{"id":"2dbc0f81-a54c-470a-8845-168d8c59f8d4","arxiv_id":"2608.09090","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A nested bisection and golden-section search over bandwidth, power, CPU frequency, and local accuracy minimizes the completion time of federated unlearning under wireless channel uncertainty.","lead":"This paper designs a resource allocation algorithm that minimizes how long a federated learning system takes to erase a client's data over a wireless network, under imperfect channel knowledge. It combines the unlearning procedure's convergence behavior with device computation and transmission constraints, and reports about 10 percent delay reductions over baseline schemes.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lemma 1's round bound J(η) is only valid when measured constants satisfy 0<ξ≤γ/(Lβ); the paper never reports γ, L, or β for the blog feedback dataset, so the simulated operating point may lie outside the theorem's valid regime.","rationale":"I read the paper as a resource-allocation contribution whose central claim is that Algorithm 5 minimizes the modeled federated unlearning delay with polynomial complexity. The Appendix A proof of Lemma 1 is internally consistent: the contraction argument, the use of β, the local-accuracy condition (5), and the final round bound all check out under the stated assumptions. Lemma 4's monotonicity argument is essentially correct, and Lemma 5's monotonicity in T is almost trivial because any feasible allocation for T remains feasible for T'>T, so the outsourcing of Lemma 5 to reference [56] is not the main risk. The genuinely load-bearing gap is the status of the constants in Lemma 1. The bound J(η) is only valid for γ-strongly convex, L-smooth losses with a known β satisfying Eq. (9), and with ξ ≤ γ/(Lβ). The paper gives no measurement, no literature value, and no sensitivity analysis for these constants on the blog feedback dataset; Section IV fixes ξ=0.1 without demonstrating that the theorem's condition holds. Since β is itself defined in terms of the calibration updates produced by the algorithm, the model is not self-contained: one cannot instantiate J(η) without first running the very procedure whose round count it is supposed to predict. The numerical section compounds this by reporting delays computed from J(η) rather than from an actual unlearning run, so the claimed 4–11% reductions are not yet evidence about the real system. This is exactly the concern the reader identified as the weakest assumption, and my pass confirms and sharpens it: the concrete failure mode is the unverified inequality ξ≤γ/(Lβ), which is the precondition for Lemma 1 to be a contraction. The verdict should therefore remain CONDITIONAL; the paper is a plausible framework but its central quantitative claims are conditional on unmeasured model constants. I would not move to REJECT because the optimization machinery and the derivation are coherent if the constants are supplied.","tokens_in":19793,"tokens_out":13507,"duration_ms":143771,"concrete_test":"Run a pilot implementation of Algorithm 1 on the blog feedback dataset with the paper's parameters; measure β = max_{k,j} ||h_k^{(j)}||/||hat h_k^{(j)}||, estimate γ and L from the Hessian of the regularized loss, and verify ξ=0.1 ≤ γ/(Lβ). Recompute J(η) and rerun Figs. 2–8 with the measured constants. If the inequality fails or the delay curves shift by more than the claimed 4–11% gains, the central claim is not supported by the reported simulations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is Lemma 1: Algorithm 5's J(η), and therefore every reported delay, is computed from the closed form J(η)=a/[(γ−Lξβ)(√γ−√ηL)^2+(1−η)γ^2]. The lemma is proved under Eqs. (9)–(10) and the explicit condition 0<ξ≤γ/(Lβ), stated in the lemma itself. The paper never measures or reports γ, L, or β for the blog feedback dataset, and Section IV fixes δ=0.1 and ξ=0.1 without checking this inequality. Worse, β is defined in Eq. (9) as max_{k,j} ||h_k^{(j)}||/||hat h_k^{(j)}||, so β is an output of the FU calibration run, not a known system parameter that can be fixed before the algorithm executes. If the true constants violate γ−Lξβ>0, the factor in (A.18) is not a contraction, J(η) is not a valid round bound, and Section IV's delay numbers are computed from a model the theorem does not support. Even in the valid regime, Lemma 1 gives a sufficient round count, so replacing the actual stopping time by J(η) in Eq. (18) is an unvalidated approximation; the simulations evaluate this analytical expression rather than an actual federated unlearning run.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":20089,"tokens_out":9807,"duration_ms":96071,"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":[{"comment":"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.","section":"Section IV and Lemma 1"},{"comment":"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.","section":"Eq. (18) and Section IV"},{"comment":"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":"Lemma 1 / Eq. (A.17)"},{"comment":"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.","section":"Section III-E, Eq. (29)"}],"minor_comments":[{"comment":"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.","section":"Problem (20)"},{"comment":"Line 1 of Algorithm 4 says to compute J(η) from Eq. (10); the correct reference is Eq. (11).","section":"Algorithm 4"},{"comment":"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.","section":"Fig. 8"},{"comment":"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.","section":"Algorithm 2"},{"comment":"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.","section":"Lemma 5"},{"comment":"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.","section":"Eq. (10)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope and the topic is timely. I would not reject on novelty grounds: the joint communication-computation formulation for FU is a reasonable extension of earlier FL resource-allocation frameworks. My main concern is validation discipline: the simulation section should not be the only evidence for the central delay claims, and the theorem parameters need to be checked or measured. Please also verify that reference [56] actually contains the cited Appendix E."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nSecond, 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.\n\nMinor 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.\n\nOverall, 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.","headline":"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.","tokens_in":20642,"tokens_out":2481,"would_cite":true,"duration_ms":23679,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["federated unlearning","delay minimization","resource allocation","wireless networks","CSI uncertainty","edge computing","convex optimization","bisection search"],"falsifier":"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.","tokens_in":19551,"feed_emoji":"📡","tokens_out":8800,"duration_ms":73996,"temperature":0.7,"pith_summary":"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.","feed_headline":"Resource tuning cuts federated unlearning delay about ten percent","feed_subtitle":"Jointly choosing bandwidth, power, compute speed, and local accuracy trims unlearning time under imperfect channels.","key_machinery":"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 $O\\left(MK\\log(1/\\epsilon_T)\\log(1/\\epsilon_b)\\log(1/\\epsilon_t)\\right)$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the DANE convergence machinery: Lemma 1's proof, the local iteration count, and the deferred monotonicity proof of Lemma 5 all build on it.","marker":"[56]"},{"why":"Provides FedEraser, the client-level unlearning method whose historical-update calibration Algorithm 1 implements.","marker":"[33]"},{"why":"Supplies the bounded CSI uncertainty model used in the worst-case robust rate constraint.","marker":"[58]"},{"why":"Provides the computation energy model $\\kappa f^2 A \\log(1/\\eta)$ used in the energy constraint.","marker":"[57]"},{"why":"Supplies the blog feedback dataset used in all numerical simulations.","marker":"[59]"}],"fun_headline_variants":["Federated unlearning delay slashed 10% via joint tuning","Wireless federated unlearning speeds up with smart resource mix","10% faster federated unlearning over wireless networks","Joint resource optimization trims unlearning time in wireless nets"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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].","fun_headline_variants_meta":{"raw":{"variants":["Federated unlearning delay slashed 10% via joint tuning","Wireless federated unlearning speeds up with smart resource mix","10% faster federated unlearning over wireless networks","Joint resource optimization trims unlearning time in wireless nets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000193,"raw_usage":{"total_tokens":1337,"prompt_tokens":922,"completion_tokens":415,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":538,"completion_tokens_details":{"reasoning_tokens":345}},"tokens_in":538,"tokens_out":415,"duration_ms":4145,"temperature":1.0,"reasoning_tokens":345,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T23:45:51.451393+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Energy efficient federated learning over wireless communication networks,","cited_arxiv_id":null,"evidence_quote":"Supplies the DANE convergence machinery: Lemma 1's proof, the local iteration count, and the deferred monotonicity proof of Lemma 5 all build on it."},{"cited_title":"FedEraser: Enabling efficient client-level data removal from federated learning models,","cited_arxiv_id":null,"evidence_quote":"Provides FedEraser, the client-level unlearning method whose historical-update calibration Algorithm 1 implements."},{"cited_title":"Robust resource allocation for secrecy wireless powered communication networks,","cited_arxiv_id":null,"evidence_quote":"Supplies the bounded CSI uncertainty model used in the worst-case robust rate constraint."},{"cited_title":"Dynamic computation offloading for mobile-edge computing with energy harvesting devices,","cited_arxiv_id":null,"evidence_quote":"Provides the computation energy model $\\kappa f^2 A \\log(1/\\eta)$ used in the energy constraint."},{"cited_title":"Feedback prediction for blogs,","cited_arxiv_id":null,"evidence_quote":"Supplies the blog feedback dataset used in all numerical simulations."}],"review_version":1}