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:

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 \(d<<D\). 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 that "CVAEs can easily learn a simplified data distribution" and that "both methods train CVAEs locally to capture the narrow conditional data distributions" appears well-stated. The evidence shows that:

1. When data is highly heterogeneous, each client only observes a few classes (as shown in Figure 3), creating simplified local distributions.
2. Figure 1 demonstrates how client decoders become "experts" in their local classes (e.g., client 2 excels at 4's and 7's).
3. The theoretical framework and empirical results support that CVAEs effectively learn these narrow distributions, with consistent performance across heterogeneity levels.

<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 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 \(d<<D\). 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 that "CVAEs can easily learn a simplified data distribution" in the high statistical heterogeneity setting appears well-supported but slightly overstated. While the evidence shows CVAEs can effectively learn from limited class distributions (as demonstrated in Figure 1 where clients learn specific digits), the word "easily" overstates the complexity of the task. The evidence shows CVAEs require careful architectural design, proper latent space sampling, and specific training procedures. The reviewer also points out lack of theoretical justification for why the methods work well in this setting.

<score>3</score>

Justification:
1. The figures and results support that CVAEs can learn local distributions, but don't demonstrate it's "easy":
- Figure 1 shows clients successfully learning specific digit classes
- Figure 7 demonstrates the importance of proper latent vector sampling
- The heterogeneous architecture results in Figure 4 show consistent but not trivial performance

2. Key limitations noted in reviewer comments:
- "Aside from solid empirical performance, are there any intuitive/theoretical explanations as to why the proposed methods are well suited for...high heterogeneity FL?"
- Lack of theoretical justification for why these methods should perform better

3. The evidence suggests CVAEs are effective but require careful implementation:
- Specific sampling procedures from prior distribution
- Architectural considerations for encoder/decoder
- Knowledge distillation training procedures

The claim would be better stated by removing "easily" and more precisely describing the capability of CVAEs to learn from statistically heterogeneous data distributions under proper training conditions.


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 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 \(d<<D\). 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 that "CVAEs can easily learn a simplified data distribution" appears to be well-supported but slightly overstated. While the evidence demonstrates that CVAEs can effectively learn from limited class distributions in high statistical heterogeneity settings (shown in Figures 1 and 3), the term "easily" is not fully justified. The reviewer points out a significant limitation - training CVAEs locally can be challenging with large images and limited data samples. The experimental results focus on small images with substantial local data, which doesn't fully support the broad ease of learning claimed.

<score>3</score>

Justification:
1. The evidence shows CVAEs can learn simplified distributions:
- Figure 1 demonstrates successful learning of limited digit classes per client
- Table 1 (referenced in text) shows consistent performance across heterogeneity levels

2. The "easily" claim is overstated because:
- Reviewer highlights difficulties with large images and limited data samples
- Evidence only demonstrates success with small images (MNIST, FashionMNIST, SVHN)
- Local training requires substantial data per client
- The paper acknowledges specific architectural requirements and constraints

3. The review comment directly challenges the "easily" characterization by pointing out real-world limitations in medical imaging applications with large images and limited samples.


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:

More specifically, FedCVAE-KD aggregates the models using a lightweight knowledge distillation procedure; client decoders are teachers, and the server decoder is the student.

The evidence to be evaluated is: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). Typically, the student model is trained by minimizing the discrepancy between student and teacher logits generated using a suitable auxiliary dataset (Hinton et al., 2015); KL-divergence is often chosen as the measure of discrepancy.

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).

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.

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.

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 \(\hat{\mathbf{x}}^{k}\).

While we do not explore the extended communication setting, we note that FedCVAE-KD extends naturally by communicating the server decoder parameters obtained through KD to all clients and repeating the outlined procedure for non-terminal communication rounds.

In the case of FedCVAE-Ens and FedCVAE-KD, an attacker who intercepts all client decoders and local label distributions should not be able to generate the high quality samples necessary to train a high quality classifier.

The server decoder for FedCVAE-KD has the same architecture as the client CVAEs by default, although this is not strictly necessary because FedCVAE-KD supports heterogeneous CVAE architectures.

CVAE training uses binary cross entropy and mean squared error for the reconstruction term of the objective for grayscale and RGB images, respectively; we use the same reconstruction objective for the KD loss (\(g(\cdot)\) in Equation 2).

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 server decoder matches that which is described in Section 4.1 but can be chosen arbitrarily.

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.

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.

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. Li et al. (2021) extended the use of KD with a hierarchical KD procedure with wide applicability to a variety of local model types.

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.

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.

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 \(\mathcal{D}_{\text{Ens}}:=\mathcal{D}_{\text{Ens}}^{1}\cup\mathcal{D}_{\text{ Ens}}^{2}\cup...\cup\mathcal{D}_{\text{Ens}}^{m}\)

While parameter averaging may seem like a reasonable approach for client decoder aggregation in FedCVAE-KD, it generates qualitatively poor samples (Figure 8) and fails to train a high-accuracy classifier (Table 6). 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).

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 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 that the statement "FedCVAE-KD aggregates the models using a lightweight knowledge distillation procedure; client decoders are teachers, and the server decoder is the student" is well-supported by the evidence. The papers explicitly describes this teacher-student relationship and KD procedure in detail, showing how client decoders act as teachers to train a student server decoder by minimizing reconstruction loss. Figure 2 clearly illustrates this process, and the results in Figure 8 demonstrate its effectiveness. The claim accurately represents the method 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:

More specifically, FedCVAE-KD aggregates the models using a lightweight knowledge distillation procedure; client decoders are teachers, and the server decoder is the student.

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: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). Typically, the student model is trained by minimizing the discrepancy between student and teacher logits generated using a suitable auxiliary dataset (Hinton et al., 2015); KL-divergence is often chosen as the measure of discrepancy.

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).

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.

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.

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 \(\hat{\mathbf{x}}^{k}\).

While we do not explore the extended communication setting, we note that FedCVAE-KD extends naturally by communicating the server decoder parameters obtained through KD to all clients and repeating the outlined procedure for non-terminal communication rounds.

In the case of FedCVAE-Ens and FedCVAE-KD, an attacker who intercepts all client decoders and local label distributions should not be able to generate the high quality samples necessary to train a high quality classifier.

The server decoder for FedCVAE-KD has the same architecture as the client CVAEs by default, although this is not strictly necessary because FedCVAE-KD supports heterogeneous CVAE architectures.

CVAE training uses binary cross entropy and mean squared error for the reconstruction term of the objective for grayscale and RGB images, respectively; we use the same reconstruction objective for the KD loss (\(g(\cdot)\) in Equation 2).

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 server decoder matches that which is described in Section 4.1 but can be chosen arbitrarily.

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.

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.

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. Li et al. (2021) extended the use of KD with a hierarchical KD procedure with wide applicability to a variety of local model types.

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.

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.

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 \(\mathcal{D}_{\text{Ens}}:=\mathcal{D}_{\text{Ens}}^{1}\cup\mathcal{D}_{\text{ Ens}}^{2}\cup...\cup\mathcal{D}_{\text{Ens}}^{m}\)

While parameter averaging may seem like a reasonable approach for client decoder aggregation in FedCVAE-KD, it generates qualitatively poor samples (Figure 8) and fails to train a high-accuracy classifier (Table 6). 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).

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 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:
I'll evaluate whether the claim "FedCVAE-KD aggregates the models using a lightweight knowledge distillation procedure; client decoders are teachers, and the server decoder is the student" is well-stated or overstated.

Summary:
The evidence strongly supports this claim. The text explicitly describes this relationship, showing how client decoders act as teachers to train a student server decoder through knowledge distillation. The process is well-documented with mathematical formulations (Equation 2) and clear explanations of the KD procedure. Figure 2 visually demonstrates this teacher-student relationship in the pipeline. The effectiveness is demonstrated through comparative results in Figure 8, showing superior performance over parameter averaging. The "lightweight" nature is supported by the one-shot communication design.

<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:

More specifically, FedCVAE-KD aggregates the models using a lightweight knowledge distillation procedure; client decoders are teachers, and the server decoder is the student.

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: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). Typically, the student model is trained by minimizing the discrepancy between student and teacher logits generated using a suitable auxiliary dataset (Hinton et al., 2015); KL-divergence is often chosen as the measure of discrepancy.

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).

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.

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.

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 \(\hat{\mathbf{x}}^{k}\).

While we do not explore the extended communication setting, we note that FedCVAE-KD extends naturally by communicating the server decoder parameters obtained through KD to all clients and repeating the outlined procedure for non-terminal communication rounds.

In the case of FedCVAE-Ens and FedCVAE-KD, an attacker who intercepts all client decoders and local label distributions should not be able to generate the high quality samples necessary to train a high quality classifier.

The server decoder for FedCVAE-KD has the same architecture as the client CVAEs by default, although this is not strictly necessary because FedCVAE-KD supports heterogeneous CVAE architectures.

CVAE training uses binary cross entropy and mean squared error for the reconstruction term of the objective for grayscale and RGB images, respectively; we use the same reconstruction objective for the KD loss (\(g(\cdot)\) in Equation 2).

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 server decoder matches that which is described in Section 4.1 but can be chosen arbitrarily.

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.

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.

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. Li et al. (2021) extended the use of KD with a hierarchical KD procedure with wide applicability to a variety of local model types.

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.

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.

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 \(\mathcal{D}_{\text{Ens}}:=\mathcal{D}_{\text{Ens}}^{1}\cup\mathcal{D}_{\text{ Ens}}^{2}\cup...\cup\mathcal{D}_{\text{Ens}}^{m}\)

While parameter averaging may seem like a reasonable approach for client decoder aggregation in FedCVAE-KD, it generates qualitatively poor samples (Figure 8) and fails to train a high-accuracy classifier (Table 6). 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).

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 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 that "FedCVAE-KD aggregates models using lightweight knowledge distillation with client decoders as teachers and server decoder as student" appears well-stated and accurately reflects the evidence. The evidence clearly describes this exact relationship, showing how client decoders act as teachers conveying knowledge to a student server decoder through KD training samples. Figure 2 provides a clear visualization of this process. The review comment, while raising important questions about other aspects, does not dispute this specific teacher-student relationship in the KD procedure.

<score>1</score>

Justification:
1. The evidence directly supports the claim through explicit descriptions of the teacher-student relationship
2. Figure 2 illustrates this exact process
3. The KD procedure is described in detail showing how client decoders (teachers) transfer knowledge to server decoder (student)
4. The reviewer's technical concerns focus on other aspects but don't contradict this specific claim
5. The description "lightweight" is justified as it requires only one round of communication and a straightforward KD training procedure


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:

More specifically, FedCVAE-KD aggregates the models using a lightweight knowledge distillation procedure; client decoders are teachers, and the server decoder is the student.

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: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). Typically, the student model is trained by minimizing the discrepancy between student and teacher logits generated using a suitable auxiliary dataset (Hinton et al., 2015); KL-divergence is often chosen as the measure of discrepancy.

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).

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.

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.

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 \(\hat{\mathbf{x}}^{k}\).

While we do not explore the extended communication setting, we note that FedCVAE-KD extends naturally by communicating the server decoder parameters obtained through KD to all clients and repeating the outlined procedure for non-terminal communication rounds.

In the case of FedCVAE-Ens and FedCVAE-KD, an attacker who intercepts all client decoders and local label distributions should not be able to generate the high quality samples necessary to train a high quality classifier.

The server decoder for FedCVAE-KD has the same architecture as the client CVAEs by default, although this is not strictly necessary because FedCVAE-KD supports heterogeneous CVAE architectures.

CVAE training uses binary cross entropy and mean squared error for the reconstruction term of the objective for grayscale and RGB images, respectively; we use the same reconstruction objective for the KD loss (\(g(\cdot)\) in Equation 2).

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 server decoder matches that which is described in Section 4.1 but can be chosen arbitrarily.

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.

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.

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. Li et al. (2021) extended the use of KD with a hierarchical KD procedure with wide applicability to a variety of local model types.

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.

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.

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 \(\mathcal{D}_{\text{Ens}}:=\mathcal{D}_{\text{Ens}}^{1}\cup\mathcal{D}_{\text{ Ens}}^{2}\cup...\cup\mathcal{D}_{\text{Ens}}^{m}\)

While parameter averaging may seem like a reasonable approach for client decoder aggregation in FedCVAE-KD, it generates qualitatively poor samples (Figure 8) and fails to train a high-accuracy classifier (Table 6). 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).

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 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 "FedCVAE-KD aggregates the models using a lightweight knowledge distillation procedure; client decoders are teachers, and the server decoder is the student" appears well-stated and accurately reflects the evidence. The papers shows:

1. Clear description of the KD process where client decoders act as teachers and server decoder as student
2. Visual evidence through figures showing how KD transfers knowledge from client decoders to server decoder
3. Empirical results demonstrating KD's effectiveness compared to parameter averaging
4. Technical details of the KD loss function and procedure

The reviewer comments don't dispute this specific claim about the KD procedure. The claim stays focused on describing the technical approach without overstating its capabilities or significance.

<score>1</score>