Pith. sign in

REVIEW 4 major objections 5 minor 61 references

Aequa: Fair Model Rewards in Collaborative Learning via Slimmable Networks

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read Training one slimmable network lets collaborative learning give each participant a model matched to their contribution, with provably perfect correlation in the continuous limit and no accuracy loss.

desk verdict A genuinely new mechanism for model-based rewards in federated learning, with solid experiments, but the headline fairness theorem is not actually proved and the fairness metric is partly circular. read the letter →

arxiv 2502.04850 v2 pith:RSMJZOEZ submitted 2025-02-07 cs.LG cs.DC

Nurbek Tastan , Samuel Horvath , Karthik Nandakumar This is my paper · ORCID
classification cs.LGcs.DC MSC 68T0568T07
keywords collaborativefairnessfederatedlearningslimmablenetworksmodelrewardsrewardallocationcontributionassessmentsimulatedannealing
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

Collaborative learning platforms need a way to reward participants that contribute more, and this paper's answer is to reward them with better models rather than money. The central claim is that one slimmable network, a single model that can be run at many widths with accuracy decreasing smoothly as the width shrinks, can serve both as the shared trained model and as the reward ladder. A post-training allocation algorithm assigns each participant the widest subnetwork their measured contribution earns, and the paper proves that in the continuous limit the assigned model accuracies are perfectly correlated with contributions. On six datasets and several partition schemes, Aequa matches or beats the standard FedAvg baseline on accuracy in most settings while reaching near-perfect reward-to-contribution correlation, making differentiated model rewards a realistic incentive mechanism.

What carries the argument

The load-bearing object is the slimmable neural network: a single architecture trained so that every subnetwork width $p \in [0.25, 1.0]$ reaches good accuracy, with accuracy monotonically increasing in width, so width is a physical, verifiable proxy for model quality. The allocation engine is a simulated-annealing search that minimizes the ratio of negative mean gain to gain variance over assignments; the authors show that this objective's optimum is the affine mapping $a_i = c_i + \alpha$, which is what converts an optimization problem into a perfect correlation between rewards and contributions. A secondary mechanism is the sandwich-rule-style width sampling during local training, which keeps all subnetworks trained while preserving the convergence guarantee.

What would settle it

Give a low-contribution participant an untrusted runtime and let it record every full-width model transmitted during training; if the retained model's final accuracy matches the allocation earned by high contributors, the differentiated rewards are not enforceable. Separately, measure Pearson correlation under a deliberately narrow width ladder (say only two widths, 0.25x and 1.0x): with a binary accuracy set Lemma 4's continuous-interval premise is violated, and the observed correlation will be far below one unless the contribution distribution happens to be binary too.

Watch

Extended reading notes

Core claim

The paper's discovery is that fairness and performance do not have to trade off: a slimmable network trained so that every width is accurate gives the server a built-in spectrum of rewards whose quality is controlled by width. Given contribution scores $c_i$, the allocation problem is to choose accuracies $a_i$ minimizing $f(a) = -\mathbb{E}[u(a)]/(\operatorname{Var}[u(a)] + \epsilon)$ with per-client gain $u_i(a) = a_i - c_i$, under the constraint that no client ends up worse than their standalone model. The authors prove that the optimum awards the most accurate model to the highest contributor (Lemma 3) and that, when any accuracy in the achievable interval can be realized, the optimal allocation is affine in the contributions, $a_i = c_i + \alpha$, so the Pearson correlation between allocated accuracy and contribution is exactly one (Lemma 4). They further prove that the width-sampled federated training retains the standard local-SGD convergence rate (Theorem 1) and that the simulated-annealing allocation converges to a global optimum with probability one (Theorem 2).

Load-bearing premise

The mechanism's enforcement depends on every participant training inside a trusted execution environment, so a low-contributing client can never walk away with the full-width model it receives during a communication round; the conclusion asserts that trusted hardware is not a strict requirement, but the paper gives no concrete alternative that would stop a client from keeping the full model.

Editorial extensions

If this is right

  • Platforms can now reward participants with differentiated models instead of money, with the highest contributor always guaranteed the most accurate model (Lemma 3).
  • Under continuous model performance the allocation is provably perfectly aligned with contributions ($\rho = 1$, Lemma 4); in the discrete models used in practice the observed correlations range roughly 0.81 to 1.00 across the 54 settings.
  • Fairness does not degrade the optimization guarantee: the slimmable training protocol retains local-SGD convergence (Theorem 1), and empirically Aequa records the best accuracy in 36 of 54 partition-dataset settings and the best incentivization correlation in all 54.
  • The mechanism extends to training-time rewards by broadcasting width-matched subnetworks and updating contributions each round, so low contributors never see the full model during training.
  • The scheme scales to thousands of clients (3,597 users on FEMNIST) with about a 31 percent wall-clock overhead per round and unchanged communication cost.

Reading between the lines

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

  • The $\rho = 1$ result is best read as an equality-of-gain design: the ratio objective drives every client toward the same additive gain $a_i - c_i$, so under the hood 'fair' means every participant benefits equally above their standalone baseline; a stronger proportionality reading is not what the proof establishes.
  • If no trusted hardware is available, the post-training allocation is only an honor system, since nothing stops a client that received the full model once from keeping it; the natural next step, which the paper does not take, is a cryptographic or verification-based mechanism that proves which width a client is entitled to before serving the model.
  • Because the reward is literally a network width, the same framework could price other width-sensitive resources such as inference latency, memory, or energy, allowing platforms to charge for compute rather than only for accuracy; this is an extension, not a claim of the paper.
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 / 5 minor

Summary. The paper proposes Aequa, a collaborative/federated learning framework that uses slimmable neural networks to provide differentiated final-model rewards proportional to each participant's assessed contribution. The training procedure samples random network widths during local updates and aggregates full-model parameters; after training, an allocation algorithm assigns each client a model width (and hence an accuracy level) by minimizing a mean-variance trade-off objective under an individual-rationality constraint. The authors provide convergence theorems for the training procedure and for the simulated-annealing allocation solver, a fairness lemma claiming perfect Pearson correlation between allocated accuracies and contributions, and extensive experiments on six datasets and multiple partition types, including a large FEMNIST run. A training-time reward extension is also presented, along with results using CGSV and ShapFed as contribution assessors.

Significance. If the theoretical claims held, Aequa would be a significant practical advance: it offers a concrete, non-monetary reward mechanism for collaborative learning with differentiated model access, and the experimental evidence is extensive, covering many datasets, partition regimes, and a 3,597-client FEMNIST deployment. The paper is also commendable for releasing code and for comparing against FedAvg, CGSV, and IAFL. However, the central formal guarantees are not currently supported: the proof of Lemma 4 is circular, and the convergence proof of Theorem 1 does not model the random-width sampling in Algorithm 1. In addition, the main fairness metric is partly an artifact of feeding the same contribution scores into the allocation algorithm that are later used for evaluation, and the enforcement mechanism relies on a TEE assumption that the conclusion later disclaims without a substitute. These issues are load-bearing because the paper's headline claims of 'provably fair' rewards and retained optimality hinges on them, but they appear addressable with a major revision.

major comments (4)
  1. [5.2 / Appendix A.4, Lemma 4] Lemma 4 is not proved by the argument given. Appendix A.4 defines alpha = u - c_N and asserts a*_i = c_i + alpha 'by construction,' but this equality is neither derived from the minimization of Eq. (3) nor implied by Lemma 3, which only establishes max_i a*_i = u. The equal-utility allocation has Var[u] = 0 and objective -alpha/epsilon, but it need not be the minimizer: for c = (0, 0.3, 0.8), u = 1, epsilon = 0.1, the equal-utility allocation (0.2, 0.5, 1.0) gives f = -2, whereas (1, 1, 1) gives utilities (1, 0.7, 0.2), with f = -0.633/(0.1089 + 0.1) ≈ -3.03. No bound on epsilon is stated that would exclude such cases, so the claimed Pearson correlation of exactly one is unsupported. The empirical correlations in Table 2 therefore cannot be read as validating Lemma 4.
  2. [4.1 / 5.1, Theorem 1] Theorem 1's analysis does not model Algorithm 1. The proof in Appendix A.5 invokes Lemmas 5 and 6, which are standard Local SGD bounds for full-model gradient steps, and Lemmas 1 and 2, which concern restrictions of F to a fixed coordinate subset with the remaining coordinates fixed to zero. Algorithm 1 instead samples a width p(i,k) uniformly at each local iteration and updates both the pmax parameters and the sampled-width parameters, which is not equivalent to optimizing a fixed coordinate-restricted objective. Consequently the bound in Theorem 1 is not shown to apply to the actual Aequa training procedure, and the claim that the framework retains optimality guarantees is not established.
  3. [Section 1 and Conclusion] The enforcement assumption is load-bearing and is contradicted by the conclusion. Section 1 states that each participant must have a trusted execution environment (TEE) so that local training is confidential and clients cannot retain the full model broadcast in each round. The conclusion says TEEs are 'not a strict requirement' and that Aequa 'operates securely in the absence of trusted hardware by incorporating contribution assessment methods,' but the paper provides no mechanism by which a participant without a TEE can be prevented from keeping the full-width model received at any communication round. Either the claim must be retracted or a concrete alternative enforcement mechanism must be supplied.
  4. [6.3 / Table 2] The main fairness metric is not an independent validation. The Pearson correlation in Table 2 is computed between the final allocated accuracies and the standalone accuracies that are used as the contribution scores feeding the allocation algorithm in Section 4.2, following the protocol of Wu et al. (2024). Since Aequa maps these same scores to widths and accuracies, a high correlation is an expected output of the allocation design rather than evidence that the rewards match true contributions. The paper should either evaluate on a held-out contribution measure not used in the allocation, or explicitly frame the high correlation as a sanity check of the allocation mapping rather than as confirmation of fairness.
minor comments (5)
  1. [4.2, Eq. (3)] The constant epsilon is described as 'small' but its value is never reported in the experiments; given that the optimality structure of f depends on epsilon, a sensitivity analysis or at least a stated default value should be included.
  2. [Appendix C, Algorithm 2] In the pseudocode, the line 'Send the updated weights of the p(i,t)_max-submodel' appears inside the inner k-loop; it should be placed after the local iteration loop completes.
  3. [Tables 1, 2, 5, 6] The row label 'NUMBER OF TIMES THAT PERFORMS THE BEST' is grammatically incorrect and could be simplified to 'Number of best results'; additionally, the summary counts in the main text should be reconciled with the full counts in the appendix.
  4. [Table 4] The column 'MCG±CGS' mixes two different metrics into a single cell; the paper should report mean collaboration gain and collaboration gain spread as separate columns, as done in Table 7.
  5. [6.6] The statement that communication cost is unchanged because both methods transmit identically sized model parameters is only accurate for the post-training allocation setting; in the training-time extension of Algorithm 2, clients transmit subnetwork updates of varying size, so this claim should be qualified.

Circularity Check

3 steps flagged · score 6.0 of 10

The headline fairness guarantee is asserted by construction: Lemma 4's proof assumes the optimal allocation is c+α, and the reported Pearson correlations measure the same standalone accuracies used as the allocation input against the allocated outputs.

  1. self definitional [Section 5.2, Lemma 4; Appendix A.4 (Proof of Lemma 4)]
    "Since model performances are continuous on the interval [ℓ, u] and that a⋆ N = u, we define α = u − cN > 0. By construction, for every client i, the allocation satisfies a⋆ i = ci + α. Consequently, the Pearson correlation coefficient is computed as: ρ(a⋆, c) = ρ(c + α1, c) = ρ(c, c) = 1. This proves the lemma."

    Lemma 4 claims that the minimizer of f(a) in Eq. 3 achieves perfect Pearson correlation with c. The proof does not minimize f; it asserts, with the words 'by construction', that the optimal allocation equals c + α1. That equal-utility affine form is precisely the conclusion to be established. No argument shows that the argmin of −E[u]/(Var[u]+ε) has this form; for ε above a data-dependent threshold, allocations with positive variance and higher mean utility have smaller f, so the asserted optimum is not generally the minimizer. The lemma therefore reduces the theorem to an unproved restatement of its own conclusion.

  2. fitted input called prediction [Sections 4.2 and 6.3; Table 2 and Table 6]
    "Following Wu et al. (2024), we quantify how well each algorithm aligns incentives with actual usefulness by computing the Pearson correlation coefficient (ρ) between the client model accuracies achieved after T communication rounds and their standalone accuracies. This metric also serves as a measure of fairness, as highlighted in (Xu et al., 2021; Lyu et al., 2020). Following IAFL (Wu et al., 2024), we use standalone accuracies as a surrogate for client contributions."

    In Section 4.2 the allocation input c is 'the contribution (e.g., standalone accuracy as a surrogate) of the client i', and the allocation algorithm maps c to assigned model performances a. The empirical Table 2 and Appendix D.3 then measure ρ between the final model accuracies (outputs of this mapping) and the same standalone accuracies (inputs). Any monotone allocation of widths from c will produce high ρ; by Lemma 4's assumed construction a = c + α1 the correlation is exactly one by definition. Reporting this as incentivization performance is therefore a check that the implemented map is monotone, not an independent validation that rewards are commensurate with contribution.

1 more flagged steps
  1. self definitional [Section 4.3, Eq. (5); Appendix D.6, Table 9]
    "The reward mechanism is then defined as: [Mν(c)]i = ν(ci/ max k ck) (5) where ν is a utility function that directly maps the contributions to network widths (pi)."

    Table 9 reports ρ(c, p) = 1.00 for contribution-versus-width, but p is defined by Eq. (5) as a deterministic function of the normalized contribution c_i / max_k c_k. A monotone ν makes the ordinal (and hence Pearson) correlation with c equal to one as a mathematical identity, independent of any data. Appendix D.6 acknowledges this: 'the correlation coefficient between participant contributions (input) and assigned model widths (output) is perfectly aligned, consistently achieving a correlation coefficient of 1.0'. The perfect score is a property of the construction, not a measured outcome.

full rationale

The paper contains substantial non-circular content: the slimmable-network federated training scheme, its convergence analysis (Theorem 1 under Assumptions 1-4), and the empirical accuracy comparison against FedAvg/CGSV/IAFL are independent of the fairness metric. However, the central claim that Aequa 'ensures that model rewards are proportional to client contributions' is supported in two ways that reduce by construction. Lemma 4's proof assumes the optimal allocation equals c + α1 rather than deriving it from Eq. 3, and the empirical fairness tables compute Pearson correlation between the contribution vector fed into the allocation and the allocated accuracies/widths produced by that same vector. The training-time variant makes the tautology explicit by defining width as ν(c_i / max_k c_k) and then reporting ρ(c, width) = 1.00. These steps are load-bearing because the paper's headline 'collaborative fairness' is operationalized as exactly this correlation. The slimmable-network performance-width curves (Figures 1, 5, and 6) are externally measured and do provide independent grounding for the feasibility of model rewards, which is why the circularity is partial rather than total. Score 6 reflects that the fairness 'prediction' is forced by the allocation definition while the training and performance contributions remain independent.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on strong smoothness/convexity assumptions that the experimental networks violate, on a deployment assumption (TEE) that is not universally available, and on a continuous-accuracy assumption that the discrete width buckets violate. The allocation objective also depends on several unspecified hyperparameters (epsilon, annealing schedule), which are free parameters in practice.

free parameters (5)
  • pmin = 0.25 default; 0.1 for quantity skew experiments
    Minimum slimmable network width. Controls the lowest accuracy floor allocated to low contributors and is tuned per partition to improve CGS results (see Table 8).
  • epsilon in Eq. 3 = not specified
    Small constant in the denominator of the allocation objective to avoid division by zero. Its value affects whether the degenerate equal-allocation solution is selected; no value or sensitivity analysis is given.
  • simulated annealing hyperparameters = not specified
    Initial temperature, cooling schedule, and proposal distribution are not detailed. The convergence proof (Theorem 2) assumes a specific slowly decreasing temperature, but the practical schedule is left unspecified.
  • momentum gamma in Eq. 4 = 0.5
    Momentum factor for smoothing contribution estimates over rounds in the training-time reward extension. Chosen without sensitivity analysis.
  • width discretization bucket = 0.05 for ResNet experiments
    In Appendix D.3, widths are sampled from a discrete bucket (0.25, 0.30, ...) instead of continuous values, introducing a discretization that violates the continuity assumption in Lemma 4.
assumptions (4)
  • domain assumption Local objective functions are L-smooth and convex (Assumptions 1 and 2).
    Standard in FL theory but not satisfied by the neural networks used in experiments (ResNet, CNN, LSTM), so the convergence bound does not strictly apply to the evaluated models.
  • ad hoc to paper Every participant has a trusted execution environment (TEE) to keep local training confidential.
    Introduced in Section 1 to prevent participants from retaining the full model and free-riding. No security analysis of the TEE is given, and the conclusion claims TEEs are not required without providing an alternative enforcement mechanism.
  • domain assumption Model accuracies are continuously available on [l, u] and can be shifted by a constant (Lemmas 3 and 4).
    The fairness proof assumes continuous model performance availability; in practice accuracies are discretized by width buckets, and the paper acknowledges this in Appendix D.3.
  • domain assumption The width-accuracy relationship of the slimmable network is monotonic and stable.
    The allocation assumes an assigned width yields the planned accuracy; this is empirically shown in Figure 1 but not theoretically guaranteed, and it can vary with data distribution.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Aequa: Fair Model Rewards in Collaborative Learning via Slimmable Networks." pith.science (2026). https://pith.science/paper/RSMJZOEZ

@misc{pith2026250204850,
  author       = {Pith},
  title        = {Pith review of: Aequa: Fair Model Rewards in Collaborative Learning via Slimmable Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RSMJZOEZ}},
  note         = {Machine review of arXiv:2502.04850}
}
read the original abstract

Collaborative learning enables multiple participants to learn a single global model by exchanging focused updates instead of sharing data. One of the core challenges in collaborative learning is ensuring that participants are rewarded fairly for their contributions, which entails two key sub-problems: contribution assessment and reward allocation. This work focuses on fair reward allocation, where the participants are incentivized through model rewards - differentiated final models whose performance is commensurate with the contribution. In this work, we leverage the concept of slimmable neural networks to collaboratively learn a shared global model whose performance degrades gracefully with a reduction in model width. We also propose a post-training fair allocation algorithm that determines the model width for each participant based on their contributions. We theoretically study the convergence of our proposed approach and empirically validate it using extensive experiments on different datasets and architectures. We also extend our approach to enable training-time model reward allocation.

Figures

Figures reproduced from arXiv: 2502.04850 by the authors.

Figure 1
Figure 1. Performance vs. network width (p) using CIFAR￾10 and CIFAR-100 datasets on ResNet-18 model. 2. Low variability in utility: The variability of utilities {ui(a)} should be kept low so that no client’s benefit is disproportionately high or low compared to others. 3. High average gain: The average gain across clients, 1 N PN i=1 ui(a), should be as large as possible, balanc￾ing overall performance with fairness. Definit… view at source ↗
Figure 2
Figure 2. Visualization of the correlation when contribution [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Performance comparison of our proposed methods [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: Performance vs. network width (p) using FEM￾NIST dataset using a custom CNN architecture composed of two convolutional layers followed by a fully connected layer [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: , which illustrates the same performance vs. model width relationship for four additional datasets: MNIST, FMNIST, SVHN, and SST, and under a homogeneous partitioning strategy. As described in Appendix B, these datasets are trained using different model architectures: …
Figure 7
Figure 7. Figure 7: Per-participant performance comparison of Aequa and other baseline methods on CIFAR-100 dataset under [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

61 extracted references · 41 canonical work pages

  1. [1]

    and Gavra, I

    Bouttier, C. and Gavra, I. Convergence rate of a simulated annealing algorithm with noisy observations. Journal of Machine Learning Research, 20 0 (4): 0 1--45, 2019

    work page 2019

  2. [2]

    Caldas, S., Duddu, S. M. K., Wu, P., Li, T., Konečný, J., McMahan, H. B., Smith, V., and Talwalkar, A. Leaf: A benchmark for federated settings. Workshop on Federated Learning for Data Privacy and Confidentiality (2019)., 2019. URL https://arxiv.org/abs/1812.01097

    arXiv 2019

  3. [3]

    J., Jhunjhunwala, D., Li, T., Smith, V., and Joshi, G

    Cho, Y. J., Jhunjhunwala, D., Li, T., Smith, V., and Joshi, G. To federate or not to federate: incentivizing client participation in federated learning. In Workshop on Federated Learning: Recent Advances and New Challenges (in Conjunction with NeurIPS 2022), 2022

    work page 2022

  4. [4]

    Cong, M., Yu, H., Weng, X., and Yiu, S. M. A game-theoretic framework for incentive mechanism design in federated learning. Federated Learning: Privacy and Incentive, pp.\ 205--222, 2020

    work page 2020

  5. [5]

    B., Ramage, D., and Xu, Z

    Daly, K., Eichner, H., Kairouz, P., McMahan, H. B., Ramage, D., and Xu, Z. Federated learning in practice: reflections and projections. In 2024 IEEE 6th International Conference on Trust, Privacy and Security in Intelligent Systems, and Applications (TPS-ISA), pp.\ 148--156. IEEE, 2024

    work page 2024

  6. [6]

    and Kleinberg, J

    Donahue, K. and Kleinberg, J. Optimality and stability in federated learning: A game-theoretic approach. In Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P., and Vaughan, J. W. (eds.), Advances in Neural Information Processing Systems, volume 34, pp.\ 1287--1298. Curran Associates, Inc., 2021. URL https://proceedings.neurips.cc/paper_files/paper/2021/...

    work page 2021

  7. [7]

    Confidential federated computations

    Eichner, H., Ramage, D., Bonawitz, K., Huba, D., Santoro, T., McLarnon, B., Van Overveldt, T., Fallen, N., Kairouz, P., Cheu, A., et al. Confidential federated computations. arXiv preprint arXiv:2404.10764, 2024

    arXiv 2024

  8. [8]

    P., Liu, C., and Zhang, Y

    Fan, Z., Fang, H., Zhou, Z., Pei, J., Friedlander, M. P., Liu, C., and Zhang, Y. Improving fairness for data valuation in horizontal federated learning. In 2022 IEEE 38th International Conference on Data Engineering (ICDE), pp.\ 2440--2453. IEEE, 2022

    work page 2022

Show all 61 references
  1. [9]

    and Zou, J

    Ghorbani, A. and Zou, J. Data shapley: Equitable valuation of data for machine learning. In Chaudhuri, K. and Salakhutdinov, R. (eds.), Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp.\ 2242--2251....

    2019

  2. [10]

    Profit sharing and efficiency in utility games

    Gollapudi, S., Kollias, K., Panigrahi, D., and Pliatsika, V. Profit sharing and efficiency in utility games. In ESA, 2017

    2017

  3. [11]

    Simulated annealing: A proof of convergence

    Granville, V., Kriv \'a nek, M., and Rasson, J.-P. Simulated annealing: A proof of convergence. IEEE transactions on pattern analysis and machine intelligence, 16 0 (6): 0 652--656, 1994

    1994

  4. [12]

    Deep residual learning for image recognition

    He, K., Zhang, X., Ren, S., and Sun, J. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.\ 770--778, 2016

    2016

  5. [13]

    Hyperparameter transfer learning with adaptive complexity

    Horv \'a th, S., Klein, A., Richt \'a rik, P., and Archambeau, C. Hyperparameter transfer learning with adaptive complexity. In International conference on artificial intelligence and statistics, pp.\ 1378--1386. PMLR, 2021

    2021

  6. [14]

    Fjord: Fair and accurate federated learning under heterogeneous targets with ordered dropout

    Horv\' a th, S., Laskaridis, S., Almeida, M., Leontiadis, I., Venieris, S., and Lane, N. Fjord: Fair and accurate federated learning under heterogeneous targets with ordered dropout. Advances in Neural Information Processing Systems, 34: 0 12876--12889, 2021

    2021

  7. [15]

    Maestro: Uncovering low-rank structures via trainable decomposition

    Horv \'a th, S., Laskaridis, S., Rajput, S., and Wang, H. Maestro: Uncovering low-rank structures via trainable decomposition. arXiv preprint arXiv:2308.14929, 2023

    2023 arXiv

  8. [16]

    Papaya: Practical, private, and scalable federated learning

    Huba, D., Nguyen, J., Malik, K., Zhu, R., Rabbat, M., Yousefpour, A., Wu, C.-J., Zhan, H., Ustinov, P., Srinivas, H., et al. Papaya: Practical, private, and scalable federated learning. Proceedings of Machine Learning and Systems, 4: 0 814--832, 2022

    2022

  9. [17]

    A., Hynes, N., G \"u rel, N

    Jia, R., Dao, D., Wang, B., Hubis, F. A., Hynes, N., G \"u rel, N. M., Li, B., Zhang, C., Song, D., and Spanos, C. J. Towards efficient data valuation based on the shapley value. In The 22nd International Conference on Artificial Intelligence and Statistics, pp.\ 1167--1176. P...

    2019

  10. [18]

    R., Li, W., Yang, D., Zhao, C., Nath, V., Xu, D., Dou, Q., and Xu, Z

    Jiang, M., Roth, H. R., Li, W., Yang, D., Zhao, C., Nath, V., Xu, D., Dou, Q., and Xu, Z. Fair federated medical image segmentation via client contribution estimation. arXiv preprint arXiv:2303.16520, 2023

    2023 arXiv

  11. [19]

    Kang, J., Xiong, Z., Niyato, D., Yu, H., Liang, Y.-C., and Kim, D. I. Incentive design for efficient federated learning in mobile networks: A contract theory approach. In 2019 IEEE VTS Asia Pacific Wireless Communications Symposium (APWCS), pp.\ 1--5, 2019. doi:10.1109/VTS-APW...

    2019

  12. [20]

    Tighter theory for local sgd on identical and heterogeneous data

    Khaled, A., Mishchenko, K., and Richt \'a rik, P. Tighter theory for local sgd on identical and heterogeneous data. In International Conference on Artificial Intelligence and Statistics, pp.\ 4519--4529. PMLR, 2020

    2020

  13. [21]

    Learning multiple layers of features from tiny images

    Krizhevsky, A., Hinton, G., et al. Learning multiple layers of features from tiny images. Toronto, ON, Canada, 2009

    2009

  14. [22]

    Matryoshka representation learning

    Kusupati, A., Bhatt, G., Rege, A., Wallingford, M., Sinha, A., Ramanujan, V., Howard-Snyder, W., Chen, K., Kakade, S., Jain, P., et al. Matryoshka representation learning. Advances in Neural Information Processing Systems, 35: 0 30233--30249, 2022

    2022

  15. [23]

    The mnist database of handwritten digits

    LeCun, Y. The mnist database of handwritten digits. http://yann. lecun. com/exdb/mnist/, 1998

    1998

  16. [24]

    K., Zaheer, M., Sanjabi, M., Talwalkar, A., and Smith, V

    Li, T., Sahu, A. K., Zaheer, M., Sanjabi, M., Talwalkar, A., and Smith, V. Federated optimization in heterogeneous networks. In Dhillon, I., Papailiopoulos, D., and Sze, V. (eds.), Proceedings of Machine Learning and Systems, volume 2, pp.\ 429--450, 2020. URL https://proceedi...

    2020

  17. [25]

    Ditto: Fair and robust federated learning through personalization

    Li, T., Hu, S., Beirami, A., and Smith, V. Ditto: Fair and robust federated learning through personalization. In International conference on machine learning, pp.\ 6357--6368. PMLR, 2021

    2021

  18. [26]

    Lin, X., Xu, X., Ng, S.-K., Foo, C.-S., and Low, B. K. H. Fair yet asymptotically equal collaborative learning. In Proceedings of the 40th International Conference on Machine Learning (ICML-23), 2023

    2023

  19. [27]

    A contract theory based incentive mechanism for federated learning

    Liu, Y., Tian, M., Chen, Y., Xiong, Z., Leung, C., and Miao, C. A contract theory based incentive mechanism for federated learning. In Federated and Transfer Learning, pp.\ 117--137. Springer, 2022 a

    2022

  20. [28]

    Gtg-shapley: Efficient and accurate participant contribution evaluation in federated learning

    Liu, Z., Chen, Y., Yu, H., Liu, Y., and Cui, L. Gtg-shapley: Efficient and accurate participant contribution evaluation in federated learning. ACM Transactions on intelligent Systems and Technology (TIST), 13 0 (4): 0 1--21, 2022 b

    2022

  21. [29]

    Collaborative fairness in federated learning

    Lyu, L., Xu, X., Wang, Q., and Yu, H. Collaborative fairness in federated learning. Federated Learning: Privacy and Incentive, pp.\ 189--204, 2020

    2020

  22. [30]

    McMahan, B., Moore, E., Ramage, D., Hampson, S., and y Arcas, B. A. Communication-efficient learning of deep networks from decentralized data. In Artificial intelligence and statistics, pp.\ 1273--1282. PMLR, 2017

    2017

  23. [31]

    Resource-adaptive federated learning with all-in-one neural composition

    Mei, Y., Guo, P., Zhou, M., and Patel, V. Resource-adaptive federated learning with all-in-one neural composition. Advances in Neural Information Processing Systems, 35: 0 4270--4284, 2022

    2022

  24. [32]

    Masked training of neural networks with partial gradients

    Mohtashami, A., Jaggi, M., and Stich, S. Masked training of neural networks with partial gradients. In International Conference on Artificial Intelligence and Statistics, pp.\ 5876--5890. PMLR, 2022

    2022

  25. [33]

    Y., et al

    Netzer, Y., Wang, T., Coates, A., Bissacco, A., Wu, B., Ng, A. Y., et al. Reading digits in natural images with unsupervised feature learning. In NIPS workshop on deep learning and unsupervised feature learning, number 2 in 2011, pp.\ 4. Granada, 2011

    2011

  26. [34]

    Nishio, T., Shinkuma, R., and Mandayam, N. B. Estimation of individual device contributions for incentivizing federated learning. CoRR, abs/2009.09371, 2020. URL https://arxiv.org/abs/2009.09371

    2009 arXiv

  27. [35]

    Learning ordered representations with nested dropout

    Rippel, O., Gelbart, M., and Adams, R. Learning ordered representations with nested dropout. In International Conference on Machine Learning, pp.\ 1746--1754. PMLR, 2014

    2014

  28. [36]

    Shapley, L. S. A value for n-person games. In Kuhn, H. W. and Tucker, A. W. (eds.), Contributions to the Theory of Games II, pp.\ 307--317. Princeton University Press, Princeton, 1953

    1953

  29. [37]

    Towards fairness-aware federated learning

    Shi, Y., Yu, H., and Leung, C. Towards fairness-aware federated learning. IEEE Transactions on Neural Networks and Learning Systems, 35 0 (9): 0 11922–11938, September 2024. ISSN 2162-2388. doi:10.1109/tnnls.2023.3263594. URL http://dx.doi.org/10.1109/TNNLS.2023.3263594

    2024

  30. [38]

    Fedfaim: A model performance-based fair incentive mechanism for federated learning

    Shi, Z., Zhang, L., Yao, Z., Lyu, L., Chen, C., Wang, L., Wang, J., and Li, X.-Y. Fedfaim: A model performance-based fair incentive mechanism for federated learning. IEEE Transactions on Big Data, 2022

    2022

  31. [39]

    K., Kim, D., and Kim, K

    Shyn, S. K., Kim, D., and Kim, K. Fedccea : A practical approach of client contribution evaluation for federated learning. CoRR, abs/2106.02310, 2021. URL https://arxiv.org/abs/2106.02310

    2021 arXiv

  32. [40]

    D., Ng, A

    Socher, R., Perelygin, A., Wu, J., Chuang, J., Manning, C. D., Ng, A. Y., and Potts, C. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing, pp.\ 1631--1642, 2013

    2013

  33. [41]

    Stich, S. U. Local sgd converges fast and communicates little. arXiv preprint arXiv:1805.09767, 2018

    2018 arXiv

  34. [42]

    Redefining contributions: Shapley-driven federated learning

    Tastan, N., Fares, S., Aremu, T., Horváth, S., and Nandakumar, K. Redefining contributions: Shapley-driven federated learning. In Larson, K. (ed.), Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, IJCAI-24 , pp.\ 5009--5017. Internatio...

    2024

  35. [43]

    CYCle: Choosing Your Collaborators Wisely to Enhance Collaborative Fairness in Decentralized Learning , 2025 a

    Tastan, N., Horv\'ath, S., and Nandakumar, K. CYCle: Choosing Your Collaborators Wisely to Enhance Collaborative Fairness in Decentralized Learning , 2025 a . URL https://arxiv.org/abs/2501.12344

    2025

  36. [44]

    FedPeWS: Personalized Warmup via Subnetworks for Enhanced Heterogeneous Federated Learning

    Tastan, N., Horv \'a th, S., Tak \'a c , M., and Nandakumar, K. FedPeWS: Personalized Warmup via Subnetworks for Enhanced Heterogeneous Federated Learning . In The Second Conference on Parsimony and Learning (Proceedings Track), 2025 b . URL https://openreview.net/forum?id=iYwiyS1YdQ

    2025

  37. [45]

    Progfed: Effective, communication, and computation efficient federated learning by progressive training

    Wang, H.-P., Stich, S., He, Y., and Fritz, M. Progfed: Effective, communication, and computation efficient federated learning by progressive training. In International Conference on Machine Learning, pp.\ 23034--23054. PMLR, 2022

    2022

  38. [46]

    B., Al-Shedivat, M., Andrew, G., Avestimehr, S., Daly, K., Data, D., et al

    Wang, J., Charles, Z., Xu, Z., Joshi, G., McMahan, H. B., Al-Shedivat, M., Andrew, G., Avestimehr, S., Daly, K., Data, D., et al. A field guide to federated optimization. arXiv preprint arXiv:2107.06917, 2021

    2021 arXiv

  39. [47]

    A principled approach to data valuation for federated learning

    Wang, T., Rausch, J., Zhang, C., Jia, R., and Song, D. A principled approach to data valuation for federated learning. Federated Learning: Privacy and Incentive, pp.\ 153--167, 2020

    2020

  40. [48]

    K., Stich, S., Dai, Z., Bullins, B., Mcmahan, B., Shamir, O., and Srebro, N

    Woodworth, B., Patel, K. K., Stich, S., Dai, Z., Bullins, B., Mcmahan, B., Shamir, O., and Srebro, N. Is local sgd better than minibatch sgd? In International Conference on Machine Learning, pp.\ 10334--10343. PMLR, 2020

    2020

  41. [49]

    M., Raskar, R., and Low, B

    Wu, Z., Amiri, M. M., Raskar, R., and Low, B. K. H. Incentive-aware federated learning with training-time model rewards. In The Twelfth International Conference on Learning Representations, 2024

    2024

  42. [50]

    Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms

    Xiao, H., Rasul, K., and Vollgraf, R. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747, 2017

    2017 arXiv

  43. [51]

    and Lyu, L

    Xu, X. and Lyu, L. A reputation mechanism is all you need: Collaborative fairness and adversarial robustness in federated learning. arXiv preprint arXiv:2011.10464, 2020

    2011 arXiv

  44. [52]

    S., and Low, B

    Xu, X., Lyu, L., Ma, X., Miao, C., Foo, C. S., and Low, B. K. H. Gradient driven rewards to guarantee fairness in collaborative machine learning. Advances in Neural Information Processing Systems, 34: 0 16104--16117, 2021

    2021

  45. [53]

    Asynchronous federated learning with incentive mechanism based on contract theory

    Yang, D., Ji, Y., Kou, Z., Zhong, X., and Zhang, S. Asynchronous federated learning with incentive mechanism based on contract theory. In 2024 IEEE Wireless Communications and Networking Conference (WCNC), pp.\ 1--6. IEEE, 2024

    2024

  46. [54]

    and Huang, T

    Yu, J. and Huang, T. Autoslim: Towards one-shot architecture search for channel numbers. arXiv preprint arXiv:1903.11728, 2019 a

    1903 arXiv

  47. [55]

    and Huang, T

    Yu, J. and Huang, T. S. Universally slimmable networks and improved training techniques. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), October 2019 b

    2019

  48. [56]

    Slimmable neural networks

    Yu, J., Yang, L., Xu, N., Yang, J., and Huang, T. Slimmable neural networks. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id=H1gMCsAqY7

    2019

  49. [57]

    A learning-based incentive mechanism for federated learning

    Zhan, Y., Li, P., Qu, Z., Zeng, D., and Guo, S. A learning-based incentive mechanism for federated learning. IEEE Internet of Things Journal, 7 0 (7): 0 6360--6368, 2020

    2020

  50. [58]

    Hierarchically fair federated learning, 2020

    Zhang, J., Li, C., Robles-Kelly, A., and Kankanhalli, M. Hierarchically fair federated learning, 2020. URL https://arxiv.org/abs/2004.10386

    2020 arXiv

  51. [59]

    Incentive mechanism for horizontal federated learning based on reputation and reverse auction

    Zhang, J., Wu, Y., and Pan, R. Incentive mechanism for horizontal federated learning based on reputation and reverse auction. In Proceedings of the Web Conference 2021, pp.\ 947--956, 2021

    2021

  52. [60]

    Federated learning on non-iid data: A survey

    Zhu, H., Xu, J., Liu, S., and Jin, Y. Federated learning on non-iid data: A survey. Neurocomputing, 465: 0 371--390, 2021. ISSN 0925-2312. doi:https://doi.org/10.1016/j.neucom.2021.07.098. URL https://www.sciencedirect.com/science/article/pii/S0925231221013254

    2021 doi

  53. [61]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.