{"id":"e1f3ff62-4d75-4c50-b8bc-b15a41041c1b","arxiv_id":"2506.02642","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A two-phase GNN with a penalty-based loss jointly optimizes BS beamforming, RIS phases, and DF relay beamforming under fine-grained user rate constraints in simulated MISO systems.","lead":"Engineers train a two-step graph neural network to jointly set base station beams, relay forwarding, and smart-surface phase shifts in a wireless system where users have individual minimum-speed needs. The method adds penalty terms to the training loss so more users meet their rate targets, and simulations report higher total throughput than random, particle swarm, and deep-network baselines.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The §IV GNN has no relay nodes, no group nodes, and no relay-indexed outputs, so the claimed autonomous relay selection and multi-relay beamforming are not representable by the described architecture.","rationale":"The reader's weakest_assumption correctly identifies the missing relay/group structure in the graph. I agree and find this to be the single most load-bearing concern because it attacks the paper's headline contribution, not a peripheral comparison. The paper's abstract explicitly claims the GNN 'simultaneously and autonomously' learns relay selection, and the experiments in §V.B.1 present relay selection as a source of performance gain. However, the architecture described in §IV contains exactly one RIS node and K user nodes; there are no relay nodes, no group nodes, and no output dimension indexed by relay. The loss functions in (29)-(31) sum over relay index j, and the power constraint (10b) requires per-relay beamforming matrices F_j, but the readout only produces a single f_k per user. Thus the described network cannot even represent the decision variables needed for the problem it claims to solve. This is an internal inconsistency, not a mere disagreement with external consensus. The proposed concrete test—tracing the forward-pass dimensions through the equations—would definitively settle whether any relay-indexed information enters the computation. Since the reader already conditioned the verdict on this unresolved gap, my read does not change the verdict; it should remain CONDITIONAL pending clarification or code release. I see no reason to recommend REJECT outright because the authors could potentially specify an external relay-selection mechanism or an unstated per-relay graph, but as written the central claim is unsupported.","tokens_in":20302,"tokens_out":5218,"duration_ms":50988,"concrete_test":"Set I=2, J=2, K=4 as in §V.A. Write out the forward pass of §IV for one sample: list the dimensions of every tensor through Eqs. (13)-(28) and the readout layers. Verify whether any tensor has a J-dimension or a group-indexed dimension. If none does, the network output is independent of which relay is used, so the claimed relay selection cannot be learned. Then request from the authors either (a) an explicit mapping from network outputs to F_1...F_J and to a relay-selection decision, or (b) the code used for Fig. 4(b) so the forward pass can be inspected. If the code performs relay selection outside the GNN (e.g., exhaustive search over j), the abstract's 'simultaneously and autonomously' claim should be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the two-phase GNN simultaneously learns beamforming, phase shifts, and relay selection is unsupported by the architecture in §IV. The first-phase graph (§IV.A) is explicitly 'a fully connected graph... comprising K+1 nodes... one node dedicated to the RIS... along with K nodes assigned to the users.' The second-phase graph (§IV.B) has the same structure: one RIS node and K user nodes. There are no relay nodes, no group nodes, and no variable encoding relay selection. The readout layers output at most θ ∈ C^N and g_k ∈ C^M in phase 1, and θ ∈ C^N and f_k ∈ C^L in phase 2; these tensors have no index for the J relays or the I groups. Yet the system model (§III.A) includes J DF relays and I groups, the power constraint C2 in (10b) sums over j=1..J of tr(F_j F_j^H), and the loss functions (29)-(31) sum over j=1..J of γ^R_{j,k}. Problem P1 in (10) does not define a relay-selection variable at all. Algorithm 1 line 16 says 'Select the appropriate relay to calculate the sum rate' but no selection mechanism, node, or output is specified. Consequently, the network cannot represent distinct relay beamforming matrices F_j or a relay-selection decision; relay selection could only exist as external post-processing, contradicting 'simultaneously and autonomously learn... relay selection.' This is not a minor detail: relay selection is one of the paper's three claimed outputs and a stated contribution in §I. Section V.B.1 attributes performance gains to 'GNN-based relay selection optimization,' but the described graph has no path from relay identity to the loss or output. If the authors intend a different graph (e.g., one graph per RIS or a meta-node per relay), it is not the one defined in §IV.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper considers a downlink MISO system with a multi-antenna base station, multiple RISs, multiple half-duplex DF relays, and users clustered into groups with fine-grained rate thresholds. It formulates a sum-rate maximization problem P1 with power, DF-decoding, rate-threshold, and discrete-phase constraints, and proposes an unsupervised two-phase graph neural network that takes CSI as input and outputs RIS phase shifts, BS beamforming vectors, and relay beamforming vectors. A penalty-based loss is introduced to trade off sum rate against fine-grained rate-demand satisfaction. Simulations compare the method with DNN, PSO, and random baselines and report higher sum rates and satisfaction ratios, plus generalization across different numbers of users.","tokens_in":20630,"tokens_out":5509,"duration_ms":54665,"significance":"If the architecture actually realized the claimed joint optimization, the paper would be a useful contribution: it is among the first in the reviewed comparison to combine group-level inter/intra trade-offs with per-user fine-grained rate demands, and the unsupervised penalty formulation is a simple way to control satisfaction ratio. Strengths include an explicit permutation-invariant feature design, a generalization study in Table IV, and comparison against several baselines. However, the central architectural claim is not supported by the described graph, and there are dimensional errors in the signal model; the experimental results therefore cannot be interpreted as validating the claimed method until these issues are fixed.","major_comments":[{"comment":"The message-passing graph in both phases is explicitly described as fully connected with K+1 nodes: one RIS node and K user nodes (e.g., 'comprising K+1 nodes... one node dedicated to the RIS... along with K nodes assigned to the users'). There are no relay nodes and no group nodes, and the readouts produce θ_i, g_k, and f_k with no relay index. Since the system model in §III includes J DF relays and I groups, and P1 constraint C2 in (10b) sums over j=1..J of tr(F_j F_j^H), the network cannot represent distinct relay beamforming matrices, relay-selection decisions, or group-level competition. Algorithm 1 line 16 instructs to 'Select the appropriate relay' without specifying a selection variable, node, or output. Consequently the abstract's claim of simultaneously and autonomously learning 'phase shifts, beamforming, and relay selection' is not supported by the described architecture.","section":"§IV.A, §IV.B, Algorithm 1"},{"comment":"No mechanism in the GNN encodes grouping. The graph has one RIS node and K user nodes; no node or aggregation is indexed by group i. The loss functions (29)–(31) include sums over i and group-threshold penalties, but the architecture has no group-level representation, so the claimed modelling of 'intra-group cooperation' and 'inter-group competition' (Section III, Section V.B.3) is not realized by the network. The text states 'inter-group competition is dynamically balanced through relay selection,' but relay selection itself is absent from the graph.","section":"§III.C, §IV.A, §IV.B"},{"comment":"Equation (3) is dimensionally invalid: H_i θ_i^1 is an M×1 vector while (H^B_{i,k})^T is a 1×M row vector, so the sum and the outer transpose are undefined. This error propagates into the SINR expression (4) and into the input definitions (11) for the first-phase GNN, and it prevents the model from being unambiguously instantiated. All expressions involving (H^B_{i,k})^T need to be corrected, presumably to use H^B_{i,k} or its conjugate transpose in the appropriate inner product.","section":"§III.A, Eqs. (3)–(4)"},{"comment":"The relay-dependent quantities are not consistently defined. The second-phase SINR γ^(2)_{i,k} in (8) depends only on f_k and has no relay index j, while γ^R_{j,k} in (6) depends on α_k, which itself depends on j; the notation in (6) mixes j and k indices in the denominator. The loss functions sum β over j=1..J of min(0,γ^R_{j,k}−γ^R_th), which either adds the same penalty J times if γ^R_{j,k} does not depend on j, or requires J distinct relay beamformers that the network does not output. The power constraint C2 in (10b) uses F_j while the phase-2 readout outputs f_k ∈ C^L; the relationship between F_j and f_k is never defined. These inconsistencies make the training objective not well matched to P1.","section":"§III.A, Eqs. (5)–(8), (29)–(31)"}],"minor_comments":[{"comment":"The group-granularity loss is written with weight λ, but the following sentence refers to μ as the weight coefficient; the notation should be aligned.","section":"Eq. (30)"},{"comment":"The label 'JOFG-Random' appears to be a typo for 'JOFD-Random', and the names JOGD-TG/JOCD-TG are used inconsistently across the text and figures.","section":"Fig. 5, Section V.B"},{"comment":"The abstract contains 'low date rates', which should be 'low data rates'.","section":"Abstract"},{"comment":"The penalty weights β and λ are fixed at 1000, and only λ is swept in Fig. 9; a similar sweep or ablation for β would better support the claim that the satisfaction ratio is tunable via the penalty parameter.","section":"Table III, Fig. 9"},{"comment":"The neighbor set N(k) is used, but the graph is fully connected for user nodes; clarifying that N(k) denotes all other users in the fully connected setting would improve readability.","section":"Algorithm 1, line 7"}],"recommendation":"major_revision","confidential_remarks":"The decisive issue is the mismatch between the claimed GNN capabilities and the described architecture: there are no relay or group nodes, and 'relay selection' appears only as an unexplained instruction in Algorithm 1. This is a load-bearing problem because relay selection is one of the three claimed outputs. The dimensional error in Eq. (3) adds to the concern that the model description has not been carefully validated. If the authors can revise the architecture to include relay/group nodes or clearly define an external relay-selection mechanism, and correct the signal model, the empirical comparison may become interpretable. The relation to prior GNN-based hybrid relay/RIS work in [31] should also be clarified."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core issue is that the architecture doesn't match the claims. The abstract and contributions say the GNN learns phase shifts, beamforming, and relay selection jointly. But Section IV describes a graph with one RIS node and K user nodes, with no relay nodes and no group nodes. The readout layers output theta and g_k (or f_k) with no index for relays or groups, so the network cannot represent distinct relay beamforming matrices or a relay-selection decision. The loss functions sum over j=1..J and i=1..I, but the network outputs don't carry those indices. Algorithm 1 line 16 says to select the appropriate relay, but no selection mechanism is specified. This isn't a minor detail; relay selection is one of the three claimed contributions, and the paper's conclusion repeats it.\n\nWhat is genuinely new is the loss function with penalty terms for fine-grained rate thresholds. Tuning the penalty parameter to trade off sum rate against satisfaction ratio is a sensible idea, and the figures show the expected qualitative behavior. The two-phase GNN for two-hop transmission is also a reasonable extension of the GNN beamforming line of work. But the empirical evaluation is thin: no code, no error bars, no comparison to the closely related GNN in [31], and no classical optimization baselines. The only baselines are random, PSO, and a plain DNN. The cross-K generalization results in Table IV are interesting, but without statistical reporting they carry limited weight.\n\nThere is also a dimension mismatch in Eq. (3): an M x 1 vector is added to a 1 x M transpose. That looks like a fixable typo, but it makes the equations harder to trust.\n\nOverall, the penalty-based loss is a plausible contribution, but the central claim about simultaneous relay selection and inter-group competition is not supported by the described architecture. The authors need to either clarify that the GNN is applied separately per relay and per group (and explain how selection is done), or redesign the graph to include relay and group nodes. I would still send this to review because the topic is relevant and the fix is achievable, but the current version would need major revisions before acceptance.","headline":"The fine-grained rate penalty loss is a reasonable idea, but the GNN as described cannot perform the relay selection or inter-group optimization the paper claims.","tokens_in":21251,"tokens_out":4428,"would_cite":false,"duration_ms":42486,"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":"A two-phase GNN learns RIS phase shifts, beamforming, and relay selection directly from CSI, while a penalty term balances sum rate against per-user rate demands.","keywords":["reconfigurable intelligent surface","decode-and-forward relay","graph neural network","fine-grained rate demands","relay selection","joint beamforming","MISO systems"],"falsifier":"Extend the graph with explicit relay nodes and optionally group nodes carrying relay- and group-specific channel features, retrain under the same loss, and compare relay-selection decisions, sum rate, and satisfaction ratios with the original architecture; unchanged performance would indicate the reported relay-selection gains do not come from learned message passing.","tokens_in":20063,"feed_emoji":"📶","tokens_out":8749,"duration_ms":77400,"temperature":0.7,"pith_summary":"Users in real networks are clustered and have different rate needs, but most RIS-relay optimization treats them as uniform individuals and maximizes only total throughput. The paper tries to close that gap by proposing a joint optimization model for a RIS- and DF-assisted MISO downlink with grouped users and per-user rate thresholds. It claims that a two-phase graph neural network, fed only channel state information, can simultaneously learn base-station beamforming, RIS phase shifts, relay beamforming, and relay selection, and that a penalty term in the loss lets the network trade sum rate against the fraction of users whose rate demands are met. If right, this would give a low-complexity, unsupervised way to run fine-grained quality-of-service control in RIS-relay networks without solving hard nonconvex problems per channel realization.","feed_headline":"Two-phase GNN lifts sum rate in RIS-relay MISO downlinks","feed_subtitle":"Penalty-tuned loss balances total throughput against individual user rate requirements, reaching near-100% satisfaction.","key_machinery":"The named central object is the two-phase GNN, a message-passing network with one RIS node and $K$ user nodes in each phase. In phase one, user-node features are built from the BS-to-user and BS-to-RIS channel matrices, the RIS node aggregates them with a mean operation, user nodes aggregate one another with a max operation to capture worst-case interference, and readout layers map the final features to the BS beamforming vectors $g_k$ and quantized RIS phases $\\theta_i^1$. Phase two repeats the same structure on the relay-to-user and relay-to-RIS channels to produce relay beamforming $f_k$ and $\\theta_i^2$. The carrying mechanism is the penalty-augmented loss: negative sum rate plus $\\beta \\min(0, \\gamma^R_{j,k} - \\gamma^R_{th})$ and $\\lambda \\min(0, R_{i,k} - R^{th}_{i,k})$, which is what makes the satisfaction ratio tunable. As defined, the graph contains no relay nodes, group nodes, or relay-selection variable, so relay selection is performed as a separate step after the GNN readouts rather than as a message-passing output.","core_discovery":"The paper's central claim is that jointly optimizing both transmission phases of a RIS- and DF-assisted MISO system—active beamforming at the BS and relays, passive phase shifts at the RISs, and the choice of which relay forwards—can be learned end-to-end by a two-phase GNN from CSI, while fine-grained rate demands are enforced through a penalty-augmented loss. The authors define the JOFD-TG algorithm: a first-phase graph outputs the BS beamforming matrix and the first-phase RIS phase shifts, a second-phase graph outputs the relay beamforming matrix and the second-phase phase shifts, and the loss subtracts the sum rate plus penalty terms that activate when a relay SINR or a user rate falls below its threshold. Simulations compare against random phase shifts, particle swarm optimization, and a DNN, and report that the GNN achieves higher sum rate and higher satisfaction ratios, that the fine-grained user-level granularity outperforms coarse- and group-level granularity, and that adjusting the penalty weight can drive the satisfaction ratio toward 100%.","pith_inferences":["Not pursued in the paper: making relay selection an explicit part of the learned graph by adding relay nodes and edges would test whether the reported relay-selection gains actually come from message passing or from the separate post-training selection rule.","The penalty-loss idea transfers naturally to other constrained resource-allocation problems where a hard requirement can be softened into a tunable penalty, such as latency or energy constraints in network slicing.","One could probe the fairness-optimal operating point by plotting the full trade-off curve of sum rate against satisfaction ratio as the penalty weight varies, and then choosing the weight from an operator-defined service objective.","If the graph were extended with group nodes, the claimed inter-group competition might become representable as a learned resource-allocation mechanism rather than an emergent effect of relay selection."],"forward_implications":["If the central claim holds, the same two-phase GNN can be retrained for new deployments without per-realization optimization, since it learns from CSI in an unsupervised way.","The penalty parameter $\\lambda$ provides a single dial for fairness: increasing it raises the fraction of users meeting their rate thresholds, at some cost in raw sum rate.","Fine-grained, per-user thresholds should dominate group-level or coarse thresholds in both sum rate and satisfaction, because the network can allocate resources to individual needs.","Relay placement and selection can matter more than RIS phase tuning in this two-phase topology, so system designers should prioritize relay positioning and the relay-selection rule.","The model's permutation-invariant aggregation should let it generalize to different numbers of users, with graceful degradation as the training and testing user counts diverge."],"supporting_citations":[{"why":"Graph-neural-network joint beamforming for hybrid relay and RIS multiuser systems, the architecture the two-phase design builds on.","marker":"[31]"},{"why":"System and channel model for hybrid relay and RIS assisted multiuser MISO, source of the Rician/Rayleigh channel assumptions and the two-phase transmission model.","marker":"[44]"},{"why":"Deep reinforcement learning relay selection in RIS-assisted cooperative networks, the relay-selection performance this work is compared with.","marker":"[34]"},{"why":"Unsupervised learning to reflect and beamform for an RIS, source of the GNN training paradigm and the implicit-channel-learning approach.","marker":"[30]"},{"why":"Deep-neural-network beamforming baseline that the proposed GNN must outperform.","marker":"[25]"},{"why":"Particle-swarm optimization baseline implementation used in the comparisons.","marker":"[47]"}],"fun_headline_variants":["Two-phase GNN optimizes RIS-relay MISO with rate targets","Joint learning of beamforming and phase shifts via GNN","Penalty-tuned GNN balances sum rate and per-user fairness","GNN-driven joint optimization for RIS-DF MISO systems","Two-phase graph network improves rate satisfaction in MISO"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that a message-passing graph containing only one RIS node and $K$ user nodes is enough to represent multiple relays, multiple groups, inter-group competition, and relay selection; the paper specifies no mechanism by which relay identity or group membership enters the learned variables.","fun_headline_variants_meta":{"raw":{"variants":["Two-phase GNN optimizes RIS-relay MISO with rate targets","Joint learning of beamforming and phase shifts via GNN","Penalty-tuned GNN balances sum rate and per-user fairness","GNN-driven joint optimization for RIS-DF MISO systems","Two-phase graph network improves rate satisfaction in MISO"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000201,"raw_usage":{"total_tokens":1409,"prompt_tokens":1003,"completion_tokens":406,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":619,"completion_tokens_details":{"reasoning_tokens":320}},"tokens_in":619,"tokens_out":406,"duration_ms":4197,"temperature":1.0,"reasoning_tokens":320,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:19:32.282965+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Extend the graph with explicit relay nodes and optionally group nodes carrying relay- and group-specific channel features, retrain under the same loss, and compare relay-selection decisions, sum rate, and satisfaction ratios with the original architecture; unchanged performance would indicate the reported relay-selection gains do not come from learned message passing.","supporting_citations":[{"cited_title":"Graph neural network-based joint beamforming for hybrid relay and reconfigurable intelligent surface aided multiuser systems,","cited_arxiv_id":null,"evidence_quote":"Graph-neural-network joint beamforming for hybrid relay and RIS multiuser systems, the architecture the two-phase design builds on."},{"cited_title":"Hybrid relay and reconfigurable intelligent surface assisted multiuser miso systems,","cited_arxiv_id":null,"evidence_quote":"System and channel model for hybrid relay and RIS assisted multiuser MISO, source of the Rician/Rayleigh channel assumptions and the two-phase transmission model."},{"cited_title":"Deep reinforcement learning-based relay selection in intelligent reflecting surface assisted cooperative networks,","cited_arxiv_id":null,"evidence_quote":"Deep reinforcement learning relay selection in RIS-assisted cooperative networks, the relay-selection performance this work is compared with."},{"cited_title":"Learning to reflect and to beamform for intelligent reflecting surface with implicit channel estimation,","cited_arxiv_id":null,"evidence_quote":"Unsupervised learning to reflect and beamform for an RIS, source of the GNN training paradigm and the implicit-channel-learning approach."},{"cited_title":"Deep learning-based beamforming for intelligent reflecting surface-assisted mmwave systems,","cited_arxiv_id":null,"evidence_quote":"Deep-neural-network beamforming baseline that the proposed GNN must outperform."},{"cited_title":"PySwarms, a research-toolkit for Particle Swarm Optimization in Python,","cited_arxiv_id":null,"evidence_quote":"Particle-swarm optimization baseline implementation used in the comparisons."}],"review_version":1}