Pith. sign in

REVIEW 3 major objections 5 minor 48 references

Fed-ZOE: Communication-Efficient Over-the-Air Federated Learning via Zeroth-Order Estimation

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Over-the-air federated learning can cut uplink traffic to ~0.07% by sending random projections of local updates, while keeping accuracy close to uncompressed aggregation.

desk verdict A solid, practical compression idea for over-the-air FL with an honest but fixable error in the convergence proof. read the letter →

arxiv 2412.16779 v1 pith:PVKGRC37 submitted 2024-12-21 cs.LG eess.SP

Jonggyu Jang , Hyeonsu Lyu , David J. Love , Hyun Jong Yang This is my paper · ORCID
classification cs.LGeess.SP
keywords over-the-airfederatedlearningrandomizedgradientestimationzeroth-orderoptimizationcommunicationefficiencycompressionsuperpositionpropertywirelessedge6G
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes Fed-ZOE, a method that makes over-the-air federated learning (OtA-FL) drastically more communication-efficient. Instead of transmitting the full gradient vector from every edge device, each device computes its local weight update and then transmits only a few thousand scalar inner products of that update with shared random vectors. The parameter server reconstructs a good approximation of the aggregated gradient from those scalars, and the linearity of the reconstruction preserves the superposition property that makes over-the-air aggregation possible. The paper argues that with L = 8,192 projections for a ResNet-18 model with 11 million parameters, a compression ratio of about 0.07%, the trained model reaches accuracy close to uncompressed OtA-FL while using far less uplink and downlink bandwidth. This matters because model sizes are growing rapidly and OtA-FL's main bottleneck is the number of symbols that must be exchanged each round.

What carries the argument

The central object is the randomized gradient estimator (RGE), a standard tool in zeroth-order optimization. Its key identity is $\mathbb{E}[u u^T] = I$, which lets $\frac{1}{L}\sum_{l=1}^L (u_l^T v) u_l$ approximate any vector $v$. Fed-ZOE applies this identity to the local model update vector $\Delta w_{k,t}$, producing compressed scalars $\phi_{t,k,l} = u_{t,l}^T \Delta w_{k,t}$. The same random vectors are regenerated at the server from a shared seed, so the server reconstructs the average update as a linear combination of random vectors weighted by the aggregated scalars. This linearity is what preserves the superposition property of over-the-air computation, making the method compatible with OtA-FL.

What would settle it

Run the reported ResNet-18/CIFAR-10 experiment at $L=8192$; if the final test accuracy is more than a couple of points below the full-gradient OtA-FL baseline, the paper's headline claim fails.

Watch

Extended reading notes

Core claim

The central discovery is that the randomized gradient estimator can be repurposed as a communication code. A device replaces its S-dimensional update vector with L dot products against random vectors drawn from a shared seed; the server reconstructs the update as $\frac{1}{L}\sum_{l=1}^L (u_{t,l}^T \Delta w_{k,t})u_{t,l}$. Because $\mathbb{E}[u u^T] = I$ for the spherically symmetric unit-variance random vectors, the reconstruction is unbiased in expectation, and because it is a linear function of the transmitted scalars, it preserves the superposition property needed for over-the-air aggregation. With enough projections L, the compression loss falls below the channel noise floor, so the server aggregates almost as well as if it had received full gradients, at a small fraction of the symbol cost.

Load-bearing premise

The convergence guarantee rests on the fourth-moment identity $\mathbb{E}[(u u^T)^2] = 3S I$ for the Gaussian random projection vectors, which is not the value the stated distribution actually gives.

Editorial extensions

If this is right

  • Uplink communication cost per round becomes proportional to $L$, the number of random projections, rather than the model size $S$, so OtA-FL can scale to much larger models without a linear increase in bandwidth.
  • The downlink broadcast can also be compressed: the server sends only the aggregated scalars, and devices reconstruct the global update locally from the shared random seed.
  • The convergence rate remains $O(1/\sqrt{T})$ in the number of communication rounds, matching standard FedAvg, with the compression variance controlled by $L$.
  • Unlike sparsification or quantization schemes, Fed-ZOE preserves the superposition property, so it can run entirely over the air without extra handshakes or iterative decoding.
  • Because the method works from random initialization, it is not limited to fine-tuning (as LoRA is) and can train full models from scratch.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the reconstruction error at $L=8192$ is already below the channel noise floor, the same projection count may suffice for billion-parameter models, making per-round communication nearly independent of model scale.
  • The variance decomposition suggests an optimal $L$: increase projections until compression loss is comparable to channel noise; beyond that, extra symbols buy little accuracy, which could inform adaptive resource allocation.
  • Because the reconstruction is linear and unbiased, combining Fed-ZOE with gradient sparsity in the projection domain or with error feedback across rounds might further improve accuracy per symbol.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes Fed-ZOE, an over-the-air federated learning (OtA-FL) framework in which each edge device compresses its local model update vector by transmitting L scalar inner products with shared random vectors, rather than the full S-dimensional update. The parameter server reconstructs the aggregated update via randomized gradient estimation, preserving the superposition property required for over-the-air computation. The authors provide a convergence analysis (Proposition 1 and Theorem 1), a beamforming optimization for unbiased aggregation, and extensive ResNet-18 experiments on CIFAR-10, CIFAR-100, SVHN, Tiny-ImageNet, and Brain-CT. The empirical results show that Fed-ZOE approaches the accuracy of uncompressed OtA-FL while using roughly 8,192 scalars per round for a model with about 1.1×10^7 parameters, corresponding to a per-round compression ratio of about 0.07%.

Significance. If the theoretical guarantee is made rigorous, the paper offers a simple and practical communication-reduction technique for OtA-FL. The core idea of applying a randomized gradient estimator to compress the local update vector rather than using it to replace backpropagation is a useful twist, and the method is explicitly designed to preserve the analog superposition property. The empirical evaluation is broad and includes several baselines (OtA-FL, LoRA-OtA-FL, ZO-OtA-FL) under non-IID data and varying numbers of devices. A notable strength is that the predicted dependence on the number of samples L (more samples improve convergence, and higher learning rates require larger L) is tested out-of-sample in Figures 3 and 5, giving a non-circular check of the core mechanism. However, several technical errors in the proof of Proposition 1 and Theorem 1 must be corrected before the convergence guarantee can be accepted as stated.

major comments (3)
  1. [Appendix B, Eq. (35)] The claimed fourth-moment identity is incorrect. For u ~ N(0, I_S), Isserlis' theorem gives E[(u u^T)^2]_{ij} = sum_s E[u_i u_s u_s u_j] = (S+2) δ_{ij}, not 3S δ_{ij}. For a unit-variance spherically symmetric vector with ||u||^2 = S (e.g., uniform on the scaled sphere), the value is S δ_{ij}. The equality in Eq. (35) is therefore false, so the variance expression (3S−1) in Proposition 1, Eq. (22), and the learning-rate condition involving (3S−1) in Theorem 1 are not proven as written. The result can likely be repaired because (S+2) ≤ 3S for S ≥ 1, so the compression-loss term remains an upper bound if the derivation is rewritten as an inequality, but the proof must be corrected and the theorem restated accordingly.
  2. [Appendix B, Part A (Eqs. 30–33)] The channel-noise contribution is undercounted by a factor of L. The receiver noise r^H n is a scalar added to all L entries of y_G, so the reconstruction noise is (1/L) U (1_L r^H n), whose squared norm has expectation S N_0 ||r||^2 / L, not S N_0 ||r||^2 / L^2. Consequently, the channel-noise term in Proposition 1 (Eq. 22) and the corresponding term in Theorem 1 (Eq. 23) are too small by a factor of L, and the final bound does not follow as written. This is a load-bearing issue for the stated convergence guarantee, although the qualitative O(1/√T) rate would likely survive a corrected derivation.
  3. [Appendix B, Eq. (32), inequality (a)] The bound σ_{k,t}^2 ≤ (1/L)||U_t Δw_{k,t}||^2 ≤ ||Δw_{k,t}||^2 is not valid for the random matrices used in the paper. For Gaussian or unit-variance spherical u_l, E[U U^T/L] = I, but U U^T/L is not ≤ I almost surely; for example, with L=1, the operator norm of u u^T is ||u||^2 = S, which is much larger than 1. Thus the pointwise inequality (a) in Eq. (32) is false, and the subsequent noise-variance bound in Eq. (33) does not follow. A correct derivation must handle the maximum over k more carefully, e.g., through an expectation bound on the maximum eigenvalue or by a different concentration argument; this affects the same noise term in Proposition 1 and Theorem 1.
minor comments (5)
  1. [Section III-C, Eq. (15) and Eq. (19)] The noise term is written as n 1_S^T, but y_G is L-dimensional and the additive noise during the L-symbol transmission should be an N×L noise matrix, not the N-dimensional vector n times a length-S vector. The dimensions are inconsistent and should be corrected throughout.
  2. [Algorithm 1, line 16] The algorithm body says 'Send σ_k to the PS,' while the derivation in Section III-C assumes both μ_{k,t} and σ_{k,t} are known at the PS. Please clarify that both scalars are transmitted or explain how μ is obtained.
  3. [Proposition 1, Eq. (22)] The variance expression is written as an equality, but both the intended derivation and the corrected version give an upper bound rather than an exact equality. Please state the result as a bound to avoid overclaiming.
  4. [Section V-C, last paragraph] The sentence 'as training a classifier for the given datasets is getting harder' should be rephrased, e.g., 'as the classification task becomes harder,' for clarity.
  5. [Abstract and Section I] The abstract states that Fed-ZOE requires 'at most 30% of the communication overhead of traditional approaches,' but the main compression claim is given as 0.07% per round. The origin of the 30% figure is not clearly tied to a specific comparison in the main text; please reconcile these numbers.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Fed-ZOE's RGE compression and recovery are an unbiased random projection, the convergence analysis is self-contained under explicitly stated assumptions, and the L-scaling behavior is validated out-of-sample rather than fitted.

full rationale

The derivation chain is self-contained. The compression step in Eq. (12) defines the recovered update as (1/L) sum_l u_{t,l} u_{t,l}^T Delta w_{k,t}, and Eq. (14) uses E[uu^T] = I to establish unbiasedness of the aggregated estimate. This is a standard mathematical identity, not a fitted input or a prediction forced by construction. Proposition 1 and Theorem 1 build on Assumptions A1--A4 with a variance decomposition into channel noise, compression loss, and local-update terms; no parameter is fitted to the accuracy curves, and the subsequent convergence-rate conclusion is derived rather than assumed. The empirical claim that larger L improves accuracy (Figs. 3 and 5) is an out-of-sample check of the algorithm under different projection dimensions, so it does not reduce to the fitted values used in the main figures. Citations to prior work are background or standard tools (OtA-FL [6], RGE [33], uniform-forcing beamforming [29], Isserlis' theorem [48]) and are not load-bearing for the central claim. We note as a correctness concern, not as circularity, that Eq. (35) appears to state E[(u u^T)^2] = 3S I for spherically symmetric unit-variance u in R^S; the correct diagonal value is S+2 for Gaussian and S for Rademacher vectors. This affects the constant (3S-1) in Proposition 1 and the learning-rate condition in Theorem 1, but it does not turn a prediction into its own input. The appended limitation about random-direction selection likewise concerns possible future improvements, not a hidden dependency of the presented results. Overall, no step in the paper reduces, by definition or by self-citation, to its own inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The method relies on standard FL assumptions (smoothness, bounded gradients, unbiased stochastic gradients), the sharing of a random seed to generate identical projection vectors, and exact knowledge of channel state and normalization statistics at the PS. No new physical entities are introduced. The questionable axiom is the Gaussian fourth-moment identity used in the proof, which is miscomputed.

free parameters (2)
  • L (number of RGE samples) = 8192 default; swept over 512 to 16384
    Controls the compression ratio and gradient-estimation variance. Chosen as a hyperparameter by the user, not derived from first principles.
  • learning rate = Set to 1/sqrt(T I) in the theorem; various values up to 0.3 in Fig. 3
    Tuning the learning rate is standard in deep learning and the method requires a small rate when L is small, as the authors show in Fig. 3.
assumptions (4)
  • domain assumption Global loss is lower-bounded; local losses are beta-smooth; mini-batch gradients are unbiased with bounded variance; gradient norms are bounded (Assumption 1).
    Standard assumptions in non-convex federated learning theory, invoked in the proof of Theorem 1.
  • domain assumption The random vectors u_t,l are spherically symmetric with unit variance and satisfy E[u_t,l u_t,l^T] = I and the fourth-moment identity used in Eq. (35).
    This is the key statistical assumption for the RGE reconstruction; the fourth-moment value is miscomputed in the paper.
  • domain assumption The PS has perfect channel state information and knows the normalization statistics mu and sigma of each device.
    Required to solve the beamforming problem P2 and compensate the normalization shift in Eq. (15); stated in Section III-C.
  • domain assumption All devices and the PS can generate identical random vectors from a shared random seed without additional communication.
    Central to the superposition property and the downlink reconstruction; described in Algorithm 1.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Fed-ZOE: Communication-Efficient Over-the-Air Federated Learning via Zeroth-Order Estimation." pith.science (2026). https://pith.science/paper/PVKGRC37

@misc{pith2026241216779,
  author       = {Pith},
  title        = {Pith review of: Fed-ZOE: Communication-Efficient Over-the-Air Federated Learning via Zeroth-Order Estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PVKGRC37}},
  note         = {Machine review of arXiv:2412.16779}
}
read the original abstract

As 6G and beyond networks grow increasingly complex and interconnected, federated learning (FL) emerges as an indispensable paradigm for securely and efficiently leveraging decentralized edge data for AI. By virtue of the superposition property of communication signals, over-the-air FL (OtA-FL) achieves constant communication overhead irrespective of the number of edge devices (EDs). However, training neural networks over the air still incurs substantial communication costs, as the number of transmitted symbols equals the number of trainable parameters. To alleviate this issue, the most straightforward approach is to reduce the number of transmitted symbols by 1) gradient compression and 2) gradient sparsification. Unfortunately, these methods are incompatible with OtA-FL due to the loss of its superposition property. In this work, we introduce federated zeroth-order estimation (Fed-ZOE), an efficient framework inspired by the randomized gradient estimator (RGE) commonly used in zeroth-order optimization (ZOO). In FedZOE, EDs perform local weight updates as in standard FL, but instead of transmitting full gradient vectors, they send compressed local model update vectors in the form of several scalar-valued inner products between the local model update vectors and random vectors. These scalar values enable the parameter server (PS) to reconstruct the gradient using the RGE trick with highly reduced overhead, as well as preserving the superposition property. Unlike conventional ZOO leveraging RGE for step-wise gradient descent, Fed-ZOE compresses local model update vectors before transmission, thereby achieving higher accuracy and computational efficiency. Numerical evaluations using ResNet-18 on datasets such as CIFAR-10, TinyImageNet, SVHN, CIFAR-100, and Brain-CT demonstrate that Fed-ZOE achieves performance comparable to Fed-OtA while drastically reducing communication costs.

Figures

Figures reproduced from arXiv: 2412.16779 by the authors.

Figure 1
Figure 1. Overview of the proposed gradient compression and reconstruction framework in Fed-ZOE. The left panel illustrates the gradient compression process [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Test accuracy of the trained ResNet-18 models with various values [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 2
Figure 2. Convergence evaluation of the proposed method and baseline methods. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Convergence of the proposed method for various numbers of the RGE [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 7
Figure 7. Figure 7: Convergence evaluation of the proposed method and baseline methods [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Convergence of the FL methods for various datasets: (a) Brain-CT dataset, (b) SVHN dataset, (c) Tiny-ImageNet dataset, and (d) CIFAR-100 dataset. [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Training efficiency of the FL methods for various datasets: (a) Brain-CT dataset, (b) SVHN dataset, (c) Tiny-ImageNet dataset, and (d) CIFAR-100 [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 35 canonical work pages

  1. [1]

    Challenges and opportunities for beyond-5G wireless security,

    E. Ruzomberka, D. J. Love, C. G. Brinton, A. Gupta, C.-C. Wang, and H. V . Poor, “Challenges and opportunities for beyond-5G wireless security,” IEEE Security & Privacy , 2023

    work page 2023

  2. [2]

    Key Focus Areas and Enabling Technologies for 6G

    C. G. Brinton, M. Chiang, K. T. Kim, D. J. Love, M. Beesley, M. Repeta, J. Roese, P. Beming, E. Ekudden, C. Li et al. , “Key focus areas and enabling technologies for 6G,” arXiv preprint arXiv:2412.07029 , 2024

    work page Pith review arXiv 2024

  3. [3]

    Federated learning for predicting clinical outcomes in patients with COVID-19,

    I. Dayan, H. R. Roth, A. Zhong, A. Harouni, A. Gentili, A. Z. Abidin, A. Liu, A. B. Costa, B. J. Wood, C.-S. Tsai et al., “Federated learning for predicting clinical outcomes in patients with COVID-19,” Nature Medicine, vol. 27, no. 10, pp. 1735–1743, 2021

    work page 2021

  4. [4]

    Federated learning empowered recommendation model for financial consumer services,

    P. Chatterjee, D. Das, and D. B. Rawat, “Federated learning empowered recommendation model for financial consumer services,” IEEE Trans. Consum. Electron., 2023

    work page 2023

  5. [5]

    Federated learning for connected and automated vehicles: A survey of existing approaches and challenges,

    V . P. Chellapandi, L. Yuan, C. G. Brinton, S. H. ˙Zak, and Z. Wang, “Federated learning for connected and automated vehicles: A survey of existing approaches and challenges,” IEEE Trans. Intell. Veh., 2023

    work page 2023

  6. [6]

    Federated learning via over- the-air computation,

    K. Yang, T. Jiang, Y . Shi, and Z. Ding, “Federated learning via over- the-air computation,” IEEE Trans. Wireless Commun., vol. 19, no. 3, pp. 2022–2035, 2020

    2022

  7. [7]

    Nomographic functions: Efficient computation in clustered gaussian sensor networks,

    M. Goldenbaum, H. Boche, and S. Sta ´nczak, “Nomographic functions: Efficient computation in clustered gaussian sensor networks,” IEEE Trans. Wireless Commun., vol. 14, no. 4, pp. 2093–2105, 2014

    work page 2014

  8. [8]

    Communication-efficient learning of deep networks from decentralized data,

    B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y. Arcas, “Communication-efficient learning of deep networks from decentralized data,” in Proc. Int. Conf. Artif. Intell. Stat. (AISTATS) , 2017, pp. 1273– 1282

    work page 2017

Show all 48 references
  1. [9]

    Communication-efficient fed- erated learning over MIMO multiple access channels,

    Y .-S. Jeon, M. M. Amiri, and N. Lee, “Communication-efficient fed- erated learning over MIMO multiple access channels,” IEEE Trans. Commun., vol. 70, no. 10, pp. 6547–6562, 2022

    2022

  2. [10]

    1-bit compressive sensing for efficient federated learning over the air,

    X. Fan, Y . Wang, Y . Huo, and Z. Tian, “1-bit compressive sensing for efficient federated learning over the air,”IEEE Trans. Wireless Commun., vol. 22, no. 3, pp. 2139–2155, 2022

    2022

  3. [11]

    Coded over-the-air computa- tion for model aggregation in federated learning,

    N. Zhang, M. Tao, J. Wang, and S. Shao, “Coded over-the-air computa- tion for model aggregation in federated learning,” IEEE Commun. Lett., vol. 27, no. 1, pp. 160–164, 2022

    2022

  4. [12]

    Communication-efficient federated learning over-the-air with sparse one-bit quantization,

    J. Oh, D. Lee, D. Won, W. Noh, and S. Cho, “Communication-efficient federated learning over-the-air with sparse one-bit quantization,” IEEE Trans. Wireless Commun., 2024

    2024

  5. [13]

    Communication-efficient stochastic zeroth-order optimization for fed- erated learning,

    W. Fang, Z. Yu, Y . Jiang, Y . Shi, C. N. Jones, and Y . Zhou, “Communication-efficient stochastic zeroth-order optimization for fed- erated learning,” IEEE Trans. Signal Process. , vol. 70, pp. 5058–5073, 2022

    2022

  6. [14]

    Fine-tuning language models with just forward passes,

    S. Malladi, T. Gao, E. Nichani, A. Damian, J. D. Lee, D. Chen, and S. Arora, “Fine-tuning language models with just forward passes,” Adv. Neural Inf. Process. Syst. (NeurIPS) , vol. 36, pp. 53 038–53 075, 2023

    2023

  7. [15]

    Federated full- parameter tuning of billion-sized language models with communication cost under 18 kilobytes,

    Z. Qin, D. Chen, B. Qian, B. Ding, Y . Li, and S. Deng, “Federated full- parameter tuning of billion-sized language models with communication cost under 18 kilobytes,” arXiv preprint arXiv:2312.06353 , 2023

    2023 arXiv

  8. [16]

    Federated LoRA with sparse communication,

    K. Kuo, A. Raje, K. Rajesh, and V . Smith, “Federated LoRA with sparse communication,” arXiv preprint arXiv:2406.05233 , 2024

    2024 arXiv

  9. [17]

    Pruning analog over-the-air distributed learning models with accuracy loss guarantee,

    K. Xu, H. H. Yang, Z. Zhao, W. Hong, T. Q. Quek, and M. Peng, “Pruning analog over-the-air distributed learning models with accuracy loss guarantee,” in Proc. IEEE Int. Conf. Commun. (ICC) . IEEE, 2022, pp. 5202–5207

    2022

  10. [18]

    Over- the-air federated learning via second-order optimization,

    P. Yang, Y . Jiang, T. Wang, Y . Zhou, Y . Shi, and C. N. Jones, “Over- the-air federated learning via second-order optimization,” IEEE Trans. Wireless Commun., vol. 21, no. 12, pp. 10 560–10 575, 2022

    2022

  11. [19]

    Federated learning over-the- air by retransmissions,

    H. Hellstr ¨om, V . Fodor, and C. Fischione, “Federated learning over-the- air by retransmissions,” IEEE Trans. Wireless Commun., vol. 22, no. 12, pp. 9143–9156, 2023

    2023

  12. [20]

    Federated learning over wireless channels: Dynamic resource allocation and task scheduling,

    S. Chu, J. Li, J. Wang, Z. Wang, M. Ding, Y . Zhang, Y . Qian, and W. Chen, “Federated learning over wireless channels: Dynamic resource allocation and task scheduling,” IEEE Trans. Cogn. Commun. Netw. , vol. 8, no. 4, pp. 1910–1924, 2022

    1910

  13. [21]

    Peta-scale embedded photonics architecture for distributed deep learning applications,

    Z. Wu, L. Y . Dai, A. Novick, M. Glick, Z. Zhu, S. Rumley, G. Michel- ogiannakis, J. Shalf, and K. Bergman, “Peta-scale embedded photonics architecture for distributed deep learning applications,” J. Lightw. Tech- nol., vol. 41, no. 12, pp. 3737–3749, 2023

    2023

  14. [22]

    NR; Physical Channels and Modulation,

    3GPP, “NR; Physical Channels and Modulation,” 3rd Generation Part- nership Project (3GPP), Technical Specification (TS) 38.211, 09 2018, version 15.2.0

    2018

  15. [23]

    Deep residual learning for image recognition,

    K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 2016, pp. 770–778

    2016

  16. [24]

    signSGD: Compressed optimisation for non-convex problems,

    J. Bernstein, Y .-X. Wang, K. Azizzadenesheli, and A. Anandkumar, “signSGD: Compressed optimisation for non-convex problems,” in Int. Conf. Mach. Learn. (ICML) , 2018, pp. 560–569

    2018

  17. [25]

    Rethinking DP-SGD in discrete domain: Exploring logistic distribution in the realm of signSGD,

    J. Jang, S. Hwang, and H. J. Yang, “Rethinking DP-SGD in discrete domain: Exploring logistic distribution in the realm of signSGD,” in Int. Conf. Mach. Learn. (ICML) , 2024

    2024

  18. [26]

    Deep gradient compression: Reducing the communication bandwidth for distributed training,

    Y . Lin, S. Han, H. Mao, Y . Wang, and W. J. Dally, “Deep gradient compression: Reducing the communication bandwidth for distributed training,” arXiv preprint arXiv:1712.01887 , 2017

    2017 arXiv

  19. [27]

    Feder- ated learning with compression: Unified analysis and sharp guarantees,

    F. Haddadpour, M. M. Kamani, A. Mokhtari, and M. Mahdavi, “Feder- ated learning with compression: Unified analysis and sharp guarantees,” in Proc. Int. Conf. Artif. Intell. Stat. (AISTATS) , 2021, pp. 2350–2358

    2021

  20. [28]

    Communication- efficient byzantine-resilient federated zero-order optimization,

    A. d. S. D. Neto, M. Egger, M. Bakshi, and R. Bitar, “Communication- efficient byzantine-resilient federated zero-order optimization,” arXiv preprint arXiv:2406.14362, 2024

    2024 arXiv

  21. [29]

    A uniform-forcing transceiver design for over-the-air function computation,

    L. Chen, X. Qin, and G. Wei, “A uniform-forcing transceiver design for over-the-air function computation,” IEEE Wireless Commun. Lett. , vol. 7, no. 6, pp. 942–945, 2018

    2018

  22. [30]

    Lora: Low-rank adaptation of large language models,

    E. J. Hu, Y . Shen, P. Wallis, Z. Allen-Zhu, Y . Li, S. Wang, L. Wang, and W. Chen, “Lora: Low-rank adaptation of large language models,” arXiv preprint arXiv:2106.09685 , 2021

    2021 arXiv

  23. [31]

    Over-the-air federated learning via weighted aggregation,

    S. M. Azimi-Abarghouyi and L. Tassiulas, “Over-the-air federated learning via weighted aggregation,” IEEE Trans. Wireless Commun. , 2024

    2024

  24. [32]

    Optimized power control for over-the-air computation in fading channels,

    X. Cao, G. Zhu, J. Xu, and K. Huang, “Optimized power control for over-the-air computation in fading channels,” IEEE Trans. Wireless Commun., vol. 19, no. 11, pp. 7498–7513, 2020

    2020

  25. [33]

    Random gradient-free minimization of convex functions,

    Y . Nesterov and V . Spokoiny, “Random gradient-free minimization of convex functions,” Found. Comput. Math., vol. 17, no. 2, pp. 527–566, 2017

    2017

  26. [34]

    Signature optimization for CDMA with limited feedback,

    W. Santipach and M. Honig, “Signature optimization for CDMA with limited feedback,” IEEE Trans. Inf. Theory , vol. 51, no. 10, pp. 3475– 3492, 2005

    2005

  27. [35]

    On the performance of random vector quantization limited feedback beamforming in a MISO system,

    C. K. Au-yeung and D. J. Love, “On the performance of random vector quantization limited feedback beamforming in a MISO system,” IEEE Trans. Wireless Commun., vol. 6, no. 2, pp. 458–462, 2007

    2007

  28. [36]

    Capacity of a multiple-antenna fading channel with a quantized precoding matrix,

    W. Santipach and M. L. Honig, “Capacity of a multiple-antenna fading channel with a quantized precoding matrix,” IEEE Trans. Inf. Theory , vol. 55, no. 3, pp. 1218–1234, 2009

    2009

  29. [37]

    On the convergence of sgd with biased gradients,

    A. Ajalloeian and S. U. Stich, “On the convergence of sgd with biased gradients,” arXiv preprint arXiv:2008.00051 , 2020

    2008 arXiv

  30. [38]

    Study on channel model for frequencies from 0.5 to 100 GHz,

    3GPP, “Study on channel model for frequencies from 0.5 to 100 GHz,” 3rd Generation Partnership Project (3GPP), Tech. Rep. TR 38.901, 2024

    2024

  31. [39]

    Learning multiple layers of features from tiny images,

    A. Krizhevsky, “Learning multiple layers of features from tiny images,” Master’s thesis, University of Tront , 2009

    2009

  32. [40]

    Reading digits in natural images with unsupervised feature learning,

    Y . Netzer, T. Wang, A. Coates, A. Bissacco, B. Wu, A. Y . Ng et al. , “Reading digits in natural images with unsupervised feature learning,” in NeurIPS Workshop, 2011

    2011

  33. [41]

    Brain tumor mri dataset,

    M. Nickparvar, “Brain tumor mri dataset,” 2021. [Online]. Available: https://www.kaggle.com/dsv/2645886

    2021

  34. [42]

    Tiny imagenet visual recognition challenge,

    Y . Le and X. Yang, “Tiny imagenet visual recognition challenge,” CS 231N, vol. 7, no. 7, p. 3, 2015

    2015

  35. [43]

    Rendering wireless environments useful for gradient estimators: A zero-order stochastic federated learning method,

    E. Mhanna and M. Assaad, “Rendering wireless environments useful for gradient estimators: A zero-order stochastic federated learning method,” arXiv preprint arXiv:2401.17460 , 2024

    2024 arXiv

  36. [44]

    Transmit beam- forming for physical-layer multicasting,

    N. D. Sidiropoulos, T. N. Davidson, and Z.-Q. Luo, “Transmit beam- forming for physical-layer multicasting,” IEEE Trans. Signal Process. , vol. 54, no. 6, pp. 2239–2251, 2006

    2006

  37. [45]

    On transmit beamforming for physical-layer multicasting,

    J. Li and A. P. Petropulu, “On transmit beamforming for physical-layer multicasting,” in Proc. IEEE Global Commun. Conf. (GLOBECOM) , 2011, pp. 1–5

    2011

  38. [46]

    A conic quadratic programming approach to physical layer multicasting for large-scale antenna arrays,

    L.-N. Tran, M. F. Hanif, and M. Juntti, “A conic quadratic programming approach to physical layer multicasting for large-scale antenna arrays,” IEEE Signal Process. Lett. , vol. 21, no. 1, pp. 114–117, 2013

    2013

  39. [47]

    An efficient global algorithm for single-group multicast beamforming,

    C. Lu and Y .-F. Liu, “An efficient global algorithm for single-group multicast beamforming,” IEEE Trans. Signal Process. , vol. 65, no. 14, pp. 3761–3774, 2017

    2017

  40. [48]

    On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables,

    L. Isserlis, “On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables,” Biometrika, vol. 12, no. 1/2, pp. 134–139, 1918

    1918

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.