{"id":"a3ea0b22-83e0-491f-b273-2bd44aee92ea","arxiv_id":"2506.05381","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A graph neural network method (CO-GNN) is proposed to jointly optimize beamforming, power allocation, and IRS phase shifts to maximize the sum secrecy rate of an IRS-assisted NOMA system facing external and internal eavesdroppers.","lead":"This paper trains a graph neural network to set beamforming, power, and reflecting-surface phases in an IRS-assisted NOMA wireless system, aiming to maximize the sum secrecy rate against both outside eavesdroppers and other users in the NOMA pair. The authors claim the network works directly from received signals, skipping explicit channel estimation, and report higher secrecy rates than alternating-optimization baselines in simulations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The CSI-free received-signal-to-parameters mapping in CO-GNN is ill-posed and circular, and training requires CSI while inference claims none; the central performance claim is therefore unsupported.","rationale":"I read the paper in good faith. The intended contribution is a GNN that maps received signals directly to the jointly optimized beamforming, power allocation, and IRS phases, avoiding explicit channel estimation while achieving high sum secrecy rate. For this to work, the mapping g(·) must be well-posed, learnable, and stable under the feedback that received signals depend on the outputs. The paper provides no argument for any of these properties. The weakest assumption identified by the reader—that scalar received signals carry sufficient information to determine the optimal high-dimensional parameters—is indeed the linchpin. I agree with the reader's assessment. My analysis adds two concrete technical details that strengthen the concern: (1) the dimensionality mismatch (4 real inputs vs. hundreds of output real parameters for the simulated K=2, M=5, N=100 configuration) makes identifiability implausible without additional structure, and (2) Algorithm 1 explicitly uses true CSI during training, so the network cannot be said to 'eliminate channel estimation' in the actual learning process; it simply shifts the CSI requirement to the training phase. The circular dependency is not merely a philosophical issue: it means the training distribution of Y is not the same as the deployment distribution when the network's outputs are used to generate Y. The proposed closed-loop test directly probes whether the learned mapping survives this feedback. If it does not, the central claim collapses. I also note the convergence guarantee in Section III.C is not a valid proof, and the R_min constraint is unenforced, but these are secondary to the fundamental ill-posedness. The paper merits rejection because the core contribution is unvalidated; no code, data, or error bars are provided to support the simulation results. However, if the closed-loop test were run and the performance held, a conditional acceptance with strong reproducibility requirements would be appropriate. My verdict stays UNCHANGED relative to the reader's REJECT.","tokens_in":16207,"tokens_out":4664,"duration_ms":48908,"concrete_test":"Run a closed-loop evaluation on the same test channels used in Section IV: start with a random feasible (w0, a0, Φ0), compute the received signal vector Y0 from Eq. (12), feed Y0 to CO-GNN to obtain (w1, a1, Φ1), then recompute Y1 under the new parameters and iterate until the parameter changes are below a threshold. If the fixed-point secrecy rate is substantially lower than the training-time loss computed with true CSI (e.g., the reported 30-40% gain over AO disappears), or if the iteration does not converge, then the CSI-free claim is falsified. If instead the fixed-point rate matches the paper's figures, the circularity concern is resolved for that setting.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III.B.1 asserts that the received signal 'encapsulates ample information pertaining to beamforming, power allocation, and phase shifts' and uses Y_k (Eq. 20) as the sole input to predict (w, a, Φ). However, Y_k in Eq. (12) depends on the current (w, a, Φ), on the random data symbols s_i, and on the channel H. At inference time the network must produce (w, a, Φ) before Y_k can be measured, yet Y_k is the input; no initial configuration, iterative scheme, or fixed-point condition is specified. This makes g(·) ill-posed: the mapping is not a function of the environment alone, and the same channel can produce different Y_k depending on the very parameters the network is supposed to output. Dimensionality reinforces the problem: for K=2, M=5, N=100, the input is four real scalars (two users × real/imag), while the output has hundreds of real parameters, so a deterministic map from Y to optimal parameters is massively underdetermined without additional structure that is never provided. Training sharpens the issue: Algorithm 1 takes the true channel H as input and computes the loss using H_R, H_I (lines 16-17), so CO-GNN is trained with full CSI; the claim that deployment 'eliminates the need for channel estimation' is a train-test distribution mismatch with no supporting generalization argument. Furthermore, Y is not updated when w, a, Φ change inside the training loop, so the training input distribution is inconsistent with the physical closed-loop dependence. The convergence discussion in Section III.C is not a proof: Lipschitz gradient continuity plus Adam does not guarantee convergence to a local minimum of a nonconvex problem. The constraint R_sec ≥ R_min in (19) is absent from the loss (30), so the fairness guarantee is unenforced. Because the central claimed advantage (CSI-free, low-complexity joint optimization) rests entirely on this ill-posed mapping, the simulation results in Section IV cannot be taken as evidence for the claim as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes CO-GNN, a graph neural network that maps received signals directly to BS beamforming, NOMA power allocation, and IRS phase shifts in an IRS-assisted NOMA system with both external and internal eavesdroppers, with the objective of maximizing the sum secrecy rate. The paper claims that this approach eliminates the need for channel estimation, is scalable, and outperforms alternating optimization and several GNN-based ablations, and the claims are supported by simulations for K=2 users, M=5 antennas, and N=10-100 IRS elements. The core contribution is the end-to-end learned mapping g(·) from received-signal features to the optimization variables.","tokens_in":16538,"tokens_out":6613,"duration_ms":62303,"significance":"If the method worked as claimed, a CSI-free, low-complexity GNN for secure IRS-NOMA would be a useful alternative to alternating optimization in dynamic settings. The paper does formulate a relevant problem (joint beamforming, power allocation, and phase-shift optimization with two eavesdropping modes) and includes ablation studies and a complexity comparison, which are positive elements. However, the central claim rests on an input representation that depends on the very outputs the network must produce, and the training procedure uses full CSI while inference is claimed to be CSI-free; the reported secrecy-rate gains are therefore not established. A redefinition of the network input or a rigorous fixed-point formulation, together with a statistical evaluation, would be needed before the significance of the contribution can be assessed.","major_comments":[{"comment":"The central claim of a CSI-free mapping g(·) is not well posed. Y_k in Eq. (12) is a scalar that depends on the current (w,a,Φ), on the random data symbols s_i, and on noise, not only on the channel; at inference time the network must output (w,a,Φ) before Y can be measured, yet Y is the input, and no initial configuration, iterative scheme, or fixed-point condition is specified. For K=2, M=5, N=100, each user node receives two real scalars while the output contains 2M beamforming entries, K power coefficients, and N phase shifts, so the claimed map is massively underdetermined without the structural assumptions that are never stated. This directly undermines the abstract's claim that CO-GNN 'eliminates the need for channel estimation.'","section":"Section III.B.1, Eq. (20)"},{"comment":"The training procedure contradicts the CSI-free claim. The loss is computed as LIN(HR, HI, w, a, Φ) and LEX(HR, HI, w, a, Φ) using true channel matrices HR and HI, so full CSI is available during training, while the text claims that deployment requires no channel estimation; the paper provides no generalization argument that a network trained on H can operate from Y alone. In addition, Y is initialized to 0 and is not updated when w, a, and Φ change during the training loop, so the input distribution at training time is inconsistent with the closed-loop dependence expressed in Eq. (12).","section":"Algorithm 1, lines 15–17"},{"comment":"The convergence guarantee is not a valid proof. The Lipschitz condition in Eq. (31) together with the Adam optimizer does not imply monotonic decrease of the loss or convergence to a local minimum for a non-convex objective, and the [x]+ operator in Eq. (18) is non-differentiable at 0, so the assertion in Eq. (32) that the gradient 'always exists' is false as written. The training section should either provide a rigorous convergence argument or explicitly state that only empirical convergence is observed.","section":"Section III.C, Eqs. (30)–(32)"},{"comment":"The constraint Rsec ≥ Rmin is part of the optimization problem but is absent from the loss function and from Algorithm 1. The text in Section II.B claims that CO-GNN 'dynamically adjusts' resources to meet Rmin, but no penalty term, projection, or constraint handling mechanism is described, so the fairness guarantee is unsupported.","section":"Problem (19) and Eq. (30)"},{"comment":"The performance claims are based on single-trial point estimates with no confidence intervals, error bars, or multiple-seed reporting, so the statements that CO-GNN 'significantly outperforms' and the quantitative improvements of 40% and 30% are not statistically supported. Moreover, there is no comparison against an upper bound or a known near-optimal solution, so the gains could reflect the weakness of the chosen benchmarks rather than the quality of the learned policy.","section":"Section IV.B, Figs. 4–9"}],"minor_comments":[{"comment":"The Rician model uses sqrt(κ/(1+κ)) for both the LOS and NLOS components; the NLOS coefficient should normally be sqrt(1/(1+κ)), otherwise the channel power normalization is inconsistent.","section":"Eq. (2)"},{"comment":"The entry 'Number of message passing la' is truncated and should read 'layers'.","section":"Table II"},{"comment":"Figure 11 is referenced in the text before the figure is introduced; the figure order should be adjusted.","section":"Section IV.C"},{"comment":"The complexity expression O((3×3+L)dMLPTR) uses T_R without defining it, and the notation 'PTR' is unclear; the authors should define all symbols.","section":"Section IV.D"},{"comment":"The conclusion mentions 'hardware impairments' although no hardware impairment model appears in the system model or simulations; either add such a model or remove the mention.","section":"Conclusion"},{"comment":"The first paragraph contains the typo 'IRS-assited-NOMA' and should read 'IRS-assisted-NOMA'.","section":"Section I.A"}],"recommendation":"reject","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about this paper. First, it does something genuinely new in a well-studied area: it proposes a GNN that takes received signals as input and outputs beamforming, power allocation, and IRS phases for an IRS-assisted NOMA system with both external and internal eavesdroppers. That combination is not in the cited literature, and the problem is relevant. Second, the load-bearing claim that this works without channel estimation does not hold up. The received signal in Eq. (12) depends on the very variables the network is supposed to output, so the mapping g(Y) is not a function of the environment alone. The same channel can produce different Y depending on the current configuration, and the authors never specify an initial configuration, an iterative scheme, or a fixed-point condition. At inference, the network would need the parameters before it can measure its input.\n\nThe training side makes this worse. Algorithm 1 takes the true channel H as input and computes the loss from H_R, H_I, so the network is trained with full CSI. The claim that deployment eliminates channel estimation is therefore a train-test mismatch with no generalization argument. Dimensionality reinforces the problem: with K=2, M=5, N=100, the input is four real scalars while the output has hundreds of real parameters, so the mapping is massively underdetermined without additional structure that is never provided.\n\nWhat does the paper do well? The system model is careful, the problem is relevant, and the GNN architecture—two message-passing layers with mean and max pooling—is conventional but reasonable. The complexity analysis is helpful. The simulations show consistent gains over the baselines, but the loss function is exactly the negative secrecy rate, so this is a fitted value, not an independent prediction. The fairness constraint R_sec >= R_min appears in the problem statement but not in the loss, so it is not enforced. The convergence \"guarantee\" in Section III.C is a statement, not a proof: Lipschitz continuity plus Adam does not imply convergence to a local optimum of a non-convex function. No code or data are provided, and the plots have no error bars, so the empirical claims are hard to verify.\n\nOverall, this paper is for a reader interested in ML-based physical-layer security who wants a starting point for applying GNNs to secure IRS-NOMA. They will find a novel architecture and a thorough system model, but the central claim is unsupported. I think it deserves a serious referee—the problem is important and the flaws are identifiable—but I expect rejection unless the authors substantially revise the formulation, e.g., by breaking the circular dependency and specifying the training data distribution.","headline":"Novel GNN for secure IRS-NOMA, but the CSI-free claim is undermined by a circular input-output dependence and a train-test mismatch.","tokens_in":17163,"tokens_out":4228,"would_cite":false,"duration_ms":41604,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A graph neural network can jointly set beamforming, power, and IRS phase shifts from received signals alone, beating alternating optimization in secure IRS-NOMA.","keywords":["intelligent reflecting surface","non-orthogonal multiple access","physical layer security","secrecy rate","graph neural networks","beamforming optimization","power allocation"],"falsifier":"Train CO-GNN on channels drawn from one distribution, such as user coordinates inside the training box with a Rician factor of 10 dB, and evaluate it on channels from a clearly different distribution, such as users outside that box or a Rician factor of 5 dB, comparing against the alternating-optimization baseline; if the secrecy-rate advantage shrinks or reverses, the learned received-signal-to-parameter map does not generalize and the CSI-free claim fails.","tokens_in":16000,"feed_emoji":"🔐","tokens_out":8918,"duration_ms":75848,"temperature":0.7,"pith_summary":"This paper claims that a graph neural network, called CO-GNN, can jointly choose the base-station beamforming, NOMA power split, and IRS phase shifts in an IRS-assisted NOMA system by reading the received signals directly, with no channel estimation. The setting includes two kinds of attackers: external eavesdroppers outside the NOMA pairing and internal ones that are legitimate users overhearing other users' signals. Training the network with the negative sum secrecy rate as the loss is claimed to maximize secrecy performance, and simulations are said to show CO-GNN reaching the highest secrecy rate among the compared schemes, roughly 40% above the alternating-optimization baseline for external eavesdropping and 30% for internal eavesdropping. If true, the result would offer a lower-complexity, CSI-free way to secure IRS-NOMA links in dynamic networks.","feed_headline":"Graph neural net beats alternating optimization on secure IRS-NOMA","feed_subtitle":"A CSI-free graph network jointly sets beamforming, power, and IRS phases, lifting secrecy rates 30–40 percent.","key_machinery":"The load-bearing mechanism is the CO-GNN graph representation and its end-to-end training loss. The IRS is node 0 and the $K$ users are nodes $1,\\dots,K$; user-node features are the real and imaginary parts of the received signal $Y_k$, and the IRS node feature is their mean. Two message-passing layers update user nodes by mean-pooling neighbor messages and the IRS node by max-pooling across users, so that the IRS representation emphasizes the user most exposed to eavesdropping. A fully connected output layer maps the final representations to $\\boldsymbol{\\Phi}\\in\\mathbb{C}^N$ with unit-modulus entries, $\\mathbf{w}\\in\\mathbb{C}^{M\\times K}$ normalized to satisfy the power constraint, and $\\mathbf{a}\\in\\mathbb{R}^K$ on the probability simplex. Training with $L=-\\sum_k R_k^{\\mathrm{sec}}$ as loss is what the paper argues lets the network jointly suppress both external and internal eavesdroppers without explicit channel estimation.","core_discovery":"The paper's central claim is that the non-convex joint optimization of beamforming vectors $\\mathbf{w}$, NOMA power allocation $\\mathbf{a}$, and IRS phase shifts $\\boldsymbol{\\Phi}$ for maximizing the sum secrecy rate can be replaced by a learned map $g(\\cdot)$ from received signals $\\mathbf{Y}$ to those parameters. CO-GNN represents the IRS as node 0 and the $K$ users as nodes $1,\\ldots,K$, passes the received-signal features through two message-passing layers with mean-pooling for user nodes and max-pooling for the IRS node, and outputs unit-modulus phase shifts, a normalized beamforming matrix, and power factors summing to one. The loss is the negative sum secrecy rate $-\\sum_k R_k^{\\mathrm{sec}}$, where $R_k^{\\mathrm{sec}}=[R_k-R_{\\phi\\to k}]^+$ with the eavesdropper rate taken from either an external or an internal node. Under this training, simulations show the sum secrecy rate increasing with transmit power, number of IRS elements, and number of antennas, with CO-GNN outperforming all benchmarks, including alternating optimization.","pith_inferences":["A natural stress test the paper does not run is to train on one channel distribution and test on another, such as different user locations or a different Rician K-factor; the claim that the received signal encapsulates enough information would be falsified if the secrecy-rate gain over alternating optimization disappears out of distribution.","Because training still uses simulated channel realizations to compute the loss, the no-channel-estimation property holds only at inference; the cost of obtaining realistic training data is left unquantified.","The max-pooling aggregation at the IRS node encodes the assumption that the most exposed user dominates the eavesdropping risk; with colluding or multiple eavesdroppers this design choice may need to be revisited."],"forward_implications":["If CO-GNN works as claimed, secure IRS-NOMA operation no longer requires explicit channel estimation at deployment time, because the received signal itself is the network input.","The paper's curves imply that adding IRS elements, transmit antennas, or transmit power all improve the secrecy rate under both external and internal eavesdropping, with CO-GNN consistently above the compared schemes.","CO-GNN's online complexity of $O((3\\times 3+L)d_{\\mathrm{MLP}}T_R)$ is much lower than the AO baseline's $O(I_\\lambda I_w K M^3+K^2N^2+P_o t)$, so the method is positioned for real-time resource allocation.","The permutation invariance and equivariance properties of the graph construction allow the same trained network to handle different numbers of users, easing scaling to larger NOMA groups."],"supporting_citations":[{"why":"Supplies the IRS-NOMA performance analysis and phase-shift modelling that motivates the system model.","marker":"[1]"},{"why":"Earlier IRS-aided NOMA security work with both internal and external eavesdroppers that this paper extends by jointly optimizing all three resource types.","marker":"[22]"},{"why":"Provides the message-passing aggregation and combination formalism that the CO-GNN layers implement.","marker":"[25]"},{"why":"Deep learning framework used to implement and train the CO-GNN network.","marker":"[26]"},{"why":"Adaptive optimizer whose convergence properties the training section relies on.","marker":"[27]"},{"why":"Baseline alternating-optimization pipeline whose three-stage structure CO-GNN is compared against.","marker":"[28]"},{"why":"WMMSE algorithm used as the beamforming step inside the AO baseline.","marker":"[29]"},{"why":"Riemannian conjugate gradient algorithm used as the phase-optimization step inside the AO baseline.","marker":"[30]"}],"fun_headline_variants":["CO-GNN: CSI-free graph network secures IRS-NOMA","One graph net replaces optimization for secure IRS-NOMA","No channel estimation: CO-GNN lifts secrecy rates in IRS-NOMA","CO-GNN jointly sets beamforming, power, and IRS phases for security"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper assumes that a user's received signal $y_k$, which is produced by the very beamforming, power allocation, and phase shifts the network must output, carries enough information for the network to recover the optimal $(\\mathbf{w},\\mathbf{a},\\boldsymbol{\\Phi})$ without channel estimation, and that this fixed-point-like mapping is learnable and stable.","fun_headline_variants_meta":{"raw":{"variants":["CO-GNN: CSI-free graph network secures IRS-NOMA","One graph net replaces optimization for secure IRS-NOMA","No channel estimation: CO-GNN lifts secrecy rates in IRS-NOMA","CO-GNN jointly sets beamforming, power, and IRS phases for security"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000308,"raw_usage":{"total_tokens":1790,"prompt_tokens":1002,"completion_tokens":788,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":618,"completion_tokens_details":{"reasoning_tokens":713}},"tokens_in":618,"tokens_out":788,"duration_ms":6730,"temperature":1.0,"reasoning_tokens":713,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:24:15.997200+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train CO-GNN on channels drawn from one distribution, such as user coordinates inside the training box with a Rician factor of 10 dB, and evaluate it on channels from a clearly different distribution, such as users outside that box or a Rician factor of 5 dB, comparing against the alternating-optimization baseline; if the secrecy-rate advantage shrinks or reverses, the learned received-signal-to-parameter map does not generalize and the CSI-free claim fails.","supporting_citations":[{"cited_title":"On the performance of multi-antenna irs-assisted noma networks with continuous and discrete irs phase shifting,","cited_arxiv_id":null,"evidence_quote":"Supplies the IRS-NOMA performance analysis and phase-shift modelling that motivates the system model."},{"cited_title":"Irs-aided secure noma networks against internal and external eavesdropping,","cited_arxiv_id":null,"evidence_quote":"Earlier IRS-aided NOMA security work with both internal and external eavesdroppers that this paper extends by jointly optimizing all three resource types."},{"cited_title":"How powerful are graph neural networks?","cited_arxiv_id":null,"evidence_quote":"Provides the message-passing aggregation and combination formalism that the CO-GNN layers implement."},{"cited_title":"Tensorflow: Large-scale machine learning on heterogeneous distributed systems,","cited_arxiv_id":null,"evidence_quote":"Deep learning framework used to implement and train the CO-GNN network."},{"cited_title":"Adam: A method for stochastic optimization,","cited_arxiv_id":null,"evidence_quote":"Adaptive optimizer whose convergence properties the training section relies on."},{"cited_title":"Weighted sum- rate maximization for reconfigurable intelligent surface aided wireless networks,","cited_arxiv_id":null,"evidence_quote":"Baseline alternating-optimization pipeline whose three-stage structure CO-GNN is compared against."},{"cited_title":"An iteratively weighted mmse approach to distributed sum-utility maximization for a mimo interfering broadcast channel,","cited_arxiv_id":null,"evidence_quote":"WMMSE algorithm used as the beamforming step inside the AO baseline."},{"cited_title":"Manopt, a matlab toolbox for optimization on manifolds,","cited_arxiv_id":null,"evidence_quote":"Riemannian conjugate gradient algorithm used as the phase-optimization step inside the AO baseline."}],"review_version":1}