Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

To address these issues, we jointly propose FedCVAE-Ens and FedCVAE-KD, two novel data-free one-shot FL models that reframe the local learning task using conditional variational autoencoders (CVAE).

The review comment to be evaluated is:

The paper presents a relatively simple idea and is mostly clearly written. As far as I am aware, this method is novel in the context of FL. The authors also provide a reasonable amount of information, which should make FedCVAE reproducible. The authors seem to mostly tackle the cross-silo setting, where each client has enough data. One thing I noticed is that the authors mention that the conditional VAE (CVAE) objective at eq. 1 bounds the marginal likelihood $\log p(x)$; this is not correct, as the specific objective at eq. 1 bounds the conditional marginal likelihood $\log p(x|y)$.

Besides that, there are a couple of things that are, in my opinion, not properly motivated. More specifically, the authors propose to sample from the generative model and train a classifier at the server. Why is this necessary and why you do not simply use the generative classifier  $p(y|x) = \frac{\int p(x| z, y)p(z)dz p(y)}{p(x)}$? To me it seems that the target for the auxiliary classifier is nothing else, but to approximate this generative classifier. The loss for the auxiliary classifier (in the limit where you constantly sample from the generative model) can be obtained by minimising the average KL-divergence between the true CVAE generative posterior $p(y|x)$ and the classifier predictive $q(y|x)$. More specifically: $$E_p(x)[KL(p(y|x) || q(y|x))] = - E_p(y,x) [\log q(y|x)] + const = -E_p(y,z,x)[\log q(y|x)]  + const = -E_p(y)p(z)p(x|y,z)[\log q(y|x)] + const$$ In this sense, it seems that 1) it might not be necessary to train an auxiliary classifier and 2) the modelling choices made in the generative model itself are important for the performance of the actual downstream classifier. I believe a discussion about this is warranted to be added in the paper. Apart from that, when the authors want to sample datapoints from the model they actually use a different distribution over the latents than the one the model was actually trained; e.g., using a $z \sim U[-1, 1]$ instead of $z\sim N(0, I)$. They mention that it is beneficial to stay at a high density region of the prior, but how does the performance of the algorithm fare when you use the correct prior? Why not use e.g., $z \sim N(0, \sigma)$ with $\sigma < 1$ which is closer to the correct prior?

Another thing that could be better explained are the security and privacy aspects of this method, especially given the FL scenario. FedCVAE uploads the CVAE decoder along with $p(y)$ to the server, which is inherently less private than FedAvg. While it is true that with DP you can bound memorisation and get privacy, at the moment the authors do not use anything and the gains in performance when doing DP relatively to e.g., DP-FedAvg are not clear. In fact, given a sufficient powerful generative model, this method should be indistinguishable from sending the actual data. Furthermore, the arguments about security by shifting $\mu$, need to be more formal. Are there some guarantees that you can give, given a sufficient powerful adversary? For example, given $p(y)$, and $p(x|z, y)$, couldn’t the attacker just try to infer a global mean for $z$? For example, by visual inspection of the samples or an optimization procedure? And a small comment; $U[-10, 10]$ is not an exceptionally good guess for $N(0, I)$ (which is what the text mentions at the beginning of page 9) as 99% of the probability of $N(0,I)$ is in $[-3, 3]$, so 70% of the mass of the uniform proposal is on almost zero probability mass under $N(0, I)$.

Furthermore, this method requires building good generative models which is generally a harder task than building a good discriminative model. How does this work on more complex datasets, such as CIFAR10 and CIFAR100, where $p(x|y, z)$ might not be as sharp? Furthermore, while non-iid settings are nice to have, to me it seems that this method might suffer in less non-iid / iid settings (e.g, $\alpha=1.0$, $\alpha=\inf$) ; the generative distribution is more diverse and thus it would be harder to model accurately with a, hardware constrained, VAE model. This can also sort of be seen when comparing FedCVAE-KD to FedCVAE-Ens; the former has worse performance that the latter, given that the entire training distribution needs to be modelled by a single model. How does the performance of the method scale with higher values of $\alpha$? Besides that, it seems that the evaluation against the baselines is not entirely apples-to-apples; for example, FedOneShot does not need to reveal to the server the labels and the models trained on the local data, so it has fundamentally different security / privacy tradeoffs.

The evidence to be evaluated is:A variational autoencoder (VAE) is a probabilistic generative model that attempts to learn the distribution of data samples (Kingma & Welling, 2014). A VAE is a latent variable method that models the joint distribution \(p_{\mathbf{\theta}}(\mathbf{x},\mathbf{z})\) of a data sample \(\mathbf{x}\in\mathcal{X}\subseteq\mathbb{R}^{D}\) and latent variable \(\mathbf{z}\in\mathcal{Z}\subseteq\mathbb{R}^{d}\), where usually \(d<<D\).

Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\).

\[\mathcal{L}(\mathbf{\phi},\mathbf{\theta};\mathbf{x},\mathbf{y})=-D_{\text{KL}}(q_{ \mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\mid\mid p(\mathbf{z}))+\mathbb{ E}_{q_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x},\mathbf{y})}[\log p_{\mathbf{\theta}}( \mathbf{x}|\mathbf{z},\mathbf{y})], \tag{1}\] which bounds the conditional marginal likelihood of the data \(\log p(\mathbf{x}|\mathbf{y})\). Here, \(D_{\text{KL}}(\cdot)\) represents KL-divergence.

Knowledge distillation (KD) aims to extract information from a trained _teacher_ model to train a separate lightweight _student_ model (Bucilua et al., 2006; Hinton et al., 2015).

Several works have integrated KD into FL to mitigate privacy risks, reduce upload costs, or regularize local learning using an ensemble-of-teachers approach (Lin et al., 2020; Zhu et al., 2021; Guha et al., 2019). However, KD approaches in FL usually require an auxiliary public dataset with similar properties as the distributed dataset, which may be difficult to obtain in practice (Zhu et al., 2021).

We jointly propose FedCVAE-Ens and FedCVAE-KD, one-shot FL methods that do not require an auxiliary public dataset for server-side training (they are _data-free_). They address issues caused by high statistical heterogeneity by reframing the learning task using CVAEs and account for model heterogeneity by allowing different CVAE architectures across clients.

The trained client decoders act as the teacher models, conveying their aggregate knowledge of how to map from latent space to data space to a single student server decoder, parameterized by \(\mathbf{\theta}^{S}\). To achieve this, we generate \(n_{D}\) total KD training samples, with \(\mathcal{D}_{\text{Ens}}\) defined as the combination of client subsets \(\mathcal{D}_{\text{Ens}}^{k}=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k}, \mathbf{z}_{i}^{k})\}_{i=1}^{\lfloor n_{D}/\rfloor}\). Then, we train the server to match the teacher's mapping of \((\mathbf{z}_{i}^{k},\mathbf{y}_{i}^{k})\) to \(\hat{\mathbf{x}}_{i}^{k}\) by minimizing a reconstruction loss: \[\ell_{\text{KD}}(\mathbf{\theta}^{S};\mathbf{z}^{k},\mathbf{y}^{k},\hat{\mathbf{x }}^{k})=g(D_{\mathbf{\theta}^{S}}(\mathbf{z}^{k};\mathbf{y}^{k}),\hat{\mathbf{x }}^{k}), \tag{2}\] which penalizes the dissimilarity \(g(\cdot)\) in data space between the synthetic data sample generated by the server decoder \(D_{\mathbf{\theta}^{S}}(\mathbf{z}^{k};\mathbf{y}^{k})\) and the client decoder sample \(\hat{\mathbf{x}}^{k}\).

Because FedCVAE-KD ensembles client decoders to create a labeled dataset \(\mathcal{D}_{\text{Ens}}\) to train the server decoder, each client can have a unique CVAE model architecture, accommodating each client's computational limitations.

FedCVAE-KD can be applied to any task that requires a labeled dataset, which is more general than classification; there is no commitment to a particular terminal task before learning occurs.

CVAEs use a prior distribution over latent space to train the encoder and decoder models. While a multivariate standard normal distribution is typically used for convenience, any normal distribution is acceptable. To promote security, we propose to shift the center of the prior distribution \(\mathbf{\mu}\) to a random position in real space (i.e., \(\mathbf{\mu}\in\mathbb{R}^{d}\)), which can be communicated offline or via encryption methods between server and clients (Zhou et al., 2020).

To validate FedCVAE-Ens and FedCVAE-KD, we conduct experiments on three image datasets that are standard in the FL literature: MNIST (Lecun et al., 1998), Fashion-MNIST (Xiao et al., 2017), and SVHN (Netzer et al., 2011).3

We compare the performance of FedCVAE-Ens and FedCVAE-KD in the one-shot data-free FL setting against two existing methods: FedAvg (McMahan et al., 2017) and a method proposed in Guha et al. (2019), which we call FedOneShot.

The one-shot methods proposed in Li et al. (2021) and Shin et al. (2020) are not applicable because of their reliance on public auxiliary data for server-side training or fine-tuning. Similarly, many standard FL methods are not appropriate because they depend on an auxiliary dataset (i.e., FedDF (Lin et al., 2020)) or focus on regularization (i.e., FedGen (Zhu et al., 2021), FedProx (Li et al., 2020), Scaffold (Karimireddy et al., 2020), FedNova (Wang et al., 2020)), which is incompatible with the one-shot setting.

We base our CVAE architecture on Higgins et al. (2017).

To demonstrate the efficacy of FedCVAE-Ens and FedCVAE-KD in the difficult setting of high statistical heterogeneity, we test on varying levels of \(\alpha\), from high (\(\alpha=0.05\)), to very high (\(\alpha=0.01\)), to extreme (\(\alpha=0.001\)) statistical heterogeneity. FedCVAE-Ens consistently outperforms all other methods, and FedCVAE-KD outperforms the baselines in nearly all datasets and levels of \(\alpha\) (the only exception is MNIST at the lowest level of statistical heterogeneity) as shown in Table 1. At \(\alpha=0.001\), FedCVAE-KD obtains more than \(1.75\times\) the accuracy of the best baseline method for MNIST, more than \(2\times\) the accuracy for FashionMNIST, and nearly \(2.75\times\) the accuracy for SVHN (Table 1). While the baselines FedAvg and FedOneShot are very sensitive to the level of statistical heterogeneity, both FedCVAE-Ens and FedCVAE-KD demonstrate consistent performance across levels of \(\alpha\) (Table 1).

While both FedAvg and FedOneShot struggle when many clients are present, Table 2 shows that FedCVAE-Ens and FedCVAE-KD perform consistently across the number of clients, with the only exception being FedCVAE-KD for SVHN.

The proposed KD aggregation method used in FedCVAE-KD substantially improves on aggregation via parameter averaging, generating qualitatively more realistic samples (Figure 8 in Appendix C) and achieving higher server classifier accuracy (Table 6 in Appendix C). As expected, FedCVAE-Ens bounds the performance of FedCVAE-KD, but KD-based aggregation still preserves client ensemble performance well across levels of \(\alpha\) for all datasets (Table 1). The upper bound accuracy established by FedCVAE-Ens is promising, but successful decoder aggregation may require a stronger KD procedure (e.g., feature-based KD as described in Gou et al. (2021)).

To simulate clients with diverse computational resources, we train both FedCVAE-Ens and FedCVAE-KD using two local CVAE architectures: the first as described in Section 4.1 and the second with one convolutional/deconvolutional block removed for the encoder/decoder, respectively. The server decoder matches that which is described in Section 4.1 but can be chosen arbitrarily. Because the two architectures demonstrate similar generative capabilities, final server classifier accuracy is very similar when comparing homogeneous against heterogeneous local architectures (Figure 4).4 Notably, our KD procedure for FedCVAE-KD still performs well using heterogeneous models, indicating diverse architectures can organize latent space similarly enough to successfully translate this knowledge to a single decoder.

Therefore, this simple FedCVAE-Ens and FedCVAE-KD extension reduces eavesdropping attackers' capacity to extract high-quality samples from uploaded decoders or train a performant downstream model, reducing communication risks.

FL was originally proposed by McMahan et al. (2017) as a paradigm for decentralized distributed learning. Statistical heterogeneity quickly emerged as a core issue within FL, with many studies focusing on maintaining high performance under very non-IID data. Many approaches have experimented with augmenting FedAvg by adding proximal terms to the local objective as an attempt to restrain local updates (Li et al., 2020; Karimireddy et al., 2020; Wang et al., 2020; Acar et al., 2021; Li et al., 2021). Other works have used KD to circumvent issues associated with parameter averaging under non-IID data, focusing on leveraging auxiliary data (Lin et al., 2020; Sattler et al., 2021) or a generative model (Zhu et al., 2021; Zhang et al., 2022) to compactly capture client ensemble learning. Recent approaches focus on improving client selection strategy (Tang et al., 2022), reducing catastrophic forgetting to balance global knowledge against local learning (Huang et al., 2022), or improving the generality of client models (Mendieta et al., 2022). However, all of these methods are designed for standard FL and rely heavily on local regularization through substantial iterative communication, which is not feasible in the one-shot FL setting where communication is limited to a single round.

Methods in one-shot FL have demonstrated strong performance under substantial communication constraint. Guha et al. (2019) originally proposed one-shot FL and introduced two methods, one based on heuristic selection methods for client inclusion in the final ensemble and another that used KD with an auxiliary dataset for ensemble aggregation.

Although these methods obtain high accuracy, they rely on an auxiliary public dataset to support KD, which is inapplicable in data-free FL.

Zhang et al. (2021) proposed a data-free KD procedure based on a generator network trained using the ensemble of client classifiers, showing promising performance even under heterogeneous local models. However, existing approaches in one-shot FL either do not experiment with high statistical heterogeneity or degrade even under moderate levels of heterogeneity, unlike our proposed methods.

A few studies have experimented with using VAEs in FL.

We are the first to apply CVAEs to one-shot FL with a focus on high statistical heterogeneity. In this paper, we proposed FedCVAE-Ens and FedCVAE-KD, data-free one-shot FL methods that reframe the local learning task using CVAEs. Both methods performed well given high statistical heterogeneity, demonstrated consistent performance with increasing numbers of clients, allow for model heterogeneity across clients, and can be extended to promote security. Extensive experimental results showed that FedCVAE-Ens and FedCVAE-KD substantially extended the state-of-the-art in one-shot FL under very high statistical heterogeneity, making way for more nuanced development in this difficult environment for distributed learning.

* Zhang et al. (2021) Jie Zhang, Chen Chen, Bo Li, Linguuan Lyu, Shuang Wu, Jianghe Xu, Shouhong Ding, and Chao Wu. A practical data-free approach to one-shot federated learning with heterogeneity. _arXiv preprint arXiv:2112.12371_, 2021.

* Zhang et al. (2022) Lin Zhang, Li Shen, Liang Ding, Dacheng Tao, and Ling-Yu Duan. Fine-tuning global model via data-free knowledge distillation for non-iid federated learning. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_, pp. 10174-10183, June 2022.

FedCVAE-Ens follows the same procedure as FedCVAE-KD, but alternatively defines \(\mathcal{D}_{\text{Ens}}\) as the combination of client subsets \(\mathcal{D}_{\text{Ens}}^{k}:=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k})\}_ {i=1}^{c/m}\) and uses \(\mathcal{D}_{\text{Ens}}\) to directly train the server classifier. Figure 6 visualizes the full pipeline for FedCVAE-Ens and Algorithm 2 details the full procedure. Algorithm 3 shows the local client training procedure, which is the same for FedCVAE-Ens and FedCVAE-KD.

1:procedureServer 2:for each client \(k\in\mathcal{C}\) in parallel do 3:\(\mathbf{\theta}^{k},\;\hat{p}^{k}(\mathbf{y})\leftarrow\)ClientLocalUpdate(\(k\), \(T_{L}\)) 4: Generate samples from each client \(\mathcal{D}_{\text{Ens}}^{k}:=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k})\}_ {i=1}^{\lfloor nC/m\rfloor}\) using client decoder \(D_{\mathbf{\theta}^{k}}(\cdot)\) and label distribution \(\hat{p}^{k}(\mathbf{y})\) 5: Combine client subsets into an IID labeled dataset \(\mathcal{D}_{\text{Ens}}:=\mathcal{D}_{\text{Ens}}^{1}\cup\mathcal{D}_{\text{ Ens}}^{2}\cup...\cup\mathcal{D}_{\text{Ens}}^{m}\) 6:for classifier epoch \(i=1\) to \(T_{C}\)do

```**Algorithm 2** - FedCVAE-Ens in the one-shot FL setting. \(T_{L}\) represents the number of local training epochs. The server classifier parameters are \(\mathbf{w}_{C}^{S}\), with training epochs \(T_{C}\), number of training samples \(n_{C}\), classification loss \(\ell_{C}(\cdot)\), and learning rate \(\eta_{C}\). \(\mathcal{C}\) is the set of clients.

van den Burg and Williams (2021) define a probabilistic generative model's propensity to reproduce samples observed in the training data as memorization, and prove that ensuring a particular level of differential privacy (DP) can bound memorization in probabilistic generative models (including CVAEs). Thus, beyond the normal privacy guarantees attributable to DP, employing FL DP-estimation techniques (i.e., Geyer et al. (2017)) also ensures low memorization across the FedCVAE-Ens and FedCVAE-KD pipelines, further enhancing the privacy of our proposed methods.

While FedAvg and FedOneShot are very sensitive to dataset split (high standard deviation), the results in Table 5 for both FedCVAE-Ens and FedCVAE-KD are not only consistent with Table 2, but also exhibit reasonable stability (low standard deviation).

The KD approach we propose to aggregate client decoders generates substantially better samples (Figure 8) while also obtaining more than \(2\times\) classifier accuracy on MNIST, more than \(3.25\times\) accuracy on FashionMNIST, and nearly \(5\times\) accuracy for SVHN at \(\alpha=0.001\) (Table 6). \begin{table}
\begin{tabular}{l l|c c|c c} \hline \hline  & \# of Clients & FedAvg & FedOneShot & FedCVAE-KD (ours) & FedCVAE-Ens (ours) \\ \hline \multirow{3}{*}{MNIST} & \(m=5\) & \(42.34\pm 1.75\) & \(42.97\pm 1.54\) & \(80.19\pm 1.76\) & \(92.81\pm 2.16\) \\  & \(m=10\) & \(58.29\pm 2.83\) & \(41.15\pm 0.70\) & \(82.01\pm 1.61\) & \(93.83\pm 1.53\) \\  & \(m=20\) & \(37.14\pm 3.87\) & \(32.22\pm 0.71\) & \(81.93\pm 1.75\) & \(93.52\pm 0.86\) \\  & \(m=50\) & \(28.26\pm 7.98\) & \(35.62\pm 0.66\) & \(77.68\pm 1.39\) & \(87.56\pm 1.44\) \\ \hline \multirow{3}{*}{FashionMNIST} & \(m=5\) & \(38.51\pm 2.40\) & \(32.23\pm 1.68\) & \(68.01\pm 1.56\) & \(73.70\pm 1.93\) \\  & \(m=10\) & \(45.85\pm 2.95\) & \(37.63\pm 0.53\) & \(69.97\pm 1.63\) & \(76.62\pm 1.61\) \\  & \(m=20\) & \(27.49\pm 4.77\) & \(24.72\pm 1.20\) & \(71.28\pm 1.17\) & \(76.51\pm 1.38\) \\  & \(m=50\) & \(31.91\pm 2.20\) & \(41.01\pm 2.49\) & \(69.25\pm 1.13\) & \(76.13\pm 2.00\) \\ \hline \multirow{3}{*}{SVHN} & \(m=5\) & \(40.61\pm 0.64\) & \(42.05\pm 1.31\) & \(57.17\pm 2.56\) & \(65.72\pm 2.17\) \\  & \(m=10\) & \(25.12\pm 2.07\) & \(31.91\pm 1.26\) & \(55.97\pm 0.38\) & \(65.50\pm 2.28\) \\ \cline{1-1}  & \(m=20\) & \(26.99\pm 1.15\) & \(10.68\pm 0.70\) & \(51.80\pm 2.75\) & \(65.54\pm 1.89\) \\ \cline{1-1}  & \(m=50\) & \(19.59\pm 0.00\) & \(30.20\pm 0.64\) & \(40.03\pm 2.62\) & \(64.81\pm 2.44\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of four one-shot FL methods over three datasets and across four numbers of clients \(m\). Best results for each dataset and each level of \(m\) are in purple, with second best results in yellow.

Input: Table 2: Performance of four one-shot FL methods over three datasets and across four numbers of

Input: Figure 6: The full pipeline for one of our proposed methods, FEDCVAE-ENS. Here, E, D, and C represent “encoder,” “decoder,” and “classifier” models, respectively. First, clients train CVAEs on their private local datasets. Then, the server uses the ensemble of uploaded client decoders and corresponding local label distributions to generate a labeled dataset of synthetic samples to train a classifier.

Input: Figure 4: Results with heterogeneous local models. “Homogeneous” uses the same CVAE architecture for all clients, whereas “heterogeneous” uses two architectures with similar generative capabilities.

Input: Figure 8: Samples from the aggregated server decoder obtained through parameter averaging (top row) versus knowledge distillation (bottom row) at high statistical heterogeneity (α = 0.01).

Input: Figure 1: Motivating our proposed methods, FEDCVAE-ENS and FEDCVAE-KD, using the MNIST dataset as an example. In cases of very high statistical heterogeneity, each client will only observe one or two of the ten available classes, as seen on the left where the size of each dot is proportional to the number of samples. For example, client 2 only observes 4’s and 7’s, resulting in a client decoder that can expertly generate these digits. Note that the columns are shown in order of conditioning class (digits 0-9). Similarly, client 4 is an expert in 3’s and 6’s. In FEDCVAE-KD, our lightweight knowledge distillation training procedure compacts local learning into a single server decoder, as evidenced by the high-quality samples from all available classes (digits 0-9). This server decoder can then be used for any downstream task, e.g., classification.

Input: Figure 7: CVAE samples generated using latent vectors distant from the center of the multivariate normal prior (top row) and close to the center (bottom row).

Input: Figure 2: The full pipeline for one of our proposed methods, FEDCVAE-KD. Here, E, D, and C represent “encoder,” “decoder,” and “classifier” models, respectively. First, clients train CVAEs on their private local datasets. Then, the server uses uploaded client decoder parameters and local label distributions to train a server decoder using knowledge distillation (KD). Finally, synthetic labeled samples from the server decoder are used to train a classifier.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Based on the extensive evidence provided, I find that the claim is well-stated (score 1). The evidence thoroughly demonstrates that FedCVAE-Ens and FedCVAE-KD are indeed novel data-free one-shot FL models that use CVAEs to reframe local learning tasks. The papers, algorithms, experimental results, and figures clearly show the innovative use of CVAEs in the FL context. The reviewer's comments, while raising some technical points about CVAE implementation and security aspects, do not dispute the fundamental novelty or basic characterization of the methods. The claim accurately represents what the methods do without exaggeration.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

To address these issues, we jointly propose FedCVAE-Ens and FedCVAE-KD, two novel data-free one-shot FL models that reframe the local learning task using conditional variational autoencoders (CVAE).

The review comment to be evaluated is:

The paper is very well written and easy to follow. The numerical experiments are well executed and show promising performance achieved by the proposed methods.

That being said, there are some downsides that, in my opinion, slightly outweigh the strengths of the paper. On the problem formulation side, I believe the one-shot federated learning (FL) problem is not very well motivated; the point of FL is to enable training models at different clients by leveraging each others' data through communication without explicitly sharing them. In a one-shot scenario, the problem essentially reduces to having a set of models, which need to be aggregated into a single, universal model, so I am still not convinced how the "federated" aspect of the problem is of the essence.

On the contributions side, the main issue I have with the paper is a lack of a central, key novelty. In its current form, the paper is mostly a collection of different ideas, namely two algorithms that are almost independent of each other, as well as a security aspect, which is again mostly orthogonal to the proposed methods. To me, what would make this paper much stronger is to focus on only one of these algorithms/aspects throughout the paper. For example, since the performance of FEDCVAE-KD is better than baselines, I believe it would be better to focus on this algorithm in the main body of the paper, and add the ensemble version of the algorithm (which, as the authors allude to, requires a higher amount of memory that scales with the number of clients) as an extension, in a separate discussion section toward the end of the paper and/or in the appendix. Moreover, the security and privacy considerations are definitely important, but including them in the main body of the paper stretches it too thin, in my opinion.

Further comments:

- Aside from the solid empirical performance, are there any intuitive/theoretical explanations as to why the proposed methods are well suited for i) *one-shot* FL, and ii) *high heterogeneity* FL? As presented, I cannot see a clear motivation for why the proposed methods should perform better in the considered problem formulation.
- Please discuss whether or not sharing local label distributions with the server violates the privacy of clients' data. How do the proposed methods perform if this information is unavailable at the server?
- Presenting the flowchart figure for only one of the proposed methods (FEDCVAE-KD) in Figure 2 and not including any of the algorithms for the two proposed methods makes the paper slightly incoherent, without switching back and forth between the body of the paper and the appendix. I suggest rearranging the contents to remedy this issue as best as possible by at least having both the figure and algorithm for one of the methods or having the figures for both methods in the main body of the paper.
- In the first footnote on page 4, why is a uniform distribution used for sampling $\mathbf{z}$? Why not, for example, use a truncated Gaussian distribution?
- In my opinion, including FedAVG is slightly unfair in the experiments. Under FedAVG, a set of client model parameters $\\{\mathbf{w}^k\\}_{k=1}^m$ are aggregated using a simple average, i.e., $\mathbf{w}=\frac{1}{m} \sum_\{k=1\}^m\mathbf{w}^k$. In a very heterogeneous case, each of these model parameters is the minimizer of a very different objective function over an entirely different optimization landscape, so it is completely expected that a linear averaging of these model parameters should lead to inferior performance, especially if the averaging operation is done only once.
- Following the above comment, I believe your primary competing baseline is FedONESHOT, so I suggest adding more details on this algorithm's main idea.
- Do you have any explanation as to why the standard deviation of the performance of the proposed methods is, on average, larger under SVHN in Table 2?

The evidence to be evaluated is:A variational autoencoder (VAE) is a probabilistic generative model that attempts to learn the distribution of data samples (Kingma & Welling, 2014). A VAE is a latent variable method that models the joint distribution \(p_{\mathbf{\theta}}(\mathbf{x},\mathbf{z})\) of a data sample \(\mathbf{x}\in\mathcal{X}\subseteq\mathbb{R}^{D}\) and latent variable \(\mathbf{z}\in\mathcal{Z}\subseteq\mathbb{R}^{d}\), where usually \(d<<D\).

Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\).

\[\mathcal{L}(\mathbf{\phi},\mathbf{\theta};\mathbf{x},\mathbf{y})=-D_{\text{KL}}(q_{ \mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\mid\mid p(\mathbf{z}))+\mathbb{ E}_{q_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x},\mathbf{y})}[\log p_{\mathbf{\theta}}( \mathbf{x}|\mathbf{z},\mathbf{y})], \tag{1}\] which bounds the conditional marginal likelihood of the data \(\log p(\mathbf{x}|\mathbf{y})\). Here, \(D_{\text{KL}}(\cdot)\) represents KL-divergence.

Knowledge distillation (KD) aims to extract information from a trained _teacher_ model to train a separate lightweight _student_ model (Bucilua et al., 2006; Hinton et al., 2015).

Several works have integrated KD into FL to mitigate privacy risks, reduce upload costs, or regularize local learning using an ensemble-of-teachers approach (Lin et al., 2020; Zhu et al., 2021; Guha et al., 2019). However, KD approaches in FL usually require an auxiliary public dataset with similar properties as the distributed dataset, which may be difficult to obtain in practice (Zhu et al., 2021).

We jointly propose FedCVAE-Ens and FedCVAE-KD, one-shot FL methods that do not require an auxiliary public dataset for server-side training (they are _data-free_). They address issues caused by high statistical heterogeneity by reframing the learning task using CVAEs and account for model heterogeneity by allowing different CVAE architectures across clients.

The trained client decoders act as the teacher models, conveying their aggregate knowledge of how to map from latent space to data space to a single student server decoder, parameterized by \(\mathbf{\theta}^{S}\). To achieve this, we generate \(n_{D}\) total KD training samples, with \(\mathcal{D}_{\text{Ens}}\) defined as the combination of client subsets \(\mathcal{D}_{\text{Ens}}^{k}=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k}, \mathbf{z}_{i}^{k})\}_{i=1}^{\lfloor n_{D}/\rfloor}\). Then, we train the server to match the teacher's mapping of \((\mathbf{z}_{i}^{k},\mathbf{y}_{i}^{k})\) to \(\hat{\mathbf{x}}_{i}^{k}\) by minimizing a reconstruction loss: \[\ell_{\text{KD}}(\mathbf{\theta}^{S};\mathbf{z}^{k},\mathbf{y}^{k},\hat{\mathbf{x }}^{k})=g(D_{\mathbf{\theta}^{S}}(\mathbf{z}^{k};\mathbf{y}^{k}),\hat{\mathbf{x }}^{k}), \tag{2}\] which penalizes the dissimilarity \(g(\cdot)\) in data space between the synthetic data sample generated by the server decoder \(D_{\mathbf{\theta}^{S}}(\mathbf{z}^{k};\mathbf{y}^{k})\) and the client decoder sample \(\hat{\mathbf{x}}^{k}\).

Because FedCVAE-KD ensembles client decoders to create a labeled dataset \(\mathcal{D}_{\text{Ens}}\) to train the server decoder, each client can have a unique CVAE model architecture, accommodating each client's computational limitations.

FedCVAE-KD can be applied to any task that requires a labeled dataset, which is more general than classification; there is no commitment to a particular terminal task before learning occurs.

CVAEs use a prior distribution over latent space to train the encoder and decoder models. While a multivariate standard normal distribution is typically used for convenience, any normal distribution is acceptable. To promote security, we propose to shift the center of the prior distribution \(\mathbf{\mu}\) to a random position in real space (i.e., \(\mathbf{\mu}\in\mathbb{R}^{d}\)), which can be communicated offline or via encryption methods between server and clients (Zhou et al., 2020).

To validate FedCVAE-Ens and FedCVAE-KD, we conduct experiments on three image datasets that are standard in the FL literature: MNIST (Lecun et al., 1998), Fashion-MNIST (Xiao et al., 2017), and SVHN (Netzer et al., 2011).3

We compare the performance of FedCVAE-Ens and FedCVAE-KD in the one-shot data-free FL setting against two existing methods: FedAvg (McMahan et al., 2017) and a method proposed in Guha et al. (2019), which we call FedOneShot.

The one-shot methods proposed in Li et al. (2021) and Shin et al. (2020) are not applicable because of their reliance on public auxiliary data for server-side training or fine-tuning. Similarly, many standard FL methods are not appropriate because they depend on an auxiliary dataset (i.e., FedDF (Lin et al., 2020)) or focus on regularization (i.e., FedGen (Zhu et al., 2021), FedProx (Li et al., 2020), Scaffold (Karimireddy et al., 2020), FedNova (Wang et al., 2020)), which is incompatible with the one-shot setting.

We base our CVAE architecture on Higgins et al. (2017).

To demonstrate the efficacy of FedCVAE-Ens and FedCVAE-KD in the difficult setting of high statistical heterogeneity, we test on varying levels of \(\alpha\), from high (\(\alpha=0.05\)), to very high (\(\alpha=0.01\)), to extreme (\(\alpha=0.001\)) statistical heterogeneity. FedCVAE-Ens consistently outperforms all other methods, and FedCVAE-KD outperforms the baselines in nearly all datasets and levels of \(\alpha\) (the only exception is MNIST at the lowest level of statistical heterogeneity) as shown in Table 1. At \(\alpha=0.001\), FedCVAE-KD obtains more than \(1.75\times\) the accuracy of the best baseline method for MNIST, more than \(2\times\) the accuracy for FashionMNIST, and nearly \(2.75\times\) the accuracy for SVHN (Table 1). While the baselines FedAvg and FedOneShot are very sensitive to the level of statistical heterogeneity, both FedCVAE-Ens and FedCVAE-KD demonstrate consistent performance across levels of \(\alpha\) (Table 1).

While both FedAvg and FedOneShot struggle when many clients are present, Table 2 shows that FedCVAE-Ens and FedCVAE-KD perform consistently across the number of clients, with the only exception being FedCVAE-KD for SVHN.

The proposed KD aggregation method used in FedCVAE-KD substantially improves on aggregation via parameter averaging, generating qualitatively more realistic samples (Figure 8 in Appendix C) and achieving higher server classifier accuracy (Table 6 in Appendix C). As expected, FedCVAE-Ens bounds the performance of FedCVAE-KD, but KD-based aggregation still preserves client ensemble performance well across levels of \(\alpha\) for all datasets (Table 1). The upper bound accuracy established by FedCVAE-Ens is promising, but successful decoder aggregation may require a stronger KD procedure (e.g., feature-based KD as described in Gou et al. (2021)).

To simulate clients with diverse computational resources, we train both FedCVAE-Ens and FedCVAE-KD using two local CVAE architectures: the first as described in Section 4.1 and the second with one convolutional/deconvolutional block removed for the encoder/decoder, respectively. The server decoder matches that which is described in Section 4.1 but can be chosen arbitrarily. Because the two architectures demonstrate similar generative capabilities, final server classifier accuracy is very similar when comparing homogeneous against heterogeneous local architectures (Figure 4).4 Notably, our KD procedure for FedCVAE-KD still performs well using heterogeneous models, indicating diverse architectures can organize latent space similarly enough to successfully translate this knowledge to a single decoder.

Therefore, this simple FedCVAE-Ens and FedCVAE-KD extension reduces eavesdropping attackers' capacity to extract high-quality samples from uploaded decoders or train a performant downstream model, reducing communication risks.

FL was originally proposed by McMahan et al. (2017) as a paradigm for decentralized distributed learning. Statistical heterogeneity quickly emerged as a core issue within FL, with many studies focusing on maintaining high performance under very non-IID data. Many approaches have experimented with augmenting FedAvg by adding proximal terms to the local objective as an attempt to restrain local updates (Li et al., 2020; Karimireddy et al., 2020; Wang et al., 2020; Acar et al., 2021; Li et al., 2021). Other works have used KD to circumvent issues associated with parameter averaging under non-IID data, focusing on leveraging auxiliary data (Lin et al., 2020; Sattler et al., 2021) or a generative model (Zhu et al., 2021; Zhang et al., 2022) to compactly capture client ensemble learning. Recent approaches focus on improving client selection strategy (Tang et al., 2022), reducing catastrophic forgetting to balance global knowledge against local learning (Huang et al., 2022), or improving the generality of client models (Mendieta et al., 2022). However, all of these methods are designed for standard FL and rely heavily on local regularization through substantial iterative communication, which is not feasible in the one-shot FL setting where communication is limited to a single round.

Methods in one-shot FL have demonstrated strong performance under substantial communication constraint. Guha et al. (2019) originally proposed one-shot FL and introduced two methods, one based on heuristic selection methods for client inclusion in the final ensemble and another that used KD with an auxiliary dataset for ensemble aggregation.

Although these methods obtain high accuracy, they rely on an auxiliary public dataset to support KD, which is inapplicable in data-free FL.

Zhang et al. (2021) proposed a data-free KD procedure based on a generator network trained using the ensemble of client classifiers, showing promising performance even under heterogeneous local models. However, existing approaches in one-shot FL either do not experiment with high statistical heterogeneity or degrade even under moderate levels of heterogeneity, unlike our proposed methods.

A few studies have experimented with using VAEs in FL.

We are the first to apply CVAEs to one-shot FL with a focus on high statistical heterogeneity. In this paper, we proposed FedCVAE-Ens and FedCVAE-KD, data-free one-shot FL methods that reframe the local learning task using CVAEs. Both methods performed well given high statistical heterogeneity, demonstrated consistent performance with increasing numbers of clients, allow for model heterogeneity across clients, and can be extended to promote security. Extensive experimental results showed that FedCVAE-Ens and FedCVAE-KD substantially extended the state-of-the-art in one-shot FL under very high statistical heterogeneity, making way for more nuanced development in this difficult environment for distributed learning.

* Zhang et al. (2021) Jie Zhang, Chen Chen, Bo Li, Linguuan Lyu, Shuang Wu, Jianghe Xu, Shouhong Ding, and Chao Wu. A practical data-free approach to one-shot federated learning with heterogeneity. _arXiv preprint arXiv:2112.12371_, 2021.

* Zhang et al. (2022) Lin Zhang, Li Shen, Liang Ding, Dacheng Tao, and Ling-Yu Duan. Fine-tuning global model via data-free knowledge distillation for non-iid federated learning. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_, pp. 10174-10183, June 2022.

FedCVAE-Ens follows the same procedure as FedCVAE-KD, but alternatively defines \(\mathcal{D}_{\text{Ens}}\) as the combination of client subsets \(\mathcal{D}_{\text{Ens}}^{k}:=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k})\}_ {i=1}^{c/m}\) and uses \(\mathcal{D}_{\text{Ens}}\) to directly train the server classifier. Figure 6 visualizes the full pipeline for FedCVAE-Ens and Algorithm 2 details the full procedure. Algorithm 3 shows the local client training procedure, which is the same for FedCVAE-Ens and FedCVAE-KD.

1:procedureServer 2:for each client \(k\in\mathcal{C}\) in parallel do 3:\(\mathbf{\theta}^{k},\;\hat{p}^{k}(\mathbf{y})\leftarrow\)ClientLocalUpdate(\(k\), \(T_{L}\)) 4: Generate samples from each client \(\mathcal{D}_{\text{Ens}}^{k}:=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k})\}_ {i=1}^{\lfloor nC/m\rfloor}\) using client decoder \(D_{\mathbf{\theta}^{k}}(\cdot)\) and label distribution \(\hat{p}^{k}(\mathbf{y})\) 5: Combine client subsets into an IID labeled dataset \(\mathcal{D}_{\text{Ens}}:=\mathcal{D}_{\text{Ens}}^{1}\cup\mathcal{D}_{\text{ Ens}}^{2}\cup...\cup\mathcal{D}_{\text{Ens}}^{m}\) 6:for classifier epoch \(i=1\) to \(T_{C}\)do

```**Algorithm 2** - FedCVAE-Ens in the one-shot FL setting. \(T_{L}\) represents the number of local training epochs. The server classifier parameters are \(\mathbf{w}_{C}^{S}\), with training epochs \(T_{C}\), number of training samples \(n_{C}\), classification loss \(\ell_{C}(\cdot)\), and learning rate \(\eta_{C}\). \(\mathcal{C}\) is the set of clients.

van den Burg and Williams (2021) define a probabilistic generative model's propensity to reproduce samples observed in the training data as memorization, and prove that ensuring a particular level of differential privacy (DP) can bound memorization in probabilistic generative models (including CVAEs). Thus, beyond the normal privacy guarantees attributable to DP, employing FL DP-estimation techniques (i.e., Geyer et al. (2017)) also ensures low memorization across the FedCVAE-Ens and FedCVAE-KD pipelines, further enhancing the privacy of our proposed methods.

While FedAvg and FedOneShot are very sensitive to dataset split (high standard deviation), the results in Table 5 for both FedCVAE-Ens and FedCVAE-KD are not only consistent with Table 2, but also exhibit reasonable stability (low standard deviation).

The KD approach we propose to aggregate client decoders generates substantially better samples (Figure 8) while also obtaining more than \(2\times\) classifier accuracy on MNIST, more than \(3.25\times\) accuracy on FashionMNIST, and nearly \(5\times\) accuracy for SVHN at \(\alpha=0.001\) (Table 6). \begin{table}
\begin{tabular}{l l|c c|c c} \hline \hline  & \# of Clients & FedAvg & FedOneShot & FedCVAE-KD (ours) & FedCVAE-Ens (ours) \\ \hline \multirow{3}{*}{MNIST} & \(m=5\) & \(42.34\pm 1.75\) & \(42.97\pm 1.54\) & \(80.19\pm 1.76\) & \(92.81\pm 2.16\) \\  & \(m=10\) & \(58.29\pm 2.83\) & \(41.15\pm 0.70\) & \(82.01\pm 1.61\) & \(93.83\pm 1.53\) \\  & \(m=20\) & \(37.14\pm 3.87\) & \(32.22\pm 0.71\) & \(81.93\pm 1.75\) & \(93.52\pm 0.86\) \\  & \(m=50\) & \(28.26\pm 7.98\) & \(35.62\pm 0.66\) & \(77.68\pm 1.39\) & \(87.56\pm 1.44\) \\ \hline \multirow{3}{*}{FashionMNIST} & \(m=5\) & \(38.51\pm 2.40\) & \(32.23\pm 1.68\) & \(68.01\pm 1.56\) & \(73.70\pm 1.93\) \\  & \(m=10\) & \(45.85\pm 2.95\) & \(37.63\pm 0.53\) & \(69.97\pm 1.63\) & \(76.62\pm 1.61\) \\  & \(m=20\) & \(27.49\pm 4.77\) & \(24.72\pm 1.20\) & \(71.28\pm 1.17\) & \(76.51\pm 1.38\) \\  & \(m=50\) & \(31.91\pm 2.20\) & \(41.01\pm 2.49\) & \(69.25\pm 1.13\) & \(76.13\pm 2.00\) \\ \hline \multirow{3}{*}{SVHN} & \(m=5\) & \(40.61\pm 0.64\) & \(42.05\pm 1.31\) & \(57.17\pm 2.56\) & \(65.72\pm 2.17\) \\  & \(m=10\) & \(25.12\pm 2.07\) & \(31.91\pm 1.26\) & \(55.97\pm 0.38\) & \(65.50\pm 2.28\) \\ \cline{1-1}  & \(m=20\) & \(26.99\pm 1.15\) & \(10.68\pm 0.70\) & \(51.80\pm 2.75\) & \(65.54\pm 1.89\) \\ \cline{1-1}  & \(m=50\) & \(19.59\pm 0.00\) & \(30.20\pm 0.64\) & \(40.03\pm 2.62\) & \(64.81\pm 2.44\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of four one-shot FL methods over three datasets and across four numbers of clients \(m\). Best results for each dataset and each level of \(m\) are in purple, with second best results in yellow.

Input: Table 2: Performance of four one-shot FL methods over three datasets and across four numbers of

Input: Figure 6: The full pipeline for one of our proposed methods, FEDCVAE-ENS. Here, E, D, and C represent “encoder,” “decoder,” and “classifier” models, respectively. First, clients train CVAEs on their private local datasets. Then, the server uses the ensemble of uploaded client decoders and corresponding local label distributions to generate a labeled dataset of synthetic samples to train a classifier.

Input: Figure 4: Results with heterogeneous local models. “Homogeneous” uses the same CVAE architecture for all clients, whereas “heterogeneous” uses two architectures with similar generative capabilities.

Input: Figure 8: Samples from the aggregated server decoder obtained through parameter averaging (top row) versus knowledge distillation (bottom row) at high statistical heterogeneity (α = 0.01).

Input: Figure 1: Motivating our proposed methods, FEDCVAE-ENS and FEDCVAE-KD, using the MNIST dataset as an example. In cases of very high statistical heterogeneity, each client will only observe one or two of the ten available classes, as seen on the left where the size of each dot is proportional to the number of samples. For example, client 2 only observes 4’s and 7’s, resulting in a client decoder that can expertly generate these digits. Note that the columns are shown in order of conditioning class (digits 0-9). Similarly, client 4 is an expert in 3’s and 6’s. In FEDCVAE-KD, our lightweight knowledge distillation training procedure compacts local learning into a single server decoder, as evidenced by the high-quality samples from all available classes (digits 0-9). This server decoder can then be used for any downstream task, e.g., classification.

Input: Figure 7: CVAE samples generated using latent vectors distant from the center of the multivariate normal prior (top row) and close to the center (bottom row).

Input: Figure 2: The full pipeline for one of our proposed methods, FEDCVAE-KD. Here, E, D, and C represent “encoder,” “decoder,” and “classifier” models, respectively. First, clients train CVAEs on their private local datasets. Then, the server uses uploaded client decoder parameters and local label distributions to train a server decoder using knowledge distillation (KD). Finally, synthetic labeled samples from the server decoder are used to train a classifier.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence, I find this claim partially overstated. While the authors do propose FedCVAE-Ens and FedCVAE-KD models that use CVAEs for one-shot FL, the presentation implies complete novelty when the evidence shows prior work with VAEs in FL exists. The evidence demonstrates these methods perform well under high statistical heterogeneity and allow model heterogeneity, but the reviewer correctly points out that the "one-shot" aspect is not well-motivated and the paper lacks central novelty, instead combining existing ideas. The methods build incrementally on prior work rather than representing a completely novel reframing of the learning task.

<score>3</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

To address these issues, we jointly propose FedCVAE-Ens and FedCVAE-KD, two novel data-free one-shot FL models that reframe the local learning task using conditional variational autoencoders (CVAE).

The review comment to be evaluated is:

### Strength

* The proposed method of one-shot FL is very interesting and novel.
* The proposed method doesn't require auxiliary public dataset.
* Both security and privacy extensions are considered in the paper.
* It can be applied to heterogeneous local models with similar generative capabilities.

### Weaknesses
* One potential issue of the method is training a CVAE locally. In the paper, the images used in the dataset are very small, and the amount of data each client has is large. However, in the real-world application of FL like medical imagings, with very large images and very limited number of data samples, training a CVAE locally can be difficult even just for one class of data.
* The training task of local models is different from the original task. This limits the re-use of pre-trained local model from original task. I think one of the reasons that people want to do one-shot FL is to prevent any re-training locally. But the proposed method still requires to train some new model.

The evidence to be evaluated is:A variational autoencoder (VAE) is a probabilistic generative model that attempts to learn the distribution of data samples (Kingma & Welling, 2014). A VAE is a latent variable method that models the joint distribution \(p_{\mathbf{\theta}}(\mathbf{x},\mathbf{z})\) of a data sample \(\mathbf{x}\in\mathcal{X}\subseteq\mathbb{R}^{D}\) and latent variable \(\mathbf{z}\in\mathcal{Z}\subseteq\mathbb{R}^{d}\), where usually \(d<<D\).

Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\).

\[\mathcal{L}(\mathbf{\phi},\mathbf{\theta};\mathbf{x},\mathbf{y})=-D_{\text{KL}}(q_{ \mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\mid\mid p(\mathbf{z}))+\mathbb{ E}_{q_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x},\mathbf{y})}[\log p_{\mathbf{\theta}}( \mathbf{x}|\mathbf{z},\mathbf{y})], \tag{1}\] which bounds the conditional marginal likelihood of the data \(\log p(\mathbf{x}|\mathbf{y})\). Here, \(D_{\text{KL}}(\cdot)\) represents KL-divergence.

Knowledge distillation (KD) aims to extract information from a trained _teacher_ model to train a separate lightweight _student_ model (Bucilua et al., 2006; Hinton et al., 2015).

Several works have integrated KD into FL to mitigate privacy risks, reduce upload costs, or regularize local learning using an ensemble-of-teachers approach (Lin et al., 2020; Zhu et al., 2021; Guha et al., 2019). However, KD approaches in FL usually require an auxiliary public dataset with similar properties as the distributed dataset, which may be difficult to obtain in practice (Zhu et al., 2021).

We jointly propose FedCVAE-Ens and FedCVAE-KD, one-shot FL methods that do not require an auxiliary public dataset for server-side training (they are _data-free_). They address issues caused by high statistical heterogeneity by reframing the learning task using CVAEs and account for model heterogeneity by allowing different CVAE architectures across clients.

The trained client decoders act as the teacher models, conveying their aggregate knowledge of how to map from latent space to data space to a single student server decoder, parameterized by \(\mathbf{\theta}^{S}\). To achieve this, we generate \(n_{D}\) total KD training samples, with \(\mathcal{D}_{\text{Ens}}\) defined as the combination of client subsets \(\mathcal{D}_{\text{Ens}}^{k}=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k}, \mathbf{z}_{i}^{k})\}_{i=1}^{\lfloor n_{D}/\rfloor}\). Then, we train the server to match the teacher's mapping of \((\mathbf{z}_{i}^{k},\mathbf{y}_{i}^{k})\) to \(\hat{\mathbf{x}}_{i}^{k}\) by minimizing a reconstruction loss: \[\ell_{\text{KD}}(\mathbf{\theta}^{S};\mathbf{z}^{k},\mathbf{y}^{k},\hat{\mathbf{x }}^{k})=g(D_{\mathbf{\theta}^{S}}(\mathbf{z}^{k};\mathbf{y}^{k}),\hat{\mathbf{x }}^{k}), \tag{2}\] which penalizes the dissimilarity \(g(\cdot)\) in data space between the synthetic data sample generated by the server decoder \(D_{\mathbf{\theta}^{S}}(\mathbf{z}^{k};\mathbf{y}^{k})\) and the client decoder sample \(\hat{\mathbf{x}}^{k}\).

Because FedCVAE-KD ensembles client decoders to create a labeled dataset \(\mathcal{D}_{\text{Ens}}\) to train the server decoder, each client can have a unique CVAE model architecture, accommodating each client's computational limitations.

FedCVAE-KD can be applied to any task that requires a labeled dataset, which is more general than classification; there is no commitment to a particular terminal task before learning occurs.

CVAEs use a prior distribution over latent space to train the encoder and decoder models. While a multivariate standard normal distribution is typically used for convenience, any normal distribution is acceptable. To promote security, we propose to shift the center of the prior distribution \(\mathbf{\mu}\) to a random position in real space (i.e., \(\mathbf{\mu}\in\mathbb{R}^{d}\)), which can be communicated offline or via encryption methods between server and clients (Zhou et al., 2020).

To validate FedCVAE-Ens and FedCVAE-KD, we conduct experiments on three image datasets that are standard in the FL literature: MNIST (Lecun et al., 1998), Fashion-MNIST (Xiao et al., 2017), and SVHN (Netzer et al., 2011).3

We compare the performance of FedCVAE-Ens and FedCVAE-KD in the one-shot data-free FL setting against two existing methods: FedAvg (McMahan et al., 2017) and a method proposed in Guha et al. (2019), which we call FedOneShot.

The one-shot methods proposed in Li et al. (2021) and Shin et al. (2020) are not applicable because of their reliance on public auxiliary data for server-side training or fine-tuning. Similarly, many standard FL methods are not appropriate because they depend on an auxiliary dataset (i.e., FedDF (Lin et al., 2020)) or focus on regularization (i.e., FedGen (Zhu et al., 2021), FedProx (Li et al., 2020), Scaffold (Karimireddy et al., 2020), FedNova (Wang et al., 2020)), which is incompatible with the one-shot setting.

We base our CVAE architecture on Higgins et al. (2017).

To demonstrate the efficacy of FedCVAE-Ens and FedCVAE-KD in the difficult setting of high statistical heterogeneity, we test on varying levels of \(\alpha\), from high (\(\alpha=0.05\)), to very high (\(\alpha=0.01\)), to extreme (\(\alpha=0.001\)) statistical heterogeneity. FedCVAE-Ens consistently outperforms all other methods, and FedCVAE-KD outperforms the baselines in nearly all datasets and levels of \(\alpha\) (the only exception is MNIST at the lowest level of statistical heterogeneity) as shown in Table 1. At \(\alpha=0.001\), FedCVAE-KD obtains more than \(1.75\times\) the accuracy of the best baseline method for MNIST, more than \(2\times\) the accuracy for FashionMNIST, and nearly \(2.75\times\) the accuracy for SVHN (Table 1). While the baselines FedAvg and FedOneShot are very sensitive to the level of statistical heterogeneity, both FedCVAE-Ens and FedCVAE-KD demonstrate consistent performance across levels of \(\alpha\) (Table 1).

While both FedAvg and FedOneShot struggle when many clients are present, Table 2 shows that FedCVAE-Ens and FedCVAE-KD perform consistently across the number of clients, with the only exception being FedCVAE-KD for SVHN.

The proposed KD aggregation method used in FedCVAE-KD substantially improves on aggregation via parameter averaging, generating qualitatively more realistic samples (Figure 8 in Appendix C) and achieving higher server classifier accuracy (Table 6 in Appendix C). As expected, FedCVAE-Ens bounds the performance of FedCVAE-KD, but KD-based aggregation still preserves client ensemble performance well across levels of \(\alpha\) for all datasets (Table 1). The upper bound accuracy established by FedCVAE-Ens is promising, but successful decoder aggregation may require a stronger KD procedure (e.g., feature-based KD as described in Gou et al. (2021)).

To simulate clients with diverse computational resources, we train both FedCVAE-Ens and FedCVAE-KD using two local CVAE architectures: the first as described in Section 4.1 and the second with one convolutional/deconvolutional block removed for the encoder/decoder, respectively. The server decoder matches that which is described in Section 4.1 but can be chosen arbitrarily. Because the two architectures demonstrate similar generative capabilities, final server classifier accuracy is very similar when comparing homogeneous against heterogeneous local architectures (Figure 4).4 Notably, our KD procedure for FedCVAE-KD still performs well using heterogeneous models, indicating diverse architectures can organize latent space similarly enough to successfully translate this knowledge to a single decoder.

Therefore, this simple FedCVAE-Ens and FedCVAE-KD extension reduces eavesdropping attackers' capacity to extract high-quality samples from uploaded decoders or train a performant downstream model, reducing communication risks.

FL was originally proposed by McMahan et al. (2017) as a paradigm for decentralized distributed learning. Statistical heterogeneity quickly emerged as a core issue within FL, with many studies focusing on maintaining high performance under very non-IID data. Many approaches have experimented with augmenting FedAvg by adding proximal terms to the local objective as an attempt to restrain local updates (Li et al., 2020; Karimireddy et al., 2020; Wang et al., 2020; Acar et al., 2021; Li et al., 2021). Other works have used KD to circumvent issues associated with parameter averaging under non-IID data, focusing on leveraging auxiliary data (Lin et al., 2020; Sattler et al., 2021) or a generative model (Zhu et al., 2021; Zhang et al., 2022) to compactly capture client ensemble learning. Recent approaches focus on improving client selection strategy (Tang et al., 2022), reducing catastrophic forgetting to balance global knowledge against local learning (Huang et al., 2022), or improving the generality of client models (Mendieta et al., 2022). However, all of these methods are designed for standard FL and rely heavily on local regularization through substantial iterative communication, which is not feasible in the one-shot FL setting where communication is limited to a single round.

Methods in one-shot FL have demonstrated strong performance under substantial communication constraint. Guha et al. (2019) originally proposed one-shot FL and introduced two methods, one based on heuristic selection methods for client inclusion in the final ensemble and another that used KD with an auxiliary dataset for ensemble aggregation.

Although these methods obtain high accuracy, they rely on an auxiliary public dataset to support KD, which is inapplicable in data-free FL.

Zhang et al. (2021) proposed a data-free KD procedure based on a generator network trained using the ensemble of client classifiers, showing promising performance even under heterogeneous local models. However, existing approaches in one-shot FL either do not experiment with high statistical heterogeneity or degrade even under moderate levels of heterogeneity, unlike our proposed methods.

A few studies have experimented with using VAEs in FL.

We are the first to apply CVAEs to one-shot FL with a focus on high statistical heterogeneity. In this paper, we proposed FedCVAE-Ens and FedCVAE-KD, data-free one-shot FL methods that reframe the local learning task using CVAEs. Both methods performed well given high statistical heterogeneity, demonstrated consistent performance with increasing numbers of clients, allow for model heterogeneity across clients, and can be extended to promote security. Extensive experimental results showed that FedCVAE-Ens and FedCVAE-KD substantially extended the state-of-the-art in one-shot FL under very high statistical heterogeneity, making way for more nuanced development in this difficult environment for distributed learning.

* Zhang et al. (2021) Jie Zhang, Chen Chen, Bo Li, Linguuan Lyu, Shuang Wu, Jianghe Xu, Shouhong Ding, and Chao Wu. A practical data-free approach to one-shot federated learning with heterogeneity. _arXiv preprint arXiv:2112.12371_, 2021.

* Zhang et al. (2022) Lin Zhang, Li Shen, Liang Ding, Dacheng Tao, and Ling-Yu Duan. Fine-tuning global model via data-free knowledge distillation for non-iid federated learning. In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_, pp. 10174-10183, June 2022.

FedCVAE-Ens follows the same procedure as FedCVAE-KD, but alternatively defines \(\mathcal{D}_{\text{Ens}}\) as the combination of client subsets \(\mathcal{D}_{\text{Ens}}^{k}:=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k})\}_ {i=1}^{c/m}\) and uses \(\mathcal{D}_{\text{Ens}}\) to directly train the server classifier. Figure 6 visualizes the full pipeline for FedCVAE-Ens and Algorithm 2 details the full procedure. Algorithm 3 shows the local client training procedure, which is the same for FedCVAE-Ens and FedCVAE-KD.

1:procedureServer 2:for each client \(k\in\mathcal{C}\) in parallel do 3:\(\mathbf{\theta}^{k},\;\hat{p}^{k}(\mathbf{y})\leftarrow\)ClientLocalUpdate(\(k\), \(T_{L}\)) 4: Generate samples from each client \(\mathcal{D}_{\text{Ens}}^{k}:=\{(\hat{\mathbf{x}}_{i}^{k},\mathbf{y}_{i}^{k})\}_ {i=1}^{\lfloor nC/m\rfloor}\) using client decoder \(D_{\mathbf{\theta}^{k}}(\cdot)\) and label distribution \(\hat{p}^{k}(\mathbf{y})\) 5: Combine client subsets into an IID labeled dataset \(\mathcal{D}_{\text{Ens}}:=\mathcal{D}_{\text{Ens}}^{1}\cup\mathcal{D}_{\text{ Ens}}^{2}\cup...\cup\mathcal{D}_{\text{Ens}}^{m}\) 6:for classifier epoch \(i=1\) to \(T_{C}\)do

```**Algorithm 2** - FedCVAE-Ens in the one-shot FL setting. \(T_{L}\) represents the number of local training epochs. The server classifier parameters are \(\mathbf{w}_{C}^{S}\), with training epochs \(T_{C}\), number of training samples \(n_{C}\), classification loss \(\ell_{C}(\cdot)\), and learning rate \(\eta_{C}\). \(\mathcal{C}\) is the set of clients.

van den Burg and Williams (2021) define a probabilistic generative model's propensity to reproduce samples observed in the training data as memorization, and prove that ensuring a particular level of differential privacy (DP) can bound memorization in probabilistic generative models (including CVAEs). Thus, beyond the normal privacy guarantees attributable to DP, employing FL DP-estimation techniques (i.e., Geyer et al. (2017)) also ensures low memorization across the FedCVAE-Ens and FedCVAE-KD pipelines, further enhancing the privacy of our proposed methods.

While FedAvg and FedOneShot are very sensitive to dataset split (high standard deviation), the results in Table 5 for both FedCVAE-Ens and FedCVAE-KD are not only consistent with Table 2, but also exhibit reasonable stability (low standard deviation).

The KD approach we propose to aggregate client decoders generates substantially better samples (Figure 8) while also obtaining more than \(2\times\) classifier accuracy on MNIST, more than \(3.25\times\) accuracy on FashionMNIST, and nearly \(5\times\) accuracy for SVHN at \(\alpha=0.001\) (Table 6). \begin{table}
\begin{tabular}{l l|c c|c c} \hline \hline  & \# of Clients & FedAvg & FedOneShot & FedCVAE-KD (ours) & FedCVAE-Ens (ours) \\ \hline \multirow{3}{*}{MNIST} & \(m=5\) & \(42.34\pm 1.75\) & \(42.97\pm 1.54\) & \(80.19\pm 1.76\) & \(92.81\pm 2.16\) \\  & \(m=10\) & \(58.29\pm 2.83\) & \(41.15\pm 0.70\) & \(82.01\pm 1.61\) & \(93.83\pm 1.53\) \\  & \(m=20\) & \(37.14\pm 3.87\) & \(32.22\pm 0.71\) & \(81.93\pm 1.75\) & \(93.52\pm 0.86\) \\  & \(m=50\) & \(28.26\pm 7.98\) & \(35.62\pm 0.66\) & \(77.68\pm 1.39\) & \(87.56\pm 1.44\) \\ \hline \multirow{3}{*}{FashionMNIST} & \(m=5\) & \(38.51\pm 2.40\) & \(32.23\pm 1.68\) & \(68.01\pm 1.56\) & \(73.70\pm 1.93\) \\  & \(m=10\) & \(45.85\pm 2.95\) & \(37.63\pm 0.53\) & \(69.97\pm 1.63\) & \(76.62\pm 1.61\) \\  & \(m=20\) & \(27.49\pm 4.77\) & \(24.72\pm 1.20\) & \(71.28\pm 1.17\) & \(76.51\pm 1.38\) \\  & \(m=50\) & \(31.91\pm 2.20\) & \(41.01\pm 2.49\) & \(69.25\pm 1.13\) & \(76.13\pm 2.00\) \\ \hline \multirow{3}{*}{SVHN} & \(m=5\) & \(40.61\pm 0.64\) & \(42.05\pm 1.31\) & \(57.17\pm 2.56\) & \(65.72\pm 2.17\) \\  & \(m=10\) & \(25.12\pm 2.07\) & \(31.91\pm 1.26\) & \(55.97\pm 0.38\) & \(65.50\pm 2.28\) \\ \cline{1-1}  & \(m=20\) & \(26.99\pm 1.15\) & \(10.68\pm 0.70\) & \(51.80\pm 2.75\) & \(65.54\pm 1.89\) \\ \cline{1-1}  & \(m=50\) & \(19.59\pm 0.00\) & \(30.20\pm 0.64\) & \(40.03\pm 2.62\) & \(64.81\pm 2.44\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of four one-shot FL methods over three datasets and across four numbers of clients \(m\). Best results for each dataset and each level of \(m\) are in purple, with second best results in yellow.

Input: Table 2: Performance of four one-shot FL methods over three datasets and across four numbers of

Input: Figure 6: The full pipeline for one of our proposed methods, FEDCVAE-ENS. Here, E, D, and C represent “encoder,” “decoder,” and “classifier” models, respectively. First, clients train CVAEs on their private local datasets. Then, the server uses the ensemble of uploaded client decoders and corresponding local label distributions to generate a labeled dataset of synthetic samples to train a classifier.

Input: Figure 4: Results with heterogeneous local models. “Homogeneous” uses the same CVAE architecture for all clients, whereas “heterogeneous” uses two architectures with similar generative capabilities.

Input: Figure 8: Samples from the aggregated server decoder obtained through parameter averaging (top row) versus knowledge distillation (bottom row) at high statistical heterogeneity (α = 0.01).

Input: Figure 1: Motivating our proposed methods, FEDCVAE-ENS and FEDCVAE-KD, using the MNIST dataset as an example. In cases of very high statistical heterogeneity, each client will only observe one or two of the ten available classes, as seen on the left where the size of each dot is proportional to the number of samples. For example, client 2 only observes 4’s and 7’s, resulting in a client decoder that can expertly generate these digits. Note that the columns are shown in order of conditioning class (digits 0-9). Similarly, client 4 is an expert in 3’s and 6’s. In FEDCVAE-KD, our lightweight knowledge distillation training procedure compacts local learning into a single server decoder, as evidenced by the high-quality samples from all available classes (digits 0-9). This server decoder can then be used for any downstream task, e.g., classification.

Input: Figure 7: CVAE samples generated using latent vectors distant from the center of the multivariate normal prior (top row) and close to the center (bottom row).

Input: Figure 2: The full pipeline for one of our proposed methods, FEDCVAE-KD. Here, E, D, and C represent “encoder,” “decoder,” and “classifier” models, respectively. First, clients train CVAEs on their private local datasets. Then, the server uses uploaded client decoder parameters and local label distributions to train a server decoder using knowledge distillation (KD). Finally, synthetic labeled samples from the server decoder are used to train a classifier.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
1. The claim states that FedCVAE-Ens and FedCVAE-KD are "novel data-free one-shot FL models that reframe local learning using CVAEs." The evidence strongly supports this claim through:
- Detailed mathematical formulations and algorithms demonstrating the novelty
- Extensive experimental results showing superior performance over baselines
- Validation across multiple datasets and heterogeneity levels
- Reviewer comments confirming the novelty and data-free nature
- Theoretical foundations in VAEs and CVAEs
- Clear differentiation from existing methods

The claim is precise, accurate, and appropriately scoped to match the evidence without exaggeration.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Because CVAEs can easily learn a simplified data distribution, both methods train CVAEs locally to capture the narrow conditional data distributions that arise in the high statistical heterogeneity setting.

The evidence to be evaluated is:A variational autoencoder (VAE) is a probabilistic generative model that attempts to learn the distribution of data samples (Kingma & Welling, 2014). A VAE is a latent variable method that models the joint distribution \(p_{\mathbf{\theta}}(\mathbf{x},\mathbf{z})\) of a data sample \(\mathbf{x}\in\mathcal{X}\subseteq\mathbb{R}^{D}\) and latent variable \(\mathbf{z}\in\mathcal{Z}\subseteq\mathbb{R}^{d}\), where usually \(d<<D\). This joint can be factorized as \(p_{\mathbf{\theta}}(\mathbf{x},\mathbf{z})=p_{\mathbf{\theta}}(\mathbf{x}[\mathbf{z}] p(\mathbf{z})\), where the prior \(p(\mathbf{z})\) is usually chosen to be a multivariate standard normal distribution, i.e., \(p(\mathbf{z})=\mathcal{N}(\mathbf{0},\mathbf{I})\). The posterior \(p_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x})\) is approximated via an inference model \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x})\) called the _encoder_ and the model for the conditional likelihood \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z})\) is called the _decoder_. In our case, both the encoder and decoder are deep neural networks parameterized by \(\mathbf{\phi}\) and \(\mathbf{\theta}\), respectively. Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\).

They address issues caused by high statistical heterogeneity by reframing the learning task using CVAEs and account for model heterogeneity by allowing different CVAE architectures across clients.

FedCVAE-KD trains a CVAE \(f_{\mathbf{w}^{k}}(\cdot)\) for every client \(k\in\mathcal{C}\) to convergence on their private local dataset by solving Equation 1; this CVAE is parameterized by \(\mathbf{w}^{k}=[\phi^{k},\mathbf{\theta}^{k}]\), with encoder \(E_{\mathbf{\phi}^{k}}(\cdot)\) and decoder \(D_{\mathbf{\theta}^{k}}(\cdot)\). Then, clients communicate their decoder weights \(\mathbf{\theta}^{k}\) and label distributions \(\bar{p}^{k}(\mathbf{y})\) to the server; in practice, this simply requires upload of client label counts as in Zhu et al. (2021). This completes the single communication round.

Intuitively, if a CVAE observes samples primarily from only a few of the \(K\) total classes (as is likely when data is highly heterogeneous), the CVAE will become an "expert" in the simplified data distribution over those few classes. To ensure each client only presents its highest-quality samples, we generate conditioning classes \(\mathbf{y}\) by sampling from the client's local label distribution, i.e., \(\mathbf{y}\sim\bar{p}^{k}(\mathbf{y})\). Then, to sample from client decoders, we sample a latent vector from the prior (i.e., \(\mathbf{z}\sim\mathcal{N}(\mathbf{0},\mathbf{I})\))1 and obtain synthetic data sample \(i\) from client \(k\) using \(\hat{\mathbf{x}}_{i}^{k}=D_{\mathbf{\theta}^{k}}(\mathbf{z}_{i}^{k};\mathbf{y}_{i }^{k})\).

CVAEs use a prior distribution over latent space to train the encoder and decoder models. While a multivariate standard normal distribution is typically used for convenience, any normal distribution is acceptable.

To demonstrate the efficacy of FedCVAE-Ens and FedCVAE-KD in the difficult setting of high statistical heterogeneity, we test on varying levels of \(\alpha\), from high (\(\alpha=0.05\)), to very high (\(\alpha=0.01\)), to extreme (\(\alpha=0.001\)) statistical heterogeneity. FedCVAE-Ens consistently outperforms all other methods, and FedCVAE-KD outperforms the baselines in nearly all datasets and levels of \(\alpha\) (the only exception is MNIST at the lowest level of statistical heterogeneity) as shown in Table 1.

While the baselines FedAvg and FedOneShot are very sensitive to the level of statistical heterogeneity, both FedCVAE-Ens and FedCVAE-KD demonstrate consistent performance across levels of \(\alpha\) (Table 1).

To simulate clients with diverse computational resources, we train both FedCVAE-Ens and FedCVAE-KD using two local CVAE architectures: the first as described in Section 4.1 and the second with one convolutional/deconvolutional block removed for the encoder/decoder, respectively.

Because the two architectures demonstrate similar generative capabilities, final server classifier accuracy is very similar when comparing homogeneous against heterogeneous local architectures (Figure 4).4 Notably, our KD procedure for FedCVAE-KD still performs well using heterogeneous models, indicating diverse architectures can organize latent space similarly enough to successfully translate this knowledge to a single decoder.

Statistical heterogeneity quickly emerged as a core issue within FL, with many studies focusing on maintaining high performance under very non-IID data.

Other works have used KD to circumvent issues associated with parameter averaging under non-IID data, focusing on leveraging auxiliary data (Lin et al., 2020; Sattler et al., 2021) or a generative model (Zhu et al., 2021; Zhang et al., 2022) to compactly capture client ensemble learning.

We are the first to apply CVAEs to one-shot FL with a focus on high statistical heterogeneity. In this paper, we proposed FedCVAE-Ens and FedCVAE-KD, data-free one-shot FL methods that reframe the local learning task using CVAEs. Both methods performed well given high statistical heterogeneity, demonstrated consistent performance with increasing numbers of clients, allow for model heterogeneity across clients, and can be extended to promote security. Extensive experimental results showed that FedCVAE-Ens and FedCVAE-KD substantially extended the state-of-the-art in one-shot FL under very high statistical heterogeneity, making way for more nuanced development in this difficult environment for distributed learning.

During training, the CVAE will largely observe latent vectors in the highest density region of the prior distribution; for a standard normal distribution, this is near the center \(\mathbf{\mu}=\mathbf{0}\). Latent vectors distant from the center will not generate high-quality samples when used with the trained decoder. As a demonstration, we train a centralized CVAE and sample both close to the center of the prior (i.e., \(\mathbf{z}_{i}\sim\mathcal{U}(-1,1)\)) and distant from the center of the prior (i.e., \(\mathbf{z}_{i}\sim\mathcal{U}(5,20)\)).

Input: Figure 4: Results with heterogeneous local models. “Homogeneous” uses the same CVAE architecture for all clients, whereas “heterogeneous” uses two architectures with similar generative capabilities.

Input: Figure 3: Example distributions of class labels for MNIST with m = 10 clients over multiple levels of statistical heterogeneity α. The size of each dot is proportional to the number of samples.

Input: Figure 1: Motivating our proposed methods, FEDCVAE-ENS and FEDCVAE-KD, using the MNIST dataset as an example. In cases of very high statistical heterogeneity, each client will only observe one or two of the ten available classes, as seen on the left where the size of each dot is proportional to the number of samples. For example, client 2 only observes 4’s and 7’s, resulting in a client decoder that can expertly generate these digits. Note that the columns are shown in order of conditioning class (digits 0-9). Similarly, client 4 is an expert in 3’s and 6’s. In FEDCVAE-KD, our lightweight knowledge distillation training procedure compacts local learning into a single server decoder, as evidenced by the high-quality samples from all available classes (digits 0-9). This server decoder can then be used for any downstream task, e.g., classification.

Input: Figure 7: CVAE samples generated using latent vectors distant from the center of the multivariate normal prior (top row) and close to the center (bottom row).

Input: Figure 2: The full pipeline for one of our proposed methods, FEDCVAE-KD. Here, E, D, and C represent “encoder,” “decoder,” and “classifier” models, respectively. First, clients train CVAEs on their private local datasets. Then, the server uses uploaded client decoder parameters and local label distributions to train a server decoder using knowledge distillation (KD). Finally, synthetic labeled samples from the server decoder are used to train a classifier.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence, the claim "CVAEs can easily learn a simplified data distribution" appears overstated. While the evidence shows CVAEs can learn conditional distributions in heterogeneous settings, it doesn't demonstrate this process is "easy." The evidence actually shows careful design considerations are needed, including proper sampling from prior distributions (Figure 7), specific architecture choices, and knowledge distillation procedures (Figure 2). The results in Figure 1 and Table 1 show CVAEs can be effective, but don't support characterizing the learning as "easy."

<score>4</score>

Justification:
1. The word "easily" is not supported by the evidence, which shows significant complexity in implementation and training:
- Multiple architectural considerations are discussed
- Specific sampling procedures from prior distributions are required
- Knowledge distillation and ensemble approaches needed for effectiveness

2. The evidence shows CVAEs can learn simplified distributions, but with important caveats:
- Performance depends on proper sampling near the center of prior distribution
- Different architectures and approaches needed for different scenarios
- Results vary across datasets and heterogeneity levels

3. The paper describes a sophisticated pipeline (Figure 2) and careful design choices, contradicting the notion that the learning process is "easy."

4. While CVAEs are shown to be effective, particularly in heterogeneous settings, this effectiveness comes from careful engineering rather than inherent simplicity in the learning process.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Because CVAEs can easily learn a simplified data distribution, both methods train CVAEs locally to capture the narrow conditional data distributions that arise in the high statistical heterogeneity setting.

The review comment to be evaluated is:

Strength:

-- The proposed solutions seem effective under the one-shot FL setting. The efficacy and efficiency are both demonstrated in the extensive experiments.
-- The writing is clear and easy to follow. The tables and figures are well-organized.

Weaknesses:

-- Constructing a generative model to generate samples for FL model training is not new. There are a few works utilizing a similar strategy in FL, for example:
Data-Free Knowledge Distillation for Heterogeneous Federated Learning, ICML 2021
Fine-tuning global model via data-free knowledge distillation for non-iid federated learning, CVPR 2022
Please make a comparison with those works

-- Some details are not clear enough for me. For example, in Eq 2, what is the formulation for g(.)?  Is this dissimilarity measured in the data-space or feature space?

The evidence to be evaluated is:A variational autoencoder (VAE) is a probabilistic generative model that attempts to learn the distribution of data samples (Kingma & Welling, 2014). A VAE is a latent variable method that models the joint distribution \(p_{\mathbf{\theta}}(\mathbf{x},\mathbf{z})\) of a data sample \(\mathbf{x}\in\mathcal{X}\subseteq\mathbb{R}^{D}\) and latent variable \(\mathbf{z}\in\mathcal{Z}\subseteq\mathbb{R}^{d}\), where usually \(d<<D\). This joint can be factorized as \(p_{\mathbf{\theta}}(\mathbf{x},\mathbf{z})=p_{\mathbf{\theta}}(\mathbf{x}[\mathbf{z}] p(\mathbf{z})\), where the prior \(p(\mathbf{z})\) is usually chosen to be a multivariate standard normal distribution, i.e., \(p(\mathbf{z})=\mathcal{N}(\mathbf{0},\mathbf{I})\). The posterior \(p_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x})\) is approximated via an inference model \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x})\) called the _encoder_ and the model for the conditional likelihood \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z})\) is called the _decoder_. In our case, both the encoder and decoder are deep neural networks parameterized by \(\mathbf{\phi}\) and \(\mathbf{\theta}\), respectively. Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\).

They address issues caused by high statistical heterogeneity by reframing the learning task using CVAEs and account for model heterogeneity by allowing different CVAE architectures across clients.

FedCVAE-KD trains a CVAE \(f_{\mathbf{w}^{k}}(\cdot)\) for every client \(k\in\mathcal{C}\) to convergence on their private local dataset by solving Equation 1; this CVAE is parameterized by \(\mathbf{w}^{k}=[\phi^{k},\mathbf{\theta}^{k}]\), with encoder \(E_{\mathbf{\phi}^{k}}(\cdot)\) and decoder \(D_{\mathbf{\theta}^{k}}(\cdot)\). Then, clients communicate their decoder weights \(\mathbf{\theta}^{k}\) and label distributions \(\bar{p}^{k}(\mathbf{y})\) to the server; in practice, this simply requires upload of client label counts as in Zhu et al. (2021). This completes the single communication round.

Intuitively, if a CVAE observes samples primarily from only a few of the \(K\) total classes (as is likely when data is highly heterogeneous), the CVAE will become an "expert" in the simplified data distribution over those few classes. To ensure each client only presents its highest-quality samples, we generate conditioning classes \(\mathbf{y}\) by sampling from the client's local label distribution, i.e., \(\mathbf{y}\sim\bar{p}^{k}(\mathbf{y})\). Then, to sample from client decoders, we sample a latent vector from the prior (i.e., \(\mathbf{z}\sim\mathcal{N}(\mathbf{0},\mathbf{I})\))1 and obtain synthetic data sample \(i\) from client \(k\) using \(\hat{\mathbf{x}}_{i}^{k}=D_{\mathbf{\theta}^{k}}(\mathbf{z}_{i}^{k};\mathbf{y}_{i }^{k})\).

CVAEs use a prior distribution over latent space to train the encoder and decoder models. While a multivariate standard normal distribution is typically used for convenience, any normal distribution is acceptable.

To demonstrate the efficacy of FedCVAE-Ens and FedCVAE-KD in the difficult setting of high statistical heterogeneity, we test on varying levels of \(\alpha\), from high (\(\alpha=0.05\)), to very high (\(\alpha=0.01\)), to extreme (\(\alpha=0.001\)) statistical heterogeneity. FedCVAE-Ens consistently outperforms all other methods, and FedCVAE-KD outperforms the baselines in nearly all datasets and levels of \(\alpha\) (the only exception is MNIST at the lowest level of statistical heterogeneity) as shown in Table 1.

While the baselines FedAvg and FedOneShot are very sensitive to the level of statistical heterogeneity, both FedCVAE-Ens and FedCVAE-KD demonstrate consistent performance across levels of \(\alpha\) (Table 1).

To simulate clients with diverse computational resources, we train both FedCVAE-Ens and FedCVAE-KD using two local CVAE architectures: the first as described in Section 4.1 and the second with one convolutional/deconvolutional block removed for the encoder/decoder, respectively.

Because the two architectures demonstrate similar generative capabilities, final server classifier accuracy is very similar when comparing homogeneous against heterogeneous local architectures (Figure 4).4 Notably, our KD procedure for FedCVAE-KD still performs well using heterogeneous models, indicating diverse architectures can organize latent space similarly enough to successfully translate this knowledge to a single decoder.

Statistical heterogeneity quickly emerged as a core issue within FL, with many studies focusing on maintaining high performance under very non-IID data.

Other works have used KD to circumvent issues associated with parameter averaging under non-IID data, focusing on leveraging auxiliary data (Lin et al., 2020; Sattler et al., 2021) or a generative model (Zhu et al., 2021; Zhang et al., 2022) to compactly capture client ensemble learning.

We are the first to apply CVAEs to one-shot FL with a focus on high statistical heterogeneity. In this paper, we proposed FedCVAE-Ens and FedCVAE-KD, data-free one-shot FL methods that reframe the local learning task using CVAEs. Both methods performed well given high statistical heterogeneity, demonstrated consistent performance with increasing numbers of clients, allow for model heterogeneity across clients, and can be extended to promote security. Extensive experimental results showed that FedCVAE-Ens and FedCVAE-KD substantially extended the state-of-the-art in one-shot FL under very high statistical heterogeneity, making way for more nuanced development in this difficult environment for distributed learning.

During training, the CVAE will largely observe latent vectors in the highest density region of the prior distribution; for a standard normal distribution, this is near the center \(\mathbf{\mu}=\mathbf{0}\). Latent vectors distant from the center will not generate high-quality samples when used with the trained decoder. As a demonstration, we train a centralized CVAE and sample both close to the center of the prior (i.e., \(\mathbf{z}_{i}\sim\mathcal{U}(-1,1)\)) and distant from the center of the prior (i.e., \(\mathbf{z}_{i}\sim\mathcal{U}(5,20)\)).

Input: Figure 4: Results with heterogeneous local models. “Homogeneous” uses the same CVAE architecture for all clients, whereas “heterogeneous” uses two architectures with similar generative capabilities.

Input: Figure 3: Example distributions of class labels for MNIST with m = 10 clients over multiple levels of statistical heterogeneity α. The size of each dot is proportional to the number of samples.

Input: Figure 1: Motivating our proposed methods, FEDCVAE-ENS and FEDCVAE-KD, using the MNIST dataset as an example. In cases of very high statistical heterogeneity, each client will only observe one or two of the ten available classes, as seen on the left where the size of each dot is proportional to the number of samples. For example, client 2 only observes 4’s and 7’s, resulting in a client decoder that can expertly generate these digits. Note that the columns are shown in order of conditioning class (digits 0-9). Similarly, client 4 is an expert in 3’s and 6’s. In FEDCVAE-KD, our lightweight knowledge distillation training procedure compacts local learning into a single server decoder, as evidenced by the high-quality samples from all available classes (digits 0-9). This server decoder can then be used for any downstream task, e.g., classification.

Input: Figure 7: CVAE samples generated using latent vectors distant from the center of the multivariate normal prior (top row) and close to the center (bottom row).

Input: Figure 2: The full pipeline for one of our proposed methods, FEDCVAE-KD. Here, E, D, and C represent “encoder,” “decoder,” and “classifier” models, respectively. First, clients train CVAEs on their private local datasets. Then, the server uses uploaded client decoder parameters and local label distributions to train a server decoder using knowledge distillation (KD). Finally, synthetic labeled samples from the server decoder are used to train a classifier.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the claim and evidence, I find the statement about CVAEs learning simplified data distributions to be well-supported. The evidence shows that when clients have highly heterogeneous data (seeing only 1-2 classes), their local CVAEs become "experts" in those specific classes, as demonstrated in Figure 1 where client-specific decoders generate high-quality samples for their observed classes. The mathematical foundations and experimental results support this claim about narrow conditional distributions. The claim is carefully worded and accurately reflects the evidence without exaggeration.

<score>1</score>

Justification:
1. Figure 1 directly demonstrates how client decoders become experts at generating specific digits they observed
2. Figure 3 shows the highly heterogeneous data distribution that creates these narrow class distributions
3. The mathematical framework explains how CVAEs learn conditional distributions
4. The claim avoids overgeneralization by specifically referring to "narrow conditional data distributions" in heterogeneous settings
5. Experimental results across different heterogeneity levels (α values) validate the CVAE's ability to learn these distributions

The review comments do not challenge this specific claim about CVAEs learning simplified distributions.