Pith. sign in

REVIEW 4 major objections 6 minor 62 references

FedWCM: Unleashing the Potential of Momentum-based Federated Learning in Long-Tailed Scenarios

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read FedWCM dynamically adjusts momentum from global and per-round class data to make momentum-based federated learning converge on long-tailed non-IID data.

desk verdict The adaptive momentum method is new and the experiments are extensive, but the convergence proof breaks at Lemma E.3, so the theoretical rate claim is unsupported as written. read the letter →

arxiv 2507.14980 v1 pith:URY7C7MW submitted 2025-07-20 cs.LG

Tianle Li , Yongzhi Huang , Linshan Jiang , Qipeng Xie , Chang Liu , Wenfeng Du , Lu Wang , Kaishun Wu This is my paper
classification cs.LG
keywords federatedlearningmomentumlong-taileddistributionnon-IIDdataclassimbalanceadaptiveclientweightingconvergenceanalysis
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 tries to establish that momentum-based federated learning, which normally accelerates convergence under balanced or mildly heterogeneous data, loses that property when the global class distribution is long-tailed: momentum amplifies majority-class gradients, skews the global update direction, and triggers minority collapse. It proposes FedWCM, which computes global and per-round class-distribution information and uses it to reweight client contributions and to shrink or grow the momentum coefficient from round to round. The paper proves that this dynamic momentum adjustment preserves the same convergence rate as FedAvg-M and FedCM, namely $\sqrt{L\Delta\sigma^2/(NKR)} + L\Delta/R$, and reports experiments where FedWCM keeps converging and outperforms FedAvg, BalanceFL, FedGrab, and FedCM variants as imbalance grows. A reader should care because it offers a way to keep momentum's speed benefit in exactly the federated settings where fixed momentum currently collapses.

What carries the argument

The carrying mechanism is a per-round momentum correction built from the global class distribution. Each client receives a score that sums, across classes, the absolute difference between the target class proportion and the global class proportion, weighted by that client's sample counts; the score is large when the client holds globally scarce data, and the target distribution is uniform by default but user-adjustable. A temperature-scaled softmax turns these scores into aggregation weights, and the adaptive momentum coefficient $\alpha^{r+1}$ is driven by the ratio of the current round's average score to the overall average score, so the method knows when the sampled clients under-represent minority classes. In the convergence proof, the weights are used to control the bias term $U_r$ that fixed-momentum analysis leaves uncontrolled under long-tailed skew, while Lemmas E.1-E.6 bound drift and momentum error in the same style as the FedAvg-M and FedCM analyses.

What would settle it

Run FedWCM on a long-tailed partition, for example CIFAR-10 with $\beta=0.1$ and imbalance factor 0.1, and record each round the distance from the reweighted momentum aggregate to the true global gradient alongside the distance for the unweighted FedCM aggregate; if the reweighted aggregate is not closer on average, Lemma E.3's premise fails. A second check is to record the momentum values produced by Equation (5) and compare them with the theorem's bound; if the method converges while routinely violating that bound, the stated condition is not what makes it work.

Watch

Extended reading notes

Core claim

In the paper's own terms, FedWCM resolves the non-convergence of momentum-based federated learning under long-tailed non-IID data by replacing two fixed ingredients with adaptive ones. A global class distribution is shared with clients, and each client is scored by how much its local class distribution deviates from the target global distribution; clients whose data contain globally scarce classes receive higher softmax weights in the momentum aggregation. The momentum coefficient is then recomputed each round from the ratio between the average score of the sampled clients and the overall average score, so momentum weakens in rounds where minority classes are poorly represented. The global update is the weighted average of client deltas, and local updates combine the current gradient with the global momentum using that round's coefficient. Theorem 6.1 states that under standard smoothness and stochastic-gradient assumptions FedWCM converges at the same rate as FedAvg-M and FedCM; the experiments are presented as showing that this restores convergence where fixed-momentum FedCM collapses and yields higher accuracy across datasets and imbalance factors.

Load-bearing premise

The load-bearing premise is that the clients the score and softmax upweight are exactly the clients whose local gradients deviate most from the global gradient, so reweighting moves the aggregate closer to the global direction; the paper asserts this inverse relationship in Lemma E.3 rather than deriving it, and it does not show that the algorithm's adaptively chosen momentum obeys the bounds the theorem imposes on $\alpha$.

Editorial extensions

If this is right

  • FedWCM keeps the same convergence rate as FedAvg-M and FedCM, so the extra adaptive machinery does not cost the theoretical acceleration that momentum provides.
  • Under long-tailed partitions where FedCM's accuracy drops close to random, FedWCM stays converged and outperforms FedAvg, BalanceFL, and FedGrab in the paper's comparisons.
  • The per-label accuracy results show tail classes gain the most, meaning the improvement is not only in average accuracy but in the classes that fixed momentum crushes.
  • FedWCM-X extends the method to clients with unequal data volumes by adding quantity-based weights and by rescaling the local learning rate with batch count, so the main result is not limited to balanced client data sizes.

Reading between the lines

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

  • The same score-and-temperature weighting could likely be transplanted into other momentum-based federated updates, such as server-side momentum or control-variate methods, since the failure mechanism it corrects is generic to fixed momentum under long-tailed skew; the paper does not test those combinations.
  • The neuron-concentration spikes that the paper associates with minority collapse suggest a practical early-warning rule: monitor average neuron concentration and lower momentum when a spike is detected, which would be a testable alternative to the paper's per-round score rule.
  • The method's dependence on knowing the global class distribution means its practical gain in stricter privacy settings will depend on how much accuracy survives when the distribution is estimated through homomorphic encryption or a noisy proxy; the paper measures encryption cost but does not measure accuracy under the encrypted estimate.
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

4 major / 6 minor

Summary. The paper proposes FedWCM, a momentum-based federated learning method designed for long-tailed non-IID data. It computes per-client scores from the deviation between local and global class distributions, uses a temperature-scaled softmax to reweight client updates, and adjusts the momentum coefficient per round based on the sampled clients' scores. The authors claim that FedWCM resolves the non-convergence of momentum-based FL in long-tailed settings and provably achieves the same convergence rate as FedAvg-M/FedCM, while outperforming existing methods in extensive experiments on Fashion-MNIST, SVHN, CIFAR-10, CIFAR-100, and ImageNet. The main text also contains a motivation study based on neuron-concentration analysis and an appendix with a convergence proof, a generalization variant (FedWCM-X), and a homomorphic-encryption discussion for privacy-preserving aggregation of class distributions.

Significance. If the empirical results are taken at face value, the paper makes a useful practical contribution: FedWCM is a simple plug-in momentum-correction scheme that shows consistent accuracy gains over FedAvg and several long-tail FL baselines, especially under strong imbalance, and its motivation via minority collapse is interesting. The privacy-preserving aggregation of class distributions in Appendix C is also a valuable addition. However, the paper's central theoretical claim—that FedWCM retains the convergence rate of FedAvg-M/FedCM—rests on a proof whose key lemma is not established, and the adaptive schedule used by the algorithm is not shown to satisfy the theorem's conditions. The theoretical contribution therefore does not support the paper's headline claim in its current form, notwithstanding the breadth of the experimental evaluation.

major comments (4)
  1. [Appendix E, Lemma E.3] This lemma is load-bearing for Theorem E.7, but its proof assumes the property it needs to establish. The proof sorts the weights and deviations and invokes the rearrangement inequality, yet the required inverse relationship between the softmax weights w_i (computed from class-distribution scores s_i) and the gradient deviations Delta_i = grad f(x^r) - (1/K) sum_k grad f(x^i_{r,k}) is asserted rather than derived. Moreover, Delta_i are vectors; sorting them as scalars is not legitimate, and a smaller value of sum_i w_i Delta_i does not imply a smaller L2 norm of the weighted-average gradient error. Since Lemma E.4 uses Lemma E.3 to discard the cross term, the proof of the convergence rate in Theorem E.7 collapses if this step fails. The paper provides no argument that clients with high scores (i.e., clients rich in globally scarce classes) have small gradient deviations; in fact, the opposite correlation is plausible.
  2. [Theorem 6.1 / Eq. (5) / Algorithm 1] The theorem imposes conditions on alpha_r (for example gamma L <= alpha_r/6 in Lemma E.4 and the bound alpha_r <= sqrt(N K L Delta / (sigma^2 R)) in Theorem E.7), but Algorithm 1 computes alpha_{r+1} from Eq. (5) using q_r, the per-round average score, and an unspecified term ||T/K||_1. The paper never shows that the schedule produced by Eq. (5) satisfies the theorem's conditions at every round. Consequently, even if the lemmas were correct, the proof would apply to a constant momentum schedule different from the one actually used in FedWCM.
  3. [Appendix E (Lemmas E.6-E.7) vs. Algorithm 1] The proof is written for full participation: the definitions and summations use all N clients (e.g., U_r = (1/NK) sum_{i=1}^N sum_{k=1}^K ..., Lemma E.6's Xi_r, and the final rate). Algorithm 1 samples a subset P_r of clients each round and aggregates only over P_r. Random client sampling is not modeled in the proof, so the claimed rate cannot be transferred to the implemented algorithm without additional sampling-variance terms.
  4. [Section 6 / Appendix E.7] The final rate (Eq. 10) is identical to the FedAvg-M/FedCM rate and contains no term reflecting the softmax weights, the score function, or the adaptive schedule. Thus even a fully correct proof would establish only that FedWCM inherits a known rate; it would not substantiate the introduction's claim that the adaptive weighting and momentum adjustment are what resolve the non-convergence problem. The theoretical content of the paper therefore rests almost entirely on the unproved Lemma E.3.
minor comments (6)
  1. [Eq. (5)] The notation ||T/K||_1 is undefined: T in Eq. (4) is a scalar temperature, and it is unclear what matrix or vector T refers to in Eq. (5).
  2. [Section 5.6 / Appendix A.2] Algorithms 2 and 3 are the same algorithm (both labeled FedWCM-X), and the text refers to Algorithm 3 after presenting Algorithm 2; the duplication should be removed or consolidated.
  3. [Section 7.2] The text says 'Table 1 summarizes the results on CIFAR-10', but Table 1 reports all five datasets; this makes the comparison hard to parse.
  4. [Appendix B] The left subfigure of Figure 13 is described as 'IF=0'; this should presumably be IF=1.
  5. [Appendix A.3] The sentence 'From Figure 2, we can observe...' should refer to Figure 12 in the appendix, not Figure 2.
  6. [Section 2.1 / Appendix D.1] The reference numbering for FedDyn is inconsistent: it is cited as [1] in Section 2.1 and as [2] in Appendix D.1.

Circularity Check

1 steps flagged · score 6.0 of 10

Convergence proof rests on Lemma E.3, which assumes the inverse weight–deviation relationship it needs to prove; Theorem 6.1/E.7 is therefore not a derivation of FedWCM's rate.

  1. self definitional [Appendix E, Lemma E.3 (proof); used by Lemma E.4 and Theorem E.7; Theorem 6.1 statement]
    "To prove the inequality, we will explicitly use the inverse relationship between w_i and Δ_i, along with the properties of the rearrangement inequality. ... By the rearrangement inequality, the weighted sum f(Δ,w) is minimized when w_i and Δ_i are inversely related (as given in the problem statement)."

    Lemma E.3 must prove that softmax weights w_i, computed from class-distribution scores s_i (Eq. 3), make the weighted gradient average closer to the global gradient than the uniform average. Its proof instead assumes the exact property needed for that conclusion: that w_i and Δ_i = ∇f(x^r) - (1/K) Σ_k ∇f(x^i_{r,k}) are inversely ordered. No argument connects s_i to Δ_i; a client with abundant globally scarce classes can have a large score and simultaneously a large gradient deviation, violating the assumed anti-correlation. Lemma E.4 then invokes Lemma E.3 to discard the cross term, and Theorem E.7 builds the claimed convergence rate on this chain. Thus the central claim that FedWCM has the same rate as FedCM rests on an assumed relationship, not a derived one.

full rationale

The paper's main theoretical contribution—Theorem 6.1, 'FedWCM achieves the same convergence rate as FedAvg-M/FedCM'—depends on Lemma E.3, whose proof is circular: it treats the inverse relationship between softmax weights and gradient deviations as 'given in the problem statement' when that inverse relationship is precisely what must be established. Because Lemma E.4 relies on Lemma E.3 to control the cross term, the chain leading to Theorem E.7 and Equation 10 inherits this unproved assumption. This is a load-bearing self-definitional step, not a minor gap. The experimental sections are not circular: results are compared against external baselines and do not reduce to fitted predictions. The paper also contains a separate, non-circular correctness gap—Theorem 6.1/E.7 imposes constraints on α_r that Algorithm 1's Eq. 5 update is never shown to satisfy—but that is an unsupported link rather than a circularity, so it does not raise the score further. No load-bearing self-citation or uniqueness-importation pattern was found. Overall, the central convergence proof is partially circular, warranting a score of 6.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The method relies on several free parameters and ad hoc assumptions. The most important is the unproven link between data-distribution scores and gradient deviations in Lemma E.3, which underpins the entire convergence argument. The global distribution availability is another practical assumption. No new physical or conceptual entities are introduced.

free parameters (6)
  • Temperature T in Eq. (4) = not specified
    Controls softmax sharpness; described qualitatively as computed from the discrepancy between target and actual global distribution, but no closed form is given for reproduction.
  • Base momentum alpha_0 = 0.1
    Set by hand; no sensitivity analysis except for local epochs.
  • Coefficients and exponential scale in Eq. (5) = 0.1, 0.9, 1
    The formula alpha_{r+1} = 0.1 + 0.9*(1 - exp(-||T/K||_1))*q_r uses ad hoc constants that are not derived from the convergence analysis.
  • q_r ratio in Eq. (5) = computed per round
    Ratio of the average sampled-client score to the overall average score; its scaling is heuristic and no statistical justification is provided.
  • Global target distribution p_hat = uniform by default
    Users can choose a different target; this choice affects all scores and weights and is not optimized or justified beyond the default.
  • Reference batch count B_hat in FedWCM-X = not specified
    In Algorithm 2 and 3, B_hat is used to rescale the local learning rate, but no value or procedure for setting it is given.
assumptions (7)
  • standard math L-smoothness of local objectives (Assumption 1)
    Standard for convergence proofs, invoked in Section 6 and Appendix E.
  • standard math Bounded stochastic gradient variance (Assumption 2)
    Standard assumption, invoked in Section 6.
  • domain assumption Global data distribution D_g is known and shared with clients
    Required by Section 5.1 Eq. (3); the privacy discussion offers homomorphic encryption but no evaluation of the main results under HE.
  • ad hoc to paper Score s_k correlates inversely with gradient deviation (Lemma E.3)
    The proof of Lemma E.3 assumes the relationship needed for the convergence argument; it is not derived from distributional properties.
  • ad hoc to paper Adaptive alpha_r in Eq. (5) satisfies the theorem's upper bounds
    Theorem 6.1 constrains alpha to be at most sqrt(N K L Delta / (sigma^2 R)) and requires eta and gamma conditions, but the algorithm's alpha update does not enforce these bounds.
  • ad hoc to paper Sampled clients approximate full participation in the proof
    Algorithm 1 samples a subset P_r, while the proof in Appendix E sums over all N clients; no bound on the sampling error is provided.
  • domain assumption Per-class sample counts n_{k,c} are known to clients for scoring
    Clients need their local class distribution to compute s_k in Eq. (3); in FL this is usually available locally, but it is still an assumption about the client's data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of FedWCM: Unleashing the Potential of Momentum-based Federated Learning in Long-Tailed Scenarios." pith.science (2026). https://pith.science/paper/URY7C7MW

@misc{pith2026250714980,
  author       = {Pith},
  title        = {Pith review of: FedWCM: Unleashing the Potential of Momentum-based Federated Learning in Long-Tailed Scenarios},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/URY7C7MW}},
  note         = {Machine review of arXiv:2507.14980}
}
read the original abstract

Federated Learning (FL) enables decentralized model training while preserving data privacy. Despite its benefits, FL faces challenges with non-identically distributed (non-IID) data, especially in long-tailed scenarios with imbalanced class samples. Momentum-based FL methods, often used to accelerate FL convergence, struggle with these distributions, resulting in biased models and making FL hard to converge. To understand this challenge, we conduct extensive investigations into this phenomenon, accompanied by a layer-wise analysis of neural network behavior. Based on these insights, we propose FedWCM, a method that dynamically adjusts momentum using global and per-round data to correct directional biases introduced by long-tailed distributions. Extensive experiments show that FedWCM resolves non-convergence issues and outperforms existing methods, enhancing FL's efficiency and effectiveness in handling client heterogeneity and data imbalance.

Figures

Figures reproduced from arXiv: 2507.14980 by the authors.

Figure 1
Figure 1. Client drift due to heterogeneity without momen [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Test accuracy over communication rounds on [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Illustration of global information gathering. [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figures from the paper (12 more)
Figure 6
Figure 6. Figure 6: Parameter computation and application. 5.3 Parameter Application in Training The computed parameters are applied to local model updates during each round. Clients update their models using the formula: 𝑥 𝑟 𝑏+1,𝑘 = 𝑥 𝑟 𝑏,𝑘 − 𝜂𝑙 (𝛼𝑟∇𝐹 (𝑥 𝑟 𝑏,𝑘 ;𝐷𝑏,𝑘 ) + (1 − 𝛼𝑟)Δ𝑟) (6) w…
Figure 8
Figure 8. Figure 8: Per-label accuracy comparison of various methods [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Test accuracy w.r.t the number of clients. [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: Test accuracy w.r.t local epochs [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: Data distribution under the setting of 𝛽 = 0.1, 𝐼𝐹 = 0.1, partitioned according to FedGrab. momentum. In scenarios with uneven data quantities, momentum methods may be dominated by a few clients with large datasets, potentially impacting the overall model performance …
Figure 12
Figure 12. Figure 12: Accuracy comparison of our method against six [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]
Figure 13
Figure 13. Figure 13: Average neuron concentration over rounds for [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]
Figure 16
Figure 16. Figure 16: Detailed neuron concentration changes across lay [PITH_FULL_IMAGE:figures/full_fig_p012_16.png]
Figure 14
Figure 14. Figure 14: Detailed neuron concentration changes across lay [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]
Figure 17
Figure 17. Figure 17: Top: Average neuron concentration change in [PITH_FULL_IMAGE:figures/full_fig_p013_17.png]
Figure 18
Figure 18. Figure 18: Comparison of Heterogeneous methods for train [PITH_FULL_IMAGE:figures/full_fig_p013_18.png]
Figure 19
Figure 19. Figure 19: Comparison of Heterogeneous methods for test [PITH_FULL_IMAGE:figures/full_fig_p013_19.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

62 extracted references · 40 canonical work pages

  1. [1]

    Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. 2021. Federated learning based on dynamic regularization.arXiv preprint arXiv:2111.04263(2021)

    arXiv 2021

  2. [2]

    Durmus Alp Emre Acar, Yue Zhao, Brendan Rogers, Praneeth Vepakomma, Tian Li Zhu, Matthew Mattina, Vikas Chandra, and Mehdi Joshi. 2021. Federated learning dynamics: Challenges and opportunities. InNeurIPS 2021 Federated Learning Workshop

    work page 2021

  3. [3]

    Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. 2019. Learning imbalanced datasets with label-distribution-aware margin loss.Ad- vances in neural information processing systems32 (2019)

    work page 2019

  4. [4]

    Zihan Chen, Songshang Liu, Hualiang Wang, Howard H Yang, Tony QS Quek, and Zuozhu Liu. 2022. Towards federated long-tailed learning.arXiv preprint arXiv:2206.14988(2022)

    arXiv 2022

  5. [5]

    Ziheng Cheng, Xinmeng Huang, Pengfei Wu, and Kun Yuan. 2023. Momen- tum benefits non-iid federated learning simply and provably.arXiv preprint arXiv:2306.16504(2023)

    arXiv 2023

  6. [6]

    Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. 2009. Im- ageNet: A large-scale hierarchical image database. In2009 IEEE Conference on Computer Vision and Pattern Recognition. Ieee, 248–255

    work page 2009

  7. [7]

    Jian-hui Duan, Wenzhong Li, Derun Zou, Ruichen Li, and Sanglu Lu. 2023. Fed- erated learning with data-agnostic distribution fusion. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 8074–8083

    work page 2023

  8. [8]

    Moming Duan, Duo Liu, Xianzhang Chen, Renping Liu, Yujuan Tan, and Liang Liang. 2020. Self-balancing federated learning with global imbalanced data in mobile systems.IEEE Transactions on Parallel and Distributed Systems32, 1 (2020), 59–71

    work page 2020

Show all 62 references
  1. [9]

    Moming Duan, Duo Liu, Xianzhang Chen, Yujuan Tan, Jinting Ren, Lei Qiao, and Liang Liang. 2019. Astraea: Self-balancing federated learning for improving classification accuracy of mobile deep learning applications. In2019 IEEE 37th international conference on computer design (...

    2019

  2. [10]

    Alireza Fallah, Aryan Mokhtari, and Asuman Ozdaglar. 2020. Personalized fed- erated learning with theoretical guarantees: A model-agnostic meta-learning approach.Advances in neural information processing systems33 (2020), 3557–3568

    2020

  3. [11]

    Junfeng Fan and Frederik Vercauteren. 2012. Somewhat practical fully homomor- phic encryption.Cryptology ePrint Archive(2012)

    2012

  4. [12]

    Ziqing Fan, Shengchao Hu, Jiangchao Yao, Gang Niu, Ya Zhang, Masashi Sugiyama, and Yanfeng Wang. 2024. Locally Estimated Global Perturbations are Better than Local Perturbations for Federated Sharpness-aware Minimization. arXiv preprint arXiv:2405.18890(2024)

    2024 arXiv

  5. [13]

    Cong Fang, Hangfeng He, Qi Long, and Weijie J Su. 2021. Exploring deep neu- ral networks via layer-peeled model: Minority collapse in imbalanced training. Proceedings of the National Academy of Sciences118, 43 (2021), e2103091118

    2021

  6. [14]

    Yanan Fu, Xuefeng Liu, Shaojie Tang, Jianwei Niu, and Zhangmin Huang. 2021. CIC-FL: enabling class imbalance-aware clustered federated learning over shifted distributions. InDatabase Systems for Advanced Applications: 26th International Conference, DASFAA 2021, Taipei, Taiwan,...

    2021

  7. [15]

    DaoQu Geng, HanWen He, XingChuan Lan, and Chang Liu. 2022. Bearing fault diagnosis based on improved federated learning algorithm.Computing104, 1 (2022), 1–19

    2022

  8. [16]

    Craig Gentry. 2009. Fully homomorphic encryption using ideal lattices. InProceed- ings of the forty-first annual ACM symposium on Theory of computing. 169–178

    2009

  9. [17]

    Jack Goetz and Ambuj Tewari. 2020. Federated learning via synthetic data.arXiv preprint arXiv:2008.04489(2020)

    2020 arXiv

  10. [18]

    Yukun Guo, Xiaoqiang Ma, Liang Chen, Helong Zhou, Hao Lu, and Xiang-Yang Li. 2022. FedGraB: Addressing Class Imbalance in Federated Learning through Gradient Balancer and Direct Prior Analysis.European Conference on Computer Vision(2022), 733–749

    2022

  11. [19]

    Abhinav Gupta and Saurabh Kumar. 2021. FedSMOO: Federated Smooth Opti- mizer for Learning with Heterogeneous Data.arXiv preprint arXiv:2105.08335 (2021)

    2021 arXiv

  12. [20]

    Farzin Haddadpour, Mohammad Mahdi Kamani, and Mehrdad Mahdavi. 2019. FedSpeed: Efficient Distributed Learning. InAdvances in Neural Information Processing Systems

    2019

  13. [21]

    Haibo He and Edwardo A Garcia. 2009. Learning from imbalanced data.IEEE Transactions on knowledge and data engineering21, 9 (2009), 1263–1284

    2009

  14. [22]

    Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. 2016. Deep residual learning for image recognition. InProceedings of the IEEE conference on computer vision and pattern recognition. 770–778

    2016

  15. [23]

    Youngkyu Hong, Seungju Han, Kwanghee Choi, Seokjun Seo, Beomsu Kim, and Buru Chang. 2021. Disentangling label distribution for long-tailed visual recognition. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition. 6626–6636

    2021

  16. [24]

    Eunjeong Jeong, Seungeun Oh, Hyesung Kim, Jihong Park, Mehdi Bennis, and Seong-Lyun Kim. 2018. Communication-efficient on-device machine learning: Federated distillation and augmentation under non-iid private data.arXiv preprint arXiv:1811.11479(2018)

    2018 arXiv

  17. [25]

    Sai Praneeth Karimireddy, Martin Jaggi, Satyen Kale, Mehryar Mohri, Sashank J Reddi, Sebastian U Stich, and Ananda Theertha Suresh. 2020. Mime: Mim- icking centralized stochastic algorithms in federated learning.arXiv preprint arXiv:2008.03606(2020)

    2020 arXiv

  18. [26]

    Sai Praneeth Karimireddy, Satyen Kale, Mehryar Mohri, Sashank Reddi, Sebas- tian Stich, and Ananda Theertha Suresh. 2020. Scaffold: Stochastic controlled averaging for federated learning. InInternational conference on machine learning. PMLR, 5132–5143

    2020

  19. [27]

    Vignesh Kothapalli. 2022. Neural collapse: A review on modelling principles and generalization.arXiv preprint arXiv:2206.04041(2022)

    2022 arXiv

  20. [28]

    Krizhevsky and G

    A. Krizhevsky and G. Hinton. 2009. Learning multiple layers of features from tiny images.Master’s thesis, Department of Computer Science, University of Toronto (2009)

    2009

  21. [29]

    Kan Li, Yang Li, Ji Zhang, Xin Liu, and Zhichao Ma. 2024. Federated deep long- tailed learning: A survey.Neurocomputing595 (2024), 127906

    2024

  22. [30]

    FedWCM: Unleashing the Potential of Momentum-based Federated Learning in Long-Tailed Scenarios

    Tianle Li, Yongzhi Huang, Linshan Jiang, Qipeng Xie, Chang Liu, Wenfeng Du, Lu Wang, and Kaishun Wu. 2025. Supplementary Material for “FedWCM: Unleashing the Potential of Momentum-based Federated Learning in Long-Tailed Scenarios”. https://li-tian-le.github.io/FedWCM-Supplemen...

    2025

  23. [31]

    Tian Li, Anit Kumar Sahu, Ameet Talwalkar, and Virginia Smith. 2020. Federated optimization in heterogeneous networks. InProceedings of Machine Learning and Systems 2020

    2020

  24. [32]

    Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and Piotr Dollár. 2017. Focal loss for dense object detection. InProceedings of the IEEE international conference on computer vision. 2980–2988

    2017

  25. [33]

    Wanqi Liu, Liangyu Chen, Dengfeng Ke, Yuxin Ding, Yunfeng Gao, Yaqian Li, Haoyu Ma, Heming Zhang, Xiuying Chen, Hui Xue, Tao Qin, Wei Chen, and Tie-Yan Liu. 2023. Classification Re-training Under Label Skew For Long-tailed Federated Learning.European Conference on Computer Vis...

    2023

  26. [34]

    Xiang Liu, Liangxi Liu, Feiyang Ye, Yunheng Shen, Xia Li, Linshan Jiang, and Jialin Li. 2023. FedLPA: Personalized One-shot Federated Learning with Layer-Wise Posterior Aggregation.arXiv preprint arXiv:2310.00339(2023)

    2023 arXiv

  27. [35]

    Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Aguera y Arcas. 2017. Communication-efficient learning of deep net- works from decentralized data. InArtificial intelligence and statistics. PMLR, 1273–1282

    2017

  28. [36]

    Naram Mhaisen, Alaa Awad Abdellatif, Amr Mohamed, Aiman Erbad, and Mohsen Guizani. 2021. Optimal user-edge assignment in hierarchical feder- ated learning based on statistical properties and network topology constraints. IEEE Transactions on Network Science and Engineering9, 1...

    2021

  29. [37]

    Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Baolin Wu, An- drew Y Ng, et al. 2011. Reading digits in natural images with unsupervised feature learning. InNIPS workshop on deep learning and unsupervised feature learning, Vol. 2011. Granada, 4

    2011

  30. [38]

    Pinxin Qian, Yang Lu, and Hanzi Wang. 2023. Long-Tailed Federated Learning Via Aggregated Meta Mapping. In2023 IEEE International Conference on Image Processing (ICIP). IEEE, 2010–2014

    2023

  31. [39]

    Sashank Reddi, Zachary Charles, Manzil Zaheer, Zachary Garrett, Keith Rush, Jakub Konečn`y, Sanjiv Kumar, and H Brendan McMahan. 2020. Adaptive feder- ated optimization.arXiv preprint arXiv:2003.00295(2020)

    2020 arXiv

  32. [40]

    Felix Sattler, Klaus-Robert Müller, and Wojciech Samek. 2020. Clustered feder- ated learning: Model-agnostic distributed multitask optimization under privacy constraints.IEEE transactions on neural networks and learning systems32, 8 (2020), 3710–3722

    2020

  33. [41]

    Xinyi Shang, Yang Lu, Gang Huang, and Hanzi Wang. 2022. Federated learning on heterogeneous and long-tailed data via classifier re-training with federated features.arXiv preprint arXiv:2204.13399(2022)

    2022 arXiv

  34. [42]

    Zhiyuan Shang et al. 2022. Addressing Class Imbalance in Federated Learning. arXiv preprint arXiv:2205.12345(2022)

    2022 arXiv

  35. [43]

    Jiangming Shi, Shanshan Zheng, Xiangbo Yin, Yang Lu, Yuan Xie, and Yanyun Qu. 2023. Clip-guided federated learning on heterogeneous and long-tailed data. arXiv preprint arXiv:2312.08648(2023)

    2023 arXiv

  36. [44]

    Xian Shuai, Yulin Shen, Siyang Jiang, Zhihe Zhao, Zhenyu Yan, and Guoliang Xing. 2022. BalanceFL: Addressing class imbalance in long-tail federated learning. In2022 21st ACM/IEEE International Conference on Information Processing in Sensor Networks (IPSN). IEEE, 271–284

    2022

  37. [45]

    Jianhui Sun, Xidong Wu, Heng Huang, and Aidong Zhang. 2024. On the role of server momentum in federated learning. InProceedings of the AAAI Conference on Artificial Intelligence, Vol. 38. 15164–15172

    2024

  38. [46]

    Yan Sun, Li Shen, Shixiang Chen, Liang Ding, and Dacheng Tao. 2023. Dynamic regularized sharpness aware minimization in federated learning: Approaching global consistency and smooth landscape. InInternational Conference on Machine Learning. PMLR, 32991–33013

    2023

  39. [47]

    Kaihua Tang, Jianqiang Huang, and Hanwang Zhang. 2020. Long-tailed clas- sification by keeping the good and removing the bad momentum causal effect. Advances in neural information processing systems33 (2020), 1513–1524. FedWCM: Unleashing the Potential of Momentum-based Federa...

    2020

  40. [48]

    Jiajun Wang, Yingchi Mao, Xiaoming He, Tong Zhou, Jun Wu, and Jie Wu. 2023. Accelerating Federated Learning with Two-phase Gradient Adjustment. In2022 IEEE 28th International Conference on Parallel and Distributed Systems (ICPADS). IEEE, 810–817

    2023

  41. [49]

    Jianyu Wang, Vinayak Tantia, Nicolas Ballas, and Michael Rabbat. 2019. Slowmo: Improving communication-efficient distributed sgd with slow momentum.arXiv preprint arXiv:1910.00643(2019)

    2019 arXiv

  42. [50]

    Han Xiao, Kashif Rasul, and Roland Vollgraf. 2017. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms.arXiv preprint arXiv:1708.07747(2017)

    2017 arXiv

  43. [51]

    Zikai Xiao, Zihan Chen, Liyinglan Liu, Yang Feng, Jian Wu, Wanlu Liu, Joey Tianyi Zhou, Howard Hao Yang, and Zuozhu Liu. 2024. FedLoGe: Joint Local and Generic Federated Learning under Long-tailed Data.arXiv preprint arXiv:2401.08977 (2024)

    2024 arXiv

  44. [52]

    Zikai Xiao, Zihan Chen, Songshang Liu, Hualiang Wang, Yang Feng, Jin Hao, Joey Tianyi Zhou, Jian Wu, Howard Yang, and Zuozhu Liu. 2024. Fed-grab: Federated long-tailed learning with self-adjusting gradient balancer.Advances in Neural Information Processing Systems36 (2024)

    2024

  45. [53]

    Jing Xu, Sen Wang, Liwei Wang, and Andrew Chi-Chih Yao. 2021. Fedcm: Federated learning with client-level momentum.arXiv preprint arXiv:2106.10874 (2021)

    2021 arXiv

  46. [54]

    Yibo Yang, Shixiang Chen, Xiangtai Li, Liang Xie, Zhouchen Lin, and Dacheng Tao. 2022. Inducing neural collapse in imbalanced learning: Do we really need a learnable classifier at the end of deep neural network?Advances in neural information processing systems35 (2022), 37991–38002

    2022

  47. [55]

    Mang Ye, Xiuwen Fang, Bo Du, Pong C Yuen, and Dacheng Tao. 2023. Hetero- geneous federated learning: State-of-the-art and research challenges.Comput. Surveys56, 3 (2023), 1–44

    2023

  48. [56]

    Chengliang Zhang, Suyi Li, Junzhe Xia, Wei Wang, Feng Yan, and Yang Liu

  49. [57]

    Jing Zhang, Chuanwen Li, Jianzgong Qi, and Jiayuan He. 2023. A survey on class imbalance in federated learning.arXiv preprint arXiv:2303.11673(2023)

    2023 arXiv

  50. [58]

    Shulai Zhang, Zirui Li, Quan Chen, Wenli Zheng, Jingwen Leng, and Minyi Guo. 2021. Dubhe: Towards data unbiasedness with homomorphic encryption in federated learning client selection. InProceedings of the 50th International Conference on Parallel Processing. 1–10

    2021

  51. [59]

    Yu Zhang, Haoyu Ma, Hanze Dong, Xiangyu Zhu, Xiuying Chen, Heming Zhang, Yaqian Li, Hao Zhu, Yunfeng Gao, Xiong Li, and Wanli Ouyang. 2023. CLIP2FL: Enhancing Visual Long-tailed Federated Learning with Diversified Model Initial- ization. InProceedings of the IEEE/CVF Conferenc...

    2023

  52. [60]

    Liang Zheng, Siyuan Liu, and Jun Wang. 2020. FedSAM: Federated Sharpness- Aware Minimization.arXiv preprint arXiv:2009.09707(2020)

    2020 arXiv

  53. [61]

    Hangyu Zhu, Jinjin Xu, Shiqing Liu, and Yaochu Jin. 2021. Federated learning on non-IID data: A survey.Neurocomputing465 (2021), 371–390

    2021

  54. [2020]

    In2020 USENIX Annual Technical Conference (USENIX ATC 20)

    BatchCrypt: Efficient Homomorphic Encryption for Cross-Silo Federated Learning. In2020 USENIX Annual Technical Conference (USENIX ATC 20). USENIX Association, 493–506. https://www.usenix.org/conference/atc20/presentation/ zhang-chengliang

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.