ 1=1
pi (F.(0:) - -F)
N
Ps (VF o. 07) + (F(0)) - FF)
1=1
1
Σ9
(n (m [F)
100, 8711(]
(A28)
Pi
(nt + ca,cos)))
i=1
(F()) F()
N
2 Σ Pi
(Th + ca,cos (F) -F,) + 2(m: + ca,cos,))
110 0:11²]
1=1
+ ((F())
- -F"),
18

---

where the first inequality results from the convexity of Fi(-). the second inequality from AM-GM inequality, and the third inequality from Equation A21. Therefore
C V/ Σne Pi (ne ca,cos33) FT)
2(1 + concos88i) 110 - 0/11
7/t (F(O:) F*) + 4L(m) ca;cos8))
N
=m((n + cancos - 1) Σ (Fi(0)) F*))
(A29)
+ +4I(m + c0;c0881)2 + ve(ne + concos;:) L) r
#t 2(1 + carcosBi)
Pc 110 0611
S 6T 30 T +
Ps 1100 0:11
where in the last incquality, we use the following facts: (1) (Nt + carcos - I - s
and Σ Ps (8) F*) F(01) F* 0, (2) r 0, and 4L(1: c,,cos33) + 1m + The
co;coos;) < 6(1 + ca,coss:) and (3) 2(m t:0 const) S 1.
Recalling the expression of A and plugging C' into it, we have
A |00] 8 (n: co)cos3i)g'11
N Σ 1=1
S u(n + co,00883)) 00 071
Ps 00
00,11'
(A30)
+ 6(m + c0 LT.
B.3.2
Proof of Lemma
Proof.
From Assumption 3, the variance of the stochastic gradients in device is bounded.
N
E Ellg'
g/|l E
Pd V (V((O V.((O Σ
-
P () -VE(0)))
(A31)
x
19

---

B.3.3
Proof of Lemma 3
Proof.
N
N
0 - 02,11
E Σ
Pi [1 - 000 - -00 - 0h0) ||
Pe
1m
1=1
E
Pi 110 11
1=1
[-1
Σ P
Σ
(E 1)(Th + ca,cos3))
VEL [
(A32)
1=1
t=f
N
t-1
(E - () + car, c
Pi
t=
Pr + ca,, -E
4(mr + c0,c088:) (F -)
Here in the first inequality, we use E|| EXI2 s x|| with probability Pt. In the second inequality, we use Jensen inequality:
1 Et) (1-10) Σ (n con,030))))))
10%, 0'0 1= Σ (m co,,os
t=
(A33)
B.4
Proof of Convergence for Non-Convex Objectives
We next establish convergence under non-convex settings.
Proof Theorem 2. Using I-smoothhess (Assumption 1), we have for the update:
F(O+t)) < F(O)) + (VF(0)) - o3) + 2 10, 011
(A34)
Since the directions of F(0)) and V.D,e, are related, so let of egf cosp1 where is the angle of of and of-
F(0 F(0)) + (n + ca;) (0)) S 1 ((s + ca,,cos
L
(A35)
We know b112 = ||a|| + < a. +/bb Thus, < a, >= |||| b 1 1|aa b11
So let (VF(0)),g)) gf):
(F(()) = -
|sfll - (VF 12.
(A36)
Substitute Equation A36 into Equation A35, get
1)t + co
L(n + concos8:)
(IVF -
1192
2
2
(A37)
Multiply both sides of Equation A37 by cctea.cos8
we have
2
77 ca,cos
[
s (0)
2
(A38)
20

---

So we get
[VF(0))]1 - + ca,cos
|
ofl (Lm + LeaycosB - 1))lg/
(A39)
Combine Lemma 2, Lemma 4, Lemma we have
2
N E[F(O++)) - F( + > oo + (Lm, + Leaycos - G²)
BIVF(()) The + ca1cos31
(A40)
Summing over t E 10, 10,1, ... , 1 and dividing both sides by T. we have
E| < T(m + ca;cos
B[F(0)) F*] f Σ of + (Ln: + LeaycosBi - 1)p;
(A41)
Substituting the update rule and rearranging terms, combined with Lemmas 2 and yields:
min tE (O,..,--1)) E [[IVF(()) = =0 (
(A42)
B.5 Conclusion
Thus, we complete the convergence analysis for FedFree, establishing OL1/T) rates under both strongly convex and non-convex settings.
C Discussion
In this work, we address the obstacle in knowledge transfer for heterogeneous federated learning: due significant variations in device capabilities, knowledge encoded in different model archi- tectures struggles to be effectively aggregated and disseminated across the federation. To tackle this issue, we introduce FedFree, a proxy-data-free HtFL framework that proposes a reverse layer- wise knowledge transfer mechanism, aggregating heterogeneous client models into global model solely using Gaussian Gaussian-based pseudo-data, thereby eliminating reliance on real proxy datasets. Fed- Free leverages Knowledge Gain Entropy (KGE) guide targeted layer-wise knowledge aligmment, ensuring each client receives the most beneficial and cechitctuuresspciffi global updates. The effec- tiveness of approach is supported by theoretical analysis and extensive experiments conducted on various datasets and models for computer vision tasks.
Limitations remain, particularly regarding real-world applicability. While FedFree has demonstrated effectiveness in near-real-word settings, its physical deployment on actual devices and environments with extremely large models remains untested due to resource constraints. Real-world implemen- tation of FedFreee may reveal additional challenges or limitations, providing further insights into its scalability and efficiency.
D Supplementary Experimental Details and Results
This section provides additional details referenced in Section 4.
D.1 Model Architectures
Table Al details the architectures used in the HtFL experiments. "Homo. Model" refers to the standard architecture used in homogeneous settings. "Model. 1" through "Model 8 represent eight distinct architectures randomly assigned to clients in the HtFL setting. The "Global Model" architecture used the server is also shown; is designed be encompassing enough for the client models.
21

---

Table A1: Model Configurations Comparison (Homogeneous and Heterogeneous Settings).
Name
Base Architecture
Key Features
Layers
Params.
Model_1
CNN
Conv layers. FC layers
#3.2M
Model 2
ResNet18
BasicBlock,, [2.2,2,2] layers
18
*11.2M
Model.3 3
ResNet34
BasicBlock, [3,4,6,3] layers
34
*21.3M
Model_4
ResNet50
Bottleneck, [3,4,6,3] layers
50
=23.5M
Model.5
ResNet101
Bottleneck, [3,4,23.3] layers
101
R:42.5M
Model 6
ResNet152
Bottleneck, [3.8,663] layers
152
2:8.2M
Model. 7
GoogleNet
Inception modules
22
*6.8M
Model_8
MobileNetV2
Linear Bouteneeks, Depthwise Separable Conv
53
R3.5M
Global Model
CNN
2 Conv layers. FC layers
5
R3.2M
Homo. Model
CNN
Conv layers, FC layers
5
R33.2M
D.2
Hyperparameter Settings
Table A2 details the hyperparameters used for FedFree and the baseline methods. Parameters for baselines were set based on their original papers or tuned slightly for fair comparison in our experi- mental environment.
Table A2: Hyperparameter settings for FedFree and baseline methods.
Parumeter
Fedlfree
FedAvg
FedProx
płedLA
FedKD
FedGH
FefTGP
FodAvg
Local epochs
30
30
30
30
30
30
Local learning rate 7)
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
learning rate
Critcal layers k
2
KGF entroyy
Proximal term
0.01
Meta step size 3
0.01
Hypernetwork LR v/.
0.005
Prototype LR Up
0,1
Regularisation
Distillation temp.
[0.95,0.98]
Contrastive temp. Te
Optimizer
SGD 10
SGD
SGD
SGD
SGD
SGD
SGD
SGD
SGD
Batch size (local)
10
10
10
D.3 Parameter Sensitivity Study (Impact of k))
We investigate the impact of the number of critical layers selected for upload on the performance of FedFreee Experiments were conducted on CIFAR- 100 with 100 clients (HtFL setting, non-IIDI), varying & E {1, 3). Figure Al shows the mean accuracy statistics after model convergence.
Accuracy(%s 80
40
20
The value of k
Figure A1: Performance comparison for different values & (number of critical layers uploaded) on CIFAR-100, 100 clients, HtFL. setting.
The results indicate that & 2 achieves the highest mean accuracy, followed by k 1. This suggests that uploading two critical layers optimally captures effective information knowledge sharing in this setup, while uploading more layers might introduce redundancy or noise without proportional benefits, potentially due to the heterogeneity and resource constraints. Therefore, we used & = 2 as the default setting in experiments.
22

---

D.4 Parameter Sensitivity Study (Entropy Methods)
Based on the results Table A3, our proposed entropy method achieves the highest accuracy of 49.20% on CIFAR-100, outperforming both Tsallis Entropy (45.98%) and Collision Entropy (44.46%). The superior performance of Shannon entropy can be attributed its fundamental prop- erty as measure of information content. Unlike Tsallis or Collision entropy, which can be bi- ased towards the most probable events (effectively smoothing the distribution), Shannon entropy exquisitely sensitive to the entire probability distribution. This demonstrates the superior effective- ness of our approach in handling predictive uncertainty for client selection in federated learning.
Table A3; Comparison of Different Entropy Methods (CIFAR-100, 100 clients.
Entropy Type
Ours
Tsaliis Entrpy
Collision Entropy
Accuracy (9)
49.20
45.98
44,46
D.5
Additional Scalability Study (Homogeneous Models)
To isolate the effect of client numbers from model heterogeneity, we conducted scalability experi- ments under a homogeneous model setting (all clients use "Homo. Model" from Table A1).
02
CIAR-23
Figure A2: Accuracy variation with different numbers of clients in the HmFL setting (non-IIDI).
Figure A2 shows the results for 10, 20, and 100 clients. Similar to the heterogencous case, accuracy decreases slightly as the number of clients increases, primarily due to escalating statistical hetero- geneity. However, FedFree maintains high accuracy compared the HmFL baselines in Table 1, confirming its scalability even without model heterogeneity.
D.6 Additional Scalability Study (Additional Dateset)
Table A4: TinyImageNe Benchmark (100 clients).
Ours
FedKD
FelGH
FedTGP
Accuracy (%)
23.31
16.67
13.28
17.72
15.35
Memory(MB) 2,045
373
2.641
2,022
4,167
To further demonstrate the applicability of FedFree, have conducted additional experiments the TinylmageNet dataset Table A4, which is significantly more challenging due to its higher resolution, increased number of classes (200), and greater data complexity.
The results, presented below, demonstrate that FedFree consistently outperforms baseline methods on this more complex dataset, further validating its generalizability. We emphasize that FedFree model-agnostic and data-agnostic by design, relying on a layer- wise knowledge-sharing strategy that does not assume any specific model architecture input modality.
D.7 Additional Learning Curves
This subsection presents detailed learning curves corresponding to the main experimental results summarized in Table 1. These plots illustrate the convergence behavior, specifically the average
23

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(a) 10 clients
(b) 20 clients
(c) 100 clients
Figure A3: Learning curves (Average Test Accuracy Rounds) for Homogeneous Models (HmFL) on CIFAR-10 10 (non-IIDI). Comparing FedFree against FedAvg, Per-FedAvg, FedProx, and pFedLA for different numbers of clients.
Accuraoy
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356
30
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(b) 20 clients
100 clients
Figure A4: Learning curves (Average Test Accuracy vs. Rounds) for Homogeneous Models (HmFL) on CIFAR-100 (non-IID1). Comparing FedFree against FedAvg, Per-FedAvg, FedProx, and LA for different numbers of clients.
client test accuracy versus communication rounds, for FedFree compared against the relevant base- lines under different settings.
Homogeneous Model Settings (HmFL). Figures A3 and A4 show the learning curves for the homogeneous model setting (HmFL., where all clients the same CNN architecture but operate on non-IlD data (non-IID1). Comparisons are shown for 10, 20, and 100 participating clients on CIFAR-10 and CIFAR-100, respectively. Baselines included are FedAvg, Per-FedAvg, FedProx, and AFedLA. Shaded areas typically represent the standard deviation across clients or runs.
Heterogeneous Model Settings (HtFL.). Figures A5 and A6 show the learning curves for the het- erogeneous model setting (HtFL.), where clients possess different architectures (randomly assigned from Model_1-Monn 1MMoeel_8 in Table A1) and operate non-IlI data (non-IID1). Comparisons shown for 10, 20, and 100 participating clients on CIFAR-I0 10 and CIFAR- -000, respectively. Base- lines included are FedProto, FedKD, FedGH, and FedTGP.
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Figure A5: Learning curves (Average Test Accuracy vs. Rounds) for Heterogeneous Models (HtFL) on CIFAR-10 (non-IID1). Comparing FedFree against FedProto, FedKD, FedGH, and FedTGP for different numbers clients.
Accunayy%))
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(b) 20 clients
(c) 100 clients
Figure A6: Learning curves (Average Test Accuracy vs. Rounds) for Heterogeneous Models (HtFL) on CIFAR- 100 (non-IID1). Comparing FedFree against FedProto, FedKD, FedGH, and FedTGP for different numbers clients.
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Reviews:
[{"review_id": "pOk6oY3DPk", "reviewer": "Reviewer_VUC8", "summary": "In this paper, the author proposes FedFree, an innovative framework that can address the knowledge sharing barriers in heterogeneous federated learning (HiFL). This framework introduces a reverse layer-by-layer knowledge transfer mechanism. The server generates Gaussian pseudo-data and uses the gradient descent algorithm to minimize the output difference between the key client layer and the global layer on the pseudo-data, achieving knowledge sharing from local to global. The framework also innovatively uses knowledge gain entropy to quantify the difference in knowledge density between the corresponding global layer and the local layer, in order to identify the global layers with potential to enhance the client model. The author demonstrated that the convergence rate of FedFree is O(1/T) under both strongly convex and non-convex Settings, and verified on the CIFAR dataset that FedFree significantly improves its performance relative to the baseline in heterogeneous scenarios and demonstrates robustness at different non-IID levels.", "questions": "Please refer to weaknesses.", "limitations": "Please refer to weaknesses.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths：\n\n1.\tThe article innovatively proposes a framework for agent-free data, avoiding the need for real agent datasets by generating Gaussian pseudo-data.\n2.\tThe article innovatively describes the role of FedFree from two directions: local → global and global → local.\n3.\tThe article provides detailed proofs of theories such as lemma, which are highly reliable.\n\nWeaknesses：\n\n1.\tAs stated in Article 3.5, \"Our central hypothesis is that a global layer having been updated using knowledge aggregated from multiple diverse clients, is likely to develop a weight distribution that encodes a broader range of features.\" and in practice, it is assumed that higher entropy corresponds to more diverse information, without providing proof or research status. It has certain limitations.\n2.\tThe article is only verified on the CIFAR-10/100 dataset. It is hoped that more experimental data can be added to prove the applicability of the FedFree framework.\n3.\tThe article points out that agentless data can avoid some privacy issues, but there is insufficient discussion on privacy security issues. Some aspects such as how using this framework can prevent the leakage of privacy issues or resist attacks can be added to illustrate that proposing this new framework has solved some privacy problems.", "was_revised": true, "final_justification": "The authors addressed my concerns, I raise my score to 4.", "rebuttal": "We sincerely thank Reviewer VUC8 for their time, thorough review, and constructive feedback on our submission. \n\n**R1-1 (KGE Hypothesis)**: As stated in Article 3.5, \"Our central hypothesis is that a global layer having been updated using knowledge aggregated from multiple diverse clients, is likely to develop a weight distribution that encodes a broader range of features.\" and in practice, it is assumed that higher entropy corresponds to more diverse information, without providing proof or research status. It has certain limitations.\n\n**Re**: We appreciate you highlighting this point for clarification. While a formal theoretical proof establishing a direct causal link between Shannon entropy of quantized weights and the richness or diversity of learned features is challenging and remains an open research problem in general deep learning theory, within FedFree, KGE is explicitly framed as a **computationally efficient proxy** (lines 202-208) to identify global layers that are promising candidates for enhancing client models. The intuition is that layers aggregated from diverse client information are likely to contain a wider variety of patterns. The **empirical effectiveness** of KGE in guiding beneficial knowledge transfer is strongly supported by the significant performance gains observed across all our experiments in Section 4 (e.g., Table 1, Figures A3-A6) and specifically validated through the ablation study in Figure 4(a). This empirical success validates its practical utility within our framework. We will strengthen the phrasing in Section 3.5 to explicitly emphasize that KGE serves as an effective heuristic, validated by extensive empirical results, rather than implying a formally proven theoretical equivalence.\n\n### Comparison of Different Entropy Methods (CIFAR-100, 100 clients)\n\n| Entropy Type      | Ours  | Tsallis Entropy | Collision Entropy |\n|-------------------|-------|-----------------|-------------------|\n| **Accuracy (%)**  | 49.20 | 45.98           | 44.46             |\n\n*Table: Performance comparison of different entropy approaches on CIFAR-100 with 100 clients.*\n\n**R1-2 (Limited Experimental Data)**: The article is only verified on the CIFAR-10/100 dataset. It is hoped that more experimental data can be added to prove the applicability of the FedFree framework.\n\n**Re**: We acknowledge this valid point. CIFAR-10 and CIFAR-100 are standard and widely recognized benchmarks for FL, particularly for evaluating architectural heterogeneity. Our experiments already employ a wide range of complex CNN architectures (ResNet18-152, GoogleNet, MobileNetV2, etc., detailed in Table A1). To further demonstrate the applicability of FedFree, we have conducted additional experiments on the TinyImageNet dataset, which is significantly more challenging due to its higher resolution, increased number of classes (200), and greater data complexity.\n\nThe results, presented below, demonstrate that FedFree consistently outperforms baseline methods on this more complex dataset, further validating its generalizability. We emphasize that FedFree is model-agnostic and data-agnostic by design, relying on a layer-wise knowledge-sharing strategy that does not assume any specific model architecture or input modality.\n\n### TinyImageNet Benchmark (100 clients)\n\n| Method    | Accuracy (%) |\n|-----------|-------------:|\n| **Ours**  | 23.31        | \n| FedProto  | 16.67        | \n| FedKD     | 13.28        |\n| FedGH     | 17.72        |\n| FedTGP    | 15.35        |\n\n*Table: Comprehensive performance comparison showing absolute accuracy and relative improvements over baseline methods.*\n\n\n\n**R1-3 (Privacy Discussion)**: The article points out that agentless data can avoid some privacy issues, but there is insufficient discussion on privacy security issues. Some aspects such as how using this framework can prevent the leakage of privacy issues or resist attacks can be added to illustrate that proposing this new framework has solved some privacy problems.\n\n**Re**: We appreciate the emphasis on privacy, which is a critical concern in FL. We would like to clarify and highlight that a key strength of FedFree is its **inherently privacy-preserving design due to its \"data-free\" and \"model-free\" nature of knowledge sharing** (lines 8, 46, 112).\n\nSpecifically, FedFree avoids privacy leakage in the following ways:\n1) No Proxy Dataset Reliance: Unlike many existing HtFL methods (e.g., FedMD, FedDF, FedKD discussed in lines 79--84) that rely on shared proxy datasets, FedFree completely eliminates this requirement, mitigating known privacy risks associated with data exposure.\n2) Gaussian-based Pseudo-data: Knowledge sharing (local-to-global and global-to-local) is facilitated solely by server-generated **Gaussian-based pseudo-data ($X \\sim \\mathcal{N}(0, I)$)** (lines 11, 51, 168--174). As stated in line~174, \"this server-generated $X$ contains no client-specific information, thereby preserving privacy.'' This pseudo-data serves as a universal probe without seeing or inferring real client data.\n3) No Direct Model Sharing/Averaging: FedFree does not directly share or average full model parameters across clients, which could expose architectural details or combined gradients. It only transfers functional knowledge of selected critical layers.\n\nWhile privacy preservation is an inherent benefit of our design, rather than the primary focus of designing new privacy techniques, FedFree can be readily integrated with widely adopted mechanisms such as Differential Privacy (DP-FL), Secure Aggregation, or Homomorphic Encryption to further enhance its privacy guarantees. We will include an extended discussion on these inherent benefits and potential integrations in the Conclusion (Section 5, around lines 343-344) of the camera-ready version."}, {"review_id": "Tw9NVpsyS5", "reviewer": "Reviewer_wr5p", "summary": "The paper proposes FedFree, a data-free and model-free heterogeneous federated learning algorithm. In FedFree, each client uploads the top-k layers with the largest local update magnitudes (measured by the $L_2$ norm) to the server. To avoid privacy leakage caused by using proxy datasets, the server generates Gaussian-based pseudo-data, eliminating the need for real data. The authors introduce a novel metric called Knowledge Gain Entropy (KGE) and use it to identify and deliver the most informative layer from the global model to each client, thereby achieving more accurate knowledge alignment. Theoretical analysis shows that FedFree achieves a convergence rate of $\\frac{1}{T}$ under both strongly convex and non-convex settings. Extensive experiments demonstrate that FedFree outperforms existing homogeneous and heterogeneous federated learning methods.", "questions": "1. In the **Critical Layer Selection** module(Section 3.3), wouldn’t layers with more parameters naturally have an advantage due to their larger L2 norms? Why does this selection strategy empirically improve performance despite this bias? Would it be more reasonable to normalize the L2 norm by the number of parameters in each layer during computation?\n\n2. In the **Handling Dimensional Mismatches** module(Section 3.5), when a client’s corresponding layer has more parameters than the global model’s, the excess parameters are simply zeroed out. Wouldn’t this lead to potential information loss? Does this not affect the algorithm’s performance? If not, what is the underlying reason for this robustness?\n\n3. In the experiments, the test accuracy of FedAvg appears significantly lower. Is this because it was also limited to only 200 training rounds? If so, it may not have fully converged. Would it be more appropriate to compare the final test accuracy after convergence for all methods?", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper presents a clear and well-structured narrative that is easy to follow.\n\n2. It provides a sound theoretical convergence analysis.\n\n3. The proposed method effectively avoids privacy leakage caused by using proxy datasets.\n\nWeaknesses:\n\n1. In the **Targeted Knowledge Distribution** module (Section 3.5), each client must traverse all layers of the global model to identify the optimal one, which incurs significant computational and time costs. Moreover, the global model used in experiments is a shallow network with only five layers, raising concerns about the scalability of the method to larger models commonly used in real-world applications.\n\n2. The method does not consider the common federated learning setting where only a subset of clients participate in each training round.\n\n3. The homogeneous models used for comparison in the experiments are overly simplistic with only five layers.\n\n4. The paper lacks comparative experiments with algorithms related to **Architectural Adaptation and Matching**, as mentioned in the related work.", "was_revised": true, "final_justification": "I have read the rebuttal of the authors and the comments from the other reviewers, and would like to keep my original rating.", "rebuttal": "Thanks for your comments. \n\n**Weakness 1 (Computational Cost of KGE \\& Global Model Size / Critical Layer Selection Bias)**\n\n**Re**: 1) Computational Cost of KGE \\& Global Model Size: We clarify that the process in the \"Targeted Knowledge Distribution'' module (Section 3.5)  does not require traversing all layers of the global model for every client. Instead, for each client i that uploaded $k$ critical layers, the server only identifies the global layer $g_j^*$ that maximizes positive KGE with respect to any of its uploaded critical layers (lines 210--213). This means the comparison is performed only for these $k$ critical layers against relevant global layers, for $k=2$ (line 154), is a very small number. The computational cost of KGE (Shannon entropy of quantized weights, lines 199--200) and the associated forward passes for functional distillation are lightweight, involving only these selected layers. Thus, the computational overhead of KGE is **negligible compared to local model training or full model inference**.\n2) Regarding the global model's shallow architecture (Table A1), it is designed as an \"effective intermediary\" (lines 161--165) whose architecture is chosen to encompass diverse client models, not necessarily to be the largest model. The strength of FedFree lies in its layer-wise knowledge transfer and alignment, which scales differently than methods relying on full model aggregation. For larger client models, the principle of selecting $k=2$ critical layers (lines 153--154) and performing layer-wise aggregation and alignment remains efficient because the number of layers processed by the server remains constant and small. We will add a sentence in Section~3.5 or Appendix D.1 to clarify the efficiency of KGE computation.\n2) Critical Layer Selection Bias: We clarify that our selection criterion is not based on the absolute L2 norm of each layer’s weights, but rather on the **magnitude of parameter change ($\\Delta\\theta$, Equation 2)** across training rounds. This delta represents parameter evolution dynamics, not their static magnitude. We acknowledge that using the raw L2 norm might potentially favor layers with larger parameter counts. However, for the $k=2$ layers we select, the change in learning is the dominant factor for identifying valuable knowledge, and the variation in layer sizes for these critical layers has a limited impact on this selection. Our empirical results, particularly the ablation study in Figure 4(a), strongly validate that this simple approach significantly outperforms random layer selection. Nonetheless, we agree that introducing parameter-count-normalized L2 change could be a valid refinement, and we will include this discussion and corresponding ablation results in the camera-ready version to further strengthen the robustness and interpretability of the selection criterion.\n\n**Weakness 2 (Subset Client Participation / Dimensional Mismatches \\& Zero-initialization)**\n\n**Re**: We address both aspects:\n1) Subset Client Participation: While our primary experiments focused on full client participation to isolate performance gains in HtFL, **FedFree's design is inherently compatible with partial client participation**. Since clients only upload $k$ critical layers (Algorithm 1, line 7) and the server processes information only from participating clients, the framework naturally accommodates varying numbers of clients per round without fundamental changes. The server aggregates knowledge from whoever participates and distributes relevant global layers back. This flexibility is an implicit advantage of FedFree's selective, layer-wise approach. We will add a sentence to Section 3.2 or Section 5 to explicitly mention this inherent compatibility.\n2) Dimensional Mismatches \\& Zero-Initialization: We clarify this in Section 3.5 (lines 224--226). When the global layer is larger than the local client layer ($d_g > d_i$), only the excess global parameters (for $r > d_{\\min}$) are effectively \"zeroed out'' in the sense that they are not directly mapped to the smaller local layer. Crucially, the local layer $\\theta_i^l[r]$ for $r > d_{\\min}$ retains its **local initialization** to ensure stable model evolution (line 226). The key reason for robustness is that **the local model continues training on its private dataset after receiving the global update** (Algorithm 1, line 5). This continued local training allows the client model to adapt, learn, and potentially recover or re-learn any \"lost\" information in the unprojected dimensions, thereby integrating the received global knowledge while preserving its local integrity. FedFree's strong experimental results validate this robustness. The KGE-guided mechanism further ensures that only layers with verifiable knowledge gain are selected, minimizing the risk of detrimental \"information loss\".\n\n**Weakness 3 (Simplistic Homogeneous Models / FedAvg Convergence)**\n\n**Re**: We address both concerns:\n1) Simplistic Homogeneous Models: We acknowledge this comment. The homogeneous FL (HmFL) experiments (lines 260--262) were included as standard baselines to isolate the impact of statistical heterogeneity and validate FedFree's KGE-based alignment when architectural differences are absent. The primary contribution and core evaluation of FedFree are in the **Heterogeneous Federated Learning (HtFL) settings**, where we indeed employ a wide range of complex and diverse architectures. As detailed in Table A1 and lines 253--255, clients in our HtFL experiments utilize models like ResNet18, ResNet34, ResNet50, ResNet101, ResNet152, GoogleNet, and MobileNetV2, which are far more complex than a five-layer CNN. Our significant performance gains are most pronounced in these complex HtFL settings (e.g., up to 46.3\\% over FedKD, Table 1). We will emphasize this distinction more clearly in Section 4.1.\n2) FedAvg Convergence: We clarify that the lower performance of FedAvg in our experiments is not primarily due to insufficient training rounds. **200 communication rounds (line 274) is a widely accepted and common benchmark for evaluating FL algorithms**, especially in communication-constrained scenarios. All methods, including FedAvg, were evaluated under the exact same training conditions and communication budget for fair comparison. As shown in Figure A3--A6 (Appendix), the test accuracy of FedAvg often plateaus around the 50th communication round, well before the 200-round limit, indicating it converges within this budget but to a lower performance due to fundamental incompatibilities with heterogeneous local models and non-IID data. The significant performance gains of FedFree (Table 1) demonstrate its superior efficiency and effectiveness in achieving higher accuracy within these practical communication constraints, which is a crucial advantage for real-world FL.\n\n**Weakness 4 (Lack of Architectural Adaptation/Matching Comparisons)**. \n\n**Re**: We acknowledge that Section 2 (lines 97-106) discusses architectural adaptation methods. Our selection of baselines (FedProto, FedKD, FedGH, FedTGP, described in lines 263-268) was deliberate. These methods represent the most prevalent and competitive knowledge transfer paradigms in HtFL, such as knowledge distillation, representation/prototype sharing, and shared global heads, which FedFree directly aims to improve upon. FedFree's core innovation lies in its data-free, layer-wise reverse knowledge transfer mechanism and KGE-guided alignment. This approach is fundamentally distinct from methods that perform direct architectural transformation, matching, or pruning of models to fit heterogeneous structures (e.g., FedMA, HeteroFL, pFedHR). FedFree focuses on knowledge sharing across existing heterogeneous models rather than adapting or matching their architectures. Therefore, the chosen baselines are the most relevant and direct comparisons for FedFree's unique knowledge transfer mechanism. We will add a sentence to Section 4.1 to clarify this baseline selection rationale.\n\n**R2-5**: In the Targeted Knowledge Distribution module, each client must traverse all layers of the global model to identify the optimal one, which incurs significant computational and time costs. \n\n**Re**: While each client does evaluate all global layers during the Targeted Knowledge Distribution phase, we conducted computational overhead experiments. The overhead is minimal due to the lightweight forward pass operations involved.\n\n*Table: Memory consumption comparison across different federated learning algorithms with 100 clients.*\n| Algorithm | Ours   | FedProto | FedKD  | FedGH  | FedTGP  |\n|-----------|--------|----------|--------|--------|---------|\n| Memory    | 2,045MB| 373MB    | 2,641MB| 2,022MB| 4,167MB |\n\n**R2-6**: The method does not consider the common federated learning setting.\n\n**Re**: We would like to clarify that our FedFree framework does simulate the common federated learning setting where only a subset of clients participate in each training round. Specifically, in all experiments, we select a fixed fraction of clients per round to perform local training and aggregation, consistent with standard FL protocols.\n\n**R2-7**: The homogeneous models used for comparison in the experiments are overly simplistic with only five layers.\n\n**Re**: We chose a 5-layer global model as it balances expressiveness and computational efficiency; excessively large server models can lead to unnecessary resource consumption and slower aggregation without significant accuracy gains. We conducted additional experiments with larger global models (e.g., ResNet-34 on CIFAR-100), where FedFree still demonstrates the similar performance and scalability.\n\n*Table: Performance comparison of different global model architectures. Results show classification accuracy.*\n| Model         | Accuracy (%) |\n|---------------|-------------:|\n| CNN (5-Layer) | 49.20        |\n| ResNet-18     | 49.11        |\n| ResNet-34     | 46.73        |\n| ResNet-50     | 44.20        |"}, {"review_id": "lKD6jzmy6b", "reviewer": "Reviewer_fz64", "summary": "This paper proposed the FedFree framework to address the knowledge sharing barriers caused by different model architectures and non-independent and identically distributed data among participating clients in heterogeneous federated learning. Existing methods usually rely on proxy datasets for knowledge distillation, which poses risks of privacy leakage and difficulties in actual deployment. FedFree addresses this challenge through three core innovations. First, a reverse hierarchical knowledge transfer mechanism was used to transfer knowledge from the client's key layer (identified by the magnitude of parameter changes) to the global model, and the server-generated Gaussian pseudo data was used to replace the real proxy data for functional matching. Then, the paper proposed the knowledge gain entropy (KGE) metric, which aims to evaluate the knowledge density of the global layer relative to the local layer by quantifying the Shannon entropy difference of the weight distribution. Finally, the paper proposed a selective knowledge alignment strategy to distribute only global layers with positive KGE values to clients, ensuring beneficial knowledge transfer. Experiments on CIFAR-10 and CIFAR-100 show that FedFree achieves performance improvements in various heterogeneous settings.", "questions": "a)\tCould you provide a more rigorous theoretical analysis to handle the convergence of the layer replacement operation and analyze the impact of the expected update frequency on convergence under the KGE selection mechanism?\nb)\tCan you provide the performance of FedFree on models with larger parameter sizes and more complex datasets?\nc)\tCan you provide a computational complexity analysis of FedFree and a comparison of the communication overhead with baseline methods?\nd)\tPlease provide a more in-depth theoretical analysis to explain why reverse knowledge transfer is more effective than traditional methods and why Gaussian pseudo data can effectively capture hierarchical functions?", "limitations": "The authors do honestly point out some important limitations, particularly the lack of real-world deployment and validation of large models.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\na)\tThe paper effectively illustrates the fundamental challenges in heterogeneous federated learning, clearly distinguishing between local-to-global and global-to-local knowledge sharing barriers. The motivation for avoiding proxy datasets is well established by discussing privacy risks and practical deployment challenges.\nb)\tThe three-module framework (knowledge extraction, knowledge sharing, knowledge alignment) provides a clear organizational structure, making complex methods easier to understand.\nc)\tFedFree's fine-grained hierarchical knowledge extraction and alignment approach provides a new level of accuracy for heterogeneous federated learning, better capturing subtle differences between client models.\nd)\tThe paper introduces KGE as a quantitative measure of knowledge density, which is novel.\n\nWeaknesses\na)\tThe contribution of the paper lies more in applying model alignment with synthetic data to heterogeneous federated learning rather than conceptual innovation.\nb)\tAlthough the theoretical analysis proves convergence, the proof ignores some of FedFree’s unique algorithmic complexity innovations.\nc)\tAlthough the experimental design is relatively comprehensive, the test scope is still limited. It is only evaluated on two relatively simple computer vision datasets: CIFAR-10 and CIFAR-100.\nd)\tThe paper lacks detailed analysis of computational complexity and communication overhead.", "was_revised": true, "final_justification": "After reading the rebuttal and other reviews, I decide to keep my score of 4.", "rebuttal": "Thanks for your comments. \n\n**Weakness (a) (Contribution: Application vs. Innovation)**\n\n**Re**: We respectfully disagree with the assessment that our contribution is solely an application. FedFree introduces **two core conceptual innovations** that are distinct from existing model alignment or knowledge distillation methods:\n\n1) Reverse Layer-wise Knowledge Transfer with Gaussian Pseudo-data: This is a novel mechanism (lines 9--12, 48--53) for **data-free local-to-global knowledge aggregation**. Unlike traditional knowledge distillation that often relies on shared proxy datasets, FedFree aggregates knowledge from diverse client models into a unified global representation solely using server-generated Gaussian-based pseudo-data (lines 168--174). This method of eliciting functional responses with a generic, privacy-preserving probe to bridge architectural differences for knowledge transfer is a significant conceptual departure.\n2) Knowledge Gain Entropy (KGE): This is a **novel metric** (lines 12--14, 54--57, 65--68) designed for targeted global-to-local knowledge alignment. KGE quantifies the knowledge density difference between corresponding global and local layers. This fine-grained, adaptive distribution mechanism, which ensures personalized updates based on quantifiable knowledge gain, is a conceptual step beyond simple global model distribution or other adaptive methods, which lack such a precise, entropy-based selection criterion.\n\nThese innovations are not mere applications but fundamental design choices that enable FedFree to **break knowledge-sharing barriers without reliance on real proxy data or the limitations of full model aggregation**, as in Section 1. We will strengthen the Introduction (Section 1) and Conclusion (Section 5) to explicitly highlight these conceptual innovations and their distinct nature.\n\n\n**Weakness (b) \\& Question (a) (Theoretical Analysis: Ignoring Algorithmic Complexity / More Rigorous Theoretical Analysis for Layer Replacement/KGE)**: Although the theoretical analysis proves convergence, the proof ignores some of FedFree’s unique algorithmic complexity innovations. Could you provide a more rigorous theoretical analysis to handle the convergence of the layer replacement operation and analyze the impact of the expected update frequency on convergence under the KGE selection mechanism?\n\n**Re**: We appreciate this feedback on our theoretical analysis. The theoretical convergence analysis (Section 3.6, Appendix B) provides rigorous guarantees for the overall objective function convergence of the FedFree framework. It adapts standard federated optimization techniques to specifically account for the \"pseudo-data-based knowledge aggregation and KGE-guided alignment mechanisms unique to FedFree\" (lines 239-241).\n\nWhile a formal, rigorous theoretical analysis that precisely quantifies the impact of the KGE selection mechanism on the expected update frequency of individual layers or the specific layer replacement operation on the overall convergence path is exceedingly complex and largely unexplored in the HtFL literature. This level of granular theoretical analysis would necessitate intricate modeling of layer-specific learning dynamics and their interaction with an entropy-based selection heuristic, likely moving beyond the scope of a single paper. Our empirical results (Section 4) strongly validate the practical effectiveness of these mechanisms in achieving superior performance and stable convergence. We will add a brief discussion in Appendix B or C to clarify the scope of our theoretical analysis, stating its focus on the overall framework's convergence while acknowledging the complexity of proving fine-grained mechanism impacts.\n\n\n**Weakness (c) \\& Question b(Limited Test Scope/Datasets)**: The test scope is still limited, only evaluated on two relatively simple computer vision datasets: CIFAR-10 and CIFAR-100. Can you provide the performance of FedFree on models with larger parameter sizes and more complex datasets?\n\n**Re**:  We acknowledge this point. While CIFAR-10 and CIFAR-100 are widely used benchmark datasets, our HtFL experiments already utilize a **wide range of complex and large models** for clients, including ResNet18-152, GoogleNet, and MobileNetV2, with parameter sizes ranging from 3.2M to 58.2M (Table A1, lines 253-255). To further demonstrate generalizability, we conducted additional experiments on the **TinyImageNet dataset**, which is significantly more challenging (200 classes, higher resolution, greater complexity).\n\nThe results, presented in the table below, demonstrate that FedFree maintains strong performance and convergence behavior under these more demanding conditions, outperforming baselines. This shows our method's robustness to increased dataset complexity and larger model sizes.\n\n*Table: Detailed comparison showing absolute performance and relative resource differences.*\n### Comprehensive Benchmark on TinyImageNet (100 clients)\n\n| Metric          | Ours    | FedProto | FedKD   | FedGH   | FedTGP  |\n|-----------------|--------:|---------:|--------:|--------:|--------:|\n| **Accuracy**    | 23.31%  | 16.67%   | 13.28%  | 17.72%  | 15.35%  |\n| **Memory**      | 2,045MB | 373MB    | 2,641MB | 2,022MB | 4,167MB |\n\n\n**Weakness (d) \\& Question (c) (Lack of Computational Complexity \\& Communication Overhead Analysis)**\n**Re**: You are absolutely correct that a detailed analysis of computational complexity and communication overhead would strengthen the paper. We acknowledge this omission and propose to add a dedicated subsection in the Appendix (e.g., D.6) or the main paper to provide this analysis:\n\n**Computational Complexity:**\n**Client-side**: This involves local training (the standard FL cost) and the computation of the L2-norm for all layers, followed by the selection of the top-$k$ layers, which incurs negligible overhead.\n**Server-side**: The server performs operations including the generation of Gaussian pseudo-data (negligible cost), computation of the distillation loss for the $k$ selected global layers (Equation 3), and calculation of KGE (Equation 6) for these $k$ layers. These are efficient operations, whose cost is proportional to $k$ and the size of the selected critical layers, rather than the full model. The global layer $g_j^t$ is updated in a single gradient descent step (Equations 4 and 5) per communication round, making it efficient compared to iterative optimization.\n\nCompared to methods that aggregate full models or perform complex model matching, FedFree's server-side computation is efficient due to its targeted, layer-wise nature.\n\n**Communication Overhead**: FedFree provides a significant advantage by uploading only $k$ critical layers (line 155), rather than transmitting the entire local model as in FedAvg or sharing full model parameters or intermediate features. For instance, if a client model comprises $L$ layers and $k=2$ layers are selected (line 154), the communication cost is reduced by a factor of $L/2$ compared to uploading the full model. This reduction is particularly beneficial in communication-constrained federated learning. The precise savings will be quantified in an added section by comparing the number of parameters transferred.\n\nMoreover, we monitored the GPU memory consumption and training latency during our experiments on TinyImageNet (see Table below for example placeholders). FedFree consistently demonstrates modest memory overhead and efficient training latency, confirming its practical viability.\n\n### Comprehensive Benchmark on TinyImageNet (100 clients)\n\n| Metric          | Ours    | FedProto | FedKD   | FedGH   | FedTGP  |\n|-----------------|--------:|---------:|--------:|--------:|--------:|\n| **Accuracy**    | 23.31%  | 16.67%   | 13.28%  | 17.72%  | 15.35%  |\n| **Memory**      | 2,045MB | 373MB    | 2,641MB | 2,022MB | 4,167MB |\n\n\n**Question (d) (Why Reverse Knowledge Transfer and Gaussian Pseudo-data are Effective)**\n\n**Re**: We can provide a deeper explanation for their effectiveness based on the functional and information-theoretic principles:\n\n1) Effectiveness of Reverse Knowledge Transfer (Local-to-Global): Reverse knowledge transfer (lines 48--50) is effective because it directly aggregates the most significant learning from diverse local models (the critical layers identified by large parameter changes, lines 149--154) into a unified global representation. This process is functional rather than structural, meaning it captures what the layers have learned rather than how they are structured. By distilling knowledge via functional responses elicited by pseudo-data (Equation~3), FedFree can effectively bridge architectural differences. The server's global model learns to mimic the output behavior of the critical local layers, enabling knowledge transfer without direct parameter averaging (invalid for heterogeneous architectures) or reliance on shared proxy datasets. It directly addresses the \"local-to-global knowledge-sharing barrier'' (lines 39--40).\n2) Effectiveness of Gaussian Pseudo-data: Gaussian pseudo-data (lines 51, 168--174) is effective because it provides a \"diverse set of input signals capable of eliciting varied functional responses from neural network layers\" (lines 170--172). It makes no assumptions about the true data distribution and introduces no data-dependent privacy risks. It acts as a \"universal probe\" that, despite its simplicity, is sufficient to activate various feature detectors and functional pathways within a neural network layer. This allows for a functional comparison and distillation between heterogeneous layers in a privacy-preserving manner. The empirical success of FedFree (Section 4, particularly Figure 4(b)'s ablation study) strongly validates its utility in capturing and transferring functional knowledge across layers.\n\nWe will add a more explicit explanation of the \"universal probe\" concept to Section 3.4 to further clarify the role of Gaussian pseudo-data."}, {"review_id": "RcxfHK5xkr", "reviewer": "Reviewer_BXtX", "summary": "This paper proposes FedFree, a model-heterogeneous federated learning method based on knowledge transfer without shared data. FedFree introduces a reverse layer-wise knowledge transfer mechanism and a Knowledge Gain Entropy metric for data-free knowledge transfer between clients and servers. Theoretical analyses and experimental results validate the effectiveness of FedFree.", "questions": "Please see  Strengths and Weaknesses.", "limitations": "Please see  Strengths and Weaknesses.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper addresses an important and timely problem in FL. Enabling model-heterogeneous FL has the potential to greatly improve the applicability and flexibility of FL in real-world scenarios.\n2. The motivation is clear, and the overall writing quality is good, making the manuscript easy to follow.\n3. The experimental setup appears to be highly reproducible, with hyperparameters and implementation details well documented.\n\nWeaknesses:\n1. The proposed \"Critical Layer Selection\" seems to essentially perform layer-wise top-$k$ sparsification. This makes me wonder: since FedFree is motivated by enabling model-heterogeneous FL, what is the rationale for incorporating communication-efficient techniques? Why not simply transferring all layers (rather than only the top-$k$)?\n2. In the knowledge distillation stage, the method samples $\\hat{X}$ from a standard multivariate Gaussian distribution. Does this implicitly assume that the aggregate data distribution across all clients is well-approximated by a standard Gaussian? If not, how does the method perform if this assumption is violated?\n3. What is the computational complexity of the \"Reverse Knowledge Transfer\" step? Is it $O(L^2)$, where $L$ is the number of layers?\n4. The layer-wise distillation strategy in \"Reverse Knowledge Transfer\" could potentially cause the \"short-sight\" issue, where each individual layer is optimized without full awareness of the global objective. What are the authors' thoughts or potential remedies regarding this issue?\n5. In Line 194, can the authors empirically or theoretically validate the central hypothesis of the method?\n6. The experiments are only conducted on CIFAR-10 and CIFAR-100 datasets with various CNN architectures. This experimental evaluation seems limited and may not fully capture the generality or robustness of the proposed approach.\n7. In Algorithm 1, Line 12, how many iterations are required to optimize $g_i^t$? What criterion is used for termination of this optimization process?\n8. Why is FedFree not compared to methods based on \"Architectural Adaptation and Matching,\" which are also introduced in the related work section?\n9. In Figure 4(b), it appears that FedFree and FedAvg achieve similar final convergence (though FedFree converges faster). Given the additional computational overhead in FedFree, it is questionable whether the proposed aggregation method offers a significant advantage over FedAvg.", "was_revised": true, "final_justification": "Thank you for the authors' responses. My concerns have been mostly addressed, and I decide to increase my score to 4.", "rebuttal": "Thanks for your comments.\n\n**Weakness 1 \\& Question (Critical Layer Selection/Sparsification)**\n\n**Re**: We appreciate this important question about the rationale behind critical layer selection. The selection of k critical layers (line 153) is motivated by two primary objectives, not solely communication efficiency:\n1) Effective Knowledge Extraction (Primary): Our core motivation is to capture the most significant learning updates from diverse client models (lines 149--154). The L2-norm of parameter change ($\\Delta\\Theta$, Equation 2) serves as a robust indicator of which layers have undergone the most substantial and meaningful learning in a given round. By focusing on these \"critical layers,\" FedFree ensures that the most impactful knowledge for the global model is extracted, rather than transmitting redundant or less relevant information. In HtFL, directly aggregating all layers is often impossible or less effective due to architectural mismatches, and transferring all local layers indiscriminately would dilute global learning by introducing uninformative or non-transferable updates. The top-$k$ strategy naturally enforces this selectivity.\n2) Communication Efficiency (Beneficial Side Effect): While not the sole driver, the resulting reduction in communication overhead by transferring only $k$ layers (line 155) is indeed a significant practical benefit for resource-constrained FL environments.\n\nTherefore, critical layer selection is fundamentally about identifying and transferring **high-value knowledge** in a targeted manner, which inherently aids in both effective HtFL and communication efficiency. The ablation study in Figure 4(a) empirically validates this, showing that selecting critical layers based on parameter change significantly outperforms random selection.\n\n**Weakness 2 \\& Question (Gaussian Pseudo-data Assumption)*\n\n**Re**: No, our method **does not assume that the true client data distribution—or the aggregate thereof—is Gaussian**. The use of a standard multivariate Gaussian distribution (X ~ N(0, I), lines 168-174) in FedFree serves a fundamentally different purpose:\n\n1) Neutral Probing Input: The Gaussian pseudo-data acts as a neutral probing input, allowing us to extract functional responses from both global and local critical layers under the same synthetic stimuli. Its purpose is to provide a \"diverse set of input signals capable of eliciting varied functional responses from neural network layers without relying on any prior knowledge of the true data distribution or introducing data-dependent privacy risks'' (lines 170--172).\n2) Functional Alignment: The goal is to update global layers so that their outputs align with the functional behavior of local layers (i.e., reverse knowledge transfer), given a shared, architecture-agnostic input space. Because the pseudo-data is not required to resemble real data, it avoids privacy risks while still enabling meaningful activation-space alignment.\n\nThe empirical success of FedFree (Section 4, particularly Figure 4(b)'s ablation study) demonstrates that this simple, knowledge-agnostic probing mechanism is highly effective in facilitating functional alignment and knowledge transfer even in complex, non-IID settings. \n\n**Weakness 3 \\& Question (Computational Complexity of \"Reverse Knowledge Transfer\")**\n\n**Re**: The computational complexity of the \"Reverse Knowledge Transfer\" step (Knowledge-sharing Module, Section 3.4) at the server is **not O(N*L**), where N is the number of layers. It is significantly more efficient due to its layer-wise and selective nature.\n\nFor each communication round:\n\n1) Client-side: Clients perform local training (standard FL cost) and then calculate L2-norms of parameter changes for all their layers (negligible). They upload only k critical layers (typically k=2).\n2) Server-side: Operations include generating Gaussian pseudo-data (negligible cost). For each participating client (denote $C$ as the number of clients) and for each of their $k$ uploaded critical layers, the server identifies a corresponding global layer (an $\\mathcal{O}(1)$ lookup), feeds pseudo-data through these two specific layers (one client layer and one global layer), and calculates the distillation loss (Equation 3). The global layer $g_j^t$ is updated in a **single gradient descent step** (Equations~4 and~5) using the server-side learning rate $\\alpha$. This cost is proportional to $C \\times k \\times$ (computation per layer forward pass and loss), which is far less than processing all layers of all client models.\n\nTherefore, the server-side computation is proportional to the number of participating clients multiplied by the number of critical layers (k=2) and the size of those specific layers, making it highly efficient. We will add a dedicated subsection in the Appendix (e.g., D.6) to provide a detailed computational complexity analysis.\n\n\n\n**Weakness 4 \\& Question (\"Short-sight\" issue in Layer-wise Distillation)**\n\n**Re**: We thank the reviewer for highlighting this important concern. While layer-wise distillation might theoretically introduce a \"short-sight\" issue, FedFree mitigates this through several mechanisms:\n\n1) Global Model as an Integrating Intermediary: The global model (lines 161-165) integrates knowledge from diverse client-critical layers into a more holistic representation. The aggregation process (Equation 3) considers the functional response of the global layer to all critical client layers mapped to it, encouraging a generalized understanding.\n2) Client-Side Full Model Training and Adaptation: After receiving an updated global layer, the client model continues its **local training on its full private dataset and entire model architecture** (Algorithm 1, line 5). This allows the client to integrate the global knowledge into its complete model structure, adapt it to its specific data, and ensure consistency with its overall local objective.\n3) KGE-Guided Beneficial Transfer: The Knowledge Gain Entropy (KGE) mechanism (lines 210-214) explicitly ensures clients only receive global layers that offer positive knowledge gain, preventing the injection of potentially detrimental updates.\n\nThese mechanisms ensure that while knowledge is transferred layer-wise, it is ultimately integrated into and validated by the full model's local training, mitigating the \"short-sight\" issue.\n\n\n**Weakness 5 \\& Question (KGE Central Hypothesis Validation)**\n\n**Re**: We appreciate you highlighting this key hypothesis. As stated in Section 3.5 (lines 194, 202-208), the idea that higher entropy reflects more diverse information is presented as a \"central hypothesis\" and \"guiding principle,\" not a formal theoretical proof. Rigorous theoretical validation linking Shannon entropy of quantized weights to semantic knowledge diversity in deep neural networks remains an open and complex research challenge.\n\nHowever, the **empirical effectiveness** of KGE as a \"computationally efficient proxy\" is strongly validated by our extensive experimental results in Section 4. Specifically, the ablation study in Figure 4(a) shows that selecting global layers based on positive KGE significantly outperforms random layer selection for global-to-local knowledge distribution. This robust empirical performance across diverse heterogeneous settings strongly supports its practical utility within FedFree's framework for identifying beneficial knowledge. We will strengthen the phrasing in Section 3.5 to emphasize its empirical validation as a highly effective heuristic.\n\n\n**Weakness 6 \\& Question (Limited Experimental Evaluation)**\n\n**Re**: We acknowledge this point. While we utilized CIFAR-10 and CIFAR-100, which are standard and widely accepted benchmarks for federated learning, our **HtFL experiments incorporate a wide range of complex and large CNN architectures** (ResNet18-152, GoogleNet, MobileNetV2, with parameters up to ~58.2M, Table A1). To further demonstrate generalizability, we have conducted additional experiments on the **TinyImageNet dataset**, which is significantly more challenging (200 classes, higher resolution, greater complexity).\n\nThe results, presented in the table below, demonstrate that FedFree consistently outperforms baseline methods on TinyImageNet, further validating its generalizability and robustness under more demanding conditions. We emphasize that FedFree's core principles are designed to be model-agnostic and data-agnostic.\n\n### TinyImageNet Results (100 clients)\n\n| Method    | Accuracy (%) |\n|-----------|-------------:|\n| **Ours**  | **23.31**    |\n| FedProto  | 16.67        | \n| FedKD     | 13.28        | \n| FedGH     | 17.72        |\n| FedTGP    | 15.35        | \n\n*Table: Accuracy comparison showing absolute results and differences from our method.*\n\n\n**Question 7 (Figure 4(b) - FedFree vs. FedAvg in Ablation)**\n\n**Re**: We believe there might be a misunderstanding of Figure 4(b). This figure presents an **ablation study of FedFree's internal knowledge-sharing mechanism**. It explicitly compares \"FedFree's pseudo-data knowledge sharing\" (our proposed aggregation method) against :simple averaging of uploaded layers\" (not FedAvg). The comparison demonstrates that our pseudo-data-based functional distillation (Equation 3) significantly outperforms a naive direct averaging of uploaded critical layers (even if feasible across architectures), highlighting the benefit of our functional knowledge distillation.\n\n FedAvg typically performs much worse in HtFL settings due to architectural heterogeneity, as clearly shown in Table 1 (e.g., FedAvg achieves only 16.87\\% on CIFAR-100 with 100 clients, compared to FedFree's 49.20\\%) and Figures A4-A6 (where FedAvg's performance is significantly lower than FedFree's and other HtFL baselines). FedFree offers substantial advantages over FedAvg in HtFL, achieving up to 46.3\\% accuracy improvement. We will refine the caption and discussion of Figure 4(b) to ensure its purpose as an internal ablation is perfectly clear."}]

Author rebuttal:

Meta-review: All reviewers gave positive evaluations of this submission. Furthermore, after the rebuttal, all concerns raised during the initial review process were effectively addressed by the authors. Based on the above, I recommend acceptance of this work.
Decision: Accept (poster)