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HASFL: Heterogeneity-aware Split Federated Learning over Edge Computing Systems

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that per-device batch sizes and model split points, chosen from a new convergence bound, minimize the training time of split federated learning on heterogeneous edge devices.

desk verdict Solid first convergence bound for SFL with per-device batch sizes, but the latency-minimization claim rests on an unverified tightness assumption. read the letter →

arxiv 2506.08426 v1 pith:NZZ4EQIC submitted 2025-06-10 cs.LG cs.AIcs.DC

Zheng Lin , Zhe Chen , Xianhao Chen , Wei Ni , Yue Gao This is my paper
classification cs.LGcs.AIcs.DC
keywords federatedlearningsplitbatchsizemodelsplittingmobileedgecomputingstragglereffectconvergenceboundlatencyoptimization
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

This paper claims that the straggler bottleneck in split federated learning can be overcome by giving each edge device its own batch size and its own model split point, and that the right choices can be computed from a convergence bound rather than tuned by hand. The authors derive an upper bound on the average squared gradient norm of the global loss that depends explicitly on every device's batch size and on the depth of the client-side cut layer. They then treat this bound as an exact predictor of the number of training rounds needed to reach a target accuracy, turning latency minimization into a joint, tractable optimization over batch sizes and split points. If the bound is tight enough, the resulting schedules cut training time by at least 4x and improve accuracy by about 1% on standard image benchmarks.

What carries the argument

The load-bearing object is the convergence bound of Theorem 1 together with its inversion in Corollary 1. The bound decomposes the optimization error into three terms: an initial-optimization-gap term $\frac{2\vartheta}{\gamma R}$ that shrinks with more rounds, a mini-batch variance term $\frac{\beta\gamma}{N^2}\sum_i\sum_j \sigma_j^2/b_i$ that shrinks when any device raises its batch size, and a staleness term $4\beta^2\gamma^2I^2\sum_{j=1}^{L_c}G_j^2$ that appears only when client-side sub-models are aggregated every $I>1$ rounds and grows with the client-side split depth $L_c$. Because the variance term depends on the sum of $\sigma_j^2/b_i$ over devices, the bound predicts that batch sizes compensate across devices: a fast device can carry a large batch while a slow device uses a small one without changing the worst-case convergence guarantee. This bound converts the system design problem into the transformed program $P''$, solved by alternating a closed-form batch-size update (Proposition 1, using the Newton-Jacobi method) with a Dinkelbach-based split-point update.

What would settle it

Record, on the paper's CIFAR-10/VGG-16 setting, the round at which the average squared gradient norm first drops below a target $\varepsilon$ and compare it with the value $R$ predicted by Corollary 1 using the same estimated parameters; a ratio far from 1 across different batch-size assignments would show the bound is too loose for the equality assumption to hold.

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Extended reading notes

Core claim

Under $\beta$-smoothness of the local losses and bounded per-layer gradient variance and second moments, the paper proves (Theorem 1) that the average squared gradient norm after $R$ rounds satisfies $\frac{1}{R}\sum_{t=1}^R \mathbb{E}\|\nabla f(w^{t-1})\|^2 \le \frac{2\vartheta}{\gamma R} + \frac{\beta\gamma}{N^2}\sum_{i=1}^N \sum_{j=1}^L \frac{\sigma_j^2}{b_i} + \mathbf{1}_{\{I>1\}} 4\beta^2 \gamma^2 I^2 \sum_{j=1}^{L_c} G_j^2$. Inverting this bound (Corollary 1) gives a lower bound on the rounds $R$ needed to reach accuracy $\varepsilon$, and the paper asserts that the optimal schedule is obtained when this lower bound holds with equality. Substituting that expression for $R$ into a per-round latency model that includes client forward/backward passes, activation upload/download, and the periodic client-side model aggregation yields an explicit latency objective, which is then minimized over per-device batch sizes $b_i$ and binary split-point variables $\mu_{i,j}$. The paper claims this is the first convergence bound for SFL with both varied batch sizes and cut layers, and that the resulting heterogeneity-aware schedule is what enables the reported speedups.

Load-bearing premise

The paper assumes the convergence upper bound is tight enough that the round count it predicts is the round count really needed, so minimizing the bound is the same as minimizing training time; if the bound is loose, the optimized batch sizes and split points can lower the surrogate without lowering real latency.

Editorial extensions

If this is right

  • If the bound is tight, the optimal schedule assigns faster devices larger batch sizes and slower devices smaller ones, with each device's cut layer chosen to balance smashed-data communication cost against aggregation frequency.
  • For aggregation interval $I>1$, the bound predicts that shallower client-side splits accelerate convergence, so the optimizer sends more layers to the server even when that increases activation traffic, stopping where the latency trade-off balances.
  • Because the batch-size rule is nearly closed-form, the schedule can be recomputed cheaply each aggregation round, letting HASFL adapt to drifting device speeds and channel rates during training.
  • The experiments report at least 4x faster convergence and about 1% higher accuracy than benchmarks that randomize batch sizes, split points, or both.

Reading between the lines

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

  • The paper never verifies its equality assumption: a reader who logs predicted versus actual rounds to reach $\varepsilon$ on the paper's own testbed could check whether the optimized schedule is truly latency-optimal or only optimal for the surrogate.
  • The per-layer variance assumption ($\sigma_j^2/b$ per layer, summed over layers) is a strong structural condition; if modern layers with normalization or adaptive optimizers violate it, the batch-size compensation rule could mis-rank devices.
  • Because the server-side common sub-model is assumed to synchronize every round for free, the analysis applies to a single edge server; a hierarchical or multi-hop version of SFL would need a modified staleness term.
  • A direct stress test is to compare HASFL's end-to-end measured latency against a brute-force grid search over batch sizes and split points on a small model; the size of any gap quantifies how much is lost by treating the upper bound as exact.
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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 HASFL, a heterogeneity-aware split federated learning framework that adaptively controls per-device batch sizes and model split points to minimize the training latency required to reach a target convergence accuracy. The authors derive a convergence upper bound for SFL with heterogeneous batch sizes and cut layers (Lemma 1 and Theorem 1), then use the lower bound on the required number of training rounds obtained from this bound (Corollary 1, Eq. (27)) to formulate a latency minimization problem. The problem is decomposed into batch-size and model-splitting subproblems, solved alternately by a block-coordinate descent algorithm (Algorithm 2). Experiments on CIFAR-10 and CIFAR-100 with VGG-16 and ResNet-18 report faster convergence and higher accuracy than several benchmarks.

Significance. If the optimization-to-latency bridge were valid, the paper would make a useful contribution to resource-efficient split federated learning: it provides the first convergence bound for SFL with jointly varied batch sizes and cut layers, and the proposed system-level optimization is evaluated across a broad set of scenarios. The theoretical derivations in Lemma 1 and Theorem 1 follow standard smoothness and bounded-variance machinery and appear algebraically sound. The experimental study is extensive and consistently shows improvements over the chosen benchmarks. However, the central claim that the proposed optimization minimizes actual training latency is not established, because the optimization is built on an unexamined equality assumption that replaces the convergence bound with an exact round-count prediction; the evaluation does not validate this assumption. The significance of the paper therefore hinges on a load-bearing point that currently lacks support.

major comments (3)
  1. [Section VI, Eqs. (27) and (43)] The paper converts a lower bound into an exact equality. Corollary 1 establishes only that R >= R_bound(epsilon, b, mu) for the average squared gradient norm to be at most epsilon; it does not establish that the actual number of rounds equals R_bound. The statement in Section VI that 'the objective function is minimized if and only if (27) holds as an equality' is therefore unsupported. Since Eqs. (42)-(45) and the entire subsequent optimization minimize Theta(b, mu) = R_bound * [T_S + T_A/I], the claimed latency optimality is for a surrogate objective. The manuscript provides no tightness analysis, no comparison of predicted R_bound against observed rounds, and no argument that the ranking of configurations by R_bound matches the ranking by actual R. This is load-bearing for the paper's main claim, and the issue cannot be dismissed as a minor technicality because the bound contains worst-case constants and is derived through multiple relaxations in Lemma 1 and Theorem 1.
  2. [Section VI, Proposition 1] Proposition 1 claims 'The optimal BS decision' is given by Eq. (48), obtained by solving the first-order condition with the Newton-Jacobi method. The proof, however, only demonstrates that for each i', holding all other batch sizes fixed, the objective is initially decreasing and then increasing in b_i' (Eqs. (49)-(50)). This establishes coordinate-wise unimodality, not joint convexity or global optimality of the simultaneous root. The optimal solution under the coupling constraints C4, R3, and R4 may lie on the boundary even when the unconstrained root does not; the correction using kappa_i is heuristic. The remark's claim that exhaustive search over 3^N combinations identifies the global optimum is also inconsistent with the algorithm actually deployed, which solves the nonlinear system and applies a one-time correction. Consequently, the guarantee that P1 is solved exactly in the BCD algorithm is not proven.
  3. [Section VII-B, Figs. 5-6] The empirical evaluation does not test the key theoretical bridge. Corollary 1 concerns the average squared gradient norm condition (Eq. (26)), but the convergence criterion in the experiments is a test-accuracy plateau (e.g., 'test accuracy increases by less than 0.02 percent across five consecutive training rounds'). Therefore, the measured speedups in Figs. 5-6 cannot validate the assertion that Eq. (27) accurately predicts the number of rounds required to reach epsilon. The paper should report the actual versus predicted round counts, or measure the gradient-norm criterion directly, to support the equality assumption that underlies the optimization.
minor comments (5)
  1. [Section II] There is a typo in the related-work discussion: 'incentive mechanisms to to balance the training load' should read 'incentive mechanisms to balance the training load'.
  2. [Section VI, Eq. (40)] The approximation ceil(R/I) ≈ R/I is used without an error bound. Since the optimization can, in principle, select small R values, the relative error of this approximation should be quantified or justified.
  3. [Section VI, Proposition 1 remark] The remark states that the optimal solution can be obtained by exhaustive search over 3^N combinations, but the described algorithm solves the nonlinear system and performs a correction step. These two statements describe different procedures, and the paper should clarify which one is implemented and what guarantees each provides.
  4. [Algorithm 2 and Section VI] Algorithm 2 terminates when the objective change is below epsilon, but no convergence analysis of the BCD scheme is provided. This is acceptable for a heuristic, but the text should avoid implying that the final solution is globally optimal.
  5. [Figures 2 and 3] The x-axis in Figs. 2(a) and 3(a) is labeled 'Training Rounds' while the captions say 'epochs'; the terminology should be made consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the optimization is built on a derived (and possibly loose) bound, but the bound is not fitted to, nor defined by, the predicted outcome.

full rationale

Theorem 1 is derived directly from Assumptions 1 and 2 using a standard smoothness/descent argument, and the proof is given in full, so the convergence bound is not imported from prior work by construction. Corollary 1 is a rearrangement of Theorem 1's upper bound into a lower bound on the number of rounds R. Section VI substitutes this lower bound into the latency expression and solves the resulting problem P'/P''. The statement that 'the objective function is minimized if and only if (27) holds as an equality' is a tightness/surrogacy assumption: if the bound is loose in a configuration-dependent way, the optimized solution may minimize the surrogate rather than actual wall-clock time. That is a validity concern, not circularity. The bound is not fitted to the experimental outcome, and no equation in the derivation chain is defined in terms of the quantity it is supposed to predict. The constants beta, sigma_j^2, and G_j^2 are estimated following external prior work [24], not tuned to make HASFL's claims true. The self-citations [21] and [23] appear in the introduction and in the justification for per-round server-side common sub-model aggregation, but the convergence proof and the optimization are self-contained and do not rest on those papers. No uniqueness theorem is imported from the authors. The experimental comparisons use external datasets and benchmarks, so the central claim has independent content.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard stochastic-optimization assumptions (smoothness, bounded variance), a deterministic edge-latency model, and an unproven tightness assumption that converts the convergence upper bound into an exact round-count predictor. The paper introduces no new physical or mathematical entities.

free parameters (3)
  • β, σ_j², G_j² (loss smoothness and gradient statistics) = estimated following the approach in [24]
    These constants are required to instantiate the convergence bound and the objective Θ'. The paper does not derive them from first principles; it estimates them from local gradient statistics using a method from prior work. The optimized BS/MS depends on these estimates.
  • Learning rate γ = 5e-4 in simulations
    Chosen by hand for all experiments. The convergence bound requires γ ≤ 1/β, but the numerical latency results depend on the chosen value.
  • Client-side aggregation interval I = 15 in simulations
    Chosen by hand. The drift term in the bound and the aggregation latency term scale with I, so the reported gains are sensitive to this choice.
assumptions (6)
  • domain assumption Each local loss function f_i is β-smooth.
    Assumption 1 in Section IV, used in the descent lemma and in bounding the drift term.
  • domain assumption Stochastic gradients have bounded per-layer variance σ_j²/b and bounded second moments Σ G_j².
    Assumption 2 in Section IV, used in Lemma 1 and Theorem 1 to bound noise and drift.
  • domain assumption Stochastic gradients are unbiased estimates of the true gradients.
    Stated in Section III-A and used throughout the proof of Theorem 1 (e.g., Eq. (22)(b)).
  • domain assumption Per-round training latency is the max over devices of compute+communication times plus the serial server time, and compute/communication times scale linearly with batch size.
    Section V-A, Eqs. (28)-(40) define the objective T(b,μ); the whole optimization rests on this deterministic latency model.
  • ad hoc to paper The convergence bound in Corollary 1 can be used as an equality to predict the required number of training rounds R.
    Section VI states 'the objective function is minimized if and only if (27) holds as an equality'. This assumes the upper bound is tight, which is not proven; it is a modeling choice specific to this paper.
  • domain assumption Device memory constraint C4 is modeled as a sum of activation, gradient, optimizer state, and model parameter sizes.
    Constraint C4 in Section V-B, used in the BS subproblem to bound κ_i.

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Cite this review

Pith. "Pith review of HASFL: Heterogeneity-aware Split Federated Learning over Edge Computing Systems." pith.science (2026). https://pith.science/paper/NZZ4EQIC

@misc{pith2026250608426,
  author       = {Pith},
  title        = {Pith review of: HASFL: Heterogeneity-aware Split Federated Learning over Edge Computing Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NZZ4EQIC}},
  note         = {Machine review of arXiv:2506.08426}
}
read the original abstract

Split federated learning (SFL) has emerged as a promising paradigm to democratize machine learning (ML) on edge devices by enabling layer-wise model partitioning. However, existing SFL approaches suffer significantly from the straggler effect due to the heterogeneous capabilities of edge devices. To address the fundamental challenge, we propose adaptively controlling batch sizes (BSs) and model splitting (MS) for edge devices to overcome resource heterogeneity. We first derive a tight convergence bound of SFL that quantifies the impact of varied BSs and MS on learning performance. Based on the convergence bound, we propose HASFL, a heterogeneity-aware SFL framework capable of adaptively controlling BS and MS to balance communication-computing latency and training convergence in heterogeneous edge networks. Extensive experiments with various datasets validate the effectiveness of HASFL and demonstrate its superiority over state-of-the-art benchmarks.

Figures

Figures reproduced from arXiv: 2506.08426 by the authors.

Figure 1
Figure 1. The illustration of HASFL over edge computing systems, where a1) [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The impact of BS on training performance and per-round training [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. The impact of MS on computing and communication overhead as well [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: An illustration of split training and client-side model aggregation [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: The training performance for CIFAR-10 and CIFAR-100 datasets [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 8
Figure 8. Figure 8: The converged time versus network communication resources on [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 6
Figure 6. Figure 6: The converged accuracy and time for CIFAR-10 and CIFAR-100 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: The converged time versus network computing resources on CIFAR [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 11
Figure 11. Figure 11: Ablation experiments for HAMS scheme on the CIFAR-10 dataset [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 10
Figure 10. Figure 10: Ablation experiments for HABS strategy on the CIFAR-10 dataset [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

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Reference graph

Works this paper leans on

55 extracted references · 46 canonical work pages · cited by 3 Pith papers

  1. [24]

    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. , vol. 37, no. 6, pp. 1205–1221, Mar. 2019

    work page 2019

  2. [1]

    Optimiz- ing Parameter Mixing Under Constrained Communications in Parallel Federated Learning,

    X. Liu, Z. Yan, Y . Zhou, D. Wu, X. Chen, and J. H. Wang, “Optimiz- ing Parameter Mixing Under Constrained Communications in Parallel Federated Learning,” IEEE/ACM Trans. Networking, vol. 31, no. 6, pp. 2640–2652, Dec. 2023

    work page 2023

  3. [2]

    HSplitLoRA: A Heterogeneous Split Parameter- Efficient Fine-Tuning Framework for Large Language Models,

    Z. Lin, Y . Zhang, Z. Chen, Z. Fang, X. Chen, P. Vepakomma, W. Ni, J. Luo, and Y . Gao, “HSplitLoRA: A Heterogeneous Split Parameter- Efficient Fine-Tuning Framework for Large Language Models,” arXiv preprint arXiv:2505.02795, 2025

    arXiv 2025

  4. [3]

    Actions at the Edge: Jointly Optimizing the Resources in Multi-access Edge Computing,

    Y . Deng, X. Chen, G. Zhu, Y . Fang, Z. Chen, and X. Deng, “Actions at the Edge: Jointly Optimizing the Resources in Multi-access Edge Computing,” IEEE Wireless Commun., vol. 29, no. 2, pp. 192–198, Apr. 2022

    work page 2022

  5. [4]

    Federated Learning over Multihop Wireless Networks with In-network Aggregation,

    X. Chen, G. Zhu, Y . Deng, and Y . Fang, “Federated Learning over Multihop Wireless Networks with In-network Aggregation,”IEEE Trans. Wireless Commun., vol. 21, no. 6, pp. 4622–4634, Apr. 2022

    work page 2022

  6. [5]

    Communication-efficient Learning of Deep Networks From Decentral- ized Data,

    B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. Arcas, “Communication-efficient Learning of Deep Networks From Decentral- ized Data,” in Proc. AISTATS, Apr. 2017

    work page 2017

  7. [6]

    Federated Learning: Strategies for Improving Communica- tion Efficiency,

    J. Kone ˇcn`y, H. B. McMahan, F. X. Yu, P. Richt ´arik, A. T. Suresh, and D. Bacon, “Federated Learning: Strategies for Improving Communica- tion Efficiency,” arXiv preprint arXiv:1610.05492 , Oct. 2016

    arXiv 2016

  8. [7]

    FedSN: A Federated Learning Framework over Heterogeneous LEO Satellite Networks,

    Z. Lin, Z. Chen, Z. Fang, X. Chen, X. Wang, and Y . Gao, “FedSN: A Federated Learning Framework over Heterogeneous LEO Satellite Networks,” IEEE Trans. Mobile Comput. , 2024

    work page 2024

Show all 55 references
  1. [8]

    Accelerating Federated Learning with Model Segmentation for Edge Networks,

    M. Hu, J. Zhang, X. Wang, S. Liu, and Z. Lin, “Accelerating Federated Learning with Model Segmentation for Edge Networks,” IEEE Trans. Green Commun. Netw., 2024

    2024

  2. [9]

    Automated Federated Pipeline for Parameter-efficient Fine-tuning of Large Lan- guage Models,

    Z. Fang, Z. Lin, Z. Chen, X. Chen, Y . Gao, and Y . Fang, “Automated Federated Pipeline for Parameter-efficient Fine-tuning of Large Lan- guage Models,” arXiv preprint arXiv:2404.06448 , 2024

    2024 arXiv

  3. [10]

    Leo-Split: A Semi-Supervised Split Learning Framework over LEO Satellite Networks,

    Z. Lin, Y . Zhang, Z. Chen, Z. Fang, C. Wu, X. Chen, Y . Gao, and J. Luo, “Leo-Split: A Semi-Supervised Split Learning Framework over LEO Satellite Networks,” arXiv preprint arXiv:2501.01293 , 2025

    2025 arXiv

  4. [11]

    Gemini: A Family of Highly Capable Multimodal Models,

    G. Team, R. Anil, S. Borgeaud, J.-B. Alayrac, J. Yu, R. Soricut, J. Schalkwyk, A. M. Dai, A. Hauth, K. Millican et al. , “Gemini: A Family of Highly Capable Multimodal Models,” arXiv preprint arXiv:2312.11805, Dec. 2023

    2023 arXiv

  5. [12]

    Split Learning for Health: Distributed Deep Learning without Sharing Raw Patient Data,

    P. Vepakomma, O. Gupta, T. Swedish, and R. Raskar, “Split Learning for Health: Distributed Deep Learning without Sharing Raw Patient Data,” arXiv preprint arXiv:1812.00564 , Dec. 2018

    2018 arXiv

  6. [13]

    Pipelining Split Learning in Multi-hop Edge Networks,

    W. Wei, Z. Lin, T. Li, X. Li, and X. Chen, “Pipelining Split Learning in Multi-hop Edge Networks,” arXiv preprint arXiv:2505.04368 , 2025

    2025

  7. [14]

    Pushing Large Language Models to the 6G Edge: Vision, Challenges, and Opportunities,

    Z. Lin, G. Qu, Q. Chen, X. Chen, Z. Chen, and K. Huang, “Pushing Large Language Models to the 6G Edge: Vision, Challenges, and Opportunities,” IEEE Commun. Mag. , 2023

    2023

  8. [15]

    Optimal Resource Allocation for U-Shaped Parallel Split Learning,

    S. Lyu, Z. Lin, G. Qu, X. Chen, X. Huang, and P. Li, “Optimal Resource Allocation for U-Shaped Parallel Split Learning,” in Proc. IEEE Globecom Wkshps , 2023, pp. 197–202

    2023

  9. [16]

    Splitfed: When Federated Learning Meets Split Learning,

    C. Thapa, P. C. M. Arachchige, S. Camtepe, and L. Sun, “Splitfed: When Federated Learning Meets Split Learning,” in Proc. AAAI, Feb. 2022

    2022

  10. [17]

    Distributed Learning in Wireless Networks: Recent Progress and Future Challenges,

    M. Chen, D. G ¨und¨uz, K. Huang, W. Saad, M. Bennis, A. V . Feljan, and H. V . Poor, “Distributed Learning in Wireless Networks: Recent Progress and Future Challenges,” IEEE J. Sel. Areas Commun. , Dec. 2021

    2021

  11. [18]

    Time-sensitive Learning For Heterogeneous Federated Edge Intelligence,

    Y . Xiao, X. Zhang, Y . Li, G. Shi, M. Krunz, D. N. Nguyen, and D. T. Hoang, “Time-sensitive Learning For Heterogeneous Federated Edge Intelligence,” IEEE Trans. Mobile Comput. , vol. 23, no. 2, pp. 1382– 1400, 2023

    2023

  12. [19]

    Speeding Up Distributed Machine Learning Using Codes,

    K. Lee, M. Lam, R. Pedarsani, D. Papailiopoulos, and K. Ramchandran, “Speeding Up Distributed Machine Learning Using Codes,” IEEE Trans. Inf. Theory, vol. 64, no. 3, pp. 1514–1529, Mar. 2017

    2017

  13. [20]

    Split learning over Wireless Networks: Parallel Design and Resource Management,

    W. Wu, M. Li, K. Qu, C. Zhou, X. Shen, W. Zhuang, X. Li, and W. Shi, “Split learning over Wireless Networks: Parallel Design and Resource Management,” IEEE J. Sel. Areas Commun. , vol. 41, no. 4, pp. 1051– 1066, Feb. 2023

    2023

  14. [21]

    AdaptsFL: Adaptive Split Federated Learning in Resource-Constrained Edge Networks,

    Z. Lin, G. Qu, W. Wei, X. Chen, and K. K. Leung, “AdaptsFL: Adaptive Split Federated Learning in Resource-Constrained Edge Networks,” arXiv preprint arXiv:2403.13101 , 2024

    2024 arXiv

  15. [22]

    Game-Theoretic Joint Incentive and Cut Layer Selection Mechanism in Split Federated Learning,

    J. Lee, J. Cho, W. Lee, M. Seif, and H. V . Poor, “Game-Theoretic Joint Incentive and Cut Layer Selection Mechanism in Split Federated Learning,” arXiv preprint arXiv:2412.07813 , 2024

    2024 arXiv

  16. [23]

    Hi- erarchical Split Federated Learning: Convergence Analysis and System Optimization,

    Z. Lin, W. Wei, Z. Chen, C.-T. Lam, X. Chen, Y . Gao, and J. Luo, “Hi- erarchical Split Federated Learning: Convergence Analysis and System Optimization,” IEEE Trans. Mobile Comput. , Apr. 2025

    2025

  17. [25]

    Adaptive Batchsize Selection and Gradient Compression For Wireless Federated Learning,

    S. Liu, G. Yu, R. Yin, J. Yuan, and F. Qu, “Adaptive Batchsize Selection and Gradient Compression For Wireless Federated Learning,” in Proc. GLOBECOM, 2020

    2020

  18. [26]

    Adaptive Batch Size For Federated Learning in Resource-constrained Edge Computing,

    Z. Ma, Y . Xu, H. Xu, Z. Meng, L. Huang, and Y . Xue, “Adaptive Batch Size For Federated Learning in Resource-constrained Edge Computing,” IEEE Trans. Mobile Comput. , vol. 22, no. 1, pp. 37–53, Jan. 2021

    2021

  19. [27]

    DYNAMITE: Dynamic Interplay of Mini-batch Size and Aggregation Frequency For Federated Learning with Static and Streaming Datasets,

    W. Liu, X. Zhang, J. Duan, C. Joe-Wong, Z. Zhou, and X. Chen, “DYNAMITE: Dynamic Interplay of Mini-batch Size and Aggregation Frequency For Federated Learning with Static and Streaming Datasets,” IEEE Trans. Mobile Comput. , vol. 23, no. 7, pp. 7664–7679, 2023

    2023

  20. [28]

    To Talk or to Work: Dynamic Batch Sizes Assisted Time Efficient Federated Learning over Future Mobile Edge Devices,

    D. Shi, L. Li, M. Wu, M. Shu, R. Yu, M. Pan, and Z. Han, “To Talk or to Work: Dynamic Batch Sizes Assisted Time Efficient Federated Learning over Future Mobile Edge Devices,” IEEE Trans. Wireless Commun. , vol. 21, no. 12, pp. 11 038–11 050, Dec. 2022

    2022

  21. [29]

    Don’t Decay the Learning Rate, Increase the Batch Size,

    S. L. Smith, P.-J. Kindermans, and Q. V . Le, “Don’t Decay the Learning Rate, Increase the Batch Size,” in Proc. ICLR, Feb. 2018

    2018

  22. [30]

    On the Computation and Communication Complexity of Parallel SGD with Dynamic Batch Sizes for Stochastic Non-convex Optimization,

    H. Yu and R. Jin, “On the Computation and Communication Complexity of Parallel SGD with Dynamic Batch Sizes for Stochastic Non-convex Optimization,” in Proc. ICML, Jun. 2019

    2019

  23. [31]

    Efficient Parallel Split Learning over Resource-constrained Wireless Edge Networks,

    Z. Lin, G. Zhu, Y . Deng, X. Chen, Y . Gao, K. Huang, and Y . Fang, “Efficient Parallel Split Learning over Resource-constrained Wireless Edge Networks,” IEEE Trans. Mobile Comput. , 2024

    2024

  24. [32]

    Convergence Analysis of Split Federated Learning on Heterogeneous Data,

    P. Han, C. Huang, G. Tian, M. Tang, and X. Liu, “Convergence Analysis of Split Federated Learning on Heterogeneous Data,” in Proc. NIPS , 2025

    2025

  25. [33]

    Unleashing the Tiger: Inference Attacks on Split Learning,

    D. Pasquini, G. Ateniese, and M. Bernaschi, “Unleashing the Tiger: Inference Attacks on Split Learning,” in Proc. CCS, Nov. 2021

    2021

  26. [34]

    On the Convergence Properties of A K-step Averaging Stochastic Gradient Descent Algorithm for Nonconvex Optimization,

    Karimireddy, Sai Praneeth and Kale, Satyen and Mohri, Mehryar and Reddi, Sashank and Stich, Sebastian and Suresh, Ananda Theertha, “On the Convergence Properties of A K-step Averaging Stochastic Gradient Descent Algorithm for Nonconvex Optimization,” in Proc. IJCAI, Jul. 2018

    2018

  27. [35]

    On the Linear Speedup Analysis of Communication Efficient Momentum SGD For Distributed Non-convex Optimization,

    H. Yu, R. Jin, and S. Yang, “On the Linear Speedup Analysis of Communication Efficient Momentum SGD For Distributed Non-convex Optimization,” in Proc. ICML, Jun. 2019, pp. 7184–7193

    2019

  28. [36]

    Scaffold: Stochastic Controlled Averaging for Federated Learn- ing,

    S. P. Karimireddy, S. Kale, M. Mohri, S. Reddi, S. Stich, and A. T. Suresh, “Scaffold: Stochastic Controlled Averaging for Federated Learn- ing,” in Proc. ICLR, Apr. 2020

    2020

  29. [37]

    Communication-efficient Algorithms for Statistical Optimization,

    Y . Zhang, M. J. Wainwright, and J. C. Duchi, “Communication-efficient Algorithms for Statistical Optimization,” in Proc. NIPS, Jun. 2012

    2012

  30. [38]

    Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent,

    X. Lian, C. Zhang, H. Zhang, C.-J. Hsieh, W. Zhang, and J. Liu, “Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent,” in Proc. NIPS, Jun. 2017

    2017

  31. [39]

    Perturbed Iterate Analysis for Asynchronous Stochastic Optimization,

    H. Mania, X. Pan, D. Papailiopoulos, B. Recht, K. Ramchandran, and M. I. Jordan, “Perturbed Iterate Analysis for Asynchronous Stochastic Optimization,” SIAM J. Optim., vol. 27, no. 4, pp. 2202–2229, Jan. 2017

    2017

  32. [40]

    Don’t Use Large Mini- batches, Use Local SGD,

    T. Lin, S. U. Stich, K. K. Patel, and M. Jaggi, “Don’t Use Large Mini- batches, Use Local SGD,” in Proc. ICLR, Dec. 2019

    2019

  33. [41]

    QSFL: Two-Level Communication-Efficient Federated Learning on Mobile Edge Devices,

    L. Yi, G. Wang, X. Wang, and X. Liu, “QSFL: Two-Level Communication-Efficient Federated Learning on Mobile Edge Devices,” IEEE Trans. Serv. Comput. , 2024

    2024

  34. [42]

    Joint Device Scheduling and Resource Allocation for Latency Constrained Wireless Federated Learning,

    W. Shi, S. Zhou, Z. Niu, M. Jiang, and L. Geng, “Joint Device Scheduling and Resource Allocation for Latency Constrained Wireless Federated Learning,” IEEE Trans. Wireless Commun., vol. 20, no. 1, pp. 453–467, Sep. 2020

    2020

  35. [43]

    Federated-learning-based Client Scheduling for Low-latency Wireless Communications,

    W. Xia, W. Wen, K.-K. Wong, T. Q. Quek, J. Zhang, and H. Zhu, “Federated-learning-based Client Scheduling for Low-latency Wireless Communications,” IEEE Wireless Commun. , vol. 28, no. 2, pp. 32–38, Apr. 2021

    2021

  36. [44]

    Horus: Interference-aware and Prediction-based Scheduling in Deep Learning Systems,

    G. Yeung, D. Borowiec, R. Yang, A. Friday, R. Harper, and P. Garraghan, “Horus: Interference-aware and Prediction-based Scheduling in Deep Learning Systems,” IEEE Trans. Parallel Distrib. Syst. , vol. 33, no. 1, pp. 88–100, May. 2021

    2021

  37. [45]

    Pipeline Network Simulation Calculation based on Improved Newton Jacobian Iterative Method,

    Z. Geng, C. Wei, Y . Han, Q. Wei, and Z. Ouyang, “Pipeline Network Simulation Calculation based on Improved Newton Jacobian Iterative Method,” in Proc. AICS, Jul. 2019

    2019

  38. [46]

    On Nonlinear Fractional Programming,

    W. Dinkelbach, “On Nonlinear Fractional Programming,” Manage. Sci., vol. 13, no. 7, pp. 492–498, Mar. 1967. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 16

    1967

  39. [47]

    A Reformulation-linearization Method for the Global Optimization of Large-scale Mixed-Integer Linear Fractional Programming Problems and Cyclic Scheduling aApplication,

    D. Yue and F. You, “A Reformulation-linearization Method for the Global Optimization of Large-scale Mixed-Integer Linear Fractional Programming Problems and Cyclic Scheduling aApplication,” in Proc. ACC, Jun. 2013

    2013

  40. [48]

    Extensions of Dinkelbach’s Algorithm for Solving Non-linear Fractional Programming Problems,

    R. G. R ´odenas, M. L. L ´opez, and D. Verastegui, “Extensions of Dinkelbach’s Algorithm for Solving Non-linear Fractional Programming Problems,” Top, vol. 7, pp. 33–70, Jun. 1999

    1999

  41. [49]

    Convergence of A Block Coordinate Descent Method for Nondifferentiable Minimization,

    P. Tseng, “Convergence of A Block Coordinate Descent Method for Nondifferentiable Minimization,” J Optim Theory Appl , vol. 109, pp. 475–494, Jun. 2001

    2001

  42. [50]

    Learning Multiple Layers of Features From Tiny Images,

    A. Krizhevsky, G. Hinton et al., “Learning Multiple Layers of Features From Tiny Images,” Tech. Rep., Apr. 2009

    2009

  43. [51]

    Broadband analog aggregation for low-latency federated edge learning,

    G. Zhu, Y . Wang, and K. Huang, “Broadband analog aggregation for low-latency federated edge learning,” IEEE Trans. Wireless Commun. , vol. 19, no. 1, pp. 491–506, Oct. 2019

    2019

  44. [52]

    Energy Efficient Federated Learning over Wireless Communication Networks,

    Z. Yang, M. Chen, W. Saad, C. S. Hong, and M. Shikh-Bahaei, “Energy Efficient Federated Learning over Wireless Communication Networks,” IEEE Trans. Wireless Commun. , vol. 20, no. 3, pp. 1935–1949, Nov. 2020

    1935

  45. [53]

    Very Deep Convolutional Networks for Large-scale Image Recognition,

    K. Simonyan and A. Zisserman, “Very Deep Convolutional Networks for Large-scale Image Recognition,” in Proc. ICLR, 2015

    2015

  46. [54]

    Deep Residual Learning for Image Recognition,

    K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” in Proc. CVPR, Jun. 2016, pp. 770–778

    2016

  47. [55]

    CoopFL: Accelerating Federated Learning with DNN Partitioning and Offloading in Hetero- geneous Edge Computing,

    Z. Wang, H. Xu, Y . Xu, Z. Jiang, and J. Liu, “CoopFL: Accelerating Federated Learning with DNN Partitioning and Offloading in Hetero- geneous Edge Computing,” Comput. Netw., vol. 220, p. 109490, Jan. 2023

    2023

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.