From: ICLR.cc/2023/Conference/Program_Chairs
title: Paper Decision
decision: Accept: poster
metareview:_summary,_strengths_and_weaknesses: This paper designs communication-efficient federated learning using random sparsification of the network weights (without training the weights). The main idea of the work is to find a good subnetwork by estimating a sparsifying probabilistic mask. Each client runs gradient descent to estimate the best mask and only a binary sample from the estimated probability vector on each client is communicated back to the server.  Bayesian estimator is used to produce a global model from the received random masks from clients.


+ The main strength of this work is in the presented empirical improvements on the considered benchmarks. The proposed method is shown to outperform all competitors both in terms of test accuracy and communication efficiency. 

+ The committee recognizes the idea and contribution of transferring mask by sampling (which is communication efficient) and reconstruction at server. 

- The committee has concerns that the paper selects a set of ideas and a lot of major design choices that are not well justified (but reviewers agree that some are addressed in the author responses). In particular, there are complaints about lack of understanding of why the method performs well and whether it will generalize to other problems. Although the empirical behaviors are studied, they are not on complex models or real-world data and thus may not extend to newer models or datasets.  Along this direction, in the current form of this paper, the issue of simplistic benchmarks is unaddressed even with the added ResNet-18 experiments. 

- Reviewers have raised concerns about the technical novelty of this work. The aggregation strategy and the stochastic mask estimation have been proposed before in prior works. 

- There is also a minor concern that the proposed method does not reduce the download volume. But the reviewers agree that upload volume reduction is more relevant given internet speeds around the world.

justification_for_why_not_higher_score: - The committee has concerns that the paper selects a set of ideas and a lot of major design choices that are not well justified (but reviewers agree that some are addressed in the author responses). In particular, there are complaints about lack of understanding of why the method performs well and whether it will generalize to other problems. Although the empirical behaviors are studied, they are not on complex models or real-world data and thus may not extend to newer models or datasets.  Along this direction, in the current form of this paper, the issue of simplistic benchmarks is unaddressed even with the added ResNet-18 experiments. 

- Reviewers have raised concerns about the technical novelty of this work. The aggregation strategy and the stochastic mask estimation have been proposed before in prior works. 

- There is also a minor concern that the proposed method does not reduce the download volume. But the reviewers agree that upload volume reduction is more relevant given internet speeds around the world.

justification_for_why_not_lower_score: + The main strength of this work is in the presented empirical improvements on the considered benchmarks. The proposed method is shown to outperform all competitors both in terms of test accuracy and communication efficiency. 

+ The committee recognizes the idea and contribution of transferring mask by sampling (which is communication efficient) and reconstruction at server. 
note_from_PC: if the above contains the word "oral" or "spotlight" please see: "oral" presentation means -> notable-top-5% and "spotlight" means -> notable-top-25%. As stated in our emails, we are disassociating presentation type from AC recommendations

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: Thank you for the increased score! 
comment: We thank the reviewer for carefully reviewing our paper, revisiting their evaluation upon our revision and response, and raising their score!

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: Thank you for the increased score! 
comment: We thank the reviewer for carefully reviewing our paper, revisiting their evaluation upon our revision and response, and raising their score!

From: ICLR.cc/2023/Conference/Paper1274/Reviewer_iZTn
title: Response to rebuttal
comment: I would like to thank the authors for the extensive response that addresses most of my concerns. While, I am still not convinced about the technical novelty of this work (e.g., [2] proposes the same aggregation strategy and [1] also employs stochastic mask estimation), I am willing to increase my score to a 6 due to the improved clarity on the bias-correction mechanism, the intuitions on the Beta priors and the new experiments.

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: Thank you for the increased score!
comment: We thank the reviewer for revisiting their evaluation upon our response, and raising their score!

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: Thank you for the increased score!
comment: We thank the reviewer for the careful review of our paper, revisiting their evaluation upon our revision and response, and raising their score!

From: ICLR.cc/2023/Conference/Paper1274/Reviewer_Un54
title: Thank you for the rebuttal
comment: I have read the rebuttal, the authors have addressed my concerns and I raise my score.

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 4/4] Thank you for the feedback and suggestions! Let us know if there are any remaining concerns.
comment: ### **Bias-correction mechanism**
Again, we are very glad to notice that the reviewer provides us with meaningful insights into our work and exposition. We realize that how the bias-correction scheme works in practice was indeed not clear. As correctly stated by the reviewer, the proposed bias-correction scheme described in Appendix C is based on the derived formula, which depends on $\sigma$, $\theta$, and $C$, i.e., the clipping extremes. To apply the scheme in our simulation, we consider $\sigma$ and $C$ as secret information between the server and the clients. Indeed, these two parameters are set and secretly shared at the beginning of the training process, and never modified or shared during the process. Then, at the server, we sample points $\theta_1, \dots,  \theta_Q$ of the function $E [\hat{\theta}]$ for the chosen and fixed values of $\sigma$ and $C$, for $Q$-many values of $\theta$ (depending on the needed precision, in all our scenarios  $Q = 100$ was enough, i.e., with a precision of 0.01). Once the server obtains an empirical estimate of  $\hat{\theta}$ at the end of one round, it maps that value to the closest $\theta_i$. Basically, by knowing $\sigma$ and $C$, we invert the map by using a lookup table approach, and given that the range $[c, 1-c]$ of $\hat{\theta}$ is not so large, it is possible to efficiently solve it by just storing $Q=100$ values. Thanks to the accurate comments of the reviewer, we improved the clarity of our scheme by explicitly adding these passages to the manuscript in Appendix C.

----------
We again thank the reviewer for the valuable suggestions and questions that helped us improve the manuscript. We hope to have addressed the reviewer's concerns. We are happy to engage in further discussion if there are any remaining concerns. If our response is satisfactory, we kindly ask the reviewer to revisit their evaluation of our submission.

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 3/4] Thank you for the feedback and suggestions! We tried to address your concerns. 
comment: ### **Beta priors $\alpha$ and $\beta$ and resetting strategy**
We thank the reviewer for the valuable suggestion and for pointing out that the resetting policy could be conveyed more clearly. We added Section 4.3, where an ablation study on the resetting frequency is performed, and insights into the adopted strategy are explicitly reported. We thus sincerely thank the reviewer for raising meaningful concerns about our method explanation and motivation, which helped us increase the quality and clarity of the exposition. 

As briefly mentioned in the old version of the paper, the Bayesian aggregation strategy is particularly beneficial with partial participation. The reason is when the server resets the priors, the new updates are aggregated without considering the history, i.e., the values of the previous updates. On the contrary, if the server does not reset the priors, the new global model updates, i.e., the modes of the Beta distributions, contain information on the previous rounds, thus aggregating the data among clients over time. Specifically, we argue that, if, with IID data split and full client participation, the mask updates contain meaningful and large information; then with partial participation and non-IID data split, the information gathered during one round may be too skewed (due to the skewed distributions of the local datasets) to provide meaningful updates. Consequently, being able to aggregate the information on several rounds in the updates helped in providing more meaningful global updates to the clients before continuing with local training. We called this value, i.e., the number of rounds before resetting the priors, with $\gamma$. We claim that to have a rough estimate of a good value for $\gamma$, the important quantity to consider is the client participation ratio $\rho$. In particular, if $\rho$ is 50%, a good value for $\gamma$ should be ~2 or ~3, as on average, at least 2 rounds are needed to collect data from all clients if we consider uniform client sampling. The ablation analyses in Section 4.3 also report the case in which $\gamma$ is equal to the total number of rounds, i.e., no resetting during the whole training process. As guessed by the reviewer, in this case, the initial updates (which may be very noisy and skewed in single rounds) add up quickly to steer the Beta priors behind the Bernoulli parameters toward some specific values, e.g., very high values of some $\alpha$‘s and/or $\beta$‘s, that are sub-optimal in terms of the final performance. However, if further training rounds suggest new updates on the probability masks ( for instance, a parameter $\theta_i$ that is close to one is actually supposed to move close to 0), then it becomes difficult and slow for the server to invert the beliefs on those parameters and update the global mask accordingly. For this reason, a resetting step before a general round t is helpful to start again from a uniform prior, thus aggregating the data coming from the clients to synthesize the new Bernoulli parameters in the probability masks $\theta$, and providing fresh global updates. 

Regarding the specific values for $\alpha$ and $\beta$, we chose them to be equal, i.e., uniform prior, and specifically equal to 1. The motivation behind the uniform prior is that we do not want to inject any prior information before seeing the new updates (after the resetting).

Please find in the new Section 4.3 of the revised paper, the explanation of the concepts discussed here, corroborated by an ablation study on the resetting schemes.

----------------------
Please see the rest of our response in the fourth box "[Response 4/4]..."

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 2/4] Thank you for the feedback and suggestions! We tried to address your concerns. 
comment: ### **Download cost**
We now start addressing the other comments and suggestions raised by the reviewer. First of all, we want to comment on the following sentence from the reviewer’s summary:

*“The download cost of FedPM is the same as FedAvg (since the probabilities are real values and one for each weight).”*

As observed by the reviewer, it is true that in the server-to-client downlink communication,  updates are not compressed since they represent the new probability mask $\theta^{g,t}$ which are, in general, real numbers. However, notice that the maximum (worst-case) number of bits needed to losslessly describe one parameter’s global update $\theta^{g,t}_i$ is equal to K, where K is the number of sampled clients. Therefore, when the number of clients participating in each round is small enough (smaller than the precision of the framework to represent a real value), the server could represent the updated global probability mask $\theta^{g,t}$ by communicating only the binary samples from the clients at the previous round $m^{k, t}$. Then each client can recover the updated global Bernoulli parameter with the same aggregation method the server is using. As the reviewer correctly pointed out, our work focuses primarily on the client-to-server communication cost as it has been shown to be the main communication bottleneck. More concretely, please check the survey in [3], Section 3.5:

*“Among them, (a)[i.e., compression during upload] has the potential for the most significant practical impact in terms of total runtime. This is both because clients’ connections generally have slower upload than download bandwidth* – and thus there is more to be gained, compared to (b)[i.e., compression during download] – and because the effects of averaging across many clients can enable more aggressive lossy compression schemes.”*

and also Section 2.2.2 and Section 2.2.3 from [4]:

*“The BS [the Base Station, i.e., the central authority in general (e.g., a server)],  broadcasts the global prediction model parameters to all users in the downlink. Due to the high power of the BS and large downlink bandwidth, we ignore the downlink time.”*

We also confirm the reviewer’s point regarding the comparison between FedAvg and our framework FedPM. Indeed in FedAvg, each client communicates a real number per parameter, while our framework requires only one-bit communication per parameter from the clients.

### **Not all communication-efficient methods provide computation efficiency or compressed final model**
The reviewer correctly stated in their summary that our framework improves both communication and computation. We would like to emphasize that the computation efficiency is not a byproduct of all communication-efficient frameworks, for instance, entropy encoding and decoding the model updates would make the communication efficient; however, the computation cost would stay the same. Similarly, outputting a small-sized final model is not an immediate outcome of communication efficiency and indeed, many communication-efficient methods output a noncompressed large final model, resulting in a high cost for representing the final model. So, we want to make it very clear that computation efficiency at inference time, small final model, and communication efficiency during training are separate contributions of our framework and should be appreciated individually. 

### **Straight-through gradient estimator**
We thank the reviewer for pointing out the missing explicit reference to the straight-through estimator to compute the gradient on the mask parameters. We’ve updated the manuscript accordingly. 

### **Bernoulli Function**
We agree that the expression Bernoulli function might have been unclear as it was not previously defined in the manuscript. We were referring to the Bernoulli sampling operation, and we clarified the terminology in the revised paper.

### **Random Weights Re-scaling at Initialization**
Regarding the $\sigma$ values adopted to sample the random weights, we did not scale the values considering the sparsity level.

The references [1] [2] [3] and [4] are provided in the first response "[Response 1/4]...".

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Please see the rest of our response in the third box "[Response 3/4]..."

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 1/4] Thank you for the feedback and suggestions! We tried to address your concerns. 
comment: We thank the reviewer for their meticulous review, for putting effort into understanding the details of our work, and for recognizing the strengths of our framework, which rely on its simplicity and superior empirical performance over baselines. We try to address their concerns in detail below.

### **Novelty:**
We first would like to respond to the reviewer’s comment on the novelty of our work as we sincerely hope that the reviewer would agree that the framework we are promising is a **unique** one that achieves higher accuracy, smaller bitrate, faster convergence, and smaller final model size than existing baselines, consistently across all the experiments (including the new results on ResNet-18 in the revised paper). The practical benefits and the simplicity of our framework are already praised by the reviewer. However,  they argue that it is a mixture of previously discovered methods. If we do agree that FedPM is built on top of older ideas, we strongly believe that the way those building blocks were designed, optimized, and merged together to obtain a communication-efficient federated learning strategy, outperforming state-of-the-art baselines, such as QSGD, DRIVE, EDEN, on different tasks, datasets, and scenarios, present itself a clear element of novelty, specifically in the original aspect of **exploiting and discovering** the fact that in a resource-constrained environment (i.e., limited communication and storage budget), the information encoded in the topology of random networks is enough to obtain better performance when compared to the best compression methods applied to the original dense models. Please also see Reviewer Un54’s comment praising the novel aspect of our work. **We believe, if this was a straightforward combination of previous methods without any additional insights, then this framework would have been proposed way earlier, given that** 
 -  **it outperforms the state-of-the art methods in several aspects that many researchers work on providing improvements for, and** 
 - **the most recent of the papers listed by the reviewer dates back more than a year ago.** 

Moreover, we do agree on the similarities of our work with the methods in [1] and [2], but still, there are substantial differences among the proposed analyses, e.g., in [1], the adopted Bayesian model is not the Beta-Bernoulli model used in our framework, and more importantly, both [1] and [2] apply those methods on the weights’/gradients’ estimation, and not on a stochastic mask optimization problem. 

[1] Louizos et al., “An Expectation-Maximization Perspective on Federated Learning,” arXiv:2111.10.192, 2021.

[2] Ferreira et al., “Bayesian SignSGD Optimizer for Federated Learning, “ 1st NeurIPS Workshop on New Frontiers in Federated Learning (NFFL 2021).

[3] P. Kairouz, H.B. McMahan et al., “Advances and Open Problems in Federated Learning,” Foundations and Trends in Machine Learning, Vol 14, Issue 1-2, June 2021.

[4] Z. Yang et al., “Delay Minimization for Federated Learning Over Wireless Communication Networks,” International Conference on Machine Learning (ICML) 2020.

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Please see the rest of our response in the second box "[Response 2/4]..."

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 2/2] Thank you for the feedback and suggestions! Let us know if you have any remaining concerns.
comment: ### **Ablations for Bayesian aggregation and motivation behind the resetting strategy:**
We thank the reviewer for the meaningful question, and for suggesting a supporting ablation study that helped us improve the manuscript.  As briefly mentioned in the paper, the Bayesian aggregation strategy is particularly beneficial with partial participation. Indeed, whenever the server resets the priors, the new updates are aggregated without considering the history, i.e., the values of the previous updates. On the contrary, if the server does not reset the priors, the new global model updates, i.e., the modes of the Beta distributions, contain information on the previous rounds, thus aggregating the data among clients, and over time. Specifically, we argue that, if the mask updates contain meaningful and large information with IID data split and full client participation, then with partial participation and non-IID data split, the information gathered during one round may be too skewed (due to the skewed distributions of the local datasets) to provide meaningful updates. Consequently, being able to aggregate the information on several rounds in the updates helped in providing more meaningful global updates to the clients before continuing with local training. We denoted this value, i.e., the number of rounds before resetting the priors, with $\gamma$. We claim that to have a rough estimate of a good value for $\gamma$, the important quantity to consider is the client participation ratio $\rho$. In particular, if $\rho$ is 50%, a good value for $\gamma$ should be ~2 or ~3, as on average, at least 2 rounds are needed to collect data from all clients if we consider uniform client sampling. 

However, we do agree with the reviewer’s comments, and we clarified these concepts in Section 4.3 in the revised manuscript, devoted to providing a more detailed explanation of the Bayesian aggregation strategy and an ablation study to answer the following questions:

1. Is Bayesian aggregation strategy really necessary?

2. What is the effect of resetting frequency on the final accuracy and convergence? 
 
In our ablation experiments, we study the training behavior with various $\gamma$ and $\rho$ values and demonstrate that Bayesian aggregation is indeed helpful when $\rho<1$, i.e., only a fraction of the clients participate in each round. Our results in Figure 4 also show how the resetting frequency $\gamma$ affects the final accuracy and convergence. For instance, $\gamma=1$ corresponds to resetting the priors at every iteration, which is equivalent to the aggregation method presented in Section 3.1.2. On the other extreme, $\gamma=200$ indicates that the priors are never reset (the total number of rounds is 200). It is seen that $\gamma=1$ curves fluctuate significantly and never converge to the best accuracy in any setting, while $\gamma=200$ curves look smoother but converge to the lowest accuracy in all settings. Hence, $\gamma$ should be carefully tuned, we give a rule of thumb for this in Section 4.3.

### **Clarification on the initialization code:**
We sincerely thank the reviewer for the very nice comments and observations on our work and manuscript quality, and for the detailed analysis of our effort, including the inspection of the uploaded code. As correctly pointed out by the reviewer, $\sigma$'s in the values of the weight distribution present a term $e$ in place of $\sqrt{2}$. This particular change did not affect the results and was the result of an empirical ablation study we performed in the weight distributions. However, as similar analyses had been previously done in several papers (see [1] and [3]), we did not report the results in the manuscript, being consistent with the old results. Of course, it is fundamental for the final performance that the range of the distribution values is of the same order of magnitude as the standard deviation of the Kaiming Normal distribution, as suggested by the reviewer. 

### **Parameter configurations:**
We thank the reviewer for the suggestions. We added a new zip file of the code with additional params_{}.yaml files that could be used to reproduce our results. The right params_{}.yaml file should be specified in main.py. 

The references [1] [2] and [3] are provided in the previous response.

--------------
We again thank the reviewer for the careful reading of our manuscript and for the valuable suggestions that improved our work. We hope our additional experiments with ResNet models, ablation studies, and a larger number of clients resolve the reviewer's concerns. We are happy to engage in further discussions if there is any remaining issue. If our response is satisfactory for the reviewer, we kindly ask them to revisit their score, encouraged by the reviewer's following statement in their review: 

*"I am happy to raise my score should the authors provide experiments with more modern network architectures and FL settings with a larger number of clients."*

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 1/2] Thank you for the feedback and suggestions! We tried to address your concerns. 
comment: We thank the reviewer for reading and understanding the details of our paper, appreciating the novelty of our work, and the exhaustive set of experiments with different levels of data heterogeneity and partial client participation. Based on the comments and the questions, the reviewer clearly read our work in great detail and appreciated the strengths of our work. We followed the reviewer's suggestions and conducted several additional experiments that we explain below.

### **Additional experiments with larger models and larger number of users:**
We do agree with the reviewer that we may have considered a larger set of clients and wider models. However, given the novelty of the method and the peculiarity of the training framework, we decided to start analyzing the performance of the framework in simpler yet practical scenarios. While the analyzed CNN models are inspired by the works in [1][2], we also introduced additional larger models like CONV10. 

Nevertheless, given the legitimate requests of the reviewer, we ran additional experiments with N=100 clients in the system, and with a wider ResNet-18 network. The results with N=100 clients are also added to Table 1 and Table3 (under $\rho=0.2$ column), and it can be verified that our framework continues to consistently outperform the baselines with a large number of users on challenging settings, such as the one we studied: K=20 out of N=100 users participate in each round with data non-iid distribute. We thank the reviewer for suggesting this experiment since we believe it also demonstrates the scalability of our framework 

We provide the results with the ResNet-18 model on CIFAR-10 and CIFAR-100 in Appendix E.1 in the revised manuscript and observe that the empirical gains in terms of accuracy, bitrate, convergence, and final model size over the baselines carry over to ResNet models as well. We thank the reviewer for suggesting these experiments, which we believe, made our manuscript stronger as it shows the improvements of our framework generalize to ResNet models.


[1] Zhou et al., “Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask,” 33rd Conference on Neural Information Processing Systems (NeurIPS 2019).

[2] Frankle et al., “The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks,” International Conference on Learning Representation 2019.

[3] Ramanujan et al., “What’s Hidden in a Randomly Weighted Neural Network?,” IEEE / CVF Computer Vision and Pattern Recognition Conference 2020.

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Please see the rest of our response in the second box "[Response 2/2]..."

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 3/3] Thank you for the feedback and suggestions! Let us know if you have any remaining concerns.
comment: ### **Why do we choose to use a score mask instead of regularization?**
We apologize for the confusion about training $\theta$ using regularization. We understand that our statement on regularizing $\theta$ was not clear enough, and we revised this in the updated manuscript. In a centralized training setting (training at the server without clients), training with regularization could indeed give the same result as using a score mask and Sigmoid function. However, in the federated setting, when the $\theta$ values are outside [0,1] range in the initial stages of training, we would need to clip $\theta$ to take a Bernoulli sample for efficient communication. This clipped $\theta$ would result in a biased estimate for the mean of $\theta$. Since we need unbiased estimates with bounded error for fast convergence, we did not go with the regularization option. This is indeed an important design choice in our algorithm, and we thank the reviewer for flagging that it is unclear why we choose a score mask over regularization. We clarified this in the revised manuscript, and we hope that our explanation resolves the reviewer’s concern.

### **Difference between capital $M$ and lower case $m$:**
We apologize for the confusion. As we stated in the first paragraph of Section 3, we use capital letters for random variables and small letters for their realizations. Hence, we used $m$ when we were talking about a deterministic binary mask after the realization happens; and we used $M$ when we were referring to the binary mask as a random variable separate from the realization. In short, $M$ and $m$ refer to the same mask, one is used for the general random variable, and the other one is used for the realization.

### **Notation in the update rule:**
The score notation in the update rule is not a typo, but rather a general consensus on the notation for updating a parameter. Specifically, we used the same indices in both sides of the update rule as those operations are performed at the same client $k$ during the same round $t$. The values are updated $\tau$ times, where $\tau$ is the number of local iterations. We deliberately avoided adding the local iteration number $\tau$ to keep the notation simpler. We may switch to a new notation if the reviewer thinks this may confuse the general reader.

### **Resolution of the Figures:**
We thank the reviewer for bringing this to our attention. We added higher-quality plots in the revised manuscript. We apologize if the resolution is still not perfect, we had to use small figures to fit the main material within the page limit. 

----------------------
We again thank the reviewer for the valuable suggestions and questions that helped us improve the manuscript. We hope to have addressed the reviewer's concerns. We are happy to engage in further discussion if there are any remaining concerns. If our response is satisfactory, we kindly ask the reviewer to revisit their evaluation of our submission.

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 2/3] Thank you for the feedback and suggestions! We tried to address your concerns.
comment: ### **The justification behind our empirical discovery:**
We also understand the reviewer’s concern about not having enough reasoning on why we sometimes choose method A over method B. To provide more insights and evidence for our choices, we added ablation study experiments in Section 4.3 to explore and answer two questions: 
1. Is Bayesian aggregation really necessary?
2. What is the effect of resetting frequency on the convergence rate and the final accuracy?

(We also discussed the choice of going with a score mask instead of realization, but we elaborate on this below.) We hope this resolves the reviewer’s concern about our design choices. However, we also note that in machine learning research, we sometimes go with a reasonable design choice even though there are (infinitely many) other alternatives. Then, the empirical success of the design may lead to important theoretical questions to justify the results in future work. In our case, why there exist subnetworks inside a randomly initialized network that perform well in a federated setting on non-iid data, and why they perform better than existing compression baselines, are interesting open questions that we introduce to the community, and we will be happy to further analyze in future work. Indeed, these questions are also still an open and active area of research even in the centralized setting on iid data, where there are many evidences that these subnetworks exist (in a centralized setting on iid data), but there is little understanding of why, how, and when they exist. We honestly think that not answering all these questions (that an entire research field is trying to explore) in a single paper should not be considered a weakness, as our work already has two important contributions (that we explained above). Please see the recent work at ICLR, ICML, ECCV... [1]-[3], that mainly report similar interesting observations on sparsifying networks (and random networks) with the goal of 
1. reporting an interesting and unexpected observation that has scientific value,  and
2. motivating other researchers to do more fundamental research in this direction. 

We believe our algorithm and its surprisingly well performance against state-of-the-art will serve the same purpose. Hence, we believe that proposing this algorithm to obtain a communication-efficient framework in a federated learning setting, reporting surprisingly good results, and outperforming the existing state-of-the-art baselines on non-iid data, are valuable contributions, since we motivate a new research direction by **showing that an unusual training approach outperforms state-of-the-art compression algorithms.**

We also would like to remind the reviewer that the history of top-level ML conferences, like ICLR, presents many papers whose research methodology is based on intuition, carefully designed and evaluated empirical experiments, conveying interesting messages, obtaining good empirical results, and suggesting promising research directions, as we do, sometimes by leaving further fundamental understanding to future work, e.g., the lottery ticket hypothesis work [1], [3], random networks [2], regularization method for FL [4], dropout [5], pruning [6], just to name a few. Among these, we would like to specifically highlight the lottery ticket hypothesis work [3], which was selected as the best paper at ICLR 2019, since the reviewer mentions this work in their review. We would like to remind the reviewer that this undoubtedly impactful work also reports surprising empirical observations without being able to fully justify why and how. However, it is clearly an important scientific contribution since it led to many interesting open questions that shifted the direction of a whole research field.  

[1] Zhou et al., “Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask,” 33rd Conference on Neural Information Processing Systems (NeurIPS 2019).

[2] Ramanujan et al., “What’s Hidden in a Randomly Weighted Neural Network?,” IEEE / CVF Computer Vision and Pattern Recognition Conference 2020.

[3] Frankle et al., “The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks,” International Conference on Learning Representation 2019.

[4] Xu et al., “Acceleration of Federated Learning with Alleviated Forgetting in Local Training,” International Conference on Learning Representation 2022.

[5] Srivastava et al., “Dropout: A Simple Way to Prevent Neural Networks from Overfitting,” Journal of Machine Learning Research 15 (2014) 1929-1958.

[6] Liu et al., “The Unreasonable Effectiveness of Random Pruning: Return of the Most Naive Baseline For Sparse Training,”  International Conference on Learning Representation 2022.

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Please see the rest of our response in the third box "[Response 3/3]..."

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 1/3] Thank you for the feedback and suggestions! We tried to address your concerns.
comment: We thank the reviewer for their valuable feedback and for raising important questions. Below, we respond to their concerns in detail.

### **A clarification on a potential misunderstanding:**
We would like to start by clarifying a potential misunderstanding of our work based on the reviewer’s summary. Specifically, the reviewer said, “The main idea of the work is to use the lottery ticket hypothesis and…”. We want to clarify that the subnetworks found by FedPM are not to be considered lottery tickets, as the weights of the subnetworks are frozen at the random values, and they are not supposed to be re-trained to convergence by using standard SGD-like optimizers on the sparsified network. They are also not found by training the full model as opposed to the lottery tickets, but by optimizing the topology of a randomly initialized network. Since we never modify the random weights, we gain efficiency not only via the sparsity of the final model (sparse models may offer efficient inference) but also by representing the final model with a smaller bitrate using the learned binary mask. Please recall that after training, the random weights in the final model (which are kept frozen once generated at initialization) can be reproduced at any node by using a single real value that represents the SEED – a negligible overhead compared to the size of the final model. Hence, the size of the final model is approximately equal to the size of the binary mask, which is at most 1 bit per parameter. This is a gain in the final model size that lottery tickets cannot provide due to weight training.

### **Our empirical discovery and contribution:**
Our motivations are clear and two-fold: 
1. providing a communication-efficient federated learning framework with consistent empirical gains in accuracy, bitrate, convergence rate, and size of the final model; 
2. achieving all this with an unusual federated training strategy, namely by finding subnetworks inside a randomly initialized global network that would work well on different clients’ heterogeneous datasets. 

We believe the first one is a practically valuable contribution, which is the target of many papers and recognized by the reviewer, and the second one opens interesting questions in the federated learning research, as it shows an alternative and unusual training method with practical benefits. Discovering that this training approach works is in itself interesting, but we also show that we can use it to have communication efficiency, faster convergence, and accuracy gains, with additional potential benefits such as differential privacy. We believe this work will motivate researchers to design new algorithms exploiting all these directions. 

As the reviewer stated, we outperform the most popular baselines, such as QSGD, and the most recent baselines, such as EDEN, with a novel idea using an unusual training strategy. We believe this should deserve the right appreciation as, instead of following an incremental approach, we propose a different and unusual federated training strategy to outperform the best baselines. This is a non-trivial empirical discovery that we believe will motivate further investigation into the conditions for the existence of these subnetworks and the optimal ways of finding them.

--------------------------------------
Please see the rest of our response in the second box "[Response 2/3]..."

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: Thank you for the constructive feedback! Let us know if you have any remaining concerns. 
comment: We thank all the reviewers for their constructive feedback, valuable suggestions, and meaningful questions, which helped us improve our manuscript. Specifically, we thank Reviewer EaNE for praising the empirical improvements we provide; Reviewer Un54 for complimenting our work for its novelty, clarity, and technical contributions; Reviewer 19LP for finding our framework novel, unexplored, important, and clear; and Reviewer iZTn for the empirical contributions and clarity of writing. 

Based on the suggestions from the reviewers, we made a number of changes in our manuscript (the updated text is marked with blue), including:

- **Additional Experiments on Larger Models:** We conducted additional experiments with ResNet-18 on CIFAR-10 and CIFAR-100 datasets and reported the results in Appendix E.1. Our findings indicate that FedPM (our framework) provides similar improvements in accuracy, bitrate, convergence, and final model size to the gains we reported in Section 4.1. We thank the reviewers for suggesting this experiment since it shows that our framework generalizes to ResNet architectures.

- **Ablation Studies:** We added Section 4.3 in the revised manuscript to provide an ablation study regarding the Bayesian aggregation strategy. In particular, we tried to answer the following two questions:
    1. Is Bayesian aggregation really necessary?
    2. What is the effect of resetting frequency on the final accuracy and convergence?

    To answer these questions, letting $\gamma$ denote the number of rounds before resetting the priors, we plot the training curves for different $\gamma$ with different client participation ratios. As we explain in our responses to the reviewers and Section 4.3 in the revised manuscript, Bayesian aggregation is indeed helpful in the case of non-IID data split and partial client participation. We provide both intuitive arguments and empirical results to support this finding. 

We address the reviews in our individual responses to each reviewer.

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 3/3] Let us know if you have any remaining concerns.
comment: Now, we would like to respond to the third point raised by the reviewer. While we are not sure if it makes sense (or even possible) to get samples from ternary support with a single parameter $tanh(\theta)$, we see other immediate major drawbacks of the scheme described by the reviewer. Specifically, the reviewer suggests communicating a sampled value {-1, 0, 1} which can take 3 different possible values, as opposed to 2 different possible values for the binary samples in our method. It is not clear to us how this would improve the communication cost. More precisely, in our framework, a binary random variable represents whether a parameter should stay in the subnetwork or not. Since this random variable has low entropy, as discussed in the manuscript, we observe large gains in the communication cost – bitrate decreasing below 1 bpp. (Note that 1 bpp is the worst-case bitrate when we compress a binary vector.) In the case of communicating ternary values {-1, 0, 1}, as suggested by the reviewer, we still need to spend the same number of bits to distinguish whether the sampled value is from {0} or {-1, 1}. However, the new scheme requires further distinguishing between -1 and 1 by spending extra bits. Due to symmetry between -1 and 1, or equivalently $-\sigma$ and $\sigma$, we would expect to spend about 1 bit to specify whether a non-zero sampled value is -1 or 1. Therefore, the bitrate of the scheme described by the reviewer should have a larger communication cost than the bitrate in our framework. Moreover, once having a realization of the ternary random variable {-1, 0, 1}, there is actually no need to distinguish between -1 and 1 since the server already knows which parameters are $-\sigma$, and which are $\sigma$. Hence, it is actually sufficient to communicate whether the sampled parameter is zero or not. This is exactly what our algorithm is doing. Hence, we do not see how the scheme described by the reviewer would provide any gains over our framework. If we misunderstood the suggested scheme, we are happy to discuss it further with the reviewer.

We hope that we addressed all the concerns raised by the reviewer. If there are any remaining questions or concerns, we are happy to discuss them further. Specifically, we hope that the reviewer will revisit their points 1 and 2 upon our response and update their score accordingly.

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 2/3] Thank you for your feedback! We tried to address your main concerns in points 1&2.
comment: Continuing from "[Response 1/3]" to explain why we mainly study the uplink communication cost:

- Lastly, regarding the reviewer’s comments in point 2, as we mention in the first bullet point above, all of our baselines share the same approach as ours, namely they compress the model updates in the uplink communication from the client to the server, and they communicate the model (or the update) without compression in the downlink communication from the server to the client. Our baselines have similar (mostly larger) communication costs to our method in total while underperforming our method consistently with a slower convergence rate. Given that our method also outputs a final model with a smaller size (i.e., the random network can be generated by using just the SEED and the learned binary mask) compared to any of the other baselines, whose final models is still a dense real-valued network, our method outperforms all the baselines in all aspects. Note that our baselines include one of the most popular algorithms, QSGD, which has been the state-of-the-art in federated and distributed learning; and also the most recent algorithms, such as DRIVE and EDEN.  **Consequently, our experimental results on the performance gain with respect to the reported state-of-the-art baselines are consistent, fair, and empirically evident.**

We hope that the reviewer will now appreciate why we should focus mainly on the uplink communication from the client to the server (like in the majority of communication-efficient federated learning papers) since it makes a significantly larger impact on the total runtime, as noted by many survey papers and reports, including the ones quoted above. 

To conclude, we would like to specify again that, even when considering both uplink and downlink communication, our analysis and simulations are valid, as the same (if not smaller) number of bits for downlink communication is consumed by our scheme, when compared to our baselines. 

Since these points were the basis of the reviewer’s current score, we hope that the reviewer will reconsider their evaluation and update their score.

We provide our response to the reviewer's suggestion in point 3 in the third box "[Response 3/3]".

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: [Response 1/3] Thank you for your feedback! We tried to address your main concerns in points 1&2.
comment: We thank the reviewer for their feedback and for raising meaningful questions about the main communication challenges in federated learning. 

Based on the reviewer's comments in points 1-2, the reviewer’s main question seems to be whether there is a valid reason why we compress the model updates during uplink communication from the client to the server but communicate non-compressed models during the downlink communication from the server to the client. There is indeed a reason, which we did not discuss in the manuscript since we assumed some familiarity with the communication-efficient federated learning research. However, since the reviewer raised this concern, we would like to resolve this misunderstanding of (1) the main communication bottleneck in federated learning, and (2) the communication gains the existing methods, including our baselines, provide. We elaborate on these below and explain

1. why the uplink communication cost is the main communication bottleneck in federated learning, and 
2. why our comparisons are valid and fair. 

In fact, similar to our framework, our baselines also reduce the communication cost only in uplink, and not in downlink communication. Since the reviewer mentioned that these concerns were the basis of their score, we kindly ask the reviewer to revisit their evaluation of our paper, specifically given that the reviewer recognized its major strengths.

We would like to start by explaining why we mainly study the uplink communication cost, i.e., the average number of bits needed for communicating the model updates from the client to the server, and why our framework is an important contribution to the communication-efficient federated learning attempts:

- First and foremost, **all the other existing baselines are compressing model updates in the uplink communication from the client to the server while communicating non-compressed updates in the downlink communication from the server to the client.** This is also true for our baselines SignSGD, TernGrad, QSGD, DRIVE, EDEN, and FedMask. (There are only a few exceptions that study compression in both downlink and uplink in the literature, but they achieve worse performance.)  We are sorry that the reviewer had a confusion about this. The reason why we did not emphasize this in the manuscript is that we assumed some familiarity with the recent literature on communication-efficient federated learning, where the focus is on the uplink communication cost. We will make this distinction more clear in the revised manuscript (to be uploaded soon). Below, we explain why the main focus is on the uplink communication.

- The main communication bottleneck to be considered is indeed the one during model uploads from the clients to the server in the uplink communication. Quoting from the survey in [1], Section 3.5: 
>“Among them, (a)[i.e., compression during upload] has the potential for the most significant practical impact in terms of total runtime. This is both because clients’ connections generally have slower upload than download bandwidth* – and thus there is more to be gained, compared to (b)[i.e., compression during download] – and because the effects of averaging across many clients can enable more aggressive lossy compression schemes.”

- Furthermore, if we assume a scenario in which the devices are connected to the same wireless network [2], we need to consider that each device has to communicate a local version of its model to the server. Consequently, if the size of the model is of S bits, and K clients are participating to the training round, S x K bits need to be communicated through the network during the model upload from the clients to the server, using the same shared wireless medium. On the other hand, the server can broadcast the **same** model to all the clients using the same wireless medium, and so the total number of bits to be communicated through the downlink wireless channel is only S, i.e., the common global model. Please refer to [2] for more details. Specifically, please have a look at [2] Section 2.2.2 and Section 2.2.3, quoting 
>“The BS [the Base Station, i.e., the central authority in general (e.g., a server)],  broadcasts the global prediction model parameters to all users in the downlink. Due to the high power of the BS and large downlink bandwidth, we ignore the downlink time.”

- Please see the rest of our response in the second box "[Response 2/3]..."



*https://www.speedtest.net/global-index



[1] P. Kairouz, H.B. McMahan et al., “Advances and Open Problems in Federated Learning,” Foundations and Trends in Machine Learning, Vol 14, Issue 1-2, June 2021.

[2] Z. Yang et al., “Delay Minimization for Federated Learning Over Wireless Communication Networks,” International Conference on Machine Learning (ICML) 2020.

From: ICLR.cc/2023/Conference/Paper1274/Authors
title: Thank you for the feedback! We are working on a revision.
comment: We thank the reviewers for their constructive feedback and for praising our work in terms of novelty (Reviewer Un54, EaNE, 19LP), empirical contributions through consistent improvements over existing baselines (Reviewer EaNE, iZTn), introducing new insights to an important problem (Reviewer Un54, 19LP), and clarity and writing (Reviewer EaNE, Un54, 19LP). The reviewers made valuable suggestions for additional experiments, ablation studies, and clarification on some parts of the methodology. We are working on them. We will upload a revised manuscript soon and will try to address the reviewers' comments in the individual responses.

From: ICLR.cc/2023/Conference/Paper1274/Reviewer_EaNE
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: **UPDATE**  
I thank the authors for providing an extensive response. I carefully read it and discussed with the other reviewers. I'm glad the authors clarified their major design choices and supported them with new experiments. One issue that remains is that of limited evaluations, but with the extra support added in the new version of the paper, I feel more confident that the proposed methodology will generalize to other setups.

---------
This paper studies communication-efficient federated learning with random sparsification of the network weights. The main idea of the work is to use the lottery ticket hypothesis and try to find a good subnetwork by estimating a sparsifying mask. The mask parameterized by a vector of probabilities $\theta$, which, in turn, are estimated using a score mask $s$, whose softmax gives us $\theta$. Moreover, the authors use multiple clients that run gradient descent to estimate the best mask and then communicate only the binary vector produced randomly from the local estimate. By receiving multiple random masks, the authors build a Bayesian estimator to produce a global model.
strength_and_weaknesses: The main strength of this work is in the presented empirical improvements on the considered benchmarks. The proposed method is shown to outperform all competitors both in terms of test accuracy and communication efficiency.

What makes me concerned is the way the method was derived and studied. Most of the ideas do not look well-motivated. For instance, the authors explain that the mask $\theta$ cannot be used with regularization because it may lead to a performance drop, so they instead use softmax. However, it is not apparent to me why there would be a performance drop with regularization but no performance drop with score mask. In the majority of cases, I think that an ablation study is required to show that the made choices were the right ones. As of now, the paper just selects a set of ideas that are not justified using theory and then proceed to study the empirical behaviour of the resulting method. I am left with the feeling that I do not understand why the method performs well and if it will generalize to other problems. This is especially troubling since the evaluations are limited to simple problems (CIFAR-10/100, EMNIST, small networks).
clarity,_quality,_novelty_and_reproducibility: I do not see major issues with paper writing. The novelty aspect is explained quite well.

Some minor issues:  
Pages 4-5: I do not understand why the authors sometimes write $M^{k,t}$ and sometimes $m^{k,t}$  
Page 4: there seems to be a typo in the update rule for $s^{k,t}$ because both sides have the same indices  
Can the authors use a higher resolution for Figures 2, 3, and 4? It'd be even better if the figures were produced from pdf files

summary_of_the_review: While the work clearly explains the points that are novel, they do not seem justified or derived in an intuitive manner. The proposed modifications to prior work are somewhat arbitrary and do not follow a rigorous mathematical derivation or empirical evaluation of different options. While the experiments show that the resulting method performs better on a number of problems, it is not apparent that the same improvement would hold universally and where exactly the improvement comes from. For instance, the method converged to better test accuracy on conv10-cifar100, but why it is not explained why it is so.
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 6: marginally above the acceptance threshold

From: ICLR.cc/2023/Conference/Paper1274/Reviewer_Un54
confidence: 5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.
summary_of_the_paper: The paper proposes a combination of ideas and methods to enable low-bit-width communication in federated learning. 
The authors combine the idea of learning a sparse sub-network of a randomly initialized model through a binary mask with a stochastic sampling scheme of said mask to communicate with the server and further a bayesian aggregation scheme. These algorithms exist in the literature but not applied successfully to FL as presented here. 


strength_and_weaknesses: This paper's strength lie in the excellent exposition and description of the method. The paper is very pleasant to read, easy to follow and written in a convincing way. 

The weakness of the paper lies in the experimental evaluation. The model & data-set combinations are not up-to-date with the literature. Generally speaking, (wide) ResNet or more edge-device friendly models would be more realistic than these VGG-type models. Especially with respect to the compression angle, I would like to understand how wider networks are influenced by the subnet-selection problem in the federated setting - also I'm curious if convolutional-only models (such as ResNets) perform equally well. 
The data-set setting does consider partial participation and heterogeneity through label-skew and differing dataset-sizes, which is highly commendable. At the same time, most FL papers consider settings with >50 clients, such as Femnist (3.6k clients) or even NLP tasks on the Stackoverflow dataset with approx 340k clients. Alternatively, I'd be curious to understand how, staying with the experimental theme of the paper, TinyImagenet (64x64) split across several hundred clients performs here. 
That being said, the existing experiments do convince me of the value of the proposed algorithm.

In terms of ablations, I would have liked the authors to provide more guidance on the resetting of the server-side $\alpha$ and $\beta$. What is happening to require the resetting in the first place? How does the frequency of resets influence the convergence? And how does non-iid data influence this behaviour? This heuristic seemingly is very important to good results, so I am curious to learn more. Please provide more detail on your statement: "... design an improved aggregation strategy with a Bayesian approach so that the previous masks at the server are not hard replaced – a useful strategy specifically in unbalanced non-IID splits"

clarity,_quality,_novelty_and_reproducibility: Clarity & quality of the writing is extremely high. I truly enjoyed reading the paper. 
The novelty of the work is good, it feels like a successful combination of existing ideas with additional insights.
The authors provided code with this submission:
I have looked at the code and while it is not complete in the sense that it enables replicating all experiments, it allows me to gain additional insights and re-implement in my own code-base. 
I noticed that the initialization scheme discussed in the paper does not correspond to the implementation. In the paper, the authors detail initializing by randomly choosing between $-\sigma$ and $\sigma$ where $\sigma$ corresponds to the standard deviation of the Kaiming Normal distribution. For ReLu activation, $\sigma$ should be $\sqrt{(2/n_l)}$, however the authors choose $e \sqrt{(1/n_l)}$, which is ever-so-slightly different. I am curious about that choice. 

I would encourage the authors to append additional `params.yaml` that allow the reproduction of all experiments in this paper. 


summary_of_the_review: Very interesting paper with a convincing story. The experimental section could be improved. I am happy to raise my score should the authors provide experiments with more modern network architectures and FL settings with a larger number of clients. 

-- post rebuttal -- 
I have read the rebuttal and revised manuscript. The authors have addressed my concerns and I have raised my score
correctness: 4: All of the claims and statements are well-supported and correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: Not applicable
flag_for_ethics_review: NO.
recommendation: 8: accept, good paper

From: ICLR.cc/2023/Conference/Paper1274/Reviewer_19LP
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: The paper proposes a new approach to communication efficient federated learning. They keep the weights of the model fixed after random initialization via a SEED. and then only train the probabilistic mask over the model in collaboration with all the clients. They reduce the communication of requirement to less1bpp during model upload from clients to server. I have a couple of questions for the authors, 


1. The paper argues that they reduce the communication cost to less than 1bpp every round. However, there are two communication steps in each round: server to clients in before each round and clients to server. While in the second step the communication is less than 1bpp as instead of communicating the masks, clients communicate a sample from the probabilistic mask, as per the paper ( algorithm line “Receive..”, section 3.1.1 first line), clients receive the actual probability mask  (not a sample)  from the server. Then the total cost of communicating 2xmodel_size in usual FL is reduced to only (model_size (download) + mask (upload)). Are we assuming large discrepancies in download and upload bitrates ? 

2. If the above assumption is incorrect, then the comparison baselines which were chosen to be  1bpp should also be revised and compared with baselines with larger communication footprint including naive FL which has 2xmodel_size communication.

3. In section 3.3, paper mentions that they use a discrete support for P_w for improving inference storage cost. However if the final weights are ternary, we can eliminate the managing the mask and directly use this for better communication ( at-least client to server communication) . The paradigm would be as follows, each maintains the floating-point models \theta_i, the final weights are used after applying an activation like tanh. Then while communicating the model to server, you sample from this tanh(theta) to have a support of {-1, 0, 1} (you can consider the factor of sigma separately).  I am curious what the authors think about this.


strength_and_weaknesses: [strength]
1. The approach is novel and unexplored. 
2. the problem being tackled is important 
3. paper is well written
[weaknesses]
1. See the points 1-2 above
clarity,_quality,_novelty_and_reproducibility: See above
summary_of_the_review: The major concern for me is that I am not sure if communication is really being reduced. While volume of upload data is surely reduced, the volume of download data is clearly not. I would like to understand the rationale behind this and if i am missing something. This is the basis of my current score.

[post rebuttal] The authors have sufficiently addressed my concerns. i am raising my score.
correctness: 2: Several of the paper’s claims are incorrect or not well-supported.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: Not applicable
flag_for_ethics_review: NO.
recommendation: 6: marginally above the acceptance threshold

From: ICLR.cc/2023/Conference/Paper1274/Reviewer_iZTn
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: This work proposes FedPM, a scheme for communication (and as a byproduct, computation) efficient federated learning. Instead of training the neural network weights with, e.g., FedAvg, the authors propose to freeze the network at its random initialisation and then only train a *binary* mask over the weights, to prune some connections, in a federated fashion. The benefit of this approach is that the client-to-server communication now becomes much cheaper, due to communicating (potentially encoded) binary vectors instead of full precision weights. To train the binary mask, the authors propose to employ a distribution over masks, the probabilities of which are a server side parameter. On each round, this distribution is communicated to each client, which then optimises it locally on their own data by 1) sampling binary masks according to this probability distribution, 2) sparsifying the weight according to the sampled mask, 3) doing the forward pass with the sparsified network and 4) approximating the gradient of the loss with respect to the parameters of the probability distribution with the straight-through estimator [1](although the authors do not explicitly mention it). The reduction in the upload costs comes from having each client communicate to the server a random sample from the locally training distribution over the masks (which is binary) instead of the actual distribution over the masks. The download cost of FedPM is the same as FedAvg (since the probabilities are real values and one for each weight). To aggregate the binary masks at the server, the authors propose to use the Bayesian aggregation from Ferreira et. al. Finally, to accommodate for computationally fast inference, the authors also propose to randomly initialise the weights to be binary with a specific scaling that leads to better behaved gradients. 

[1] Bengio et al. Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation, 2013
strength_and_weaknesses: Strengths
- Simple method
- Good results

Weaknesses
- Limited technical novelty
- Some clarity concerns 
clarity,_quality,_novelty_and_reproducibility: This submission is mostly clearly written and I believe has enough information to allow for reproducibility. A couple of things that could be better elaborated / improved upon are the following:
- The gradient estimator the authors use is an instance of the straight-through estimator (STE) described at [1], with quite a lot of follow-up literature (especially on the sparsity / quantization in neural networks front). I would therefore encourage the authors to update their text accordingly. It should be noted that the STE estimator is a biased estimator, thus it is unclear how this affects convergence of the local training. 
- The authors mention at the end of page 4 the “Bernoulli” function; does that refer to the Bernoulli probability mass function? If yes, the author should probably use the latter, otherwise they should elaborate. 
- I believe more discussion is warranted for the $\alpha$, $\beta$ parameters of the Beta distribution. For example, why do they need to be reinitialised? Is there collapse otherwise? How do you handle the bimodality when alpha, beta < 1 (i.e., what do you pick as the mode)?
- The authors propose to use the Kaiming He initialisation to control the variance of the neuron outputs when initializing the frozen network. How does the sparsity of the layer affect this? 
- A question on appendix C; as far as I understand, the bias correction requires the true theta (which is private) so how can you use it in practice?

Finally regarding the novelty. I believe that the novelty of this work is on the experimental evaluation and comparison with other relevant baselines and not on the technical side. First of all, having a probability distribution over random masks at the server, communicating it to the client to optimise it and then having the client send back a random binary sample from the optimised distribution (and computing the average at the server) is not new and has been proposed before at [2]. The extra addition of this work then is to consider frozen weights (which has been proposed at Zhou et al.) and the Bayesian aggregation at the server, which, as far as I understand, was already proposed in Ferreira et al. The privacy analysis seems to again be taken directly from Imola & Chaudhuri, so the main extra novelty seems to be the bias correction term, which however is not part of the main paper. 

[2] An Expectation-Maximization Perspective on Federated Learning, Louizos et al., 2021

summary_of_the_review: Given the aforementioned comments, I am leaning towards not recommending acceptance of this work; the technical novelty is small (as it is a combination of prior ideas) and the empirical novelty, while appreciated, is not enough for me to push this work over the acceptance threshold.

correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 6: marginally above the acceptance threshold