{"id":"45ae6ec7-5815-46fc-9d5a-12c7886cd433","arxiv_id":"2511.11949","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A cyclic scheduling framework for energy-harvesting federated learning that claims large energy savings, with a convergence analysis that appears internally inconsistent.","lead":"This paper proposes FedBacys, a battery-aware federated learning scheme that splits clients into cyclic groups and schedules local training around energy-harvesting deadlines, plus an 'odd-chances' variant that trains half as often. The authors claim large energy savings and provide a convergence bound, but the proof has internal inconsistencies and the abstract describes experiments the body does not report.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1 mis-scales participation: with q_i=1/N (Eq. 5), E[Σq_i]≤η, not Nη; Eq. (11)'s Nη coefficient is unsupported and the full-participation check forces η=1/N, contradicting Lemma 4. The stationarity bound does not follow.","rationale":"The reader's weakest assumption identifies the same load-bearing flaw: the proof's participation normalization is inconsistent with the definition of q_i. This is decisive because it is the step that converts a bound on individual participation probabilities into a bound on the global-model descent. The full-participation sanity check makes the contradiction crisp: with q_i=1/N, the proof's target BNη∇f equals B∇f only when Nη=1, while Lemma 4 demands η≥1/(6√N), which is incompatible for N>36. Since Theorem 1 and Theorem 2 rest on this descent inequality, the central theoretical claim is unsupported. Secondary concerns (no code/data, absent non-IID label-skew experiments) also weaken the empirical claim, but the algebraic inconsistency alone justifies rejection. I recommend keeping the reader's REJECT verdict.","tokens_in":21823,"tokens_out":5047,"duration_ms":48404,"concrete_test":"Full-participation consistency check: set S_t=U for one epoch. Then q_i=1/N (Eq. 5), so the aggregate in Eq. (7) equals (1/N)Σ_i Δ_i and Σ_i q_i=1. Substitute into Eq. (11): the target must be B·Σ_i q_i·∇f = B∇f, yet the proof uses BNη∇f, forcing Nη=1. Compare with Lemma 4, which requires η≥1/(6√N); for N=100 this is η≥1/60, while Nη=1 gives η=1/100. This contradiction demonstrates the proof cannot hold for the stated q_i. As a second check, recompute the descent inequality using E[Σ_i q_i]≤η: replace Nη in Eq. (11) with η, propagate through Eqs. (12)-(15), and verify whether the coefficient of E||∇f(x_{t,0})||² remains positive under γ≤1/(12BLN). If it does not, Theorem 1 requires an additional factor-N correction and the stated O(F/(BNTγη)) rate is not established.","verdict_should_be":"REJECT","load_bearing_attack":"q_i^t is defined in Eq. (5) as 1/N for participants, 0 otherwise. Lemma 3 bounds any user's participation probability by η≤1; therefore E[Σ_i q_i^t] = E[#participants]/N ≤ η. The proof of Theorem 1 (Appendix B-A, Eq. (11)) nevertheless centers the decomposition on BNη∇f(x_{t,0}) and divides by 2BNη, i.e. it treats the expected weighted participant sum as Nη. This inflates the descent term by a factor of N and propagates into Eqs. (14)-(15), where the coefficient of E||∇f||² is 4BNγη/15. The inconsistency is not a minor notation issue: if q_i were an indicator (so EΣq_i≤Nη), then Σ(q_i)^2 ≤ ρ²<1 would forbid more than one participant per round; if q_i=1/N, the factor Nη is wrong. A concrete contradiction: when all N clients participate, Σ_i q_i=1, so consistency of Eq. (11)'s target requires Nη=1, i.e. η=1/N, but Lemma 4 guarantees η≥1/(6√N), impossible for N>36. Lemma 3's own 'tighter' bound is vacuous (η≤1; for FedBacys-Odd η→1/2), so the claimed finite-horizon staleness bound is not what carries the proof. Without a correct descent lemma, Theorem 1 and Theorem 2's rate are unsupported, undermining the advertised convergence guarantee.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes FedBacys and FedBacys-Odd, energy-harvesting federated learning algorithms that organize clients into cyclically scheduled groups with pipelined intra-group aggregation. The main claimed contributions are (i) a convergence bound on the stationarity gap (Theorem 1) and a PL-based rate (Theorem 2) under a multi-slot local training model, and (ii) an experimental demonstration that the schemes, especially FedBacys-Odd, reduce cumulative energy consumption relative to several FL/EHFL baselines. The scheduling idea is interesting and the experimental setup is fairly broad, but the central convergence proof contains a scaling inconsistency in the participation weights that invalidates the advertised theorems as stated.","tokens_in":22284,"tokens_out":6979,"duration_ms":62082,"significance":"If the convergence claims were valid, the paper would make a useful contribution to EHFL by addressing the under-modeled cost of multi-slot local training and by showing that cyclic, battery-aware scheduling can preserve convergence while reducing energy. The experimental study, which includes several baselines and a range of charging probabilities, provides suggestive evidence that the proposed algorithms are energy-efficient in practice. However, the theoretical guarantee is the primary scientific claim of the paper, and the proof of Theorem 1 is not correct as written. No code or machine-checked proofs are provided, so the experiments are not independently reproducible from the manuscript alone. The significance of the paper therefore rests on a convergence result that is currently unsupported.","major_comments":[{"comment":"The proof of Theorem 1 mis-scales the expected participant sum. Eq. (5) defines q_i^t = 1/N for participating clients and 0 otherwise. Lemma 3 bounds each client's participation probability by η≤1, so E[Σ_i q_i^t] = (1/N)Σ_i P(i participates) ≤ η. Eq. (11) nevertheless centers the decomposition on BNη∇f(x_{t,0}) and divides by 2BNη, i.e. it treats the expected weighted sum as Nη. The justification given ('expectation of the size of the participant subset ... bounded above by Nη') confuses the number of participants with the weighted sum Σ q_i. This changes the descent coefficient by a factor of N and propagates into Eqs. (14)-(15). Concretely, full participation gives Σ_i q_i^t = 1, so consistency with Eq. (11)'s target would require Nη=1, i.e. η=1/N, contradicting Lemma 4's η ≥ 1/(6√N) for N>36. Thus Theorem 1, and consequently Theorem 2, are not established.","section":"Appendix B-A, Eq. (11); §V Eq. (5)"},{"comment":"Lemma 3 is advertised as giving a 'significantly tighter' upper bound η on participation probability, but its proof only derives the trivial bound η≤1. Since η is the sole parameter encoding battery dynamics in the convergence bound, the claimed finite-horizon staleness bound and the stated dependence of Theorem 1 on system parameters are unsupported. Additionally, the 'Impact of the odd-chances-only policy' paragraph asserts without proof that η decays from 1 to 1/2 as T→∞; if this is a modeling assumption rather than a theorem, it should be labeled as such and its effect on the bound quantified. As written, η acts as an arbitrary free parameter in the proof, not as a derived system quantity.","section":"Appendix C, Lemma 3; §V"}],"minor_comments":[{"comment":"The notation q_i^t is used both as an aggregation weight (1/N) and, in the text, as a participation probability. This conflation is likely the source of the N-scaling error in the proof; please rename or explicitly distinguish the weight from the participation indicator.","section":"§V, Eq. (5)"},{"comment":"The pseudo-code for FedBacys-Odd is hard to follow: the LOCALTRAIN call appears in both the general condition branch and the odd-chance branch, making it unclear when a client actually trains. A cleaner separation of the two policies would help.","section":"Algorithm 1"},{"comment":"The energy and accuracy results appear to be from single runs. Reporting multiple seeds with error bars would strengthen the empirical claims, especially for the 'roughly half energy' comparison.","section":"§VI, Table I and Fig. 3"},{"comment":"The symbol E_t is used for both the conditional expectation E[·|F_t] and the battery level E_s^{(i)} in Section III. Please use distinct notations to avoid confusion.","section":"Appendix B-A"}],"recommendation":"reject","confidential_remarks":"The main convergence proof has a concrete scaling inconsistency that cannot be dismissed as a typo: it changes the central descent coefficient by a factor of N and contradicts the stated participation bounds. The advertised stationarity-gap and PL rates therefore do not follow. The experimental study is suggestive, but without a valid theoretical guarantee the paper does not meet the bar for publication. A resubmission with a corrected descent lemma and a re-derived bound, or with the theory substantially weakened and clearly separated from heuristics, could be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe short version: the FedBacys idea is worth a look, but the paper's main convergence guarantee is broken. The proof of Theorem 1 has a scaling error: the paper defines q_i^t as 1/N for participants (Eq. 5), so the expected sum of q_i over users is at most η, not Nη. Yet Eq. (11) centers everything on BNη∇f and divides by 2BNη, treating the expected participant sum as Nη. The all-client-participate sanity check forces η=1/N, which contradicts Lemma 4's lower bound η≥1/(6√N) for N>36. That means the stationarity bound does not follow, and Theorem 2 inherits the problem. Lemma 3's \"tighter\" upper bound is also vacuous (η≤1), so the paper's advertised contribution to the convergence analysis of cyclic EHFL is unsupported.\n\nWhat is worthwhile: the κ-slot local training energy model is a sensible correction to the usual single-slot assumption, and the pipelined cyclic scheduling with battery-level awareness is a reasonable engineering idea. FedBacys-Odd's odd-chances heuristic is simple but effective in the experiments, cutting cumulative energy roughly in half. The empirical comparison against CyCP, MIFA, FedSeq, and FLDA under varying charging probabilities is useful, even though FedBacys's advantage over CyCP at higher δ is mostly structural (training less often).\n\nOther soft spots: the abstract claims experiments under non-IID and severe label skew, but the body's setup doesn't describe data heterogeneity—just varying δ. There are no error bars, no code, no data, and the results are single runs. The Algorithm 1 pseudocode for FedBacys-Odd looks garbled (it seems to train in the FedBacys branch and then again on odd counts), which needs fixing.\n\nBottom line: this is a paper with a timely problem and a plausible practical recipe, but the theory as written is wrong. I would not send it to review in its current form; a desk reject with an invitation to resubmit after a corrected proof and more rigorous experiments seems right. If the authors fix the participation scaling and rerun, the scheduling piece could be salvageable as a systems paper.","headline":"The FedBacys scheduling idea and energy experiments are plausible, but Theorem 1's proof has a participation-scaling error that invalidates the advertised convergence guarantee.","tokens_in":22725,"tokens_out":6691,"would_cite":false,"duration_ms":57340,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Cyclic, battery-aware scheduling can roughly halve the energy cost of energy-harvesting federated learning, and a selective variant that trains only on odd-numbered eligible chances does so without sacrificing accuracy.","keywords":["federated learning","energy harvesting","cyclic scheduling","battery-aware","client participation","stationarity gap","convergence analysis","energy efficiency"],"falsifier":"Recompute Eq. (11) under the paper's own definition q_i^t = 1/N for participants: the target BNη∇f requires E[Σ_i q_i^t] = Nη, whereas the definition gives E[Σ_i q_i^t] = η, so the identity claimed in step (a) fails unless q_i is silently redefined. Separately, rerun the Table I setting (CIFAR-10, N=100, S=30, κ=20, δ=1.0, G=5): if FedBacys-Odd's total energy is not close to 524,850 battery units with final accuracy near FedBacys, the empirical energy claim is falsified.","tokens_in":21725,"feed_emoji":"🔋","tokens_out":8723,"duration_ms":72199,"temperature":0.7,"pith_summary":"This paper aims to show that federated learning on energy-harvesting devices can be made practical when local training is explicitly modeled as a multi-slot, battery-draining operation. FedBacys groups clients by battery level and runs them through a rotating pipeline: each group's hub aggregates local updates and passes the model to the next group, so recharging in one group overlaps with computation in another. The paper proves a stationarity-gap bound for this cyclic schedule and argues that the pipeline's finite horizon avoids the exponential staleness factors that plague asynchronous FL analyses. Its FedBacys-Odd variant trains only on odd-numbered eligible chances, and the CIFAR-10 experiments show it reaches the same target accuracy as the full schedule while consuming roughly half the cumulative network energy at high charging probabilities.","feed_headline":"Training only on odd chances halves FL energy use","feed_subtitle":"Battery-aware cyclic scheduling reaches target accuracy with roughly half the cumulative energy of standard baselines.","key_machinery":"The load-bearing object is the cyclic group pipeline: clients are split into G groups, each group is given R = floor(S/G) slots, and at the final slot of its window the group hub aggregates local updates and multicasts the intermediate model to the next group, with the last group relaying to the server. A deadline condition forces local training to start κ slots before the upload window, so clients train with a fresher reference model and avoid redundant work. The analysis compresses the causal, memory-dependent battery dynamics into a single bounded participation probability η (Lemma 3), and FedBacys-Odd adds an odd-chance counter that skips every other eligible training start, conserving κ","core_discovery":"Under standard smoothness, bounded-variance, and gradient-divergence assumptions, FedBacys satisfies a stationarity-gap bound of the form min_t E||∇f(x_[t,0])||^2 = O( F/(BNTγη) + ρ²(ζ²+σ²)/(Nη²) + higher-order terms ), where η is a per-client upper bound on the probability of successful participation derived from the charging probability δ, local training cost κ, epoch length S, and battery capacity. The cyclic structure makes stale updates at most one epoch old, so the analysis avoids exponential staleness factors typical of asynchronous methods. Under the Polyak–Łojasiewicz condition the optimization error decays as O(1/T²) to a neighborhood set by noise and heterogeneity. Empirically, th","pith_inferences":["Extension: the odd-chance rule is a generic 'skip until fresher' principle, so the same counter-based selection could be applied to communication-constrained FL, where the scarce resource is uplink budget rather than battery energy.","Extension: the bound's dependence on η suggests a testable prediction: as the charging probability δ decreases, performance should degrade through the η² term in the floor, and the paper's threshold condition marks where that floor starts to dominate; experiments below that threshold would test the theory.","Extension: the deadline-cramming rule could be made per-client by allowing heterogeneous κ values, letting slower or larger-model devices participate without forcing a single global epoch length S; this is a direct generalization of the scheduling mechanism.","Extension: because the error floor contains heterogeneity terms ζ² and β̃², grouping clients by data distribution in addition to battery level could shrink the floor; the paper lists semantics-aware adaptation as future work but does not test this combination."],"forward_implications":["If the bounds hold, battery-aware cyclic scheduling can replace random client selection in EHFL without losing convergence guarantees: performance is controlled by a finite-horizon staleness term rather than exponential asynchrony factors.","The odd-chance rule implies that deliberately skipping a large fraction of training opportunities can preserve accuracy, because conserved battery energy is spent later on fresher updates rather than wasted on stale ones.","The condition 1 - F_Binomial(κ-1; S, δ) ≥ 1/(6√N) gives a concrete design rule: choose the epoch length S long enough that a client starting with an empty battery can harvest κ units by its upload deadline with probability at least 1/(6√N).","The reported energy savings come from scheduling alone, not from compression or quantization, so systems that already use compression could expect additional savings on top of those techniques.","Under the PL condition, the convergence error decays as O(1/T²) down to a floor set by client heterogeneity and participation variability, identifying stable participation and balanced scheduling as the levers that shrink that floor."],"fun_headline_variants":["Pipelined cyclic scheduling halves FL energy","Battery-aware FL: same accuracy, half the energy","Cyclic groups cut FL energy, skip stale gradient slowdown","Energy-harvesting FL gets a recharge-friendly loop","Cyclic FL pipeline dodges staleness, halves energy"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The proof's central norm-splitting identity, Eq. (11), assumes the expected participation sum is Nη, but Eq. (5) defines q_i^t as 1/N for a participating client, which makes the expected sum equal to η, not Nη; if q_i is not redefined as an indicator, Theorem 1 does not follow from the given algebra.","fun_headline_variants_meta":{"raw":{"variants":["Pipelined cyclic scheduling halves FL energy","Battery-aware FL: same accuracy, half the energy","Cyclic groups cut FL energy, skip stale gradient slowdown","Energy-harvesting FL gets a recharge-friendly loop","Cyclic FL pipeline dodges staleness, halves energy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001036,"raw_usage":{"total_tokens":4207,"prompt_tokens":765,"completion_tokens":3442,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":509,"completion_tokens_details":{"reasoning_tokens":3364}},"tokens_in":509,"tokens_out":3442,"duration_ms":21075,"temperature":1.0,"reasoning_tokens":3364,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T22:06:47.554448+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute Eq. (11) under the paper's own definition q_i^t = 1/N for participants: the target BNη∇f requires E[Σ_i q_i^t] = Nη, whereas the definition gives E[Σ_i q_i^t] = η, so the identity claimed in step (a) fails unless q_i is silently redefined. Separately, rerun the Table I setting (CIFAR-10, N=100, S=30, κ=20, δ=1.0, G=5): if FedBacys-Odd's total energy is not close to 524,850 battery units with final accuracy near FedBacys, the empirical energy claim is falsified.","supporting_citations":[],"review_version":1}