{"id":"a83b236a-0693-43e8-ba45-b5594853441d","arxiv_id":"2608.01426","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A cluster-aware over-the-air FL framework for energy-harvesting devices uses user clusters both to schedule diverse participants for a fair global model and to train personalized models per cluster, with convergence bounds and simulations on MNIST, FMNIST, and CIFAR-10.","lead":"This paper proposes a unified cluster-aware framework for over-the-air federated learning with energy-harvesting devices, covering both fair global model training and personalized cluster-specific models. A smart generalist would read it to see how user data similarity can be exploited through the same wireless aggregation mechanism for two opposite goals, fairness and personalization.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"LSE-based scheduling requires full-column-rank participation matrix; low-energy users can be unidentifiable, a regime the paper neither states nor tests.","rationale":"The reader's weakest assumption identifies exactly this LSE identifiability issue. My stress-test agrees: this is the most load-bearing concern because Mode I with unknown distributions depends on recovering per-user representations from aggregated OTA signals, and the EH participation process directly determines whether A has full column rank. The paper does not state the requirement, does not analyze the low-energy regime, and its simulations use parameter values where the problem is unlikely to appear. Other weaknesses (e.g., absent error bars, no strong baselines) are less decisive: the numerical claims in the tested regime are plausible and the framework is coherent. The identifiability concern does not overturn the reader's conditional verdict; it reinforces it, so the verdict should remain unchanged.","tokens_in":26367,"tokens_out":7080,"duration_ms":70920,"concrete_test":"Simulate the estimation phase of §III.C with MNIST, M=40, T=100, and p_e ∈ {0.25, 0.10, 0.05}. For each p_e, compute the empirical rank of A and the number of users with zero participation; then run the LSE-based scheduler and compare its final accuracy against entropy-based scheduling and no-scheduling baselines. If any zero-participation user occurs and LSE scheduling no longer consistently outperforms no-scheduling, the missing identifiability analysis is a real gap.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Section III.C, the PS estimates user representations by solving the LSE for Θ_rep in Eq. (28), Θ_PS = A Θ_rep + N*, with A ∈ {0,1}^{T×M}. The implicit estimator requires A^T A invertible: every user's column must be nonzero and the participation patterns must span R^M. This is not stated. Under the Bernoulli EH model with arrival probability p_m^e(t), the probability that user m is never active in the T-round estimation window is (1-p_m^e)^T, which is non-negligible for low p_m^e (e.g., ≈37% for p=0.01, T=100; ≈0.6% for p=0.05, T=100, which matters with M=100). For such users, no representation is identifiable, cosine-similarity clustering is blind to them, and the diversity-aware scheduler may systematically ignore exactly the users whose data is underrepresented. The numerical evaluation uses p_e=0.25 with T=100/200 (expected 25–50 participations per user), so the issue is masked. Since the unknown-distribution mode is a central part of the unified framework, this implicit identifiability assumption is load-bearing for the claimed fairness improvement in general EH settings.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a unified cluster-aware over-the-air federated learning (OTA-FL) framework for energy-harvesting (EH) mobile devices. In Mode I, cluster structure guides diversity-aware scheduling to train a fair global model; in Mode II, the same cluster structure defines cluster-level objectives and OTA recovery targets for personalized clustered FL. The authors provide convergence analysis for the global training mode, propose entropy-based scheduling for known data distributions and least-squares-based user-representation estimation for unknown distributions, and develop MMSE/CWC combining schemes for personalized clustered OTA-FL under full or partial CSI at the parameter server. Numerical experiments on MNIST, FMNIST, and CIFAR-10 support the claims of improved fairness or personalization with reduced communication overhead.","tokens_in":26685,"tokens_out":4756,"duration_ms":52023,"significance":"If the proposed framework and its analysis hold, the paper offers a useful unified treatment of two usually separate FL objectives—fair global training and personalized clustered training—under practical OTA and EH constraints. The convergence analysis is honest: it explicitly states that the finite-K decaying-stepsize bound does not establish convergence and that the constant-stepsize floor decomposes into OTA noise, data heterogeneity, and participation-bias terms. The manuscript also benefits from extensive simulations across multiple datasets, a clear treatment of different CSI levels, and the absence of fitted numerical constants in the theory. These are genuine strengths. However, two load-bearing technical points need attention: the LSE-based representation estimator implicitly requires a full-column-rank participation matrix, and the convergence bound depends on an unspecified constant c in Lemma 4. Both issues are addressable, but they currently limit the strength of the central claims.","major_comments":[{"comment":"The LSE estimator for Theta_rep is defined via A in {0,1}^{T x M}. Solving the least-squares problem requires A^T A invertible, i.e., every user must participate at least once during the estimation window and the participation patterns must span R^M. This identifiability condition is never stated. Under the Bernoulli EH model, user m is absent from the entire T-round estimation window with probability (1-p_m^e)^T. For p_m^e=0.01 and T=100 this is about 0.37; for p_m^e=0.05 it is about 0.006, which is not negligible with M=100. In that regime the corresponding user representation is unidentifiable, cosine-similarity clustering is blind to that user, and the diversity-aware scheduler may systematically ignore exactly the users whose data is underrepresented. The simulations use p_m^e(t)=0.25 with T=100 or 200 (expected 25-50 participations per user), which masks this regime. Please add the","section":"Section III.C, Eq. (28)"},{"comment":"Lemma 4 bounds the cross term as (eta^2 tau(tau-1)LG + eta tau epsilon)c, where c is only described as 'some constant ... related to Gamma, G and mu'. No expression or computable bound for c is provided. Since c appears linearly in B_1 = 2(tau-1)Gamma + tau epsilon-bar c, the asymptotic residual neighborhood in Corollary 1 and the interpretation in Remark 1 depend on an unspecified quantity. As stated, the result establishes the form of the bound but not a concrete quantitative neighborhood. Please make c explicit or replace it with a computable bound, or clearly state that the asymptotic neighborhood is only qualitative.","section":"Appendix A, Lemma 4, Eq. (55)"},{"comment":"The LSE-based representation estimation is central to the unknown-distribution scheduling mode, but no consistency or error guarantee is provided for Theta_hat_rep. The only evidence is the single MNIST visualization in Fig. 2. Even when A has full column rank, the quality of the estimate depends on T, on the magnitude of Theta_diff,j relative to Theta_rep, and on the statistical properties of N*. The paper should state the assumptions under which the estimated representations are reliable and ideally give an error bound or sample-complexity result. Without this, the claim that LSE-based scheduling 'minimizes' or even 'reduces' the gradient approximation error epsilon in (16) is not supported by the theory.","section":"Section III.C, Eqs. (24)-(28)"}],"minor_comments":[{"comment":"The definition of epsilon appears with a norm whose squared value is then used in Eq. (15). Please clarify whether epsilon is the norm or the squared norm, and use consistent notation.","section":"Eq. (16)"},{"comment":"In the partial-CSI MMSE subsection, X_c,n in C^H is described as 'the matrix of transmitted cluster updates' but it is a vector per symbol. Please correct the wording.","section":"Section IV.B.1"},{"comment":"Lemmas 3 and 4 are justified by reference to [24, Lemma 1] rather than proved. Given that Lemma 4 contains the unspecified constant c, a full proof or at least a more detailed derivation would improve self-containedness.","section":"Appendix A"},{"comment":"The sentence about clustering 'with the expected number of users per cluster determined by each cluster's energy distribution' is vague. Please specify how the cluster sizes are computed from energy arrival probabilities.","section":"Section III.C"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope and the overall direction is promising. The main reasons for major revision are the unstated full-rank identifiability condition in the LSE mode and the unspecified constant c in the convergence bound. Both are fixable within the manuscript's scope, and I do not see a need for rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: this is a genuinely useful unification, not a breakthrough. The authors take the user-cluster structure that arises under heterogeneous data and use it in two complementary modes: diversity-aware scheduling to train a fair global model, and clustered personalized training with simultaneous over-the-air recovery. Most prior work treats these separately, so the unified framing is the main novelty. The LSE-based estimation of user representations from aggregated OTA signals is the most interesting piece, and the partial-CSI combiners (MMSE and CWC) are practical.\n\nThe convergence analysis is honest. Theorem 1 and its corollaries decompose the bound into OTA noise, heterogeneity, and gradient-approximation terms, and Corollary 1 states plainly that the finite-K decaying-stepsize bound does not converge; that is a good sign. The lemmas are borrowed from [11] and [24], and Lemma 4 has an unspecified constant c. That is a real weakness, but not fatal, because the scheduler design is still motivated by the epsilon term.\n\nThe main soft spot is an unstated identifiability requirement in the LSE-based scheduling. The estimation phase assumes the T x M participation matrix A has full column rank. For a user with energy-arrival probability p, the chance of never participating in T estimation rounds is (1-p)^T. With p=0.01 and T=100, that is about 37%; with M=100 users, several users would be unidentifiable. The numerical evaluation uses p_e=0.25 with T=100 or 200, where each user appears tens of times, so the problem is masked. Since the unknown-distribution mode is central to the fairness claim, the paper should either state the condition or analyze the low-energy regime.\n\nMinor issues: no error bars, no code released, and baselines are only no-scheduling and a single global model. The comparison set is thinner than ideal, but the improvements over those baselines look real.\n\nWho should read it: people working on OTA computation, energy harvesting, and federated edge learning. It deserves a serious referee; the identifiability point is addressable and should be part of the review.","headline":"A useful unified cluster-aware framework for OTA FL with energy harvesting; the main soft spot is an unstated identifiability requirement in the LSE-based scheduling that fails for low-energy users.","tokens_in":27116,"tokens_out":3053,"would_cite":true,"duration_ms":27287,"reading_group":"yes","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 user clusters turn over-the-air federated learning with energy-harvesting devices into either fairer global training or personalized per-cluster training.","keywords":["federated learning","over-the-air computation","energy harvesting","diverse client scheduling","clustered federated learning","personalization","data heterogeneity","blind transmitters"],"falsifier":"Run the LSE-based scheduler with $M=40$ users, one class per user, an estimation window of $T=100$ iterations, and energy arrival probabilities $p^m_e=0.25$ for most users but near zero for a few. If those low-energy users never appear in the participation matrix $A$, the least-squares estimate $\\hat{\\Theta}_{\\text{rep}}$ is not identifiable and the estimated cosine-similarity clusters will not reflect their data; fairness should then degrade to or below the no-scheduling baseline. Checking the rank of $A$ in that run settles whether the paper's identifiability assumption holds.","tokens_in":26299,"feed_emoji":"📡","tokens_out":10685,"duration_ms":87154,"temperature":0.7,"pith_summary":"The paper aims to show that the natural cluster structure among users with similar data can serve as one shared mechanism for two different goals in over-the-air federated learning with energy-harvesting devices: making a single global model fairer, and producing personalized models per user group. For the global-model goal, cluster information drives scheduling that picks a representative subset of active users, reducing the gap between the scheduled gradient and the full-participation gradient. For the personalization goal, the same clusters define separate learning targets, and the parameter server recovers all clusters' updates simultaneously from one superimposed wireless signal using MMSE or cluster-wise weighted combining. The convergence analysis decomposes the error into contributions from OTA channel noise, data heterogeneity, and gradient approximation error, which motivates the scheduling and combining designs. Numerical experiments on MNIST, FMNIST, and CIFAR-10 indicate that the framework improves fairness or personalization while lowering communication overhead.","feed_headline":"Cluster structure makes over-the-air FL fair or personalized","feed_subtitle":"One server, one channel: cluster-aware scheduling either cuts data bias or trains per-cluster models.","key_machinery":"The carrying mechanism is the user-cluster structure, a grouping of devices by similarity of their label distributions or update directions. In Mode I it enters through cluster-aware scheduling: entropy-based selection when label distributions are known, and least-squares estimation of user representations from the noisy aggregated signal when they are not. In Mode II it is encoded in the cluster-assignment matrix $A$ and its projector $P = A(A^\\top A)^{-1}A^\\top$; the server's MMSE or cluster-wise weighted combining recovers each cluster's average update from the same received signal. The convergence analysis centers on the gradient-approximation error $\\epsilon$, the gap between the full-p","core_discovery":"The paper's central claim is that user-cluster structure is one abstraction that resolves a tension in over-the-air federated learning: data heterogeneity can be treated either as bias to be removed or as structure to be exploited, and the same clusters serve both goals. For a fair global model, the server either uses known label distributions to pick the active-user subset with highest label entropy, or, when distributions are unknown, estimates each user's update representation from $T$ aggregated over-the-air signals by least squares ($\\hat{\\Theta}_{PS}=A\\,\\Theta_{\\text{rep}}+N^*$) and clusters users by cosine similarity; scheduling then samples across clusters. For personalization, the s","pith_inferences":["Beyond the paper: the full-column-rank identifiability requirement is a hidden constraint; an adaptive estimation window that lengthens until every user has participated enough times would be a natural extension the paper does not analyze.","Beyond the paper: the same cluster abstraction could carry into hierarchical federated learning or multi-task learning, where clusters become task groups; the paper mentions such directions only as future work.","Beyond the paper: a testable prediction is that the gap between LSE-based scheduling and entropy-based scheduling shrinks as the estimation window $T$ grows and as energy arrival probabilities become more balanced across users."],"forward_implications":["One parameter server can train multiple cluster-specific models simultaneously over one multiple-access channel, avoiding separate transmissions or multiple servers for personalized FL.","In energy-harvesting settings, cluster-aware scheduling makes partial participation more representative, so fairness improves most when data heterogeneity is strongest, as shown by the CIFAR-10 experiments with strong Dirichlet skew.","The error-bound decomposition yields concrete design rules: increasing the number of server antennas $K$ or the minimum scheduled-set size $S_{\\min}$ suppresses the OTA noise floor, while the heterogeneity floor $2(\\tau-1)\\Gamma/(\\mu\\tau)$ cannot be removed by stepsize tuning.","Even with no CSI at the transmitters and only cluster-level CSI at the server, the CWC and partial-MMSE combiners still beat a single-global-model baseline, so personalization is feasible under realistic channel knowledge.","The LSE representation phase uses only participation patterns and aggregated noisy updates, so scheduling can be made diversity-aware without requiring users to disclose their data distributions."],"supporting_citations":[{"why":"Supplies the blind-transmitter OTA aggregation model and the channel-combining lemmas reused in the proof of Theorem 1.","marker":"[11]"},{"why":"Provides the over-the-air FL analysis whose smoothness and strong-convexity assumptions are adopted for the convergence bounds.","marker":"[13]"},{"why":"Supplies the gradient-approximation error formulation and the principle that a diverse subset approximates full aggregation, used in the scheduling design.","marker":"[24]"},{"why":"Introduces clustered sampling based on update similarity, the basis for grouping users and sampling across clusters in Mode I.","marker":"[23]"},{"why":"Defines clustered federated learning and the model-agnostic client partitioning that Mode II extends to the over-the-air setting.","marker":"[25]"},{"why":"Provides the clustered minimization formulation and convergence properties used for the cluster-level objectives.","marker":"[26]"},{"why":"Earlier over-the-air clustered FL with beamforming and compression, which the paper extends to energy harvesting, blind transmitters, and partial CSI.","marker":"[27]"},{"why":"Supplies the energy-harvesting device model with unit battery and the assumption that energy arrivals are shared with the parameter server.","marker":"[17]"}],"fun_headline_variants":["Cluster-aware OTA FL: fair global or personalized local models","One channel, two goals: cluster-aware FL for fairness or personalization","Fair global model or personalized clusters? One framework does both","Cluster-aware scheduling: pick fair users or train per-cluster models","Over-the-air FL: clusters for either fairness or personalization"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The weakest load-bearing premise is that the $T\\times M$ participation matrix $A$ in Eq. (28) has full column rank, so every user's update representation is recoverable from aggregated over-the-air signals during the estimation window; users with very low energy-arrival probabilities may rarely or never participate, making their representations unidentifiable and the diversity-aware scheduler blind to their data.","fun_headline_variants_meta":{"raw":{"variants":["Cluster-aware OTA FL: fair global or personalized local models","One channel, two goals: cluster-aware FL for fairness or personalization","Fair global model or personalized clusters? One framework does both","Cluster-aware scheduling: pick fair users or train per-cluster models","Over-the-air FL: clusters for either fairness or personalization"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000714,"raw_usage":{"total_tokens":3051,"prompt_tokens":752,"completion_tokens":2299,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":496,"completion_tokens_details":{"reasoning_tokens":2211}},"tokens_in":496,"tokens_out":2299,"duration_ms":14196,"temperature":1.0,"reasoning_tokens":2211,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T00:11:44.982290+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the LSE-based scheduler with $M=40$ users, one class per user, an estimation window of $T=100$ iterations, and energy arrival probabilities $p^m_e=0.25$ for most users but near zero for a few. If those low-energy users never appear in the participation matrix $A$, the least-squares estimate $\\hat{\\Theta}_{\\text{rep}}$ is not identifiable and the estimated cosine-similarity clusters will not reflect their data; fairness should then degrade to or below the no-scheduling baseline. Checking the rank of $A$ in that run settles whether the paper's identifiability assumption holds.","supporting_citations":[{"cited_title":"Blind federated edge learning,","cited_arxiv_id":null,"evidence_quote":"Supplies the blind-transmitter OTA aggregation model and the channel-combining lemmas reused in the proof of Theorem 1."},{"cited_title":"Over-the- air federated edge learning with hierarchical clustering,","cited_arxiv_id":null,"evidence_quote":"Provides the over-the-air FL analysis whose smoothness and strong-convexity assumptions are adopted for the convergence bounds."},{"cited_title":"Diverse client selection for federated learning via submodular maxi- mization,","cited_arxiv_id":null,"evidence_quote":"Supplies the gradient-approximation error formulation and the principle that a diverse subset approximates full aggregation, used in the scheduling design."},{"cited_title":"Clustered sampling: Low-variance and improved representativity for clients selection in federated learning,","cited_arxiv_id":null,"evidence_quote":"Introduces clustered sampling based on update similarity, the basis for grouping users and sampling across clusters in Mode I."},{"cited_title":"Clustered federated learning: Model-agnostic distributed multitask optimization under privacy con- straints,","cited_arxiv_id":null,"evidence_quote":"Defines clustered federated learning and the model-agnostic client partitioning that Mode II extends to the over-the-air setting."},{"cited_title":"An efficient framework for clustered federated learning,","cited_arxiv_id":null,"evidence_quote":"Provides the clustered minimization formulation and convergence properties used for the cluster-level objectives."},{"cited_title":"Over-the-air clustered federated learning,","cited_arxiv_id":null,"evidence_quote":"Earlier over-the-air clustered FL with beamforming and compression, which the paper extends to energy harvesting, blind transmitters, and partial CSI."},{"cited_title":"Joint client selection and receive beamforming for over-the-air federated learning with energy harvesting,","cited_arxiv_id":null,"evidence_quote":"Supplies the energy-harvesting device model with unit battery and the assumption that energy arrivals are shared with the parameter server."}],"review_version":1}