arxiv: 2604.09680 · v1 · submitted 2026-04-03 · 💻 cs.NI

Recognition: 2 theorem links

· Lean Theorem

Hybrid Hierarchical Federated Learning over 5G/NextG Wireless Networking

Haiyun Liu, Jiahao Xue, Jie Xu, Yao Liu, Zhuo Lu

Authors on Pith no claims yet

Pith reviewed 2026-05-13 19:09 UTC · model grok-4.3

classification 💻 cs.NI

keywords hybrid hierarchical federated learning5G wireless networksCoMP transmissionnon-IID datamodel convergenceedge serversfederated learning

0 comments

The pith

Allowing clients to aggregate models with multiple edge servers at once speeds hierarchical federated learning when coverage overlaps.

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

The paper proposes hybrid hierarchical federated learning so that clients located where multiple edge servers overlap can send model updates to all of them simultaneously. Traditional hierarchical federated learning forces each client to pick only one server, leaving unused the coordinated multi-point capability already present in 5G and NextG networks. A convergence upper bound is derived, and experiments with non-IID data show up to twice the speed to target accuracy when fifteen of fifty-seven clients reach more than one server and each server sees data from only two of ten classes. A sympathetic reader would care because this change turns an existing network feature into faster training without requiring new base-station hardware.

Core claim

HHFL relaxes the single-server association rule of hierarchical federated learning so that clients in overlapping coverage areas perform model aggregation with every reachable edge server at the same time. This produces richer inter-server knowledge transfer that reduces divergence caused by non-IID data partitions across servers. The paper supplies a rigorous convergence upper bound and reports that the resulting training process reaches the same accuracy in roughly half the rounds under the tested non-IID configuration.

What carries the argument

Simultaneous multi-edge-server model aggregation performed by clients in coverage overlap zones

If this is right

Convergence reaches target accuracy in up to half the rounds when each edge server sees data from only two of ten classes.
Inter-edge-server knowledge sharing increases because overlapping clients carry updates across server boundaries.
The approach applies directly to any CoMP-enabled 5G or NextG deployment without hardware changes.
A new convergence upper bound is established for the hybrid multi-server association case.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same multi-association pattern could be tested in other multi-access wireless settings such as Wi-Fi 6 or satellite networks.
Client mobility patterns that change overlap regions over time would likely require dynamic association rules.
Reducing the number of global communication rounds may also lower total energy consumed by clients.

Load-bearing premise

Clients can communicate with multiple edge servers at the same time without interference, synchronization overhead, or extra bandwidth costs that would cancel the reported convergence gains.

What would settle it

An experiment on the same non-IID partition that adds realistic multi-link interference and coordination latency and shows that total training time increases rather than decreases.

Figures

Figures reproduced from arXiv: 2604.09680 by Haiyun Liu, Jiahao Xue, Jie Xu, Yao Liu, Zhuo Lu.

**Figure 2.** Figure 2: Coordinated multi-point technique. A. Motivation and Architecture Design With the increasing densification of wireless infrastructures and the growing demand for seamless coverage in 5G and NextG communication systems, overlapping regions among BSs have become increasingly common [26]–[29]. The coordinated multi-point (CoMP) transmission and reception technique has been proposed [30] as an enhanced techni… view at source ↗

**Figure 3.** Figure 3: The actual distribution of clients and the number of clients assigned to each ES under the HFL architecture. The [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 5.** Figure 5: It can be observed that HHFL consistently outperforms [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: Client actual distribution and the number of clients assigned to each ES for the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: Convergence curves under different numbers of clients [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

**Figure 9.** Figure 9: Test accuracy versus wall-clock time across six cases (time is normalized such that one unit corresponds to the time for a client to complete E local updates). 0 0.5 1 1.5 2 2.5 Total data transmitted 104 84 86 88 90 Test accuracy (%) HFL: (IID, IID) HFL: (non-IID-1, IID) HFL: (non-IID-2, IID) HHFL: (IID, IID) HHFL: (non-IID-1, IID) HHFL: (non-IID-2, IID) (a) ES IID scenario, convex loss function 0 0.5 1 1… view at source ↗

**Figure 11.** Figure 11: Efficiency gain of HHFL over HFL across Cases 1- [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗

**Figure 13.** Figure 13: Efficiency gain of HHFL over HFL with varying [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗

**Figure 15.** Figure 15: Test accuracy versus wall-clock time across six cases on the CIFAR-10 dataset (time is normalized such that one unit corresponds to the time for a client to complete E local updates). 0 2 4 6 8 10 Total data transmitted 104 0 20 40 60 80 Test accuracy (%) HFL: (IID, IID) HFL: (non-IID-1, IID) HFL: (non-IID-2, IID) HHFL: (IID, IID) HHFL: (non-IID-1, IID) HHFL: (non-IID-2, IID) (a) ES IID scenario 0 2 4 6 8… view at source ↗

read the original abstract

Today's 5G and NextG wireless networks are moving toward using the coordinated multi-point (CoMP) transmission and reception technique, where a client can be simultaneously served by multiple base stations (BSs) for better communication performance. However, traditional hierarchical federated learning (HFL) architectures impose the constraint that each client can be associated with only one edge server (ES) at a time. If we keep using the traditional HFL architectures in modern hierarchical networks for model training, the benefits of the CoMP technique would remain unexploited and leave room for further improvements in training efficiency. To address this issue, we propose hybrid hierarchical federated learning (HHFL), which allows clients in overlapping regions to simultaneously communicate with multiple edge servers (ESs) for model aggregation. HHFL is able to enhance inter-ES knowledge sharing, thereby mitigating model divergence and improving training efficiency. We provide a rigorous theoretical convergence analysis with a convergence upper bound to validate its effectiveness. Experimental results show that HHFL outperforms traditional HFL, particularly when the data across different ESs is not independent and identically distributed (non-IID). For example, when each ES is dominated by only two of the ten classes and 15 out of the 57 clients can connect to multiple ESs, HHFL achieves up to 2x faster convergence under the same configuration. These results demonstrate that HHFL provides a scalable and efficient solution for FL model training in today's and NextG wireless networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

HHFL relaxes the single-ES rule in hierarchical FL so overlapping clients can aggregate with multiple servers in CoMP 5G setups, claiming 2x faster convergence in one non-IID case, but the bound treats extra links as cost-free.

read the letter

The main thing here is that the paper lets clients in CoMP overlap zones aggregate models with more than one edge server at a time instead of sticking to the usual single-ES association in hierarchical federated learning. This is pitched as a way to move knowledge across servers faster when data is non-IID, and they report up to 2x quicker convergence in a setup where each server sees only two of ten classes and 15 of 57 clients have multi-ES links. The idea is a direct extension that uses existing 5G infrastructure rather than inventing new hardware. They also sketch a convergence upper bound to back it up. That part is useful for people thinking about real wireless deployments because it ties the architecture to CoMP without requiring major changes. The soft spots are in the details that are missing from the abstract. The bound does not appear to include the extra latency, interference, or bandwidth costs that simultaneous multi-ES communication would create under a realistic scheduler, which could erase the round-count savings in wall-clock time. The experiments are described at a high level with no error bars, no full baseline list, and no mention of how the simulation handles resource allocation for the multi-connected clients. This leaves the 2x number hard to evaluate. The work is aimed at researchers who build federated learning systems on top of 5G or NextG networks and care about non-IID performance in practice. It is not a deep theoretical shift, but the architectural point is clear enough that a referee should look at the full math and simulations to see whether the overheads are modeled and whether the bound holds. I would send it out for review rather than desk reject.

Referee Report

3 major / 3 minor

Summary. The manuscript proposes hybrid hierarchical federated learning (HHFL) for 5G/NextG networks, extending traditional HFL by allowing clients in overlapping coverage areas to simultaneously aggregate models with multiple edge servers via CoMP. It claims a rigorous convergence upper bound and reports up to 2x faster convergence versus standard HFL in a specific non-IID regime (each ES dominated by only two of ten classes, with 15/57 clients multi-connected).

Significance. If the central claim holds after accounting for realistic communication costs, the work would be significant for FL over wireless networks by leveraging CoMP to improve inter-ES knowledge sharing and mitigate non-IID divergence. The specific speedup result in a challenging non-IID setting and the attempt at a theoretical bound are strengths, but the idealized treatment of multi-link overheads limits the result's immediate impact.

major comments (3)

[Convergence analysis] Convergence analysis section: The upper bound is presented as validating faster training when multi-ES clients are allowed, yet the derivation (as summarized) treats simultaneous uploads/downloads as cost-free with zero added latency, interference, or bandwidth penalty. This assumption is load-bearing for the 2x speedup claim, as any realistic CoMP scheduler would impose orthogonal resource allocation or SINR degradation that increases wall-clock time per round.
[Experimental results] Experimental results section: The reported 2x faster convergence for the non-IID case (each ES dominated by two classes, 15/57 multi-connected clients) lacks error bars, detailed baseline descriptions, and any simulation of CoMP scheduling overheads. The idealized setup does not close the loop on whether the reduction in rounds-to-convergence survives realistic per-round time increases, directly undermining the practical claim.
[System model] System model section: The assumption that clients can simultaneously communicate with multiple ESs without prohibitive synchronization, interference, or bandwidth costs is stated without quantitative analysis or ablation; this is load-bearing because the abstract's speedup example relies on 15 multi-connected clients whose extra links are treated as free.

minor comments (3)

[Abstract] The abstract states a 'rigorous theoretical convergence analysis with a convergence upper bound' but supplies no equation numbers or derivation outline for inspection.
[Experimental results] Convergence curves in the experimental figures should include confidence intervals or multiple runs to support the 2x speedup claim.
[System model] Notation for multi-ES aggregation (e.g., how models from overlapping clients are combined across ESs) is not clearly defined in the system model.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the scope and limitations of our work. We address each major comment point by point below, indicating where revisions will be made to strengthen the manuscript while preserving the core contributions on HHFL and its convergence benefits in non-IID settings.

read point-by-point responses

Referee: Convergence analysis section: The upper bound is presented as validating faster training when multi-ES clients are allowed, yet the derivation (as summarized) treats simultaneous uploads/downloads as cost-free with zero added latency, interference, or bandwidth penalty. This assumption is load-bearing for the 2x speedup claim, as any realistic CoMP scheduler would impose orthogonal resource allocation or SINR degradation that increases wall-clock time per round.

Authors: We thank the referee for this observation. Our convergence analysis derives an upper bound on the number of communication rounds to reach a target accuracy, showing that multi-ES aggregation reduces the client-drift term in non-IID data. The bound itself is agnostic to per-round wall-clock time and focuses on iteration complexity. We agree that the presentation should explicitly separate round count from elapsed time. In the revision we will (i) clarify this distinction in the analysis section, (ii) add a short analytical discussion of CoMP scheduling overhead (e.g., resource partitioning factor), and (iii) include a remark that the reported speedup is measured in rounds while noting the practical trade-off. These changes will be marked as partial revisions. revision: partial
Referee: Experimental results section: The reported 2x faster convergence for the non-IID case (each ES dominated by two classes, 15/57 multi-connected clients) lacks error bars, detailed baseline descriptions, and any simulation of CoMP scheduling overheads. The idealized setup does not close the loop on whether the reduction in rounds-to-convergence survives realistic per-round time increases, directly undermining the practical claim.

Authors: We agree that error bars, clearer baseline descriptions, and an overhead sensitivity study are needed. In the revised manuscript we will: add standard-deviation error bars from five independent runs; expand the experimental setup subsection with explicit descriptions of all baselines (including communication-round definitions); and introduce a new ablation that scales per-round latency by factors of 1.0x–1.5x to simulate CoMP overhead. Under these moderate overheads the round reduction still yields net wall-clock improvement in the reported non-IID regime. These additions constitute a full revision of the experimental section. revision: yes
Referee: System model section: The assumption that clients can simultaneously communicate with multiple ESs without prohibitive synchronization, interference, or bandwidth costs is stated without quantitative analysis or ablation; this is load-bearing because the abstract's speedup example relies on 15 multi-connected clients whose extra links are treated as free.

Authors: The system model is grounded in the 5G CoMP framework, where joint transmission/reception is already standardized with coordinated resource allocation. We will strengthen the section by adding (i) a brief quantitative discussion citing 5G CoMP literature on typical synchronization and bandwidth overheads, and (ii) an ablation varying the fraction of multi-connected clients (0–15) while holding total bandwidth fixed. This will quantify the sensitivity of the speedup to the number of extra links without altering the core model assumptions. The change will be a partial revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives a convergence upper bound for HHFL by extending standard HFL analysis to permit simultaneous multi-ES aggregation for overlapping clients. No equations or steps are exhibited that reduce this bound to fitted parameters, self-definitions, or load-bearing self-citations by construction. The 2x convergence claim is supported by separate experimental results under the stated non-IID regime, and the theoretical extension treats multi-link communication as an added degree of freedom without circular re-use of the target outcome. The derivation remains self-contained against external HFL benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the feasibility of simultaneous multi-ES communication and on the validity of an unspecified convergence bound; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)

domain assumption Clients located in coverage overlap can communicate simultaneously with multiple edge servers without prohibitive interference or overhead
Invoked to justify the HHFL architecture in CoMP networks

pith-pipeline@v0.9.0 · 5572 in / 1154 out tokens · 52304 ms · 2026-05-13T19:09:32.434180+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
HHFL algorithm: wt0i = 1/|Si| Σn∈Si wt0(n); edge aggregation wt0+E(n) = Σi∈Cn (1/♢n) pi/|Si| vt+1i; convergence bound E[F(wt)]−F∗≤L/2 Z/(t+α) with Z containing σi2, Γ, and drift term 22G+1H2(GE+G−2)[(GE−1)+E2(G−1)]
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
Assumptions 1–4 (L-smooth, μ-strongly convex, bounded variance, bounded gradients) and virtual global model wt = Σi pi wti

Reference graph

Works this paper leans on

92 extracted references · 92 canonical work pages

[1]

Federated learning for uavs- enabled wireless networks: Use cases, challenges, and open problems,

B. Brik, A. Ksentini, and M. Bouaziz, “Federated learning for uavs- enabled wireless networks: Use cases, challenges, and open problems,” IEEE Access, 2020

work page 2020
[2]

Federated learning for internet of things: A compre- hensive survey,

D. C. Nguyen, M. Ding, P. N. Pathirana, A. Seneviratne, J. Li, and H. Vincent Poor, “Federated learning for internet of things: A compre- hensive survey,”IEEE Commun. Surv. Tutor., 2021

work page 2021
[3]

Fedloc: Federated learning framework for data-driven cooperative localization and location data processing,

F. Yin, Z. Lin, Q. Kong, Y . Xu, D. Li, S. Theodoridis, and S. R. Cui, “Fedloc: Federated learning framework for data-driven cooperative localization and location data processing,”IEEE Open J. Signal Process., 2020

work page 2020
[4]

Traffic analysis of a local area network with a star topology,

M. K. Mehmet-Ali, J. F. Hayes, and A. K. Elhakeem, “Traffic analysis of a local area network with a star topology,”IEEE Trans. Commun., 1988

work page 1988
[5]

A large hierarchical network star—star topology design algorithm,

J. Petrek and V . Sledt, “A large hierarchical network star—star topology design algorithm,”Eur. Trans. Telecommun., 2001

work page 2001
[6]

Nacrp: A connectivity protocol for star topology wireless sensor networks,

L. Goratti, T. Baykas, T. Rasheed, and S. Kato, “Nacrp: A connectivity protocol for star topology wireless sensor networks,”IEEE Wirel. Commun. Lett., 2015

work page 2015
[7]

An active star topology for improving fault confinement in can networks,

M. Barranco, J. Proenza, G. Rodr ´ıguez-Navas, and L. Almeida, “An active star topology for improving fault confinement in can networks,” IEEE Trans Ind. Informat., 2006

work page 2006
[8]

A comparative study of topological properties of hypercubes and star graphs,

K. Day and A. Tripathi, “A comparative study of topological properties of hypercubes and star graphs,”IEEE Trans. Parallel Distrib. Syst., 2002

work page 2002
[9]

Parameterized hierarchical layer topology construction for wireless networks,

J. Lessmann and A. Krishnamurthy, “Parameterized hierarchical layer topology construction for wireless networks,” inIEEE ICSNC, 2007

work page 2007
[10]

Adaptive hierarchical federated learning over wireless networks,

B. Xu, W. Xia, W. Wen, P. Liu, H. Zhao, and H. Zhu, “Adaptive hierarchical federated learning over wireless networks,”IEEE Trans. Veh. Technol., 2021

work page 2021
[11]

Hierarchical organization in complex networks,

E. Ravasz and A.-L. Barab ´asi, “Hierarchical organization in complex networks,”APS Physical review E, 2003

work page 2003
[12]

Performance analysis for downlink transmission in multiconnectivity cellular v2x networks,

L. Jiao, J. Zhao, Y . Xu, T. Zhang, H. Zhou, and D. Zhao, “Performance analysis for downlink transmission in multiconnectivity cellular v2x networks,”IEEE Internet Things J., 2023

work page 2023
[13]

Multi- connection to the sky: Energy-efficient beamforming for multi-satellite uplink transmission with lens antenna array,

N. Ye, X. Cao, X. Ding, J. Li, D. Zhao, and Q. Ouyang, “Multi- connection to the sky: Energy-efficient beamforming for multi-satellite uplink transmission with lens antenna array,”IEEE Trans. Green Com- mun. Netw., 2023

work page 2023
[14]

Space-air-ground integrated wireless networks for 6g: Basics, key technologies and future trends,

Y . Xiao, Z. Ye, M. Wu, H. Li, M. Xiao, M.-S. Alouini, A. Al- Hourani, and S. Cioni, “Space-air-ground integrated wireless networks for 6g: Basics, key technologies and future trends,”IEEE J. Sel. Areas Commun., 2024

work page 2024
[15]

Research on 6g mobile communication system,

G. Xu, “Research on 6g mobile communication system,” inJournal of Physics: Conference Series. IOP Publishing, 2020

work page 2020
[16]

Federated learning for 6g: Applications, challenges, and opportunities,

Z. Yang, M. Chen, K.-K. Wong, H. V . Poor, and S. Cui, “Federated learning for 6g: Applications, challenges, and opportunities,”Elsevier Engineering, 2022

work page 2022
[17]

6g wire- less communication systems: Applications, requirements, technologies, challenges, and research directions,

M. Z. Chowdhury, M. Shahjalal, S. Ahmed, and Y . M. Jang, “6g wire- less communication systems: Applications, requirements, technologies, challenges, and research directions,”IEEE Open J. Commun. Soc., 2020

work page 2020
[18]

6g and beyond: The future of wireless communications systems,

I. F. Akyildiz, A. Kak, and S. Nie, “6g and beyond: The future of wireless communications systems,”IEEE access, 2020

work page 2020
[19]

6g wireless communications: Vision and potential techniques,

P. Yang, Y . Xiao, M. Xiao, and S. Li, “6g wireless communications: Vision and potential techniques,”IEEE network, 2019

work page 2019
[20]

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,” inPMLR AISTATS, 2017. 15

work page 2017
[21]

Advances and open problems in federated learning,

P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. N. Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cummingset al., “Advances and open problems in federated learning,”Found. Trends Mach. Learn., 2021

work page 2021
[22]

Practical secure aggregation for privacy-preserving machine learning,

K. Bonawitz, V . Ivanov, B. Kreuter, A. Marcedone, H. B. McMahan, S. Patel, D. Ramage, A. Segal, and K. Seth, “Practical secure aggregation for privacy-preserving machine learning,” inACM CCS, 2017

work page 2017
[23]

Federated optimization in heterogeneous networks,

T. Li, A. K. Sahu, M. Zaheer, M. Sanjabi, A. Talwalkar, and V . Smith, “Federated optimization in heterogeneous networks,” inMLSys, 2020

work page 2020
[24]

Federated multi-task learning,

V . Smith, C.-K. Chiang, M. Sanjabi, and A. S. Talwalkar, “Federated multi-task learning,”Adv. Neural Inf. Process. Syst., 2017

work page 2017
[25]

Client-edge-cloud hierarchical federated learning,

L. Liu, J. Zhang, S. Song, and K. B. Letaief, “Client-edge-cloud hierarchical federated learning,” inIEEE ICC, 2020

work page 2020
[26]

Network densification: the dominant theme for wireless evolution into 5g,

N. Bhushan, J. Li, D. Malladi, R. Gilmore, D. Brenner, A. Damnjanovic, R. T. Sukhavasi, C. Patel, and S. Geirhofer, “Network densification: the dominant theme for wireless evolution into 5g,”IEEE Commun. Mag., 2014

work page 2014
[27]

A survey on coverage enhancement in cellular networks: Challenges and solutions for future deployments,

R. Borralho, A. Mohamed, A. U. Quddus, P. Vieira, and R. Tafazolli, “A survey on coverage enhancement in cellular networks: Challenges and solutions for future deployments,”IEEE Commun. Surv. Tutor., 2021

work page 2021
[28]

A survey on handover and mobility management in 5g hetnets: current state, challenges, and future directions,

Y . Ullah, M. B. Roslee, S. M. Mitani, S. A. Khan, and M. H. Jusoh, “A survey on handover and mobility management in 5g hetnets: current state, challenges, and future directions,”Sensors, 2023

work page 2023
[29]

A survey of handover management in mobile hetnets: Current challenges and future direc- tions,

A. U. Rehman, M. B. Roslee, and T. Jun Jiat, “A survey of handover management in mobile hetnets: Current challenges and future direc- tions,”Applied Sciences, 2023

work page 2023
[30]

Enhancing the cellular downlink capacity via co-processing at the transmitting end,

S. Shamai and B. M. Zaidel, “Enhancing the cellular downlink capacity via co-processing at the transmitting end,” inIEEE VTC Spring, 2001

work page 2001
[31]

A comprehensive review on coordinated multi-point operation for lte-a,

F. Qamar, K. B. Dimyati, M. N. Hindia, K. A. B. Noordin, and A. M. Al- Samman, “A comprehensive review on coordinated multi-point operation for lte-a,”Computer Networks, 2017

work page 2017
[32]

Co- ordinated multi-point transmission in 5g and beyond heterogeneous networks,

F. Irram, M. Ali, Z. Maqbool, F. Qamar, and J. J. Rodrigues, “Co- ordinated multi-point transmission in 5g and beyond heterogeneous networks,” inIEEE INMIC, 2020

work page 2020
[33]

Comp enhanced subcarrier and power allocation for multi-numerology based 5g-nr networks,

L.-H. Shen, C.-Y . Su, and K.-T. Feng, “Comp enhanced subcarrier and power allocation for multi-numerology based 5g-nr networks,”IEEE Trans. Veh. Technol., 2022

work page 2022
[34]

Generalized coordinated multipoint framework for 5g and beyond,

M. S. J. Solaija, H. Salman, A. B. Kihero, M. ˙I. Sa ˘glam, and H. Arslan, “Generalized coordinated multipoint framework for 5g and beyond,” IEEE Access, 2021

work page 2021
[35]

The road towards 6g: A comprehensive survey,

W. Jiang, B. Han, M. A. Habibi, and H. D. Schotten, “The road towards 6g: A comprehensive survey,”IEEE Open J. Commun. Soc., 2021

work page 2021
[36]

Hfel: Joint edge asso- ciation and resource allocation for cost-efficient hierarchical federated edge learning,

S. Luo, X. Chen, Q. Wu, Z. Zhou, and S. Yu, “Hfel: Joint edge asso- ciation and resource allocation for cost-efficient hierarchical federated edge learning,”IEEE Trans. Wireless Commun., 2020

work page 2020
[37]

Personalized client-edge-cloud hierarchical federated learning in mobile edge computing,

C. Ma, X. Li, B. Huang, G. Li, and F. Li, “Personalized client-edge-cloud hierarchical federated learning in mobile edge computing,”Springer J. Cloud Comput., 2024

work page 2024
[38]

Hiflash: Communication-efficient hierarchical federated learning with adaptive staleness control and heterogeneity-aware client-edge associa- tion,

Q. Wu, X. Chen, T. Ouyang, Z. Zhou, X. Zhang, S. Yang, and J. Zhang, “Hiflash: Communication-efficient hierarchical federated learning with adaptive staleness control and heterogeneity-aware client-edge associa- tion,”IEEE Trans. Parallel Distrib. Syst., 2023

work page 2023
[39]

Security assessment of hierarchical federated deep learning,

D. S. Alqattan, R. Sun, H. Liang, G. Nicosia, V . Snasel, R. Ranjan, and V . Ojha, “Security assessment of hierarchical federated deep learning,” inSpringer ICANN, 2024

work page 2024
[40]

Timely asynchronous hierarchical federated learning: Age of convergence,

P. Mitra and S. Ulukus, “Timely asynchronous hierarchical federated learning: Age of convergence,” inIEEE WiOpt, 2023

work page 2023
[41]

Analyzing grant-free access for urllc service,

Y . Liu, Y . Deng, M. Elkashlan, A. Nallanathan, and G. K. Karagiannidis, “Analyzing grant-free access for urllc service,”IEEE J. Sel. Areas Commun., 2020

work page 2020
[42]

Fedmes: Speeding up federated learning with multiple edge servers,

D.-J. Han, M. Choi, J. Park, and J. Moon, “Fedmes: Speeding up federated learning with multiple edge servers,”IEEE J. Sel. Areas Commun., 2021

work page 2021
[43]

Submodel partitioning in hierar- chical federated learning: Algorithm design and convergence analysis,

W. Fang, D.-J. Han, and C. G. Brinton, “Submodel partitioning in hierar- chical federated learning: Algorithm design and convergence analysis,” inIEEE ICC, 2024

work page 2024
[44]

On the convergence of fedavg on non-iid data,

X. Li, K. Huang, W. Yang, S. Wang, and Z. Zhang, “On the convergence of fedavg on non-iid data,”arXiv preprint, 2019

work page 2019
[45]

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., 2022

work page 2022
[46]

Adaptive federated learning in resource constrained edge computing systems,

S. Wang, T. Tuor, T. Salonidis, K. K. Leung, C. Makaya, T. He, and K. Chan, “Adaptive federated learning in resource constrained edge computing systems,”IEEE J. Sel. Areas Commun., 2019

work page 2019
[47]

Fast-convergent federated learning,

H. T. Nguyen, V . Sehwag, S. Hosseinalipour, C. G. Brinton, M. Chiang, and H. V . Poor, “Fast-convergent federated learning,”IEEE J. Sel. Areas Commun., 2020

work page 2020
[48]

Convergence of update aware device scheduling for federated learning at the wireless edge,

M. M. Amiri, D. G ¨und¨uz, S. R. Kulkarni, and H. V . Poor, “Convergence of update aware device scheduling for federated learning at the wireless edge,”IEEE Trans. Wireless Commun., 2021

work page 2021
[49]

Fedpaq: A communication-efficient federated learning method with periodic averaging and quantization,

A. Reisizadeh, A. Mokhtari, H. Hassani, A. Jadbabaie, and R. Pedarsani, “Fedpaq: A communication-efficient federated learning method with periodic averaging and quantization,” inPMLR AISTATS, 2020

work page 2020
[50]

Communication-efficient algorithms for statistical optimization,

Y . Zhang, M. J. Wainwright, and J. C. Duchi, “Communication-efficient algorithms for statistical optimization,”Adv. Neural Inf. Process. Syst., 2012

work page 2012
[51]

Local sgd converges fast and communicates little,

S. U. Stich, “Local sgd converges fast and communicates little,”arXiv preprint, 2018

work page 2018
[52]

Towards federated learning at scale: Syste m design,

K. Bonawitz, “Towards federated learning at scale: Syste m design,” arXiv preprint, 2019

work page 2019
[53]

Federated learning with non-iid data,

Y . Zhao, M. Li, L. Lai, N. Suda, D. Civin, and V . Chandra, “Federated learning with non-iid data,”arXiv preprint, 2018

work page 2018
[54]

Threats to federated learning: A survey,

L. Lyu, H. Yu, and Q. Yang, “Threats to federated learning: A survey,” arXiv preprint, 2020

work page 2020
[55]

Final draft etsi es 203 228 v1. 2.0 (2017-02),

E. STANDARD, “Final draft etsi es 203 228 v1. 2.0 (2017-02),” 2017

work page 2017
[56]

Bridge the present and future: A cross-layer matching game in dynamic cloud- aided mobile edge networks,

H. Qi, M. Liwang, X. Wang, L. Li, W. Gong, J. Jin, and Z. Jiao, “Bridge the present and future: A cross-layer matching game in dynamic cloud- aided mobile edge networks,”IEEE Trans. Mobile Comput., 2024

work page 2024
[57]

An in-depth measurement analysis of 5g mmwave phy latency and its impact on end-to-end delay,

R. Fezeu, A. Brunstrom, M. Flores, and M. Fiore, “An in-depth measurement analysis of 5g mmwave phy latency and its impact on end-to-end delay,” inSpringer PAM, 2023

work page 2023
[58]

Next generation 5g wireless networks: A comprehensive survey,

M. Agiwal, A. Roy, and N. Saxena, “Next generation 5g wireless networks: A comprehensive survey,”IEEE Commun. Surv. Tutor, 2016

work page 2016
[59]

Hierarchical federated learning across heterogeneous cellular networks,

M. S. H. Abad, E. Ozfatura, D. Gunduz, and O. Ercetin, “Hierarchical federated learning across heterogeneous cellular networks,” inIEEE ICASSP, 2020

work page 2020
[60]

Hierarchical personalized federated learning for user modeling,

J. Wu, Q. Liu, Z. Huang, Y . Ning, H. Wang, E. Chen, J. Yi, and B. Zhou, “Hierarchical personalized federated learning for user modeling,” in ACM Web Conf., 2021

work page 2021
[61]

Hhhfl: Hierarchical heterogeneous horizontal federated learning for electroen- cephalography,

D. Gao, C. Ju, X. Wei, Y . Liu, T. Chen, and Q. Yang, “Hhhfl: Hierarchical heterogeneous horizontal federated learning for electroen- cephalography,”arXiv preprint, 2019

work page 2019
[62]

Min-max cost optimization for efficient hierarchical federated learning in wireless edge networks,

J. Feng, L. Liu, Q. Pei, and K. Li, “Min-max cost optimization for efficient hierarchical federated learning in wireless edge networks,”IEEE Trans. Parallel Distrib. Syst., 2021

work page 2021
[63]

Enhancing privacy via hierarchical federated learning,

A. Wainakh, A. S. Guinea, T. Grube, and M. M ¨uhlh¨auser, “Enhancing privacy via hierarchical federated learning,” inIEEE EuroS&PW, 2020

work page 2020
[64]

Toward robust hierarchical federated learning in internet of vehicles,

H. Zhou, Y . Zheng, H. Huang, J. Shu, and X. Jia, “Toward robust hierarchical federated learning in internet of vehicles,”IEEE Trans. Intell. Transp. Syst., 2023

work page 2023
[65]

Mobility-aware cluster federated learning in hierarchical wireless net- works,

C. Feng, H. H. Yang, D. Hu, Z. Zhao, T. Q. Quek, and G. Min, “Mobility-aware cluster federated learning in hierarchical wireless net- works,”IEEE Trans. Wireless Commun., 2022

work page 2022
[66]

Hierarchical federated learning with social context clustering-based participant selection for internet of medical things applications,

X. Zhou, X. Ye, K. I.-K. Wang, W. Liang, N. K. C. Nair, S. Shimizu, Z. Yan, and Q. Jin, “Hierarchical federated learning with social context clustering-based participant selection for internet of medical things applications,”IEEE Trans. Comput. Soc. Syst., 2023

work page 2023
[67]

Optimal user-edge assignment in hierarchical federated learning based on statistical properties and network topology constraints,

N. Mhaisen, A. A. Abdellatif, A. Mohamed, A. Erbad, and M. Guizani, “Optimal user-edge assignment in hierarchical federated learning based on statistical properties and network topology constraints,”IEEE Trans. Netw. Sci. Eng., 2021

work page 2021
[68]

Privacy vs. efficiency: Achieving both through adaptive hierarchical federated learning,

Y . Guo, F. Liu, T. Zhou, Z. Cai, and N. Xiao, “Privacy vs. efficiency: Achieving both through adaptive hierarchical federated learning,”IEEE Trans. Parallel Distrib. Syst., 2023

work page 2023
[69]

Context-aware online client selection for hierarchical federated learning,

Z. Qu, R. Duan, L. Chen, J. Xu, Z. Lu, and Y . Liu, “Context-aware online client selection for hierarchical federated learning,”IEEE Trans. Parallel Distrib. Syst., 2022

work page 2022
[70]

Accelerating federated learning with cluster construction and hierarchical aggrega- tion,

Z. Wang, H. Xu, J. Liu, Y . Xu, H. Huang, and Y . Zhao, “Accelerating federated learning with cluster construction and hierarchical aggrega- tion,”IEEE Trans. Mobile Comput., 2022

work page 2022
[71]

Smartpc: Hierarchical pace control in real-time federated learning system,

L. Li, H. Xiong, Z. Guo, J. Wang, and C.-Z. Xu, “Smartpc: Hierarchical pace control in real-time federated learning system,” inIEEE RTSS, 2019

work page 2019
[72]

Hed-fl: A hierarchical, energy efficient, and dynamic approach for edge federated learning,

F. De Rango, A. Guerrieri, P. Raimondo, and G. Spezzano, “Hed-fl: A hierarchical, energy efficient, and dynamic approach for edge federated learning,”Pervasive and Mobile Computing, 2023

work page 2023
[73]

Time minimization in hierarchical federated learning,

C. Liu, T. J. Chua, and J. Zhao, “Time minimization in hierarchical federated learning,” inIEEE/ACM SEC, 2022

work page 2022
[74]

Hierarchical federated learning with multi-timescale gradient correction,

W. Fang, D.-J. Han, E. Chen, S. Wang, and C. Brinton, “Hierarchical federated learning with multi-timescale gradient correction,”Adv. Neural Inf. Process. Syst., 2024

work page 2024
[75]

Quantized hierarchical fed- erated learning: A robust approach to statistical heterogeneity,

S. M. Azimi-Abarghouyi and V . Fodor, “Quantized hierarchical fed- erated learning: A robust approach to statistical heterogeneity,”arXiv preprint, 2024. 16

work page 2024
[76]

Personalized hierarchical split federated learning in wireless networks,

M.-F. Pervej and A. F. Molisch, “Personalized hierarchical split federated learning in wireless networks,”arXiv preprint, 2024

work page 2024
[77]

Federated learning with hierarchical clustering of local updates to improve training on non-iid data,

C. Briggs, Z. Fan, and P. Andras, “Federated learning with hierarchical clustering of local updates to improve training on non-iid data,” inIEEE IJCNN, 2020

work page 2020
[78]

Dynamic edge association and resource allocation in self-organizing hierarchical federated learning networks,

W. Y . B. Lim, J. S. Ng, Z. Xiong, D. Niyato, C. Miao, and D. I. Kim, “Dynamic edge association and resource allocation in self-organizing hierarchical federated learning networks,”IEEE J. Sel. Areas Commun., 2021

work page 2021
[79]

Joint adaptive aggregation and resource allocation for hierarchical federated learning systems based on edge-cloud collaboration,

Y . Su, W. Fan, Q. Meng, P. Chen, and Y . Liu, “Joint adaptive aggregation and resource allocation for hierarchical federated learning systems based on edge-cloud collaboration,”IEEE Trans. Cloud Comput., 2025

work page 2025
[80]

Compressed hierarchical federated learning for edge-level imbalanced wireless networks,

Y . Liu, Z. Qu, and J. Wang, “Compressed hierarchical federated learning for edge-level imbalanced wireless networks,”IEEE Trans. Comput. Soc. Syst., 2025

work page 2025

Showing first 80 references.