{"id":"de6b45b6-b47a-4bfa-a186-58b971e6e8d7","arxiv_id":"2508.15185","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"An ISCC-enabled Air-FEEL convergence bound is derived, and an alternating optimization algorithm for batch size and resource allocation is proposed to maximize per-round loss decrease.","lead":"This paper studies federated learning over wireless networks where devices sense radar data, compute local updates, and aggregate them over the air in one go. It derives convergence bounds affected by sensing noise and over-the-air distortion, then designs a joint resource allocation algorithm to speed up training.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lemma 1's variance bound is invalid: c_k is common to all b_k samples of device k, so its variance contribution scales as b_k^2, not b_k; Lemma 2, Theorem 1, and the P1 objective built on this bound are therefore unsupported.","rationale":"The reader's weakest assumption identifies exactly the load-bearing flaw: Eq. (2) makes c_k common to all samples of a device, yet the proof of Lemma 1 bounds its variance as though each sample carried an independent contribution, giving a b_k rather than b_k^2 scaling. This is not a matter of looseness or of an unusual regime; it is an internal inconsistency between the model definition and the proof. The bound in Eq. (31) is used directly in Lemma 2's proof (Eq. (59)), in Theorem 1's proof (Eq. (62)), and as the objective of P1/P2. If the variance term is b_k times larger, the stated convergence rate, the multiplicative effect of batch size and sensing SNR, and the resource-allocation solutions all become unsubstantiated. The simulations in Section V demonstrate empirical trends but do not test the specific variance formula, so they do not provide independent support for the faulty step. No amount of internal consistency in Appendices C and D compensates: those appendices optimize a quantity whose derivation is invalid. A corrected analysis would need to either assume c_k is independent across samples (contradicting Eq. (2)) or redo the variance bound with the b_k^2 scaling, which would change the optimization problem and likely the qualitative conclusions about sensing power versus batch size. Given that the central claim rests on this lemma, the appropriate verdict is REJECT, matching the reader's assessment.","tokens_in":24805,"tokens_out":2658,"duration_ms":32256,"concrete_test":"Re-derive Eq. (34) for the simplest case that isolates the common-clutter issue. Set K=1, b_1=b, P_{1,s}→∞ (no sensing noise), c_1 ~ N(0, δ_c^2 I), and choose a quadratic loss F(w;x)=½‖w−x‖² so that Ĥ_{1,i}=−I (hence ‖Ĥ_{1,i}‖_F=1=A) for every i. Then Eq. (30) gives g̃ = g + (1/b)∑_{i=1}^b (−I)c_1 = g − c_1, so the exact variance contribution is E‖g̃−g‖² = δ_c^2. The paper's Lemma 1 bound (31) gives δ_c^2/b. For b=100, the bound is 100× too small. If this symbolic or numerical computation confirms the discrepancy, Lemma 1 is false as stated, and the convergence theorem and optimization problem built on it must be reworked.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's central theoretical device is Lemma 1, which bounds the variance of the aggregated gradient. In the sensing model, Eq. (2) defines the i-th sample as x̂_{k,i} = x_{k,i} + c_k + n_s/√P_{k,s}, with c_k carrying no sample index i: the residual clutter is common to all b_k samples of device k. In the proof of Lemma 1, the third term in Eq. (32) is the squared norm of (1/b^{(t)}) ∑_k ∑_i Ĥ_{k,i} (c_k + n_s/√P_{k,s}). For fixed k, the c_k contribution is (1/b^{(t)}) (∑_{i=1}^{b_k} Ĥ_{k,i}) c_k. Even under Assumption 1, ‖∑_i Ĥ_{k,i}‖_F ≤ b_k A, so the variance of this term scales as b_k^2 A^2 δ^2_{k,c}/b^2, not b_k A^2 δ^2_{k,c}/b^2 as claimed in Eq. (34). The cross terms do not vanish in general because the Ĥ_{k,i} are Hessian-type matrices evaluated at distinct clean samples and are not assumed to be zero-mean or independent; they are deterministic functions of the data samples. Equation (31) therefore understates the sensing-distortion variance by a factor of roughly b_k. Since Eq. (31) is the only variance bound used in Lemma 2 (via Eq. (59)) and Theorem 1 (via Eq. (62)), the per-round loss-degradation bound, the convergence rate, and the optimization objective P1/P2 (which minimizes exactly this incorrect variance expression) all inherit the error. The algebraic derivations in Appendices C and D optimize an invalid objective, so they do not rescue the core claim. The empirical simulations may show plausible trends, but they cannot compensate for a false analytical bound that drives the claimed contribution.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an ISCC-based over-the-air federated edge learning (Air-FEEL) framework in which edge devices acquire sensing data contaminated by wireless sensing noise, compute local gradients, and transmit them to a server via AirComp. The main analytical contribution is a convergence analysis: Lemma 1 gives a variance bound for the aggregated gradient, Lemma 2 converts it into a per-round loss-degradation bound, and Theorem 1 gives an O(1/sqrt(T)) convergence bound. These results are then used to formulate an optimization problem P1/P2 that jointly optimizes batch sizes, sensing power, computation frequency, and AirComp receive power, solved by alternating convex optimization. Simulations on a human-motion recognition dataset are used to validate the convergence behavior and the proposed resource allocation.","tokens_in":25334,"tokens_out":7951,"duration_ms":98312,"significance":"The topic is timely: integrating sensing, communication, and computation for Air-FEEL is an important direction, and the paper provides a clean system model and a plausible alternating optimization framework. The empirical study, using a real sensing dataset and comparing with several baselines, is a positive feature. If the convergence analysis were correct, the claimed first characterization of wireless sensing noise on Air-FEEL convergence would be valuable. However, the central variance bound in Lemma 1 is invalid as stated, and the downstream convergence theorem and optimization objective inherit the flaw. The paper does not provide machine-checked proofs or reproducible code, so the analytical claims rest on the derivations themselves, which contain a load-bearing error.","major_comments":[{"comment":"Lemma 1's variance bound is not valid. In Eq. (2), the residual clutter c_k^{(t)} carries no sample index i and is therefore common to all b_k^{(t)} samples of device k. In the proof, the third term of Eq. (32) is E || (1/b^{(t)}) \\sum_k \\sum_{i=1}^{b_k} \\hat{H}_{k,i} (c_k + n_s / \\sqrt{P_{k,s}}) ||^2. For fixed k, the clutter contribution is (1/b^{(t)}) (\\sum_{i=1}^{b_k} \\hat{H}_{k,i}) c_k. Even under Assumption 1, ||\\sum_i \\hat{H}_{k,i}||_F can be as large as b_k A, so the variance contribution scales as b_k^2 A^2 \\delta_{k,c}^2 / b^2, not b_k A^2 \\delta_{k,c}^2 / b^2 as claimed in Eq. (34). The cross terms between different i for the same c_k do not vanish; only cross terms between c_k and n_s vanish under the zero-mean/independence assumptions. The bound in Eq. (31) therefore undercounts the sensing-distortion variance by roughly a factor of b_k. Since Eq. (31) is the only variance b","section":"Section III-B, Eq. (2) and Eqs. (31)-(34)"},{"comment":"The first-order Taylor expansion in Eq. (24) contains a higher-order remainder, but Eq. (28) drops this remainder and the resulting approximate expression is subsequently used as an equality in Eq. (30), including for the unbiasedness claim E[\\tilde{g}^{(t)}] = g^{(t)} in Lemma 1. No bound on the Taylor remainder is provided, so even if the common-clutter issue were fixed, the gradient estimate could be biased and the variance bound would not be rigorous. The authors should state the neglect of the remainder as an explicit assumption and, ideally, propagate an error term through Lemma 1, Lemma 2, and Theorem 1.","section":"Section III-A.2, Eq. (28)"},{"comment":"The theorem asserts lim_{T->infty} G_T = 0. This requires some boundedness or sublinear-growth condition on the per-round distortion terms \\delta_u^2 / \\eta^{(t)} and \\sum_k b_k^{(t)}(\\sigma^2 + A^2(\\delta_{k,c}^2 + \\delta_s^2/P_{k,s}))/b^{(t)2}, but no such assumption is stated. In addition, Lemma 2 is an expectation bound, while the left-hand side of Eq. (37) is written without an expectation. These are formal gaps that would need to be repaired even setting aside the Lemma 1 error.","section":"Theorem 1, Eq. (37)"}],"minor_comments":[{"comment":"The uploading energy E_{k,u} is written with H_k = E[h_k^2] in the denominator, but the transmit power in Eq. (11)-(12) is set using the instantaneous channel magnitude h_k. If h_k is random, E[1/h_k^2] is not 1/E[h_k^2]. This should be clarified: either h_k is a known deterministic channel magnitude or the expectation should be computed accordingly.","section":"Eq. (17)"},{"comment":"The primal-dual updates in Eqs. (68)-(70) and (81)-(82) are stated without step-size choices or a convergence proof. The claim of O(K^2) complexity relies on these iterations converging; as written, the dual update is heuristic. Additionally, in Appendix D, the statement 'Since \\psi_k \\ne 0, \\forall k, it holds \\varphi_k \\ne 0' is not a valid implication from the displayed KKT equations. The conclusion may be repairable, but the argument needs correction.","section":"Appendices C and D"},{"comment":"The list of human motions contains a duplication: 'adult walking, child walking, adult walking' appears in the enumeration. Please correct the typo.","section":"Section V-A"},{"comment":"The text says the goal is 'maximizing the loss function degradation,' but the actual objective P1 minimizes the variance term that upper-bounds the degradation in Eq. (36). The wording should distinguish the true per-round degradation from its lower bound.","section":"Section IV-A, P1"}],"recommendation":"reject","confidential_remarks":"The central defect is in Lemma 1: the sensing model explicitly makes the clutter common to all samples of a device, and the variance bound treats it as if it were independent per sample. This is not a presentation issue but a load-bearing mathematical error that invalidates the convergence theorem and the optimization objective. A corrigendum would require changing the sensing model or substantially reworking the analysis, so I do not see a path within the current manuscript's scope. I would note for the editor that the paper builds heavily on the authors' prior ISCC models ([30], [36]); the novelty claim about sensing-noise characterization is exactly where the proof fails."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the convergence analysis is built on a variance bound that mishandles the common clutter term c_k, and that error is load-bearing. The system model, problem formulation, and algorithm design are competent, but the main theorem and the optimization objective rest on an invalid bound. Reject.\n\nWhat is actually new: the paper is the first to put wireless sensing noise into an AirComp-FEEL convergence analysis and to couple it with batch-size and resource allocation. That is an incremental but real extension of [30]-[32], and the paper is reasonably honest about its scope. The alternating optimization with closed-form KKT solutions is a sensible strategy, and the simulations use a real human-motion recognition dataset rather than a toy. The appendices are algebraically consistent: the authors clearly know how to derive KKT conditions.\n\nThe soft spot is in Lemma 1. In Eq. (2), c_k is common to all b_k samples of device k. The third variance term therefore contains (1/b^{(t)}) (\\sum_i \\hat{H}_{k,i}) c_k, whose squared norm scales as b_k^2 under Assumption 1, not b_k as claimed in Eq. (34). That factor of b_k propagates into Lemma 2, Theorem 1, and the P1/P2 objective. The optimization is minimizing a bound that is too small by a factor of b_k for each device, so the resource-allocation conclusions are unsupported. The first-order Taylor truncation in Eq. (25) is also unvalidated, and the simulations do not show statistical variability across runs. These are secondary.\n\nThe paper is not without merit: the framing of ISCC for Air-FEEL is clear, and the problem is real. But the central theoretical contribution does not hold. An editor should send this to peer review rather than desk-reject, because the error is technical and the framework could be salvaged with a corrected bound or a revised sensing model. I would not cite it in its current form, and I would only bring it to a reading group as a case study in how a common-cause assumption changes variance scaling.","headline":"The convergence analysis is built on a variance bound that mishandles the common clutter term c_k; that invalidates the main theorem and the optimization, so reject despite a solid system model and real problem framing.","tokens_in":25765,"tokens_out":4758,"would_cite":false,"duration_ms":51979,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that in over-the-air federated edge learning, convergence speed is set jointly by sensing SNR, AirComp SNR, and total batch size, and that these three compete for the same per-round time and energy.","keywords":["over-the-air federated edge learning","integrated sensing communication and computation","AirComp","convergence analysis","sensing noise","batch size control","resource allocation","loss function degradation"],"falsifier":"Fix one residual clutter vector per device, add independent sensing noise, and measure the empirical variance of the AirComp-aggregated gradient while sweeping each device's batch size with everything else fixed. If the variance grows like b_k, Lemma 1 stands; if it grows like b_k^2, the bound in Eq. (31) fails and the Theorem 1 convergence constant needs reworking.","tokens_in":24722,"feed_emoji":"📡","tokens_out":6600,"duration_ms":75096,"temperature":0.7,"pith_summary":"This paper studies a federated edge learning system in which edge devices acquire their own training data by wireless sensing, compute local gradients, and send them to an edge server using over-the-air computation (AirComp), so model updates are aggregated in one shot. The central claim is that the convergence rate is governed by three quantities—sensing SNR, AirComp SNR, and the total number of freshly sensed training samples—and that these three consume the same per-round time and energy budgets, so they trade off against one another. The authors derive a per-round lower bound on the loss decrease (Lemma 2) and a convergence theorem (Theorem 1), and claim this is the first characterization of how sensing-noise-corrupted data samples degrade convergence in Air-FEEL. On that basis they propose an alternating optimization scheme that allocates batch sizes, sensing power, computation frequency, and AirComp receive power, with per-subproblem complexity O(K^2). Simulations on a human motion recognition task confirm the predicted trends and show that the joint scheme beats baselines that optimize only one subsystem.","feed_headline":"Convergence speed tied to sensing SNR, upload SNR, and batch size","feed_subtitle":"One bound splits the loss drop among sensing, over-the-air aggregation, and on-device compute; the paper uses it to allocate time and energy","key_machinery":"The engine of the paper is the first-order Taylor expansion of the local loss around the clean data sample, which turns sensing noise into a bounded perturbation of each local gradient. That perturbation is controlled by a bounded mixed-Hessian assumption, giving the linear sensing model c_k + n_s/sqrt(P_{k,s}) a gradient-space variance contribution. The global recovered gradient then admits a variance decomposition (Lemma 1) whose three terms—AirComp noise, stochastic gradient noise, and sensing corruption—drive the per-round loss bound (Lemma 2) and the convergence theorem (Theorem 1). The optimization side then decomposes the resulting non-convex problem into two convex sub-problems, batc","core_discovery":"The paper's central discovery is an explicit mean-square bound on the global gradient recovered at the server: the recovered gradient is unbiased, and its variance separates into an AirComp channel-noise term, a per-sample gradient stochasticity term, and a sensing-corruption term produced by residual radar clutter and sensing noise in the freshly acquired samples. This variance bound feeds an L-smooth descent argument that gives a per-round loss-degradation lower bound and an O(1/sqrt(T)) convergence bound on the average squared gradient norm. The paper claims these are the first convergence results for Air-FEEL that explicitly include the quality of wireless sensing data acquisition, and i","pith_inferences":["If the residual clutter c_k is indeed a single fixed corruption shared by all b_k samples of a device, its contribution to the gradient variance scales with b_k^2 rather than b_k; a corrected Lemma 1 would then penalize large per-device batches more heavily and could shift the optimal batch sizes downward.","The variance decomposition suggests a device-scheduling rule that the paper only assumes in advance: drop devices with the largest per-sample corruption contribution (b_k/b^2)(delta^2_{k,c}+delta^2_s/P_{k,s}) before spending resources on them.","A curriculum-style schedule might start with large, low-SNR batches early in training and switch to smaller, higher-SNR batches later; the paper's per-round objective treats every round identically, so this remains an untested extension."],"forward_implications":["Higher sensing SNR, higher AirComp SNR, and larger total batch size each accelerate convergence, but because they consume the same per-round time and energy they cannot all be maxed out at once.","For each device the optimal computation speed is the slowest one that still meets the round deadline; any faster speed only burns energy that could go to sensing or uploading.","Larger batch sizes call for lower sensing power per sample, so the system faces a data-quantity versus data-quality frontier rather than a single best operating point.","Because AirComp aggregates in one shot, the communication latency does not grow with the number of devices, so scaling the network adds sensing samples and computation without adding aggregation delay."],"supporting_citations":[{"why":"Supplies the task-oriented ISCC-FEEL framework, the human-motion sensing dataset, and the OMA baseline the proposed AirComp scheme is compared against.","marker":"[30]"},{"why":"Supplies the linear sensing signal model with residual clutter and sensing noise that equation (2) adopts for the data acquisition process.","marker":"[36]"},{"why":"Establishes broadband analog aggregation for low-latency federated edge learning, the AirComp mechanism the paper uses for one-shot model aggregation.","marker":"[6]"},{"why":"Introduces MIMO over-the-air computation, the waveform-superposition aggregation principle behind the AirComp step.","marker":"[10]"},{"why":"Provides the optimized power-control design for Air-FEEL whose per-round loss-degradation objective this work extends to ISCC.","marker":"[9]"},{"why":"Justifies the first-order Taylor approximation of the loss and the bounded mixed-Hessian assumption (Assumption 1).","marker":"[40]"},{"why":"Supplies the unbiased and variance-bounded stochastic gradient assumptions (Assumption 2) used in Lemma 1.","marker":"[42]"}],"fun_headline_variants":["Sensing noise and AirComp distortions slow federated edge learning convergence","Over-the-air learning slows when sensing noise and aggregation noise mix","Sensing noise, upload noise, and compute share blame for slow learning","New bound separates sensing noise from upload noise in federated learning","Federated edge learning: sensing noise and upload noise throttle convergence"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The proof of Lemma 1 treats the residual radar clutter c_k as if its contribution to variance grew with the batch size b_k, but Eq. (2) defines c_k as one fixed corruption shared by all b_k samples of device k; the contribution should grow with b_k^2, so the variance bound in Eq. (31), and with it the convergence theorem and the optimization objective, rests on an unproven scaling.","fun_headline_variants_meta":{"raw":{"variants":["Sensing noise and AirComp distortions slow federated edge learning convergence","Over-the-air learning slows when sensing noise and aggregation noise mix","Sensing noise, upload noise, and compute share blame for slow learning","New bound separates sensing noise from upload noise in federated learning","Federated edge learning: sensing noise and upload noise throttle convergence"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000819,"raw_usage":{"total_tokens":3468,"prompt_tokens":838,"completion_tokens":2630,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":582,"completion_tokens_details":{"reasoning_tokens":2540}},"tokens_in":582,"tokens_out":2630,"duration_ms":19938,"temperature":1.0,"reasoning_tokens":2540,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T18:04:21.454215+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fix one residual clutter vector per device, add independent sensing noise, and measure the empirical variance of the AirComp-aggregated gradient while sweeping each device's batch size with everything else fixed. If the variance grows like b_k, Lemma 1 stands; if it grows like b_k^2, the bound in Eq. (31) fails and the Theorem 1 convergence constant needs reworking.","supporting_citations":[{"cited_title":"To- ward ambient intelligence: Federated edge learning with task-oriented sensing, computation, and communication integration,","cited_arxiv_id":null,"evidence_quote":"Supplies the task-oriented ISCC-FEEL framework, the human-motion sensing dataset, and the OMA baseline the proposed AirComp scheme is compared against."},{"cited_title":"Task- oriented sensing, computation, and communication integration for multi- device edge AI,","cited_arxiv_id":null,"evidence_quote":"Supplies the linear sensing signal model with residual clutter and sensing noise that equation (2) adopts for the data acquisition process."},{"cited_title":"Broadband analog aggregation for low-latency federated edge learning,","cited_arxiv_id":null,"evidence_quote":"Establishes broadband analog aggregation for low-latency federated edge learning, the AirComp mechanism the paper uses for one-shot model aggregation."},{"cited_title":"MIMO over-the-air computation for high- mobility multimodal sensing,","cited_arxiv_id":null,"evidence_quote":"Introduces MIMO over-the-air computation, the waveform-superposition aggregation principle behind the AirComp step."},{"cited_title":"Optimized power control design for over-the-air federated edge learning,","cited_arxiv_id":null,"evidence_quote":"Provides the optimized power-control design for Air-FEEL whose per-round loss-degradation objective this work extends to ISCC."},{"cited_title":"Compressed-vfl: Communication-efficient learning with vertically partitioned data,","cited_arxiv_id":null,"evidence_quote":"Justifies the first-order Taylor approximation of the loss and the bounded mixed-Hessian assumption (Assumption 1)."},{"cited_title":"Stochastic first-and zeroth-order methods for nonconvex stochastic programming,","cited_arxiv_id":null,"evidence_quote":"Supplies the unbiased and variance-bounded stochastic gradient assumptions (Assumption 2) used in Lemma 1."}],"review_version":1}