Federated Unlearning Over Wireless Networks

Mingzhe Chen; Wei Xu; Yixuan Chen; Zhaohui Yang; Zhaoyang Zhang; Zhouxiang Zhao

REVIEW 4 major objections 6 minor 59 references

Federated Unlearning Over Wireless Networks

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper shows that the delay of federated unlearning over wireless links can be minimized by jointly choosing bandwidth, transmit power, CPU frequency, and local accuracy, and it gives a polynomial-time algorithm that finds…

desk verdict A credible first physical-layer-aware resource allocation framework for federated unlearning, but the delay gains are analytical predictions under unverified convexity constants, so the paper needs referee scrutiny before the numbers are trusted. read the letter →

arxiv 2608.09090 v1 pith:FV46E7ZY submitted 2026-08-10 cs.IT math.IT

Yixuan Chen , Zhouxiang Zhao , Mingzhe Chen , Wei Xu , Zhaoyang Zhang , Zhaohui Yang This is my paper · ORCID

classification cs.ITmath.IT

keywords federatedunlearningdelayminimizationresourceallocationwirelessnetworksCSIuncertaintyedgecomputingconvexoptimizationbisectionsearch

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

When a user asks to be deleted from a federated model, the remaining devices must run calibration rounds to erase that user's influence; over wireless links these rounds are slow and unreliable, and standard federated-learning resource allocation ignores them. This paper targets that gap by modeling the full chain: the convergence behavior of the unlearning algorithm, local computation at energy-constrained devices, and worst-case robust transmission under bounded channel-estimation error. It derives a closed-form lower bound on the number of global calibration rounds needed for a target accuracy, then solves the resulting non-convex delay-minimization problem with a nested bisection and golden-section search. The claimed result is an algorithm of polynomial-logarithmic complexity that cuts unlearning completion time by roughly 10 percent compared with retraining and fixed-resource baselines, with the largest gains in tight energy and bandwidth regimes.

What carries the argument

The load-bearing object is the global-round bound $J(\eta)=\frac{a}{(\gamma-L\xi\beta)(\sqrt{\gamma}-\sqrt{\eta L})^2+(1-\eta)\gamma^2}$, with $a=\frac{2L^2\ln(1/\epsilon_0)}{\xi\beta}$, which states how many global calibration rounds are needed for the unlearning algorithm to reach the target accuracy $\epsilon_0$ when local problems are solved to accuracy $\eta$. That bound, combined with the local iteration count $v\log_2(1/\eta)$, yields the per-round computation time and energy, and with the robust transmission rate it yields the per-user delay $T_k$. The algorithmic machinery is the hierarchy of monotone searches that exploit this structure: a golden-section search finds the transmission time minimizing each user's total energy, a bisection finds the minimum bandwidth that keeps a user feasible, an outer bisection finds the minimal delay for fixed $\eta$, and a uniform scan over $\eta$ selects the best local accuracy. This decomposition is what turns the non-convex joint problem into a polynomial-logarithmic procedure $O\left(MK\log(1/\epsilon_T)\log(1/\epsilon_b)\log(1/\epsilon_t)\right)$.

What would settle it

Run the paper's unlearning procedure on the blog feedback dataset with its stated parameters, record the actual number of global calibration rounds needed to reach $\epsilon_0 = 10^{-3}$ for a grid of $\eta$ values, and compare with $J(\eta)$; if the measured round counts fall below the bound by a large margin or if the per-user total energy $E_{\mathrm{total}}(t)$ is not convex in $t$, then the predicted delay, the optimal allocation, and the claimed gain all shift.

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Extended reading notes

Core claim

The paper's central claim is that federated unlearning delay over wireless networks can be minimized by jointly optimizing bandwidth, transmit power, CPU frequency, and local accuracy, and that the resulting non-convex problem decomposes into a hierarchy of monotone feasibility checks. Lemma 1 gives a closed-form lower bound $J(\eta)$ on the number of global calibration rounds as a function of local accuracy $\eta$, and Lemma 2 fixes the local iteration count; together they convert the unlearning process into a per-round cost that depends on $\eta$. The algorithm scans $\eta$ over a uniform grid, and for each $\eta$ uses bisection over the total delay $T$, bisection over each user's bandwidth, and a golden-section search over transmission time to find the minimum feasible delay. Numerical experiments on the blog feedback dataset report consistent reductions in completion time relative to equal-bandwidth, fixed-accuracy, and retraining baselines, with reductions around 10 percent at moderate power, bandwidth, and energy levels.

Load-bearing premise

The entire delay model assumes the number of calibration rounds is exactly the convergence bound $J(\eta)$, which requires the local loss functions to be $\gamma$-strongly convex and $L$-smooth with known $\gamma$ and $L$, and requires the historical-to-calibration update norms to fall within the known bounds $\alpha$ and $\beta$; the paper never measures these constants on the blog feedback dataset, and the monotonicity proof needed for the delay-bisection step is deferred to reference [56].

Editorial extensions

If this is right

Wireless operators can compute near-optimal unlearning resource allocations in polynomial-logarithmic time, using only channel estimates, error bounds, and energy budgets.
Joint tuning of communication and computation resources is the source of the gain: at moderate transmit power the proposed scheme is about 10.7 percent faster than retraining, 4.1 percent faster than equal-bandwidth allocation, and 5.0 percent faster than fixed-accuracy allocation.
The optimal local accuracy is not a fixed constant: it shifts with channel and energy conditions, so a system that tunes it can outperform one that hard-codes it.
The performance curves saturate at high power, bandwidth, and energy budgets, meaning the bottleneck moves from communication to computation; the algorithm still finds the best feasible point in that regime.

Reading between the lines

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

Beyond the paper, the same decomposition should apply to other iterative calibration-based unlearning methods that share the convergence structure, not just the FedEraser/DANE combination used here.
The uniform grid over $\eta$ could likely be replaced by a golden-section or bisection search if the delay-versus-$\eta$ curve is unimodal; the paper's own Fig. 8 suggests such a shape but the paper does not claim it.
A direct empirical test is to measure $\gamma$, $L$, $\alpha$, and $\beta$ on the blog feedback data; if those constants are estimated rather than assumed, the predicted $J(\eta)$ can be validated and the robustness claims made quantitative.
Extending the model to multiple simultaneous unlearning requests, which the paper lists as future work, would change the bandwidth and energy coupling and is a natural test of the framework's scalability.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First thing to know: this is a credible first cut at physical-layer-aware resource allocation for federated unlearning. It jointly allocates bandwidth, power, CPU frequency, and local accuracy under bounded CSI error, which the cited prior work does not do. The derived round bound J(η) is the load-bearing piece, and the Appendix A proof is internally coherent under the stated assumptions. The solver—uniform scan over η, nested bisection for T and b, golden-section for t_k—is standard but cleanly assembled, and the complexity O(MK log(1/ε_T) log(1/ε_b) log(1/ε_t)) is believable.

The real soft spot is that Section IV evaluates the analytical model, not an actual unlearning run. Every delay number is computed by plugging J(η) into (18), and J(η) is a sufficient round bound, not the actual stopping time. So the roughly 10% gains are predictions of the authors' model, not end-to-end measurements. That is not disqualifying, but it should be labeled as such.

Second, the theorem's validity requires 0<ξ≤γ/(Lβ) (stated in Lemma 1), and the paper fixes ξ=0.1, δ=0.1 without ever reporting γ, L, or β for the blog feedback dataset. If those constants violate the inequality, the contraction factor in (A.18) does not hold and J(η) is unsupported. Worse, β is defined in (9) as the max over historical-to-calibration update norm ratios—an output of the unlearning process itself—so treating it as a known system constant before the algorithm runs is circular unless it is measured separately. This is the main correctness risk, and it is addressable: report the constants, or at least run a sensitivity analysis over plausible ranges.

Minor issues: Lemma 5's monotonicity proof is outsourced to [56], the authors' prior FL paper; probably fine but should be stated. Optimality over η is only over a discrete grid, so the "global optimum" claim is grid-restricted. No code or data is provided.

Overall, the framework is sound under its assumptions and the contribution is genuinely useful for the FU-over-wireless niche. The paper deserves serious refereeing. The referee should ask for calibrated constants, a sensitivity analysis, and ideally a small-scale actual FU simulation to validate J(η) against real stopping times.

Referee Report

4 major / 6 minor

Summary. The paper studies delay minimization for federated unlearning (FU) over a wireless edge network, where the remaining clients calibrate the global model through a DANE-type algorithm while uploading updates under bounded CSI uncertainty. The authors derive a closed-form lower bound J(η) on the number of calibration rounds (Lemma 1), combine it with per-round computation and worst-case transmission models, and formulate a non-convex min-max delay problem. They propose an algorithm that scans the local accuracy parameter η on a grid and uses nested bisection and golden-section searches for per-user feasibility, minimum bandwidth, and minimum delay. Numerical results compare the proposed scheme with equal-bandwidth, fixed-accuracy, and retraining baselines.

Significance. The problem is timely and the decomposition strategy is well structured. The complexity analysis is transparent, and the paper identifies a relevant coupling between FU convergence rounds and wireless resource allocation. If the round bound J(η) were validated on an actual FU calibration run and the required constants were measured or certified, the framework would be a useful contribution to the emerging FU-over-wireless literature. The main weakness is that the numerical results currently validate the authors' analytical model rather than the underlying unlearning process, and the theorem's operating assumptions are not checked in simulation.

major comments (4)

[Section IV and Lemma 1] Section IV sets δ=0.1 and ξ=0.1 but never reports γ, L, or β for the blog feedback dataset, and Lemma 1 (Eq. (11)) is valid only if γ−Lξβ>0 (Eq. (A.17)). Without these constants, the reader cannot check whether the simulated operating point lies in the theorem's valid regime. In addition, β in Eq. (9) is defined as max_{k,j} ||h_k^{(j)}||/||hat h_k^{(j)}||, which is an output of the FU calibration run rather than a known system parameter; the optimization therefore assumes a quantity that is not available before the allocation is executed. Please report measured constants (or a verifiable upper bound on β) and confirm the condition, or revise the convergence bound accordingly.
[Eq. (18) and Section IV] Eq. (18) uses J(η) as the number of global rounds in the delay expression, but Lemma 1 gives only a sufficient round count for the required accuracy; the actual stopping time of Algorithm 1 may be smaller. More importantly, the simulations in Section IV compute T through the same analytical J(η) rather than running the federated unlearning calibration on the blog feedback data. The reported delay reductions therefore compare resource allocation schemes inside the authors' own model and are not an independently measured evaluation of the unlearning delay. An experiment that records the actual convergence of Algorithm 1 (or FedEraser) and compares the resulting delay against the optimized allocation is needed.
[Lemma 1 / Eq. (A.17)] Lemma 1 states the condition as 0<ξ≤γ/(Lβ), but the proof at (A.17) requires γ−Lξβ>0. If equality holds, the coefficient in (A.18) is zero, the contraction bound collapses, and the exponential bound in (A.19) is invalid. The statement should use 0<ξ<γ/(Lβ), and the simulations must respect this strict inequality.
[Section III-E, Eq. (29)] Algorithm 5 returns η* as the minimizer over a fixed grid of M points, not over the continuous interval [10^{-3}, 0.99]. The abstract and conclusion refer to 'optimal delay, bandwidth, power, and computation frequency' without this qualification. Please state that the result is grid-optimal or near-optimal, or provide an argument that the true optimum lies on the grid.

minor comments (6)

[Problem (20)] Constraint (20d) sums b_k over k∈K, but the optimization variables exclude the leaving user k_u; the sum should be over the set \tilde K.
[Algorithm 4] Line 1 of Algorithm 4 says to compute J(η) from Eq. (10); the correct reference is Eq. (11).
[Fig. 8] The caption of Fig. 8 says 'Completion time versus maximum average transmit power of each user,' but the x-axis is the local accuracy parameter η; the caption should describe the plotted trade-off.
[Algorithm 2] Line 8 of Algorithm 2 uses 0.382(b−a) and 0.618(b−a) with undefined a and b; the interval endpoints should be t_a and t_b.
[Lemma 5] The proof of Lemma 5 is cited to 'Appendix E in [56]', which is a prior FL paper and not an FU setting; either give the direct proof (the same feasible tuple remains feasible for larger T) or remove the external citation.
[Eq. (10)] The phrase 'L-Lipschitz continuous' in the sentence before Eq. (10) should be 'L-smooth (Lipschitz continuous gradient)', since the displayed condition is on the Hessian.

Circularity Check

1 steps flagged · score 4.0 of 10

Load-bearing monotonicity lemma is outsourced to the authors' own prior paper; the resource-allocation core is otherwise independent.

self citation load bearing [Section III-D, Lemma 5 (proof deferred to [56])]
"Lemma 5: The feasibility of problem (20) exhibits a strict monotonic structure with respect to T. If problem (20) is feasible for a given T, then it remains feasible for any T′>T. Conversely, if it is infeasible for T, then it is also infeasible for any T′<T. Proof: See Appendix E in [56]."

Algorithm 4's bisection on T and hence Algorithm 5's claimed minimal delay rest entirely on Lemma 5. The lemma's proof is not given in the paper; it is imported from [56], a prior paper co-authored by Z. Yang and M. Chen, two of the present authors. No derivation is shown that the assumptions of Appendix E of [56] carry over to the FU-specific feasibility set with J(η), robust CSI constraints, and the energy budget constraints. At this load-bearing step, the optimality claim therefore reduces to a self-citation rather than to a proof contained in the present paper.

full rationale

The paper does not fit parameters to data: Lemma 1 is derived in Appendix A, and the simulation uses the same analytical J(η) that appears in the optimization, so the reported gains are model-based rather than empirically validated, but that is not circularity by construction. The only genuinely load-bearing self-citation is Lemma 5, whose proof is deferred to the authors' own prior work [56]; this lemma is what licenses the bisection over T and therefore the optimal delay returned by Algorithm 5. Because the proof is not reproduced or adapted to the FUN-specific constraints, the optimality claim partially rests on a self-citation. The unmeasured γ, L, and β constants, and the fact that β in Eq. (9) is defined over the FU calibration rounds, are correctness and reproducibility risks, but they do not make the derivation equivalent to its inputs. The resource-allocation and complexity results retain independent content, so a score of 4 is appropriate rather than 6 or higher.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The delay model rests on a chain of unverified inputs: strong convexity constants, a calibration ratio bound, and known CSI error bounds. The paper does not provide values for γ, L, β, or M in the simulations, so the quantitative delay curves cannot be reproduced from the text. No new physical entity is introduced.

free parameters (6)

beta (calibration ratio upper bound)
Appears in Lemma 1's J(η) and in the condition ξ ≤ γ/(Lβ); the paper assumes such a bound exists in Eq. (9) but gives no value or measurement method.
gamma (strong convexity constant)
Required for the convergence bounds in Lemma 1 and Lemma 2; assumed known in Eq. (10) but not listed in the simulation table.
L (Lipschitz constant)
Required for the convergence bounds and for the condition δ < 2/L; assumed known but not specified in the simulations.
xi (regularization constant) = 0.1
Manually set in simulations; affects the round bound J(η) through the condition ξ ≤ γ/(Lβ).
delta (local step size) = 0.1
Manually set in simulations; Lemma 2 requires δ < 2/L.
M (number of accuracy grid points) = not specified
The uniform scan over η is discretized into M points; the reported optimal η* is only the best grid point, and M is not given in Table II.

assumptions (5)

domain assumption The local loss functions F_k are γ-strongly convex and L-smooth for all remaining users (Eq. 10).
This underpins the convergence proof of Lemma 1 and the local iteration count in Lemma 2; it is not verified for the blog feedback dataset or for general deep learning models.
ad hoc to paper There exist positive α and β bounding the norm ratios ||h_k^(j)||/||ĥ_k^(j)|| for all k and j (Eq. 9).
The calibration update eĥ_k rescales by this ratio, and β appears directly in J(η); no procedure is given to compute α and β.
domain assumption Channel estimation errors are bounded by known constants ε_k (Eq. 14).
The robust transmission constraint (16) uses the worst-case gain (|ĝ_k|−ε_k)^2; the uncertainty region must be known a priori.
domain assumption The convergence conditions ξ ≤ γ/(Lβ) and δ < 2/L hold.
Lemma 1 requires the first condition and Lemma 2 the second; the simulations set ξ=δ=0.1 without checking these against the unknown γ, L, and β.
domain assumption Downlink broadcast time and energy are negligible, and the BS has stored all historical updates h_k^(j).
The per-user delay in Eq. (18) includes only local computation and uplink transmission; downlink and storage costs are ignored.

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Pith. "Pith review of Federated Unlearning Over Wireless Networks." pith.science (2026). https://pith.science/paper/FV46E7ZY

@misc{pith2026260809090,
  author       = {Pith},
  title        = {Pith review of: Federated Unlearning Over Wireless Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FV46E7ZY}},
  note         = {Machine review of arXiv:2608.09090}
}

read the original abstract

To comply with stringent data privacy regulations, federated unlearning (FU) has emerged as a critical paradigm. However, its implementation over wireless networks introduces severe communication latency and reliability challenges due to iterative calibration requirements and physical-layer channel uncertainties. In this paper, we investigate the problem of delay minimization for federated unlearning networks (FUN). Specifically, we establish a comprehensive system model that jointly incorporates the convergence behavior of the FUN algorithm, local device computation dynamics, and a worst-case robust transmission model operating under bounded channel state information (CSI) error. To solve the resulting non-convex joint resource allocation problem, we propose an efficient iterative algorithm. By exploiting the monotonicity and convexity properties of the system constraints, the problem is decomposed via a uniform scan over the local accuracy parameter, within which the optimal delay, bandwidth, power, and computation frequency are determined utilizing nested bisection and golden-section searches. Both theoretical analysis and extensive numerical results demonstrate that the proposed algorithm achieves polynomial complexity and significantly reduces the overall unlearning completion time compared to conventional baseline schemes.

Figures

Figures reproduced from arXiv: 2608.09090 by the authors.

**Figure 1.** FU over wireless networks. wi represents the global model at the i-th FL round. At the i-th round (i = 1, 2, . . . , I), each user k trains the received model on its local dataset Dk for Ilocal epochs according to local accuracy η, producing an update h i k with respect to wi . The BS aggregates the received updates {h i 1 , h i 2 , . . . ,h i K} to obtain the new global model wi+1, which will be used in the next ro… view at source ↗

**Figure 2.** Completion time versus maximum average transmit power of each [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Completion time versus maximum CPU frequency for each user. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Completion time versus total bandwidth. 10 20 30 40 50 60 70 80 90 100 Maximum Energy Budget (J) 60 80 100 120 140 160 180 Completion time (s) Propose-FUN EB-FUN FA-FUN Retrain [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Completion time versus maximum energy budget of each user. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 8.** Figure 8: Completion time versus maximum average transmit power of each [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

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