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FedRAW: Preserving Rare-Label Influence in Asynchronous Federated Learning

Prashant Bajpai, Divya Saxena, Philippe Lalanda, German Vega

arXiv:2609.07192v1cs.LGcs.AI

TL;DR

Asynchronous federated learning can underrepresent rare-label clients in the global model even when overall accuracy appears stable. FedRAW combines server-side buffer deduplication with rarity-aware weighting, and improves rare-label accuracy across four datasets at comparable global accuracy. Its rarity scores rely on a one-time client label summary at initialization, limiting compensation to labels present then.

  • Problem

    In asynchronous federated learning, rare-label clients can lose influence through less frequent buffer entry and rarity-agnostic weighting, while overall accuracy remains largely unchanged.

    Source: §I · p. 1

  • Method

    FedRAW combines server-side client-level buffer deduplication with rarity-aware weighting, using a one-time label summary at initialization without modifying local training or communication protocols.

    Source: §I · p. 2, §VII · p. 10

  • Results

    FedRAW improves AvgRare over FedFa by +24.2 pp, +11.8 pp, +30.4 pp, and +18.0 pp on EMNIST Balanced, CIFAR-10, HAM10000, and ISIC-2019, respectively, at comparable global accuracy.

    Source: §VII · p. 10

  • Takeaways & Limitations

    The conclusion reports rare-label recovery confirmed by F1-based and client-level metrics, with O(K) rather than O(N) server-side state compared with CA2FL.

    Source: §VII · p. 10

    FedRAW assumes client label distributions are known at initialization, so it cannot compensate for labels absent then or introduced later.

    Source: §VI · p. 10

Abstract

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Asynchronous federated learning improves scalability by updating the global model from a server-side buffer of client updates as they arrive, rather than waiting for all selected clients to finish. While efficient, this arrival-driven aggregation can silently distort representation learning under heterogeneous participation. We identify silent rarity failure, a hidden failure mode in which clients holding rare labels contribute too weakly to the global model even though its overall accuracy appears largely unaffected. This failure arises from two coupled effects: rare-label clients may submit updates less frequently when they are slower or less available, creating participation bias; and once their updates enter the buffer, standard asynchronous aggregation assigns them no compensating influence, creating aggregation bias. We propose FedRAW, a fully server-side aggregation method that preserves rare-label influence without changing local training, client objectives, or communication protocols. FedRAW combines client-level update deduplication, which prevents frequently arriving clients from repeatedly dominating the update buffer, with rare-label-aware weighting, which increases the influence of clients carrying low-coverage labels. We formalize silent rarity failure through participation and aggregation bias, and show that FedRAW increases rare-label client influence over uniform aggregation while preserving convergence. Across EMNIST Balanced, CIFAR-10, HAM10000, and ISIC-2019, FedRAW improves rarelabel accuracy while preserving comparable global accuracy and adding negligible server-side computation.

I. INTRODUCTION

FedRAW targets silent rarity failure in asynchronous federated learning, where rare-label clients lose influence despite apparently stable global accuracy. It combines server-side buffer deduplication and rarity-aware weighting; across four datasets, it improves rare-label accuracy at comparable global accuracy.

I. INTRODUCTION

  • Silent rarity failure occurs when rare-label clients contribute too weakly despite stable overall accuracy, through both less frequent buffer entry and insufficient influence once included.The introduction characterizes this as a system-induced failure that can occur even when rare-label clients have sufficient local data.Source: §I · pp. 1–2
  • On EMNIST Balanced, global accuracy stays at 75–77% across settings while rare-label accuracy falls to 16.9% under aggregation bias and 2.3% when both biases are present.The controlled settings isolate aggregation bias and then combine it with slower rare-label clients.Source: §I · p. 1, Figure 1 · p. 2

III. FEDRAW: FEDERATED RARITY-AWARE WEIGHTING

  • FedRAW combines client-level deduplication, which limits repeated buffer slots for fast clients, with rare-label-aware weighting for low-coverage clients.The method is server-side and does not modify local training, client objectives, or communication protocols.Source: §I · p. 2, §III · p. 3

I. INTRODUCTION

  • FedRAW substantially improves rare-label accuracy over asynchronous baselines across EMNIST Balanced, CIFAR-10, HAM10000, and ISIC-2019, with comparable global accuracy and negligible server-side computation.The paper presents this as its benchmark-wide result.Source: §I · p. 2

A. Buffer-Based Asynchronous FL

  • Buffer-based asynchronous methods such as FedBuff and FedFa target scalability, but their rarity-agnostic aggregation can let frequent clients occupy multiple buffer positions.CA2FL improves participation coverage with cached updates, while its global correction gives each client 1/N influence.Source: A. Buffer-Based Asynchronous FL · p. 2

B. Long-Tail and Class Imbalance in FL

D. Staleness-Aware Asynchronous FL

  • Staleness-aware methods address delayed or outdated updates; FedRAW instead targets low-coverage labels and their underrepresentation in the aggregation buffer.The paper frames these as distinct challenges not directly addressed together by prior work.Source: D. Staleness-Aware Asynchronous FL · p. 3

A. Client-Level Buffer Deduplication

Deduplication prevents fast clients from repeatedly occupying server-buffer slots, improving the opportunity for distinct clients to be represented. FedRAW's rarity-aware weights then increase the influence of buffered clients carrying low-coverage labels.

A. Client-Level Buffer Deduplication

  • FedRAW keeps at most one update per client in the buffer, replacing that client's prior update when a new one arrives and otherwise using a sliding window of capacity K.This prevents repeated arrivals from fast clients from occupying multiple positions and preserves buffer presence for distinct clients.Source: A. Client-Level Buffer Deduplication · p. 3

B. Rare-Label-Aware Weighted Aggregation

  • FedRAW scores clients using the local frequency of each label weighted by inverse client coverage, then normalizes buffered clients’ scores into aggregation weights.Scores are computed once at initialization and remain fixed during training; higher scores correspond to more local data from low-coverage labels.Source: B. Rare-Label-Aware Weighted Aggregation · pp. 3–4
  • FedRAW adds O(K) work per aggregation event, computes rarity scores once in O(NL) time, and uses one hash-map lookup per arriving update for deduplication.The per-event buffer pass sums rarity scores and computes normalized weights.Source: B. Rare-Label-Aware Weighted Aggregation · p. 4

A. Participation Bias under Heterogeneous Arrival

  • Slower clients have smaller arrival rates; when rare-label clients are slower on average, their normalized arrival probability and buffer entry frequency are lower.The analysis identifies this disadvantage as participation bias before aggregation.Source: A. Participation Bias under… · p. 4

B. Aggregation Bias under Uniform Buffer Weighting

Under uniform buffer aggregation, lower buffer presence directly means lower per-event influence for rare-label clients. FedRAW addresses this through deduplication and higher aggregation weights for clients with higher rarity scores.

B. Aggregation Bias under Uniform Buffer Weighting

  • Under uniform aggregation, every buffered update receives weight 1/K, so a rare-label client with lower buffer presence probability also has lower per-event influence.The paper defines per-event influence as buffer presence probability multiplied by the client’s weight.Source: B. Aggregation Bias under Uniform… · pp. 4–5

C. Influence Preservation under FedRAW

  • FedRAW’s deduplication weakly increases the number of distinct clients represented when a frequent client would otherwise occupy multiple slots.Replacing an existing client update removes duplicate slots and reduces domination by fast clients.Source: C. Influence Preservation under FedRAW · p. 5
  • A buffered client with a larger rarity score receives a larger normalized aggregation weight; a score above the buffer average yields weight above uniform 1/K.This increases the influence of low-coverage clients conditional on their updates being in the buffer.Source: C. Influence Preservation under FedRAW · p. 5

D. Convergence under Bounded Staleness

FedRAW converges to stationary points of an influence-weighted objective under bounded staleness. Rarity weighting affects the variance term, while the bounded-staleness term remains independent of the weighting factor.

D. Convergence under Bounded Staleness

  • FedRAW's average squared gradient is bounded by a vanishing O(1/√TQ) term plus a bounded-staleness constant.Under the diminishing step-size schedule, the first three bound terms decrease as O(1/√TQ).Source: D. Convergence under Bounded Staleness · pp. 5–6
  • The guarantee assumes smooth client objectives, bounded gradient variance and heterogeneity, bounded staleness, fixed rarity scores, and stationary participation.FedRAW additionally uses a bounded-drift condition.Source: D. Convergence under Bounded Staleness · p. 5
  • FedRAW optimizes an influence-weighted objective, whose stationary points need not be those of the uniform objective.The objectives coincide only under uniform weights and uniform participation.Source: D. Convergence under Bounded Staleness · p. 5
  • The bounded-staleness term is independent of ρ, while non-uniform weighting scales the variance term by a factor bounded by ρ ∈ [1, K].The residual bounded-staleness neighborhood remains after the diminishing-schedule terms vanish.Source: D. Convergence under Bounded Staleness · pp. 5–6

V. EVALUATION RESULTS

Across four datasets, FedRAW is evaluated with client-coverage-based rare labels, multiple baseline types, and metrics for global, rare-class, and client-level performance. It improves rare-label accuracy over asynchronous baselines in the reported comparisons.

1) Datasets and Federated Partitions:

  • The evaluation covers EMNIST Balanced and CIFAR-10 with controlled rare-label partitions, plus HAM10000 and ISIC-2019 with naturally rare medical classes.Rare labels are defined by client coverage; the medical datasets assign two clients to each rare class and 20 to each common class.Source: 1) Datasets and Federated Partitions · p. 6

2) Baselines:

  • FedRAW is compared with synchronous FedAvg and q-FedAvg, asynchronous FedBuff and FedFa, and cached-update CA2FL.q-FedAvg targets loss parity rather than label-coverage scarcity; supplementary experiments address scalability, partitioning, sensitivity, and ablations.Source: 2) Baselines · p. 6

3) Evaluation Metrics:

  • GlobalAcc measures held-out global top-1 accuracy, while AvgRare averages accuracy over rare classes and is the primary rare-label preservation metric.MacroF1, RareF1, and recall-weighted RareF2 capture class and rare-class detection; Worst-10% and Local Rare/Common assess client-level utility.Source: 3) Evaluation Metrics · p. 6

1) Rare-label accuracy:

2) Rare-class detection quality:

FedRAW improves rare-class detection across four datasets while maintaining comparable global accuracy, and its benefits depend on rare clients entering the aggregation buffer often enough. Ablations indicate that rarity-aware weighting drives recovery, while deduplication makes buffer presence more reliable.

2) Rare-class detection quality:

  • RareF1 improves over FedFa from 10.5% to 37.9% on EMNIST Balanced, 28.2% to 35.9% on CIFAR-10, 15.2% to 49.9% on HAM10000, and 39.1% to 49.5% on ISIC-2019.RareF2 also improves on all four datasets, indicating fewer missed rare-class detections.Source: 2) Rare-class detection quality · p. 7

3) Global accuracy trade-off:

  • AvgRare improves over FedFa by +24.2 pp on EMNIST Balanced, +11.8 pp on CIFAR-10, +30.4 pp on HAM10000, and +18.0 pp on ISIC-2019, while GlobalAcc changes by −0.9 pp, +2.7 pp, +0.4 pp, and +0.4 pp, respectively.Source: 3) Global accuracy trade-off · p. 7

4) Client-level utility:

  • LocalRare rises over FedFa from 63.5% to 68.4% on EMNIST Balanced, 34.3% to 42.1% on CIFAR-10, and 63.9% to 66.8% on ISIC-2019.On HAM10000, the LocalRare–LocalCommon gap narrows from 7.6 pp to 5.7 pp.Source: 4) Client-level utility · p. 7

5) Participation coverage versus aggregation influence:

  • FedRAW amplifies low-coverage clients’ influence when their updates reach the buffer, whereas CA2FL preserves participation through cached updates; FedRAW also uses 3× less server-side memory.On ISIC-2019, uniform aggregation gives common clients 26/30 (86.7%) of influence and rare clients 4/30 (13.3%).Source: 5) Participation coverage versus… · p. 8

6) Device-level fairness is insufficient:

  • q-FedAvg’s synchronous device-level reweighting is not a like-for-like baseline and performs poorly on some shared partitions, indicating that device-level fairness and label-coverage rarity are distinct problems.On EMNIST Balanced it achieves 0.1% AvgRare and 0.1% RareF1 while GlobalAcc is 50.3%.Source: 6) Device-level fairness is insufficient · p. 8

7) Effect of rare-client availability:

  • FedRAW is most effective when rare-label clients enter the buffer often enough for rarity-aware weighting to act, and it cannot recover information from clients that rarely arrive.The authors identify higher variance on CIFAR-10 and HAM10000, where rare-client participation and rare-class sample counts are more limiting.Source: 7) Effect of rare-client availability · p. 8

C. Ablation Study — 1) Effect of Deduplication and Rarity Weighting:

  • Rarity weighting alone recovers 35.2% AvgRare on EMNIST and 53.8% on HAM10000, while deduplication alone yields 7.9% and 15.4%; together they provide more reliable correction.Deduplication raises BufPres from 59.9% to 72.7% on EMNIST and 46.6% to 59.0% on HAM10000, reducing dependence on stochastic buffer events.Source: 1) Effect of Deduplication and Rarity… · p. 8

2) Effect of Buffer Size; 3) Effect of Rare-Label Density:

4) Specificity to Label-Coverage Scarcity:

FedRAW improves rare-label accuracy over FedFa across four datasets at comparable global accuracy, while supplementary tests probe where its benefits hold and where they are limited. Results also identify participation bias as the dominant bottleneck under extreme speed heterogeneity and describe limitations involving rarity misreporting, similar rare classes, and initialization assumptions.

4) Specificity to Label-Coverage Scarcity:

  • When a Dirichlet split gives every client all labels, FedRAW shows no meaningful improvement over FedFa, consistent with its focus on label-coverage rarity.In this setting, rarity scores collapse toward uniform weighting.Source: 4) Specificity to Label-Coverage… · p. 9

6) Robustness to Rarity Misreporting:

  • Under a false rare-label claim, a water-filling weight cap recovers 83.5% of the GlobalAcc loss and 42.0% of the AvgRare loss, but leaves residual loss tied to buffer occupancy.A simple clip-and-renormalize cap fails to enforce the intended bound; the authors say a complete defense likely needs occupancy-aware safeguards.Source: 6) Robustness to Rarity Misreporting · p. 9

D. Effect of Staleness under Extreme Speed Heterogeneity

  • At 20× speed heterogeneity, rare-client participation falls to 1.34% under FedRAW, while deduplication still raises rare-client buffer presence to 17.9% versus 11.6% under FedFa.At 2× and 10×, buffer presence is 76.7% vs. 67.6% and 33.8% vs. 23.8%, respectively.Source: D. Effect of Staleness under Extreme… · p. 9
  • At 20×, rare-client staleness reaches 417.2 rounds while GlobalAcc is 73.59%; the analysis identifies participation bias, rather than staleness, as the dominant bottleneck.At that ratio, FedFa AvgRare is 0.00% and FedRAW is 0.83%, which the authors characterize as near-floor performance.Source: D. Effect of Staleness under Extreme… · p. 9

VI. LIMITATION

  • On CIFAR-10 with Cat and Dog as rare labels, FedRAW’s rare-label accuracy falls below competing methods despite its highest rare-client buffer presence across seeds.The authors attribute this to simultaneous amplification intensifying early competition between visually similar rare classes.Source: §VI · p. 9
  • FedRAW’s one-time label summary assumes client label distributions are known upfront, making initialization synchronous and harder to reconcile with dynamic membership or drifting labels.It cannot compensate for labels absent at initialization or introduced later; incremental or re-estimated rarity scoring is proposed for future work.Source: §VI · pp. 9–10

VII. CONCLUSION

  • Across EMNIST Balanced, CIFAR-10, HAM10000, and ISIC-2019, FedRAW improves AvgRare over FedFa by +24.2 pp, +11.8 pp, +30.4 pp, and +18.0 pp, respectively, at comparable global accuracy.The conclusion also reports competitive rare-label performance against CA2FL and attributes recovery to rarity-aware weighting, with deduplication improving rare-client buffer presence.Source: §VII · p. 10

5) Robustness to Rare-Label Choice and Scale:

  • Across rare-label choices, FedRAW recovers 17.3% AvgRare (+13.3 pp) versus FedFa’s 4.0%; at N=50 EMNIST Balanced clients, it leads by +15.2 pp (18.6% vs. 3.4%).The N=50 experiment used K=10, 3 seeds (42, 123, 456), 6 rare-label clients (2 per rare label) and 44 common-label clients; higher variance (±5.5 pp) reflects the smaller rare-client pool.Source: S-II. GENERALISATION TO ALTERNATIVE… · p. 11, SUPPLEMENTARY MATERIAL · p. 11

A. Setup and Motivation

The appendix probes when FedRAW helps or remains neutral, including uniform-coverage partitions, visually similar rare classes, and rarity misreporting. Results also show that weight capping alone cannot change which clients occupy the buffer.

B. Why FedRAW is Inert Under Dirichlet Partitioning

C. Results

B. Main Results

  • On CIFAR-10 with visually similar Cat and Dog as rare labels, FedRAW’s mean AvgRare is 14.4%, below CA2FL’s 26.5% and FedFa’s 18.5%.This contrasts with the primary airplane-and-frog setting, where FedRAW leads asynchronous baselines by +11.8 pp AvgRare.Source: B. Main Results · p. 12, Table S9 · p. 13

C. Per-Seed Breakdown and Buffer Presence

  • FedRAW has the highest rare-client buffer presence on every Cat-and-Dog seed, yet AvgRare ranges from 34.4% to 1.4% and 7.5%, consistent with seed-dependent winner-takes-all dynamics.The account attributes the instability to amplified gradient conflict between visually similar rare classes and early buffer dominance.Source: C. Per-Seed Breakdown and Buffer… · p. 12, Table S10 · p. 13

D. Confusion Matrix Analysis

  • For Cat-and-Dog, FedRAW predicts 356 of 1000 dog test samples as cat on average, while cat recall remains comparable; FedFa predicts 440 dogs correctly and 97 as cat.The passage identifies this asymmetric confusion as consistent with gradient interference under approximately 4× rarity weighting.Source: D. Confusion Matrix Analysis · p. 12, Table S11 · p. 13

C. Results

  • The naive cap recovers 13.5% of AvgRare loss and 56% of GlobalAcc loss, while water-filling recovers 42.0% and 83.5%, respectively.The comparison is under rarity misreporting on EMNIST Balanced with correlated speed, N=30, K=10, seed 42.Source: C. Results · p. 13, Table S12 · p. 13
  • Capping limits weight magnitude but not buffer occupancy: the attacker holds the maximum-weight slot in 53.8% of aggregations under both undefended and water-filling-capped conditions.With the attacker present, genuine rare clients hold that slot in 37.2% of aggregations, down from 76.7% in the unattacked run.Source: C. Results · p. 13, Table S12 · p. 13, D. Interpretation · p. 13

A. Effect of Buffer Size

  • Under correlated speed, FedFa AvgRare declines from 20.92% at K=3 to 14.08% at K=10 and 13.92% at K=20, while FedRAW retains rare-label gains at every tested buffer size.The passage links larger buffers under uniform aggregation with more opportunities for frequent common clients to occupy positions.Source: A. Effect of Buffer Size · pp. 13–14, Table S13 · p. 14

B. Effect of Rare-Label Density

Rare-label density is associated with stronger rare-class recovery, while HAM10000 results vary by seed but remain competitive with an asynchronous method that caches updates. The convergence analysis gives a bound with vanishing optimization and variance terms plus a bounded-staleness constant.

B. Effect of Rare-Label Density

  • AvgRare rises from 18.25% with one client per rare label to 52.75% with ten, while rare-client buffer presence reaches 100% by seven clients per rare label.RareF1 rises consistently with AvgRare, while MacroF1 stays within 1.5 pp of GlobalAcc.Source: B. Effect of Rare-Label Density · p. 14, Table S14 · p. 14

C. Seed-wise Analysis of HAM10000 Rare-Label Metrics

  • On HAM10000, FedRAW outperforms FedFa and FedBuff across all three seeds and remains competitive with CA2FL, despite variance from seed-dependent partitions and random arrival times.CA2FL uses cached client updates to retain influence from clients that participate less frequently.Source: C. Seed-wise Analysis of HAM10000… · p. 14, Table S15 · p. 14

S-VIII. CONVERGENCE ANALYSIS OF FEDRAW

  • The convergence bound separates a vanishing optimization-plus-variance part from a bounded-staleness constant controlled by the drift assumption.The analysis tracks leading constants explicitly and leaves only an O(1) step-size factor and the standard O(τmax/T) buffered-FL reference-reindexing term in order notation.Source: S-VIII. CONVERGENCE ANALYSIS OF FEDRAW · p. 14

C. The Influence-Weighted Objective

  • Under stationary participation, the analysis defines each client’s per-event influence as expected aggregation weight when included in the buffer, yielding a fixed influence-weighted objective.The participation probabilities need not be equal; slower rare-label clients may have smaller probabilities.Source: C. The Influence-Weighted Objective · p. 15, B. Assumptions · p. 15

D. Perturbed-Iterate Expansion

The analysis treats parameter averaging as a pseudo-gradient step and separates the update into descent, variance, and staleness-related contributions. The mean-zero buffer fluctuation drops out of the linear term, while staleness and drift remain bounded contributions.

D. Perturbed-Iterate Expansion

  • Because FedRAW averages parameters directly, the server rate is fixed at ηg=1, and the update is analyzed as a pseudo-gradient step with a staleness displacement.The displacement contributes to a bounded-staleness neighborhood term rather than vanishing with the schedule.Source: D. Perturbed-Iterate Expansion · pp. 15–16
  • The staleness displacement is bounded using the drift assumption, and the remaining pseudo-gradient terms carry descent and variance contributions.The displacement terms enter the bounded-staleness constant, while the buffer-sampling variance term carries the weight non-uniformity factor ρ.Source: D. Perturbed-Iterate Expansion · pp. 15–16

E. Bounding T1

  • The mean-zero buffer fluctuation contributes nothing to the linear term T1; its variance is instead carried in T2.Taking the buffer expectation before polarization separates the fluctuation from the staleness-and-drift residual.Source: E. Bounding T1 · p. 16

F. Bounding T3: Staleness and Drift

This section bounds the staleness displacement and local drift using the bounded-drift assumption. Convex aggregation weights cancel from the client-independent bound, so the resulting staleness term carries no factor ρ.

F. Bounding T3: Staleness and Drift

  • The pseudo-gradient contribution to the staleness distance is bounded by applying Cauchy–Schwarz over at most τmax terms, then Jensen over convex client weights and Cauchy–Schwarz over Q local steps.The local-gradient second-moment bound is used in the final step.Source: F. Bounding T3: Staleness and Drift · pp. 16–17
  • The full staleness distance is bounded by the drift constant rather than expanded into a self-referential recursion, which does not close at ηg=1.The stated approach bounds the displacement together with the pseudo-gradient contribution.Source: F. Bounding T3: Staleness and Drift · pp. 16–17
  • Convex weights sum out of the client-independent bound, so the staleness-and-drift term has no factor ρ.The analysis states that only T2 carries ρ.Source: F. Bounding T3: Staleness and Drift · p. 17

G. Bounding T2: Variance and ρ

The variance analysis retains both client-noise and buffer-fluctuation terms, with their contributions controlled by the rarity-weight factor ρ. The mean-gradient bound uses a step-size condition to keep its additive residual bounded and ρ-scaled.

G. Bounding T2: Variance and ρ

  • Client-noise variance scales with squared rarity weights, summarized by ρ, which equals 1 under uniform weights.The client weight is squared after cross terms vanish; ρ/K is the squared-weight quantity.Source: G. Bounding T2: Variance and ρ · p. 17
  • Retaining buffer fluctuation places its contribution in the β(Q)-weighted T2 term, where it vanishes at O(1/T) with bounded ρ-scaling.The passage attributes this placement to taking the expectation over H first.Source: G. Bounding T2: Variance and ρ · p. 17

H. Mean-Gradient Term and the Step-Size Condition

  • Under the stated step-size condition, the mean-gradient residual is a bounded, ρ-scaled additive term of the same order as the variance term.Both contributions are O(1/T) under the diminishing schedule and are folded into ρB′.Source: H. Mean-Gradient Term and the… · p. 17

I. Per-Step Inequality and Telescoping

The bound separates a ρ-free staleness contribution from ρ-scaled variance contributions, yielding a bounded-staleness guarantee under diminishing rates. The uniform case recovers the FedFa/FedBuff bound only with uniform participation as well as uniform weights; deduplication changes participation rather than rate constants.

I. Per-Step Inequality and Telescoping

  • Telescoping the per-step inequality yields the stated rate with a ρ-scaled variance constant and a ρ-free staleness constant.The bound uses a finite objective gap and absorbs a fixed factor into the corollary's O constants.Source: §I · pp. 17–18

J. Diminishing-Rate Corollary

  • The optimization and variance terms vanish under diminishing rates, while staleness leaves a bounded neighborhood controlled by Ψτmax and independent of ρ.The irreducible O(σ²τmax²) term reflects arrival-driven lag and is shared by FedFa/FedBuff.Source: J. Diminishing-Rate Corollary · p. 18

K. Consistency with the Uniform Case

  • Uniform weights recover the FedFa/FedBuff bound only when participation is also uniform; otherwise uniform weights descend on a participation-skewed objective.Under uniform participation, the influence-weighted objective equals the uniform objective.Source: K. Consistency with the Uniform Case · p. 18

L. Role of Deduplication

  • Deduplication raises slow rare-label clients’ buffer presence probabilities, reshaping the participation-weighted objective without changing the rate constants.It preserves the convex-combination aggregator, so the per-step bound holds unchanged.Source: L. Role of Deduplication · p. 18
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