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:

We show that without knowing the center of the prior, an eavesdropping attacker cannot train a performant classifier, thus promoting pipeline security.

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: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_).

We discuss privacy- and security-promoting extensions in Appendix B and Section 3.3, respectively. 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.

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 \(\hat{\mathbf{x}}_{i}^{k}=D_{\mathbf{\theta}^{k}}(\mathbf{z}_{i}^{k};\mathbf{y}_{i }^{k})\).

In practice, we find it useful to focus on the highest density region of the prior and instead sample from a truncated standard normal distribution with tight symmetric bounds. 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 \(\mathbf{\theta}^{S}\).

We define a secure pipeline as one where an outside attacker who obtains transferred data cannot train a performant classifier (Zhou et al., 2020). 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.

To promote security, we propose to shift the center of the prior distribution \(\mathbf{\mu}\) to a random position in real space (i.e., \(\mathbf{\mu}\in\mathbb{R}^{d}\)), which can be communicated offline or via encryption methods between server and clients (Zhou et al., 2020). As shown in Figure 7 (Appendix B), sampling latent vectors too far from the center of the normal prior produces qualitatively poor data samples, deterring eavesdropping attackers who have no knowledge of \(\mathbf{\mu}\).

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

**Promoting Security.** We verify the effectiveness of our proposed distribution shift extension for securing the uploaded information. Suppose an eavesdropping attacker is able to intercept the label distributions, decoder weights, and decoder architectures from all clients during upload. Without knowledge of the shared center of the multivariate normal prior \(\mathbf{\mu}\), we show that training a performant classifier is infeasible because it is difficult to extract high-quality samples from the client decoders. In particular, even when the attacker samples latent vectors \(\mathbf{z}\) from a broad region which overlaps with the high-density region of the prior (i.e., a uniform distribution centered on \(\mathbf{\mu}\)), the accuracy of the classifier trained on the resulting samples degrades sharply as the sampling region grows (Figure 5). Even a good guess of \(\mathcal{U}(-10,10)\) for a normal prior of \(\mathcal{N}(\mathbf{0},\mathbf{I})\) results in a \(3-30\%\) point decrease in accuracy depending on the dataset. A more realistic guess of \(\mathcal{U}(-1000,1000)\) results in a \(33-67\%\) point decrease. Therefore, this simple FedCVAE-Ens and FedCVAE-KD extension reduces eavesdropping attackers' capacity to extract high-quality samples from uploaded decoders or train a performant downstream model, reducing communication risks.

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., \(\mathbf{z}_{i}\sim\mathcal{U}(5,20)\)).

Uploading client label distributions \(\hat{p}^{k}(\mathbf{y})\) may generate additional privacy concerns. One potential solution is to mask the precise label counts for each client by adding noise before upload as in Zhang et al. (2022); to achieve this, we draw noise from a normal distribution \(\epsilon_{c}\sim\mathcal{N}(0,\gamma\cdot n_{k})\) such that the "strength" (variance) of the noise applied to class \(c\) is in proportion \(\gamma\) to the total number of training samples for client \(k\). Noise is applied to the training sample count for each class for a given client before uploading this information to the server.

As \(\gamma\to\infty\), information from the uploaded label distribution disappears; when \(\gamma=0\), the exact local label distributions are communicated. When adding a modest amount of noise to the client label distributions (i.e., \(\gamma\leq 0.1\)), accuracy for both FedCVAE-Ens and FedCVAE-KD is barely affected compared to upload with no noise; see Table 8 for \(\gamma>0\) and refer to the \(\alpha=0.01\) in Table 1 for \(\gamma=0\). The notion of uploading and harnessing client label distributions in FL is new (Zhu et al., 2021; Zhang et al., 2022) and quantifying the privacy risks that label distributions might induce is an open problem which could benefit from focused development.

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 5: Results for our proposed security-promoting extension at high heterogeneity (α = 0.05). We show the accuracy for a classifier trained on samples from the intercepted client decoders and using client label distributions when the center of the normal prior is unknown. The sampling bounds represent the parameters of the uniform distribution used for latent vector sampling, i.e., ±100 represents the distribution U(−100, 100). The prior is a multivariate standard normalN (0, I).

Input: Table 8: Performance of our proposed methods with noise added to the uploaded client label distributions. Results show the average test accuracy across 5 seeds for the random noise ± one standard deviation.

Input: Figure 9: The effect of the noise proportion γ on an example data partition at α = 0.01, m = 10 clients, and on MNIST. The original partition is in yellow (γ = 0). The size of each dot is proportional to the number of samples.

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

Output:
Based on my review of the claim "We show that without knowing the center of the prior, an eavesdropping attacker cannot train a performant classifier, thus promoting pipeline security," I find this to be somewhat overstated based on the available evidence.

While Figure 5 shows degradation in classifier accuracy as sampling bounds increase, the reviewer raises valid concerns about the security guarantees. The evidence shows that even with broad sampling (U[-10,10]), the accuracy drop is only 3-30%, suggesting some attack capability remains. The reviewer correctly points out that a sophisticated attacker could potentially infer the global mean. Additionally, there's no formal proof or guarantee provided against sufficiently powerful adversaries.

<score>4</score>

Justification:
1. The claim makes an absolute statement ("cannot train") when the evidence shows reduced but not eliminated performance
2. The reviewer highlights lack of formal security guarantees
3. Evidence shows some classifier performance remains possible even with incorrect prior center
4. The potential for attackers to infer the center is not addressed
5. The security mechanism relies on security through obscurity rather than proven cryptographic guarantees


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:

We show that without knowing the center of the prior, an eavesdropping attacker cannot train a performant classifier, thus promoting pipeline security.

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: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_).

We discuss privacy- and security-promoting extensions in Appendix B and Section 3.3, respectively. 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.

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 \(\hat{\mathbf{x}}_{i}^{k}=D_{\mathbf{\theta}^{k}}(\mathbf{z}_{i}^{k};\mathbf{y}_{i }^{k})\).

In practice, we find it useful to focus on the highest density region of the prior and instead sample from a truncated standard normal distribution with tight symmetric bounds. 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 \(\mathbf{\theta}^{S}\).

We define a secure pipeline as one where an outside attacker who obtains transferred data cannot train a performant classifier (Zhou et al., 2020). 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.

To promote security, we propose to shift the center of the prior distribution \(\mathbf{\mu}\) to a random position in real space (i.e., \(\mathbf{\mu}\in\mathbb{R}^{d}\)), which can be communicated offline or via encryption methods between server and clients (Zhou et al., 2020). As shown in Figure 7 (Appendix B), sampling latent vectors too far from the center of the normal prior produces qualitatively poor data samples, deterring eavesdropping attackers who have no knowledge of \(\mathbf{\mu}\).

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

**Promoting Security.** We verify the effectiveness of our proposed distribution shift extension for securing the uploaded information. Suppose an eavesdropping attacker is able to intercept the label distributions, decoder weights, and decoder architectures from all clients during upload. Without knowledge of the shared center of the multivariate normal prior \(\mathbf{\mu}\), we show that training a performant classifier is infeasible because it is difficult to extract high-quality samples from the client decoders. In particular, even when the attacker samples latent vectors \(\mathbf{z}\) from a broad region which overlaps with the high-density region of the prior (i.e., a uniform distribution centered on \(\mathbf{\mu}\)), the accuracy of the classifier trained on the resulting samples degrades sharply as the sampling region grows (Figure 5). Even a good guess of \(\mathcal{U}(-10,10)\) for a normal prior of \(\mathcal{N}(\mathbf{0},\mathbf{I})\) results in a \(3-30\%\) point decrease in accuracy depending on the dataset. A more realistic guess of \(\mathcal{U}(-1000,1000)\) results in a \(33-67\%\) point decrease. Therefore, this simple FedCVAE-Ens and FedCVAE-KD extension reduces eavesdropping attackers' capacity to extract high-quality samples from uploaded decoders or train a performant downstream model, reducing communication risks.

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., \(\mathbf{z}_{i}\sim\mathcal{U}(5,20)\)).

Uploading client label distributions \(\hat{p}^{k}(\mathbf{y})\) may generate additional privacy concerns. One potential solution is to mask the precise label counts for each client by adding noise before upload as in Zhang et al. (2022); to achieve this, we draw noise from a normal distribution \(\epsilon_{c}\sim\mathcal{N}(0,\gamma\cdot n_{k})\) such that the "strength" (variance) of the noise applied to class \(c\) is in proportion \(\gamma\) to the total number of training samples for client \(k\). Noise is applied to the training sample count for each class for a given client before uploading this information to the server.

As \(\gamma\to\infty\), information from the uploaded label distribution disappears; when \(\gamma=0\), the exact local label distributions are communicated. When adding a modest amount of noise to the client label distributions (i.e., \(\gamma\leq 0.1\)), accuracy for both FedCVAE-Ens and FedCVAE-KD is barely affected compared to upload with no noise; see Table 8 for \(\gamma>0\) and refer to the \(\alpha=0.01\) in Table 1 for \(\gamma=0\). The notion of uploading and harnessing client label distributions in FL is new (Zhu et al., 2021; Zhang et al., 2022) and quantifying the privacy risks that label distributions might induce is an open problem which could benefit from focused development.

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 5: Results for our proposed security-promoting extension at high heterogeneity (α = 0.05). We show the accuracy for a classifier trained on samples from the intercepted client decoders and using client label distributions when the center of the normal prior is unknown. The sampling bounds represent the parameters of the uniform distribution used for latent vector sampling, i.e., ±100 represents the distribution U(−100, 100). The prior is a multivariate standard normalN (0, I).

Input: Table 8: Performance of our proposed methods with noise added to the uploaded client label distributions. Results show the average test accuracy across 5 seeds for the random noise ± one standard deviation.

Input: Figure 9: The effect of the noise proportion γ on an example data partition at α = 0.01, m = 10 clients, and on MNIST. The original partition is in yellow (γ = 0). The size of each dot is proportional to the number of samples.

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 "without knowing the center of the prior, an eavesdropping attacker cannot train a performant classifier" appears to be overstated. While Figure 5 shows clear degradation in classifier accuracy as sampling bounds increase, the evidence indicates that attackers can still achieve some level of performance, albeit reduced. For example, with U(-10,10) sampling, the accuracy drop is only 3-30%, and even with U(-1000,1000), the classifier still maintains some performance above random chance. The claim would be better stated by specifying the degree of performance degradation rather than implying complete inability to train a classifier.

<score>4</score>

Justification:
1. The evidence shows degraded but not zero performance:
- With U(-10,10) sampling: Only 3-30% accuracy decrease
- With U(-1000,1000) sampling: 33-67% decrease, but still above random chance

2. The claim uses absolute language ("cannot train") when the evidence shows reduced but not eliminated capability

3. Figure 7 qualitatively demonstrates degraded sample quality with distant sampling, but does not show complete inability to generate usable samples

4. The reviewer comments do not specifically address this security claim, so were not factored into the assessment

5. A more precise claim would specify the degree of security protection rather than implying complete prevention of attacks


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:

We show that without knowing the center of the prior, an eavesdropping attacker cannot train a performant classifier, thus promoting pipeline security.

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: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_).

We discuss privacy- and security-promoting extensions in Appendix B and Section 3.3, respectively. 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.

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 \(\hat{\mathbf{x}}_{i}^{k}=D_{\mathbf{\theta}^{k}}(\mathbf{z}_{i}^{k};\mathbf{y}_{i }^{k})\).

In practice, we find it useful to focus on the highest density region of the prior and instead sample from a truncated standard normal distribution with tight symmetric bounds. 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 \(\mathbf{\theta}^{S}\).

We define a secure pipeline as one where an outside attacker who obtains transferred data cannot train a performant classifier (Zhou et al., 2020). 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.

To promote security, we propose to shift the center of the prior distribution \(\mathbf{\mu}\) to a random position in real space (i.e., \(\mathbf{\mu}\in\mathbb{R}^{d}\)), which can be communicated offline or via encryption methods between server and clients (Zhou et al., 2020). As shown in Figure 7 (Appendix B), sampling latent vectors too far from the center of the normal prior produces qualitatively poor data samples, deterring eavesdropping attackers who have no knowledge of \(\mathbf{\mu}\).

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

**Promoting Security.** We verify the effectiveness of our proposed distribution shift extension for securing the uploaded information. Suppose an eavesdropping attacker is able to intercept the label distributions, decoder weights, and decoder architectures from all clients during upload. Without knowledge of the shared center of the multivariate normal prior \(\mathbf{\mu}\), we show that training a performant classifier is infeasible because it is difficult to extract high-quality samples from the client decoders. In particular, even when the attacker samples latent vectors \(\mathbf{z}\) from a broad region which overlaps with the high-density region of the prior (i.e., a uniform distribution centered on \(\mathbf{\mu}\)), the accuracy of the classifier trained on the resulting samples degrades sharply as the sampling region grows (Figure 5). Even a good guess of \(\mathcal{U}(-10,10)\) for a normal prior of \(\mathcal{N}(\mathbf{0},\mathbf{I})\) results in a \(3-30\%\) point decrease in accuracy depending on the dataset. A more realistic guess of \(\mathcal{U}(-1000,1000)\) results in a \(33-67\%\) point decrease. Therefore, this simple FedCVAE-Ens and FedCVAE-KD extension reduces eavesdropping attackers' capacity to extract high-quality samples from uploaded decoders or train a performant downstream model, reducing communication risks.

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., \(\mathbf{z}_{i}\sim\mathcal{U}(5,20)\)).

Uploading client label distributions \(\hat{p}^{k}(\mathbf{y})\) may generate additional privacy concerns. One potential solution is to mask the precise label counts for each client by adding noise before upload as in Zhang et al. (2022); to achieve this, we draw noise from a normal distribution \(\epsilon_{c}\sim\mathcal{N}(0,\gamma\cdot n_{k})\) such that the "strength" (variance) of the noise applied to class \(c\) is in proportion \(\gamma\) to the total number of training samples for client \(k\). Noise is applied to the training sample count for each class for a given client before uploading this information to the server.

As \(\gamma\to\infty\), information from the uploaded label distribution disappears; when \(\gamma=0\), the exact local label distributions are communicated. When adding a modest amount of noise to the client label distributions (i.e., \(\gamma\leq 0.1\)), accuracy for both FedCVAE-Ens and FedCVAE-KD is barely affected compared to upload with no noise; see Table 8 for \(\gamma>0\) and refer to the \(\alpha=0.01\) in Table 1 for \(\gamma=0\). The notion of uploading and harnessing client label distributions in FL is new (Zhu et al., 2021; Zhang et al., 2022) and quantifying the privacy risks that label distributions might induce is an open problem which could benefit from focused development.

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 5: Results for our proposed security-promoting extension at high heterogeneity (α = 0.05). We show the accuracy for a classifier trained on samples from the intercepted client decoders and using client label distributions when the center of the normal prior is unknown. The sampling bounds represent the parameters of the uniform distribution used for latent vector sampling, i.e., ±100 represents the distribution U(−100, 100). The prior is a multivariate standard normalN (0, I).

Input: Table 8: Performance of our proposed methods with noise added to the uploaded client label distributions. Results show the average test accuracy across 5 seeds for the random noise ± one standard deviation.

Input: Figure 9: The effect of the noise proportion γ on an example data partition at α = 0.01, m = 10 clients, and on MNIST. The original partition is in yellow (γ = 0). The size of each dot is proportional to the number of samples.

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 appears to be moderately overstated. While the evidence shows that an attacker's ability to train a performant classifier is significantly reduced without knowing the center of the prior distribution, it doesn't completely prevent it. Figure 5 demonstrates that even with broad sampling bounds (±10), classifiers still achieve 20-50% accuracy across datasets. The security is proportional to how far the attacker samples from the true center - it creates difficulties but doesn't make it strictly "impossible" as implied by the strong wording "cannot train a performant classifier."

<score>4</score>

Justification:
1. The evidence shows degraded but not zero performance:
- With ±10 sampling bounds: ~55% accuracy on MNIST, ~50% on FashionMNIST, ~50% on SVHN
- Even with ±1000 bounds, accuracy is reduced by 33-67% but not eliminated

2. More measured language like "significantly impairs" or "makes it difficult" would better reflect that:
- Security depends on sampling region size
- Some classifier performance remains possible
- It's a probabilistic rather than absolute guarantee

3. The review comments don't specifically address this security claim, so weren't factored into the scoring.

The claim would be better stated by acknowledging these limitations and the gradual degradation of performance rather than suggesting a complete inability to train classifiers.


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:

In sum, our contributions are two one-shot FL methods targeted to the high statistical heterogeneity setting that: (1) perform substantially better than other baseline methods in this setting, (2) demonstrate invariance to the number of clients, (3) are data-free and can be applied to any downstream task requiring a labeled dataset, (4) allow for heterogeneous local model architectures, and (5) extend to promote pipeline security.

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

In the federated setting, we have a set of clients \(\mathcal{C}\), with \(m=|\mathcal{C}|\) clients in total. Each client \(k\) has a local private dataset \(\mathcal{D}^{k}=\{(\mathbf{x}_{i},\mathbf{y}_{i})\}_{i=1}^{n_{k}}\), with \(n_{k}=|\mathcal{D}^{k}|\) representing the number of data samples belonging to user \(k\). Traditional FL methods assume each client has a local differentiable model \(f_{\mathbf{w}^{k}}(\cdot)\), usually a deep neural network parameterized by \(\mathbf{w}^{k}\).

However, in the one-shot FL setting communication is restricted to a single round, which severely limits communication costs but also increases the difficulty of the distributed learning task (Guha et al., 2019). Notably, existing one-shot FL methods either ignore the issue of statistical heterogeneity (i.e., Guha et al. (2019)), fail to comprehensively explore the effect of statistical heterogeneity on performance (i.e., Shin et al. (2020) and Li et al. (2021)), or degrade substantially at even moderate levels of statistical heterogeneity (i.e., Zhou et al. (2020) and Zhang et al. (2021)). We jointly propose FedCVAE-Ens and FedCVAE-KD, one-shot FL methods that do not require an auxiliary public dataset for server-side training (they are _data-free_). They address issues caused by high statistical heterogeneity by reframing the learning task using CVAEs and account for model heterogeneity by allowing different CVAE architectures across clients.

We discuss privacy- and security-promoting extensions in Appendix B and Section 3.3, respectively. 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 \(\hat{\mathbf{x}}^{k}\).

Because FedCVAE-KD ensembles client decoders to create a labeled dataset \(\mathcal{D}_{\text{Ens}}\) to train the server decoder, each client can have a unique CVAE model architecture, accommodating each client's computational limitations. Furthermore, the decision of the classifier architecture can be deferred until after FL is finished and will not affect the learning procedure. FedCVAE-KD can be applied to any task that requires a labeled dataset, which is more general than classification; there is no commitment to a particular terminal task before learning occurs.

We define a secure pipeline as one where an outside attacker who obtains transferred data cannot train a performant classifier (Zhou et al., 2020). 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.

To promote security, we propose to shift the center of the prior distribution \(\mathbf{\mu}\) to a random position in real space (i.e., \(\mathbf{\mu}\in\mathbb{R}^{d}\)), which can be communicated offline or via encryption methods between server and clients (Zhou et al., 2020). As shown in Figure 7 (Appendix B), sampling latent vectors too far from the center of the normal prior produces qualitatively poor data samples, deterring eavesdropping attackers who have no knowledge of \(\mathbf{\mu}\).

To simulate statistical heterogeneity, we use the Dirichlet distribution to generate disjoint non-IID client training datasets as in Hsu et al. (2019) and Lin et al. (2020). Specifically, we sample \(\mathbf{p}^{k}\sim Dir(\alpha)\) and allocate a \(\mathbf{p}^{k}_{i}\) proportion of class \(i\) to client \(k\). The parameter \(\alpha\) controls the level of non-IID-ness, with a lower \(\alpha\) inducing more skewed label distributions across clients. To illustrate the effect of \(\alpha\) on dataset partitions across clients, we visualize the distribution of labels across \(m=10\) clients for \(\alpha=\{0.001,0.01,0.05\}\) in Figure 3.

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

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

Unless otherwise stated, we use \(m=10\) clients, \(\alpha=0.01\) (very heterogeneous), and report average test accuracy across 5 seeded parameter initializations \(\pm\) one standard deviation. The data partition is fixed unless otherwise stated. Following Zhu et al. (2021), we distribute \(50\%\) of the available training data to clients for MNIST and FashionMNIST, and \(100\%\) for SVHN. All available test data is used to evaluate the final server classifier (or ensemble for FedOneShot). We adopt the same convolutional classifier architecture as McMahan et al. (2017) for all methods.

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.

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

Because FL applications often include many participating clients (Li et al., 2020), we evaluate several values for number of clients (\(m=\{5,10,20,50\}\)). While both FedAvg and FedOneShot struggle when many clients are present, Table 2 shows that FedCVAE-Ens and FedCVAE-KD perform consistently across the number of clients, with the only exception being FedCVAE-KD for SVHN. Even though it is typical to observe FL methods' accuracy degrade with increasing numbers of clients (Zhang et al., 2021), FedAvg and FedOneShot are unstable with no clear decrease in accuracy, which we ascribe to the highly variable partitions generated at high levels of statistical heterogeneity. Experiments varying the dataset partitions reveal high variation in accuracy for FedAvg and FedOneShot, whereas both FedCVAE-Ens and FedCVAE-KD exhibit consistent accuracy (Table 5 in Appendix C).

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

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

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.

**Promoting Security.** We verify the effectiveness of our proposed distribution shift extension for securing the uploaded information. Suppose an eavesdropping attacker is able to intercept the label distributions, decoder weights, and decoder architectures from all clients during upload. Without knowledge of the shared center of the multivariate normal prior \(\mathbf{\mu}\), we show that training a performant classifier is infeasible because it is difficult to extract high-quality samples from the client decoders. In particular, even when the attacker samples latent vectors \(\mathbf{z}\) from a broad region which overlaps with the high-density region of the prior (i.e., a uniform distribution centered on \(\mathbf{\mu}\)), the accuracy of the classifier trained on the resulting samples degrades sharply as the sampling region grows (Figure 5).

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

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

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

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

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

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

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

**Privacy.** A private pipeline is one that does not leak private client data to other participating clients or the server. van den Burg and Williams (2021) define a probabilistic generative model's propensity to reproduce samples observed in the training data as memorization, and prove that ensuring a particular level of differential privacy (DP) can bound memorization in probabilistic generative models (including CVAEs). Thus, beyond the normal privacy guarantees attributable to DP, employing FL DP-estimation techniques (i.e., Geyer et al. (2017)) also ensures low memorization across the FedCVAE-Ens and FedCVAE-KD pipelines, further enhancing the privacy of our proposed methods.

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

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).

While accuracy for both FedCVAE-Ens and FedCVAE-KD degrade with less data per client, they both consistently perform better than FedAvg and FedOneShot across all tested percent subsets of the training data.

Uploading client label distributions \(\hat{p}^{k}(\mathbf{y})\) may generate additional privacy concerns. One potential solution is to mask the precise label counts for each client by adding noise before upload as in Zhang et al. (2022); to achieve this, we draw noise from a normal distribution \(\epsilon_{c}\sim\mathcal{N}(0,\gamma\cdot n_{k})\) such that the "strength" (variance) of the noise applied to class \(c\) is in proportion \(\gamma\) to the total number of training samples for client \(k\). Noise is applied to the training sample count for each class for a given client before uploading this information to the server. We visualize the effect of noise on client label distributions for several levels of \(\gamma\) in Figure 9. As \(\gamma\to\infty\), information from the uploaded label distribution disappears; when \(\gamma=0\), the exact local label distributions are communicated. When adding a modest amount of noise to the client label distributions (i.e., \(\gamma\leq 0.1\)), accuracy for both FedCVAE-Ens and FedCVAE-KD is barely affected compared to upload with no noise; see Table 8 for \(\gamma>0\) and refer to the \(\alpha=0.01\) in Table 1 for \(\gamma=0\). The notion of uploading and harnessing client label distributions in FL is new (Zhu et al., 2021; Zhang et al., 2022) and quantifying the privacy risks that label distributions might induce is an open problem which could benefit from focused development. \begin{table}
\begin{tabular}{l l|c c|c c} \hline \hline  & \# of Clients & FedAvg & FedOneShot & FedCVAE-KD (ours) & FedCVAE-Ens (ours) \\ \hline \multirow{3}{*}{MNIST} & \(m=5\) & \(42.34\pm 1.75\) & \(42.97\pm 1.54\) & \(80.19\pm 1.76\) & \(92.81\pm 2.16\) \\  & \(m=10\) & \(58.29\pm 2.83\) & \(41.15\pm 0.70\) & \(82.01\pm 1.61\) & \(93.83\pm 1.53\) \\  & \(m=20\) & \(37.14\pm 3.87\) & \(32.22\pm 0.71\) & \(81.93\pm 1.75\) & \(93.52\pm 0.86\) \\  & \(m=50\) & \(28.26\pm 7.98\) & \(35.62\pm 0.66\) & \(77.68\pm 1.39\) & \(87.56\pm 1.44\) \\ \hline \multirow{3}{*}{FashionMNIST} & \(m=5\) & \(38.51\pm 2.40\) & \(32.23\pm 1.68\) & \(68.01\pm 1.56\) & \(73.70\pm 1.93\) \\  & \(m=10\) & \(45.85\pm 2.95\) & \(37.63\pm 0.53\) & \(69.97\pm 1.63\) & \(76.62\pm 1.61\) \\  & \(m=20\) & \(27.49\pm 4.77\) & \(24.72\pm 1.20\) & \(71.28\pm 1.17\) & \(76.51\pm 1.38\) \\  & \(m=50\) & \(31.91\pm 2.20\) & \(41.01\pm 2.49\) & \(69.25\pm 1.13\) & \(76.13\pm 2.00\) \\ \hline \multirow{3}{*}{SVHN} & \(m=5\) & \(40.61\pm 0.64\) & \(42.05\pm 1.31\) & \(57.17\pm 2.56\) & \(65.72\pm 2.17\) \\  & \(m=10\) & \(25.12\pm 2.07\) & \(31.91\pm 1.26\) & \(55.97\pm 0.38\) & \(65.50\pm 2.28\) \\ \cline{1-1}  & \(m=20\) & \(26.99\pm 1.15\) & \(10.68\pm 0.70\) & \(51.80\pm 2.75\) & \(65.54\pm 1.89\) \\ \cline{1-1}  & \(m=50\) & \(19.59\pm 0.00\) & \(30.20\pm 0.64\) & \(40.03\pm 2.62\) & \(64.81\pm 2.44\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of four one-shot FL methods over three datasets and across four numbers of clients \(m\). Best results for each dataset and each level of \(m\) are in purple, with second best results in yellow.

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

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 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 5: Results for our proposed security-promoting extension at high heterogeneity (α = 0.05). We show the accuracy for a classifier trained on samples from the intercepted client decoders and using client label distributions when the center of the normal prior is unknown. The sampling bounds represent the parameters of the uniform distribution used for latent vector sampling, i.e., ±100 represents the distribution U(−100, 100). The prior is a multivariate standard normalN (0, I).

Input: Table 8: Performance of our proposed methods with noise added to the uploaded client label distributions. Results show the average test accuracy across 5 seeds for the random noise ± one standard deviation.

Input: Figure 9: The effect of the noise proportion γ on an example data partition at α = 0.01, m = 10 clients, and on MNIST. The original partition is in yellow (γ = 0). The size of each dot is proportional to the number of samples.

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

Input: Figure 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 most aspects of the claim are supported by substantial experimental results, but there is some overstatement in how definitively certain points are presented. The evidence demonstrates strong performance in heterogeneous settings and with varying numbers of clients, though there are some exceptions (e.g., FedCVAE-KD's performance decline with SVHN at higher client numbers). The security extension is demonstrated but not as comprehensively as suggested. While the methods are data-free, the claim could better acknowledge some limitations and qualifiers.

<score>2</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:

In sum, our contributions are two one-shot FL methods targeted to the high statistical heterogeneity setting that: (1) perform substantially better than other baseline methods in this setting, (2) demonstrate invariance to the number of clients, (3) are data-free and can be applied to any downstream task requiring a labeled dataset, (4) allow for heterogeneous local model architectures, and (5) extend to promote pipeline security.

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

In the federated setting, we have a set of clients \(\mathcal{C}\), with \(m=|\mathcal{C}|\) clients in total. Each client \(k\) has a local private dataset \(\mathcal{D}^{k}=\{(\mathbf{x}_{i},\mathbf{y}_{i})\}_{i=1}^{n_{k}}\), with \(n_{k}=|\mathcal{D}^{k}|\) representing the number of data samples belonging to user \(k\). Traditional FL methods assume each client has a local differentiable model \(f_{\mathbf{w}^{k}}(\cdot)\), usually a deep neural network parameterized by \(\mathbf{w}^{k}\).

However, in the one-shot FL setting communication is restricted to a single round, which severely limits communication costs but also increases the difficulty of the distributed learning task (Guha et al., 2019). Notably, existing one-shot FL methods either ignore the issue of statistical heterogeneity (i.e., Guha et al. (2019)), fail to comprehensively explore the effect of statistical heterogeneity on performance (i.e., Shin et al. (2020) and Li et al. (2021)), or degrade substantially at even moderate levels of statistical heterogeneity (i.e., Zhou et al. (2020) and Zhang et al. (2021)). We jointly propose FedCVAE-Ens and FedCVAE-KD, one-shot FL methods that do not require an auxiliary public dataset for server-side training (they are _data-free_). They address issues caused by high statistical heterogeneity by reframing the learning task using CVAEs and account for model heterogeneity by allowing different CVAE architectures across clients.

We discuss privacy- and security-promoting extensions in Appendix B and Section 3.3, respectively. 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 \(\hat{\mathbf{x}}^{k}\).

Because FedCVAE-KD ensembles client decoders to create a labeled dataset \(\mathcal{D}_{\text{Ens}}\) to train the server decoder, each client can have a unique CVAE model architecture, accommodating each client's computational limitations. Furthermore, the decision of the classifier architecture can be deferred until after FL is finished and will not affect the learning procedure. FedCVAE-KD can be applied to any task that requires a labeled dataset, which is more general than classification; there is no commitment to a particular terminal task before learning occurs.

We define a secure pipeline as one where an outside attacker who obtains transferred data cannot train a performant classifier (Zhou et al., 2020). 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.

To promote security, we propose to shift the center of the prior distribution \(\mathbf{\mu}\) to a random position in real space (i.e., \(\mathbf{\mu}\in\mathbb{R}^{d}\)), which can be communicated offline or via encryption methods between server and clients (Zhou et al., 2020). As shown in Figure 7 (Appendix B), sampling latent vectors too far from the center of the normal prior produces qualitatively poor data samples, deterring eavesdropping attackers who have no knowledge of \(\mathbf{\mu}\).

To simulate statistical heterogeneity, we use the Dirichlet distribution to generate disjoint non-IID client training datasets as in Hsu et al. (2019) and Lin et al. (2020). Specifically, we sample \(\mathbf{p}^{k}\sim Dir(\alpha)\) and allocate a \(\mathbf{p}^{k}_{i}\) proportion of class \(i\) to client \(k\). The parameter \(\alpha\) controls the level of non-IID-ness, with a lower \(\alpha\) inducing more skewed label distributions across clients. To illustrate the effect of \(\alpha\) on dataset partitions across clients, we visualize the distribution of labels across \(m=10\) clients for \(\alpha=\{0.001,0.01,0.05\}\) in Figure 3.

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

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

Unless otherwise stated, we use \(m=10\) clients, \(\alpha=0.01\) (very heterogeneous), and report average test accuracy across 5 seeded parameter initializations \(\pm\) one standard deviation. The data partition is fixed unless otherwise stated. Following Zhu et al. (2021), we distribute \(50\%\) of the available training data to clients for MNIST and FashionMNIST, and \(100\%\) for SVHN. All available test data is used to evaluate the final server classifier (or ensemble for FedOneShot). We adopt the same convolutional classifier architecture as McMahan et al. (2017) for all methods.

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.

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

Because FL applications often include many participating clients (Li et al., 2020), we evaluate several values for number of clients (\(m=\{5,10,20,50\}\)). While both FedAvg and FedOneShot struggle when many clients are present, Table 2 shows that FedCVAE-Ens and FedCVAE-KD perform consistently across the number of clients, with the only exception being FedCVAE-KD for SVHN. Even though it is typical to observe FL methods' accuracy degrade with increasing numbers of clients (Zhang et al., 2021), FedAvg and FedOneShot are unstable with no clear decrease in accuracy, which we ascribe to the highly variable partitions generated at high levels of statistical heterogeneity. Experiments varying the dataset partitions reveal high variation in accuracy for FedAvg and FedOneShot, whereas both FedCVAE-Ens and FedCVAE-KD exhibit consistent accuracy (Table 5 in Appendix C).

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

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

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.

**Promoting Security.** We verify the effectiveness of our proposed distribution shift extension for securing the uploaded information. Suppose an eavesdropping attacker is able to intercept the label distributions, decoder weights, and decoder architectures from all clients during upload. Without knowledge of the shared center of the multivariate normal prior \(\mathbf{\mu}\), we show that training a performant classifier is infeasible because it is difficult to extract high-quality samples from the client decoders. In particular, even when the attacker samples latent vectors \(\mathbf{z}\) from a broad region which overlaps with the high-density region of the prior (i.e., a uniform distribution centered on \(\mathbf{\mu}\)), the accuracy of the classifier trained on the resulting samples degrades sharply as the sampling region grows (Figure 5).

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

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

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

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

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

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

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

**Privacy.** A private pipeline is one that does not leak private client data to other participating clients or the server. van den Burg and Williams (2021) define a probabilistic generative model's propensity to reproduce samples observed in the training data as memorization, and prove that ensuring a particular level of differential privacy (DP) can bound memorization in probabilistic generative models (including CVAEs). Thus, beyond the normal privacy guarantees attributable to DP, employing FL DP-estimation techniques (i.e., Geyer et al. (2017)) also ensures low memorization across the FedCVAE-Ens and FedCVAE-KD pipelines, further enhancing the privacy of our proposed methods.

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

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).

While accuracy for both FedCVAE-Ens and FedCVAE-KD degrade with less data per client, they both consistently perform better than FedAvg and FedOneShot across all tested percent subsets of the training data.

Uploading client label distributions \(\hat{p}^{k}(\mathbf{y})\) may generate additional privacy concerns. One potential solution is to mask the precise label counts for each client by adding noise before upload as in Zhang et al. (2022); to achieve this, we draw noise from a normal distribution \(\epsilon_{c}\sim\mathcal{N}(0,\gamma\cdot n_{k})\) such that the "strength" (variance) of the noise applied to class \(c\) is in proportion \(\gamma\) to the total number of training samples for client \(k\). Noise is applied to the training sample count for each class for a given client before uploading this information to the server. We visualize the effect of noise on client label distributions for several levels of \(\gamma\) in Figure 9. As \(\gamma\to\infty\), information from the uploaded label distribution disappears; when \(\gamma=0\), the exact local label distributions are communicated. When adding a modest amount of noise to the client label distributions (i.e., \(\gamma\leq 0.1\)), accuracy for both FedCVAE-Ens and FedCVAE-KD is barely affected compared to upload with no noise; see Table 8 for \(\gamma>0\) and refer to the \(\alpha=0.01\) in Table 1 for \(\gamma=0\). The notion of uploading and harnessing client label distributions in FL is new (Zhu et al., 2021; Zhang et al., 2022) and quantifying the privacy risks that label distributions might induce is an open problem which could benefit from focused development. \begin{table}
\begin{tabular}{l l|c c|c c} \hline \hline  & \# of Clients & FedAvg & FedOneShot & FedCVAE-KD (ours) & FedCVAE-Ens (ours) \\ \hline \multirow{3}{*}{MNIST} & \(m=5\) & \(42.34\pm 1.75\) & \(42.97\pm 1.54\) & \(80.19\pm 1.76\) & \(92.81\pm 2.16\) \\  & \(m=10\) & \(58.29\pm 2.83\) & \(41.15\pm 0.70\) & \(82.01\pm 1.61\) & \(93.83\pm 1.53\) \\  & \(m=20\) & \(37.14\pm 3.87\) & \(32.22\pm 0.71\) & \(81.93\pm 1.75\) & \(93.52\pm 0.86\) \\  & \(m=50\) & \(28.26\pm 7.98\) & \(35.62\pm 0.66\) & \(77.68\pm 1.39\) & \(87.56\pm 1.44\) \\ \hline \multirow{3}{*}{FashionMNIST} & \(m=5\) & \(38.51\pm 2.40\) & \(32.23\pm 1.68\) & \(68.01\pm 1.56\) & \(73.70\pm 1.93\) \\  & \(m=10\) & \(45.85\pm 2.95\) & \(37.63\pm 0.53\) & \(69.97\pm 1.63\) & \(76.62\pm 1.61\) \\  & \(m=20\) & \(27.49\pm 4.77\) & \(24.72\pm 1.20\) & \(71.28\pm 1.17\) & \(76.51\pm 1.38\) \\  & \(m=50\) & \(31.91\pm 2.20\) & \(41.01\pm 2.49\) & \(69.25\pm 1.13\) & \(76.13\pm 2.00\) \\ \hline \multirow{3}{*}{SVHN} & \(m=5\) & \(40.61\pm 0.64\) & \(42.05\pm 1.31\) & \(57.17\pm 2.56\) & \(65.72\pm 2.17\) \\  & \(m=10\) & \(25.12\pm 2.07\) & \(31.91\pm 1.26\) & \(55.97\pm 0.38\) & \(65.50\pm 2.28\) \\ \cline{1-1}  & \(m=20\) & \(26.99\pm 1.15\) & \(10.68\pm 0.70\) & \(51.80\pm 2.75\) & \(65.54\pm 1.89\) \\ \cline{1-1}  & \(m=50\) & \(19.59\pm 0.00\) & \(30.20\pm 0.64\) & \(40.03\pm 2.62\) & \(64.81\pm 2.44\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of four one-shot FL methods over three datasets and across four numbers of clients \(m\). Best results for each dataset and each level of \(m\) are in purple, with second best results in yellow.

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

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 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 5: Results for our proposed security-promoting extension at high heterogeneity (α = 0.05). We show the accuracy for a classifier trained on samples from the intercepted client decoders and using client label distributions when the center of the normal prior is unknown. The sampling bounds represent the parameters of the uniform distribution used for latent vector sampling, i.e., ±100 represents the distribution U(−100, 100). The prior is a multivariate standard normalN (0, I).

Input: Table 8: Performance of our proposed methods with noise added to the uploaded client label distributions. Results show the average test accuracy across 5 seeds for the random noise ± one standard deviation.

Input: Figure 9: The effect of the noise proportion γ on an example data partition at α = 0.01, m = 10 clients, and on MNIST. The original partition is in yellow (γ = 0). The size of each dot is proportional to the number of samples.

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

Input: Figure 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 appears to be generally well-supported but slightly overstated in a few areas. While the methods do show strong performance with statistical heterogeneity and support for heterogeneous architectures, the claim of "substantial" improvement needs some qualification - performance varies by dataset and conditions. The security extension, while promising, shows degrading performance as sampling bounds increase. The method's data-free nature and extensibility to downstream tasks are well-demonstrated. The invariance to client numbers claim is mostly but not entirely supported, as FedCVAE-KD shows some degradation with SVHN.

<score>2</score>