{"id":"5739edb2-7346-42b6-8d13-25087128db20","arxiv_id":"2607.26038","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Federated discrete-time survival models with learned sensor representations improve remaining-useful-life predictions over locally trained models on C-MAPSS, but fall short of centralized training on the harder datasets.","lead":"This paper describes a way for several organizations to jointly train a machine-failure prediction model without sharing their sensor data. The method adapts a standard survival-analysis model so each site can compute its part locally, and tests it on four turbofan-engine datasets.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Per-window survival labels are undefined after sliding-window construction: Eq. (7)/(16) assume one event time per system, while Algorithm 1 trains on many windows per engine; the optimized objective may not correspond to any coherent survival model.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the gap between the single-event-time likelihood in Eqs. (7)-(16) and the sliding-window training in Algorithm 1. This is the most critical issue because the paper's core methodological contribution is the client-separable discrete-time survival objective; if that objective is not well-defined for the actual training instances, the empirical comparisons cannot validate the central claim. The client-separability argument itself is mathematically sound at the level of the formal likelihood, so the problem is in the mapping from that formulation to the implemented pipeline. I considered other potential concerns, such as the overclaim of parity with centralized training on FD003/FD004 (Table V shows substantial gaps) and the lack of standard RUL baselines, but these are secondary to the undefined per-window target. The proposed concrete test is a simple single-engine sanity check that would settle whether the implementation assigns the same labels to all windows of an engine or uses some unstated relative-time derivation. Since this concern directly matches the reader's assessment, the verdict remains conditional: the paper can be accepted only after the per-window survival likelihood is formally defined and the diagnostic is resolved.","tokens_in":16996,"tokens_out":6332,"duration_ms":63322,"concrete_test":"Run a diagnostic on FD001 training data: pick one engine with failure cycle T > 200. Create two length-40 windows ending at cycles 50 and 150. Compute the interval labels y_ij as the paper specifies (Eq. (7), Eq. (17)) and evaluate Eq. (16) for a fixed randomly initialized model. If the two windows have identical label sequences and identical loss contributions, then the window's temporal position is not encoded in the survival target, confirming misspecification. If a different label derivation is intended, that derivation should be written down and used to re-derive Eq. (16); the test is to show that the loss distinguishes windows with different remaining lives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires the objective in Eq. (16) to be a valid client-separable survival likelihood for the data actually used in training. The paper defines that likelihood at the level of a system i with a single event/censoring time T_i: Eq. (7) creates a binary sequence y_ij over intervals j=1..J_i covering the system's whole at-risk period, and Eq. (16) sums over systems. But Algorithm 1 line 4 constructs 'sliding-window sensor sequences of length L from {X_i}' and Section II-C2 takes the model input to be a single L-step window X_i ∈ R^{L×p}. Nowhere is it stated how a window relates to the intervals j: does each window inherit the engine's full T_i and therefore the identical y_i sequence (so early windows are labeled with outcomes for intervals before they even exist), or is each window a new pseudo-subject with its own left-truncated lifetime and a new label sequence? Neither is written. If windows inherit T_i, the loss for all windows of one engine is identical except for z_i, so the time-to-event information is not indexed by the window's position and the model is not asked to predict remaining life at different horizons; if windows are pseudo-subjects, Eq. (7)-(16) must be re-derived with a new failure time and left-truncation, which is absent. Overlapping windows from the same engine are also treated as independent samples in Eq. (16) without justification, so the effective sample size and reported standard deviations are ill-defined. Either way, the objective is not a well-defined survival likelihood for sliding-window training, and the reported C-index/IBS/MAE/RMSE comparisons in Table V are not attached to a coherent per-window target.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a federated longitudinal-survival framework for system failure prognostics. To avoid the nonseparable global risk sets of the continuous-time Cox partial likelihood, it reformulates survival learning with a discrete-time complementary-log-log hazard model whose interval-level negative log-likelihood is client-separable. An LSTM-attention encoder maps sliding-window sensor sequences to representations that feed interval-specific hazards; survival curves and expected RUL are then derived. Experiments on the four C-MAPSS subsets, with engines partitioned across ten simulated clients, report that federated training consistently improves over isolated local training and is competitive with centralized training on several metrics.","tokens_in":17395,"tokens_out":3747,"duration_ms":40809,"significance":"If the formulation is made rigorous, the paper addresses a real obstacle: continuous-time Cox partial likelihood is not client-separable, and the discrete-time cloglog likelihood does decompose across clients. The empirical study is broad, uses held-out test engines, fixes hyperparameters chosen on FD001 across all datasets, and reports mean ± std over five seeds with comparisons to centralized and local baselines. This is a substantive contribution to federated PHM, provided the training objective is actually well-defined.","major_comments":[{"comment":"The statistical unit is inconsistent. Eq. (7)–(16) define the likelihood at the level of a system i with a single event/censoring time T_i and interval index J_i. Algorithm 1 line 4 constructs sliding-window sensor sequences of length L from each system, and Section II-C.2 says the model input is a single L-step window. The manuscript never defines the per-window target sequence, how a window's intervals relate to T_i, or why overlapping windows from the same engine can be treated as independent terms in Eq. (16). If every window inherits the engine's full T_i, then all windows of one engine receive the same label sequence and the model has no supervision at different prediction horizons; if each window is a pseudo-subject, the likelihood must be re-derived with left-truncation, which is absent. Either way, the objective actually optimized in Algorithm 1 is not the likelihood in Eq. (16)","section":"Section II-C.1, II-C.2, and Algorithm 1"},{"comment":"The C-index is one of the primary metrics supporting the central empirical claim, but the 'aggregate risk score r_i' is never defined. It is not stated whether r_i is a predicted hazard at a fixed horizon, a negative expected RUL, a linear predictor, or something else. Without this definition, the reader cannot verify the discrimination results or compare them with standard survival-analysis practice. Please specify the score and the handling of ties and censoring.","section":"Section III-C, Eq. (35)"},{"comment":"Even after clarifying the window-level unit, the aggregation weights in Eq. (30) must match the local objective. Eq. (16) normalizes by N_k, the number of systems per client, and Eq. (28) weights clients by N_k/N. If the actual training data are sliding windows, the effective sample size per client is larger and depends on the number of windows. The paper should state whether the loss is averaged over systems or over windows, and adjust the FedAvg weighting accordingly; otherwise the global objective being minimized is ambiguous.","section":"Eq. (16), Eq. (28), and Algorithm 1"}],"minor_comments":[{"comment":"Eq. (18) defines pooled counts over all systems i∈N, but in the federated setting these counts are obtained by aggregating local counts in Eq. (21). Clarify that N here denotes the union over all clients, and note that the KM grid construction is part of a preliminary communication round.","section":"Eq. (18)–(22)"},{"comment":"Test trajectories with 40 or fewer cycles are excluded. Please report the number of excluded engines per subset and comment on the potential selection bias this introduces, since short trajectories are likely those with the earliest truncation.","section":"Table I and Section III-B"},{"comment":"The definitions of Local-avg, Local-best, and Local-worst are given in the table caption only as 'summaries computed across ten clients.' Clarify how seed variation is combined with client variation: are the means computed over five seeds and ten clients, or over clients within a single seed and then averaged over seeds?","section":"Table V and Fig. 5"},{"comment":"With a learned nonlinear g_ω(z_i), the formula hj(z_i)=1−exp{−exp(α_j+g_ω(z_i))} does not correspond to a standard proportional-hazards model in the strict sense unless g_ω is linear. The paper should soften the claim that the cloglog link 'preserves the proportional-hazards interpretation of the original Cox model' when the predictor is an arbitrary neural-network function.","section":"Section II-C.2, Eq. (27)"}],"recommendation":"major_revision","confidential_remarks":"The central methodological issue — the undefined window-level target construction — is fixable within the manuscript's scope but requires a precise re-formulation of the likelihood and the training procedure. I would encourage the editor to request the authors to make this explicit before publication. No code or data are provided; given the ambiguity in the objective, releasing code or at least a precise pseudocode for the window-label generation would greatly strengthen the reproducibility."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know about this paper is that the statistical core is real but the training set-up is not well-defined. The authors take the discrete-time survival objective from Andreux et al. (credited), which is client-separable because it avoids global risk sets, and embed it in a federated learning loop over C-MAPSS. The cloglog derivation is standard and correct. The genuinely new pieces are the LSTM-attention encoder, the KM-based adaptive grid computed in the federated setting, and the four-subsets C-MAPSS evaluation. That is a legitimate extension, and the paper is honest about where the idea comes from.\n\nThe soft spot is the sliding window. The likelihood in Eqs. (7)-(16) is defined for one observation per system, with a single event/censoring time T_i. Algorithm 1 then trains on every L-cycle subsequence of each engine. The paper never says what event time a window has. If a window at cycle t inherits the engine's T_i, it is labelled with failures in intervals that may predate the window, and early windows are asked to predict hazards for periods before they exist. If a window is a pseudo-subject, the likelihood needs left truncation and per-window remaining-life labels, which are absent. Overlapping windows from the same engine are also treated as independent samples in Eq. (16), so the effective sample size and the reported standard deviations are not well defined. That is load-bearing: the main empirical claim, that federated training beats local training, is attached to a model whose training loss has not been shown to be a valid survival likelihood for the data actually fed in.\n\nThe empirical evaluation is plausible but thin: no code, no standard RUL baselines, and the abstract overclaims parity with centralized training on FD003/FD004 (the body is more careful, and the performance-preservation table shows the gap). These are addressable. For applied PHM researchers this is a useful illustration; for statisticians it is a warning about undefined replication. The idea is worth engaging with; the paper deserves a serious referee, but the referee should insist on a formal re-derivation of the per-window target and the independence assumption before the numbers are taken at face value.","headline":"The federated survival idea is sound but the training objective is undefined after sliding-window construction; the paper needs a careful re-derivation before its empirical claims can be trusted.","tokens_in":17925,"tokens_out":4611,"would_cite":false,"duration_ms":47879,"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":"Switching to a discrete-time complementary log-log hazard makes survival models client-separable, so federated training beats isolated local training on every C-MAPSS subset without pooling raw data.","keywords":["federated learning","survival analysis","discrete-time Cox model","complementary log-log link","remaining useful life","prognostics and health management","C-MAPSS","longitudinal sensor data"],"falsifier":"Train the same federated model on C-MAPSS with a single non-overlapping window per engine (targets from the engine's true remaining life) versus the paper's overlapping sliding windows. If the overlapping version is sharply better, the reported federated gains are an artifact of duplicate supervision; if both behave similarly, the independence assumption is harmless.","tokens_in":16868,"feed_emoji":"⚙️","tokens_out":6013,"duration_ms":52747,"temperature":0.7,"pith_summary":"The paper tries to show that the reason survival models are hard to federate—the Cox partial likelihood's global risk sets—can be removed by switching to a discrete-time formulation with a complementary log-log link, whose interval-level likelihood splits into a sum of client-local terms. It then attaches an LSTM-with-attention encoder so that sliding windows of multivariate sensor readings produce the time-dependent risk representation, and a Kaplan-Meier-adaptive time grid provides stable interval baselines. The authors' empirical claim, on the four C-MAPSS turbofan subsets with ten simulated clients, is that this federated framework consistently improves C-index, integrated Brier score, MAE, and RMSE over isolated local training and remains close to—sometimes better than—centralized training. A sympathetic reader should care because it offers a concrete route to collaborative failure prognostics across organizations that cannot pool sensor or failure data.","feed_headline":"Discrete-time hazards unlock federated failure prediction","feed_subtitle":"A cloglog reformulation drops global risk sets; federated training beats local models on every C-MAPSS subset.","key_machinery":"The load-bearing object is the interval-level discrete-time hazard h_j(z_i)=1−exp{−exp(α_j+g_ω(z_i))}, whose complementary log-log link preserves the proportional-hazards interpretation of the Cox model. Because the binary cross-entropy loss over system–interval labels decomposes as a sum over local observations, the global objective is client-separable; the LSTM-attention encoder provides the time-dependent representation z_i, and the KM-adaptive grid supplies interval baselines α_j that allocate failures evenly across intervals.","core_discovery":"The paper's central claim is that the continuous-time Cox partial likelihood—whose risk sets couple observations across clients—can be replaced by a discrete-time complementary log-log hazard model whose interval-level likelihood is a sum of client-local terms, so federated averaging optimizes a well-defined global survival objective without any client seeing another's data. The framework couples this client-separable objective to an LSTM-with-attention encoder that turns sliding windows of multivariate sensor readings into risk representations, and a Kaplan-Meier-based adaptive time grid that stabilizes interval baseline estimates. On the four C-MAPSS subsets with ten simulated clients, the","pith_inferences":["The same client-separability argument should extend to other discrete-time survival variants—proportional-odds, competing risks, or recurrent events—since any likelihood that factors over system–interval Bernoulli trials will be federatable; the paper only demonstrates the cloglog case.","Because only aggregated binned counts are sent to build the grid, a privacy analysis is still owed: bin width controls how much failure-time information is disclosed, and the paper does not quantify the resulting privacy–utility trade-off.","A direct check of the observation-unit assumption would be to train on one non-overlapping window per engine (labels from the engine's true remaining life) and compare with the overlapping-window version; if performance collapses, the reported gains partly reflect duplicated windows rather than genuine survival learning."],"forward_implications":["A federated network of maintenance sites can train a shared failure-risk and RUL model without transmitting raw sensor streams or individual failure records; only model updates and binned event counts for grid construction are exchanged.","The discrete-time cloglog formulation removes the need for global risk sets, so the per-client loss equals the global loss under FedAvg-style weighted averaging, making standard federated optimization directly applicable to survival objectives.","The Kaplan–Meier-based grid improves calibration and RUL error relative to equidistant bins on FD001, reducing IBS by about 5.5% and RMSE by about 4.1%.","Collaborative training reduces the worst-case outcome of isolated local training: on FD001, federated C-index is 0.787 versus 0.574 for the worst local client, and RMSE improves from 36.54 to 17.70 cycles.","On the more heterogeneous FD003/FD004 subsets, federated training still beats local-only training on all metrics, though it does not fully close the gap to centralized training."],"fun_headline_variants":["Federated prognostics without risk-set sharing","Federated survival via client-separable hazards","Discrete-time hazards make federated survival learnable","No global risk sets: private collaborative failure prediction","Client-separable hazards: federated RUL without data pooling"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The likelihood assumes one independent survival observation per system, but training feeds overlapping sliding windows per engine; the paper never defines a window's interval labels or why overlapping windows are independent, so the objective being optimized is not pinned down.","fun_headline_variants_meta":{"raw":{"variants":["Federated prognostics without risk-set sharing","Federated survival via client-separable hazards","Discrete-time hazards make federated survival learnable","No global risk sets: private collaborative failure prediction","Client-separable hazards: federated RUL without data pooling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001189,"raw_usage":{"total_tokens":4739,"prompt_tokens":734,"completion_tokens":4005,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":478,"completion_tokens_details":{"reasoning_tokens":3930}},"tokens_in":478,"tokens_out":4005,"duration_ms":23881,"temperature":1.0,"reasoning_tokens":3930,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T00:45:35.104136+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train the same federated model on C-MAPSS with a single non-overlapping window per engine (targets from the engine's true remaining life) versus the paper's overlapping sliding windows. If the overlapping version is sharply better, the reported federated gains are an artifact of duplicate supervision; if both behave similarly, the independence assumption is harmless.","supporting_citations":[],"review_version":1}