{"id":"512663e9-fb79-415c-9d1b-defb6a4dd711","arxiv_id":"2502.05538","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A coalition-formation-guided heterogeneous federated learning method, using QMIX reinforcement learning and transfer learning, is proposed and simulated for RIS-assisted cell-free MIMO channel estimation, reporting lower computation and better NMSE than baselines.","lead":"An engineering paper proposes a federated learning framework for estimating wireless channels in RIS-assisted cell-free MIMO networks, where users form coalitions using deep reinforcement learning and train smaller local models. A simulation study reports a 16% cut in end-user computation and about 20% better channel estimation accuracy than the baselines tested.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The stability theorem's static-utility assumption does not match the implemented retraining-based reward, so the theoretical guarantee may not transfer to the evaluated system.","rationale":"The reader's weakest assumption correctly identifies that the potential-game proof requires static coalition-dependent errors, while the implemented DRL reward is based on one-epoch NMSE that changes with retraining. This is the most load-bearing concern because it undermines the paper's central theoretical claim (Theorem 1) and its connection to the empirical algorithm. If the theorem's assumptions are not satisfied, the paper still may present a useful engineering heuristic with plausible simulation results, but the claimed theoretical guarantee of stable, utility-maximizing coalition formation is unsupported. The empirical results are not directly invalidated, so a conditional verdict remains appropriate: the authors should either (a) clarify that the theorem applies to the converged-error game and provide evidence that the DRL approximates it, or (b) weaken the theoretical claims to a heuristic justification. Other issues (lack of code, no error bars, overclaimed privacy) are secondary and do not change the conclusion. The proposed concrete test would directly assess whether the one-epoch reward materially changes the outcome, settling whether the static-utility mismatch is merely formal or practically damaging.","tokens_in":19155,"tokens_out":16090,"duration_ms":157594,"concrete_test":"Re-run the CFFL algorithm with the reward computed from a fully converged FL model (e.g., after the same 6000 epochs used in the NMSE comparisons) instead of after one epoch, and compare the resulting coalition structure and final NMSE to the original one-epoch-reward version. If the final NMSE differs by more than the ~20% reported gain, the one-epoch reward is not a faithful implementation of the Theorem 1 utility, and the stability/improvability guarantee does not transfer. A second, cheaper test: fix one converged global model and evaluate all single-user moves under the static utility; if any unilateral move improves the two-affected-coalition welfare, the DRL output is not stable under the theorem.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Theorem 1 (Appendix A) proves existence of a stable coalition structure via an exact potential game with coalition utility U(S_j) = A - sum e_{j,p}, where e_{j,p} are fixed errors for a given membership. The proof requires that e_{j,p} (and hence U(S_j)) be a static function of the coalition's composition. In the implementation (Section III-D), however, the reward driving coalition formation is R_t = 1 - e, where e is the average NMSE after one epoch of FL training. Those errors change whenever models are retrained (Steps 1-6 in Section III-C) and whenever users move between coalitions. Thus the utility landscape is non-stationary during the DRL process, so the potential-game argument does not transparently apply. Even if a stable partition exists for the converged-error game, nothing in the paper shows that the one-epoch-reward DRL converges to it, or that the final coalition structure is stable under the theorem's altruistic criterion. This gap directly affects the paper's theoretical contribution and weakens the claim that coalition formation provably improves the FL-based channel estimation system.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a coalition-formation-guided heterogeneous federated learning (CFFL+HFL) framework for downlink channel estimation in RIS-assisted cell-free MIMO systems. Users are grouped into coalitions via distributed DRL (DQN or QMIX), each coalition trains a local FL model with heterogeneous model sizes via knowledge distillation, and transfer learning based on distance and RSRP similarity initializes the models. The authors claim a 20% improvement in channel estimation accuracy, a 16% reduction in end-user computational overhead, and improved privacy compared with centralized and homogeneous FL baselines. The paper also states Theorem 1, asserting the existence of a stable coalition structure under an altruistic criterion via an exact potential game proof in Appendix A.","tokens_in":19419,"tokens_out":7293,"duration_ms":64359,"significance":"If the stated gains are statistically robust and the stability theorem actually applied to the implemented algorithm, the framework would be a useful integrative contribution to FL-based channel estimation in RIS-assisted cell-free networks, with a plausible combination of coalition games, DRL, HFL, and transfer learning. The simulation study includes several baselines (MMSE, DML, FL, DCE, DQN+FL) and the reported NMSE/complexity trends are internally consistent. However, the theoretical guarantee is not currently connected to the implemented reward mechanism, the empirical claims lack multiple-seed statistics, and the privacy contribution is both qualitatively and quantitatively under-supported. These issues are fixable, but they are load-bearing for the paper's main claims.","major_comments":[{"comment":"The exact-potential-game proof in Appendix A assumes that the coalition utility U(S_j) = A - sum e_{j,p} is a static function of coalition membership, with fixed errors e_{j,p}. In the implemented CFFL loop, however, Section III-D defines the reward as R_t = 1 - e, where e is the average NMSE after one epoch of FL training, and those errors change whenever models are retrained (Steps 1-6 in Section III-C) or users switch coalitions. Thus the utility landscape is non-stationary during the DRL process, so Theorem 1's stable-partition guarantee does not transparently apply to the algorithm whose performance is evaluated in Section IV. Please either formulate a static coalition utility (e.g., based on channel correlation or data distribution) for which Theorem 1 holds and connect the DRL to that game, or explicitly restrict the theorem to the static setting and explain why the dynamic reward still yields the claimed stability.","section":"Section III-D and Appendix A"},{"comment":"The central quantitative claims (\"20% accuracy improvement,\" \"16% computational overhead reduction\") are reported without any error bars, multiple-seed trials, or scenario sensitivity analysis; Figures 12-16 show only single traces. It is therefore unclear whether the reported gains are within training or initialization noise. Please report means and variances over at least several independent runs and specify the exact benchmark and SNR at which the 20% figure is computed, since Section IV-C reports gains of 18% and 28% at SNR = 5 dB while Section IV-B reports a roughly 30% gain at 0-2 dB.","section":"Section IV"},{"comment":"The privacy-improvement claim is not supported and appears partially contradicted by the described method. Eq. (11) has each active UE train on raw data from Z neighboring UEs with a data-sharing ratio a, and Step 4 says the central server trains the distillation part using data collected by the edge server (uplink data), which are raw-data exchanges of the kind FL is intended to avoid. In addition, Table III shows that the HFL local model has 8,409,856 parameters versus 8,428,416 for homogeneous FL, a reduction of only 0.22%, so the assertion that HFL \"transmits only a part of model parameters\" does not amount to a meaningful privacy gain. Please specify the threat model, quantify the privacy improvement, and either justify or temper the abstract's privacy claim.","section":"Section III-A, Section III-C Step 4, and Table III"}],"minor_comments":[{"comment":"There are numerous typographical errors, including \"altruitic\" for \"altruistic\" (Definition 1, Theorem 1, Appendix A), \"for the shake of fairness\" (Section IV), \"Rewawrd\" (Figure 14 caption), \"outperfroms\" (Section IV-B), and \"Siganl\" in reference [4]; a thorough copyedit is needed.","section":"Throughout"},{"comment":"The symbol L is used for the reference distance in Eq. (12) and for the number of users in Eq. (14), and earlier as the number of paths in Eqs. (1) and (3); this overloading makes the notation hard to follow.","section":"Eq. (12) and Eq. (14)"},{"comment":"In Definition 1, the notation S1 ⊆ S and S2 ⊆ S is confusing because S is defined as a coalition structure (a set of coalitions); S1 and S2 should be elements of S rather than subsets, or the structure should be defined differently.","section":"Definition 1"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable engineering study, but the main theoretical claim is disconnected from the implemented algorithm and the empirical claims lack statistical grounding. I do not see deliberate circularity; the benchmarks are external. My main concern is that the stable-partition theorem, as stated, cannot be verified from the paper because the utility is dynamic in the algorithm. This is fixable in revision by re-scoping the theorem or changing the algorithm, so I recommend major revision rather than rejection. The heavy self-citation to the WCNC predecessor [1] is normal for an extended version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a reasonable engineering paper that puts together coalition formation games, QMIX-based distributed RL, heterogeneous FL, and RSRP+distance transfer learning for RIS-assisted cell-free MIMO channel estimation. The main empirical claims—roughly 20% NMSE improvement and 16% reduction in on-device compute—are plausible and backed by multiple baselines. The soft spot is the stability theorem: it is proven for a static utility game, while the implemented DRL reward uses one-epoch NMSE that changes as models retrain and users move. The potential-game argument does not transparently transfer. That is addressable, but it means the paper should not claim a provable stability guarantee for the system actually evaluated.\n\nWhat is genuinely new: the altruistic preference ordering for FL user grouping, the QMIX-based distributed coalition formation applied to this problem, and the RSRP+distance transfer learning combination. I do not recall another paper putting these three together for RIS channel estimation. The simulation setup is sensible: DeepMIMO, sparse and dense user distributions, and several baselines including MMSE, DML, FL, DCE, and DQN+FL. The complexity and communication-overhead tables are useful.\n\nSoft spots, in order of importance:\n1. The theorem/implementation gap. The proof defines coalition utility U(Sj) with fixed errors e_{j,p}, but Section III-D defines the DRL reward as 1 minus the average NMSE after one epoch of FL training. Those errors change whenever models are retrained or users switch coalitions, so the utility landscape is non-stationary. The authors should either state the theorem applies to a converged utility game or revise the proof to match the iterative training loop.\n2. No error bars or multiple seeds. All figures appear to be single-run. For a DRL-based method, the reported 18–28% gains could carry substantial variance.\n3. The privacy claim is qualitative and not supported by the numbers. Table III shows the total parameter count for HFL (8.409M) is barely lower than for homogeneous FL (8.428M)—a 0.22% reduction. The FLOPs reduction is 16%, but the transmitted parameter count is nearly identical, so the privacy benefit from transmitting fewer parameters is negligible.\n4. The scenario is small: 10 UEs, one RIS, four BSs. That is fine for a proof of concept, but the 20% accuracy claim should be understood in that narrow setting.\n\nMinor: Remark 1 appears to say \"homogeneous FL\" where it means heterogeneous FL, and the abstract has a grammar slip. Both should be cleaned up.\n\nBottom line: this is a publishable engineering paper with a useful combination of methods and mostly internally consistent simulations. The theoretical claim needs to be aligned with the algorithm, and the empirical claims need variance information. I would send it to peer review, but I would expect major revision focusing on the theorem gap and error bars.\n\nThe paper is for researchers working on federated learning for wireless channel estimation, especially those interested in game-theoretic user grouping. A serious referee will find enough substance to engage with.\n\nRecommendation: engage with it; accept for peer review with revision expectations.","headline":"A solid engineering combination of game-theoretic FL grouping, QMIX, and transfer learning for RIS channel estimation, with a stability theorem that doesn't quite match the implemented algorithm.","tokens_in":19942,"tokens_out":2828,"would_cite":false,"duration_ms":30370,"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":"The paper argues that federated-learning user grouping for channel estimation in RIS-assisted cell-free MIMO should be treated as a coalition-formation game solved by distributed deep reinforcement learning, and reports that this approach…","keywords":["coalition formation","heterogeneous federated learning","distributed deep reinforcement learning","QMIX","channel estimation","reconfigurable intelligent surface","cell-free MIMO","transfer learning"],"falsifier":"Freeze the local models between coalition moves and recompute the exact-potential-game stable partition; if the partition the QMIX algorithm converges to differs from that static partition, or if the algorithm's coalition choices cycle when retraining is allowed, the theorem's guarantee would not be governing the implemented system.","tokens_in":18947,"feed_emoji":"📡","tokens_out":7288,"duration_ms":69525,"temperature":0.7,"pith_summary":"The paper sets out to show that user grouping in federated channel estimation should be decided by the users themselves through coalition formation, rather than fixed in advance or handled by a central server. It claims that a coalition-formation game with altruistic preferences has at least one stable group structure, and that a distributed QMIX-based reinforcement learner can find it while training heterogeneous local models of different sizes. In the DeepMIMO-based simulation with 10 users, the reported result is an approximately 20% improvement in channel-estimation accuracy, a 16% reduction in end-user computational overhead, and a 15% reduction in per-epoch training time compared with the benchmarks, with better privacy because only part of each model is transmitted.","feed_headline":"Coalition-based federated learning cuts channel-estimation error 20%","feed_subtitle":"Grouping users with similar channels into FL coalitions shrinks local models, saves 16% compute, and improves privacy.","key_machinery":"The mechanism is a coalition formation game in which each coalition $S_j$ carries utility $U(S_j) = A - \\sum_{p \\in S_j} e_{j,p}$, where $e_{j,p}$ is the normalized mean-squared channel-estimation error of user $p$; the altruistic preference order says a user switches coalitions only when both the coalition it joins and the one it leaves improve. The stability proof identifies the game as an exact potential game with potential $\\varphi = \\sum_{j \\in S_k, S_k \\in \\mathcal{S}} u(a_{k,j})$, so every unilateral move changes the utility and the potential by the same amount, guaranteeing a pure-strategy Nash equilibrium. To find such a partition in practice, each user runs a Q-network, with individual Q-values combined in a QMIX mixing network and reward $1 - e$, where $e$ is the average NMSE after one federated-learning epoch. Heterogeneous FL is realized by distilling a large global model into a smaller local model with a shared parameter part and a distillation part, and transfer learning initializes each user's local model from neighboring central models weighted by distance and RSRP similarity.","core_discovery":"The central claim is that partitioning users into coalitions whose members have correlated fading is the right organizational principle for federated cascaded-channel estimation in RIS-assisted cell-free MIMO, and that this partition can be discovered by distributed deep reinforcement learning instead of centralized optimization. The paper formalizes user grouping as a coalition formation game, defines an altruistic preference order, and proves in Theorem 1 that at least one stable coalition structure exists, identifying the optimal decomposition of the network utility maximization problem with a stable structure. It then augments heterogeneous federated learning with a transfer-learning initialization based on distance and received-signal-power similarity, and reports that the combined framework improves channel estimation accuracy by about 20% and cuts end-user computational overhead by about 16% relative to centralized DML, homogeneous FL, and MMSE baselines.","pith_inferences":["A reader who wants to rely on the stability guarantee should check whether the learned coalition sequence converges to the static-utility stable partition; the paper reports convergence of rewards but not this comparison.","The same coalition-formation-guided grouping could be applied to other wireless federated learning tasks where a similarity metric plays the role of channel correlation, such as beam prediction, CSI feedback, or localization, since the game-theoretic machinery does not depend on the specific DNN.","The reported 20% accuracy gain and 16% compute saving are for a single 10-user DeepMIMO scenario; scaling to hundreds of users or moving users would test whether QMIX's local-observation design remains stable and whether the transfer-learning initialization still pays off."],"forward_implications":["If the framework is correct, grouping users with similar channel fading into coalitions is what yields most of the reported gain: at 5 dB SNR, CFFL is reported to outperform a single-group FL baseline by 18% and the FL+Dis transfer-learning baseline by 28% in NMSE.","Distributed QMIX decision-making should reach about 97.5% of the centralized DQN reward while eliminating the exchange of other users' coalition choices, so its communication advantage grows as the number of users increases.","Heterogeneous FL should reduce end-user FLOPs by about 16% and per-epoch training time by about 15% at a roughly 3% NMSE cost relative to homogeneous FL, which is the trade that makes the method usable on devices with limited computation.","Transfer learning that uses both distance and received-signal-power similarity should accelerate convergence and improve NMSE by 33–50% over DML, conventional FL, MMSE, and DCE baselines.","Because HFL transmits only the shared part of local model parameters, the paper's privacy claim is that less user data is exposed than in homogeneous FL or centralized learning."],"supporting_citations":[{"why":"Supplies the baseline federated-learning approach for RIS-assisted channel estimation that the proposed coalition-guided framework extends and compares against.","marker":"[23]"},{"why":"Provides the distributed machine-learning downlink channel estimation baseline and motivates the move to federated training.","marker":"[22]"},{"why":"Gives the weighted-gradient aggregation formula used in the federated-learning model updates.","marker":"[35]"},{"why":"Supplies the DeepMIMO dataset used for all reported channel-estimation experiments.","marker":"[39]"},{"why":"Provides the exact-potential-game theorem that underpins the claim that a stable coalition structure exists.","marker":"[40]"},{"why":"Demonstrates the feasibility of combining coalition formation with channel estimation and serves as a direct precedent for the proposed framework.","marker":"[30]"}],"fun_headline_variants":["Coalition FL cuts channel error 20%, compute 16% in RIS MIMO","Stable coalitions via DRL improve channel estimates 20%","Distributed RL groups users into FL coalitions for better channels","20% better channel estimation via RL-formed FL coalitions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The stability theorem assumes each coalition's utility is a fixed function of membership, but in the implemented algorithm the utility is the channel-estimation error measured after one round of retraining, which changes every time models update or users switch groups.","fun_headline_variants_meta":{"raw":{"variants":["Coalition FL cuts channel error 20%, compute 16% in RIS MIMO","Stable coalitions via DRL improve channel estimates 20%","Distributed RL groups users into FL coalitions for better channels","20% better channel estimation via RL-formed FL coalitions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000936,"raw_usage":{"total_tokens":4021,"prompt_tokens":981,"completion_tokens":3040,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":597,"completion_tokens_details":{"reasoning_tokens":2963}},"tokens_in":597,"tokens_out":3040,"duration_ms":22718,"temperature":1.0,"reasoning_tokens":2963,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T18:55:41.801873+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Freeze the local models between coalition moves and recompute the exact-potential-game stable partition; if the partition the QMIX algorithm converges to differs from that static partition, or if the algorithm's coalition choices cycle when retraining is allowed, the theorem's guarantee would not be governing the implemented system.","supporting_citations":[{"cited_title":"Federated learning for channel estimation in conventional and RIS-assisted massive MIMO,","cited_arxiv_id":null,"evidence_quote":"Supplies the baseline federated-learning approach for RIS-assisted channel estimation that the proposed coalition-guided framework extends and compares against."},{"cited_title":"Distributed machine learning based downlink channel estimation for RIS assisted wireless communications,","cited_arxiv_id":null,"evidence_quote":"Provides the distributed machine-learning downlink channel estimation baseline and motivates the move to federated training."},{"cited_title":"Communication-efficient learning of deep networks from decentralized data,","cited_arxiv_id":null,"evidence_quote":"Gives the weighted-gradient aggregation formula used in the federated-learning model updates."},{"cited_title":"Deepmimo: A generic deep learning dataset for mil- limeter wave and massive mimo applications,","cited_arxiv_id":null,"evidence_quote":"Supplies the DeepMIMO dataset used for all reported channel-estimation experiments."},{"cited_title":"Joint design of coalition formation and semi-blind channel estimation in fog radio access networks,","cited_arxiv_id":null,"evidence_quote":"Demonstrates the feasibility of combining coalition formation with channel estimation and serves as a direct precedent for the proposed framework."}],"review_version":1}