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

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

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

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

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

The claim to be assessed is:

To the best of our knowledge, we are the first to thoroughly address very high statistical heterogeneity in one-shot FL.

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: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)).

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

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

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.

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.

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.

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

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

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. Footnote 4: We choose not to baseline against FedOneShot, which supports heterogeneous local models, because our notion of “heterogeneous model” is different; FedOneShot supports heterogeneous local classifiers while our two methods defer the choice of classifier to after FL is complete and instead support heterogeneous local CVAEs.

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.

Guha et al. (2019) originally proposed one-shot FL and introduced two methods, one based on heuristic selection methods for client inclusion in the final ensemble and another that used KD with an auxiliary dataset for ensemble aggregation. Li et al. (2021) extended the use of KD with a hierarchical KD procedure with wide applicability to a variety of local model types. Although these methods obtain high accuracy, they rely on an auxiliary public dataset to support KD, which is inapplicable in data-free FL. Secure dataset transfer has been applied in several studies: Zhou et al. (2020) achieved this through dataset distillation, which requires a shared model architecture, and Shin et al. (2020) provided limited experiments using XOR-based data augmentation techniques. 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.

Wen et al. (2020) and Gu and Yang (2021) used VAEs to protect against malicious clients, but only included limited experimental results with respect to statistical heterogeneity, relied on multiple communication rounds, and, in the case of Wen et al. (2020), did not use KD for server-side aggregation. 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.

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 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. \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 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:
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 "To the best of our knowledge, we are the first to thoroughly address very high statistical heterogeneity in one-shot FL" appears well-supported. The evidence demonstrates:
- Systematic testing across multiple heterogeneity levels (α=0.001, 0.01, 0.05)
- Comprehensive experiments varying client numbers (m=5,10,20,50)
- Superior performance over baselines, especially in high heterogeneity
- Thorough literature review showing prior work's limitations with heterogeneity
- Clear experimental validation with detailed results

The review comments don't dispute this claim's validity, though they note some practical limitations.

<score>1</score>

The claim is well-stated and accurately reflects the evidence without exaggeration. The authors thoroughly tested and demonstrated their approach's effectiveness in handling statistical heterogeneity in one-shot FL, backed by comprehensive experimentation and clear comparisons to existing methods.


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:

Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity.

The evidence to be evaluated is:Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\). A CVAE is trained by maximizing the variational lower bound: \[\mathcal{L}(\mathbf{\phi},\mathbf{\theta};\mathbf{x},\mathbf{y})=-D_{\text{KL}}(q_{ \mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\mid\mid p(\mathbf{z}))+\mathbb{ E}_{q_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x},\mathbf{y})}[\log p_{\mathbf{\theta}}( \mathbf{x}|\mathbf{z},\mathbf{y})], \tag{1}\]

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

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

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

Output:
After reviewing the evidence, I find that the claim "Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity" is well-stated and supported by the evidence. The evidence comprehensively demonstrates how both FedCVAE-Ens and FedCVAE-KD utilize CVAEs to handle statistical heterogeneity:

1. The mathematical formulation shows how CVAEs are integrated into the approaches
2. Tables 1 and 2 demonstrate improved performance under high heterogeneity conditions
3. The results consistently show better handling of heterogeneous data compared to baselines
4. Visual evidence in Figure 1 illustrates how the CVAE-based approach effectively handles heterogeneous data distribution

<score>1</score>


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

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

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

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

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

The claim to be assessed is:

Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity.

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:Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\). A CVAE is trained by maximizing the variational lower bound: \[\mathcal{L}(\mathbf{\phi},\mathbf{\theta};\mathbf{x},\mathbf{y})=-D_{\text{KL}}(q_{ \mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\mid\mid p(\mathbf{z}))+\mathbb{ E}_{q_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x},\mathbf{y})}[\log p_{\mathbf{\theta}}( \mathbf{x}|\mathbf{z},\mathbf{y})], \tag{1}\]

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

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

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

Input:
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, the claim "Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity" is well-stated and accurately reflects the evidence. The paper demonstrates:

1. Detailed mathematical formulation of how CVAEs are used (Equation 1)
2. Clear explanation of how CVAEs help with heterogeneity by becoming "experts" in specific class distributions
3. Experimental results showing consistent performance across different heterogeneity levels (α values in Table 1)
4. Visual evidence in Figure 1 showing how CVAEs effectively handle heterogeneous data
5. Reviewer comments acknowledge the effectiveness of the approaches

The claim does not overreach and is firmly grounded in the presented theoretical foundation and empirical results.

<score>1</score>


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

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

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

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

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

The claim to be assessed is:

Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity.

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:Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\). A CVAE is trained by maximizing the variational lower bound: \[\mathcal{L}(\mathbf{\phi},\mathbf{\theta};\mathbf{x},\mathbf{y})=-D_{\text{KL}}(q_{ \mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\mid\mid p(\mathbf{z}))+\mathbb{ E}_{q_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x},\mathbf{y})}[\log p_{\mathbf{\theta}}( \mathbf{x}|\mathbf{z},\mathbf{y})], \tag{1}\]

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

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

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

Output:
Based on the evidence provided, including the detailed paper text, tables, figures, and reviewer comments, I find that the claim "Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity" is well-stated. The evidence strongly supports this through:

1. Clear mathematical formulation of the CVAE approach
2. Experimental results showing improved performance under high heterogeneity conditions
3. Detailed explanation of how CVAEs help handle heterogeneous data
4. Reviewer acknowledgment of the method's novelty and effectiveness

While the reviewer points out some technical concerns about CVAE implementation details, these don't contradict the fundamental claim about reframing the learning task using CVAEs.

<score>1</score>


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

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

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

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

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

The claim to be assessed is:

Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity.

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:Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\). A CVAE is trained by maximizing the variational lower bound: \[\mathcal{L}(\mathbf{\phi},\mathbf{\theta};\mathbf{x},\mathbf{y})=-D_{\text{KL}}(q_{ \mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\mid\mid p(\mathbf{z}))+\mathbb{ E}_{q_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x},\mathbf{y})}[\log p_{\mathbf{\theta}}( \mathbf{x}|\mathbf{z},\mathbf{y})], \tag{1}\]

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

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

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

Input:
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 "Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity" is well-stated and supported by the evidence. The paper clearly demonstrates that both FedCVAE-Ens and FedCVAE-KD utilize CVAEs at their core, showing how they handle heterogeneous data distributions across clients. The experimental results in Tables 1 and 2 validate their effectiveness in addressing high statistical heterogeneity, consistently outperforming baselines across different heterogeneity levels (α values). The reviewer's comments, while critical of other aspects, do not dispute this specific claim.

<score>1</score>


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

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

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

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

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

The claim to be assessed is:

Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity.

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:Conditional VAEs (CVAEs) extend the basic VAE by conditioning the encoder and decoder on the one-hot encoding of the class label \(\mathbf{y}\in\mathcal{Y}=\{1,2,...,K\}\) corresponding to data sample \(\mathbf{x}\), resulting in the conditional encoder \(q_{\mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\) and conditional decoder \(p_{\mathbf{\theta}}(\mathbf{x}|\mathbf{z},\mathbf{y})\). A CVAE is trained by maximizing the variational lower bound: \[\mathcal{L}(\mathbf{\phi},\mathbf{\theta};\mathbf{x},\mathbf{y})=-D_{\text{KL}}(q_{ \mathbf{\phi}}(\mathbf{z}|\mathbf{x},\mathbf{y})\mid\mid p(\mathbf{z}))+\mathbb{ E}_{q_{\mathbf{\theta}}(\mathbf{z}|\mathbf{x},\mathbf{y})}[\log p_{\mathbf{\theta}}( \mathbf{x}|\mathbf{z},\mathbf{y})], \tag{1}\]

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

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

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

Output:
I've reviewed the claim "Both approaches reframe the local learning task using a conditional variational autoencoder (CVAE) to address high statistical heterogeneity" against the provided evidence and review comments.

The evidence strongly supports this claim. The paper clearly demonstrates that both FedCVAE-Ens and FedCVAE-KD use CVAEs to handle statistical heterogeneity, with mathematical formulations and experimental results showing consistent performance across different heterogeneity levels (α values). The evidence shows that the CVAE approach helps clients become "experts" in their local data distribution while maintaining good overall performance. While the reviewer notes potential limitations with CVAE training on large images with limited data, this doesn't affect the accuracy of the original claim about reframing the learning task.

<score>1</score>