{"id":"d576360e-55a2-45fe-add1-57a73cd687ed","arxiv_id":"2502.10149","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"An IRS-MEC vehicular offloading problem is recast as a Stackelberg game and solved with a generative diffusion model, but the diffusion model is never trained and the solution network is left undefined.","lead":"The paper proposes a diffusion-model-based Stackelberg game approach to jointly reduce delay and energy in IRS-assisted vehicular edge computing. It claims large gains over random and PPO baselines, but the method as written lacks a training procedure and an actual denoising network.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The load-bearing gap is that the diffusion model's denoising network is never defined or trained; the forward phase is explicitly omitted, so Algorithm 1 cannot generate informed strategies and the central performance claim is unsupported.","rationale":"The reader's weakest_assumption identifies precisely the load-bearing problem: the denoising network εδ is never defined, trained, or specified, and the forward phase—which is essential for generating training data in DDPM—is explicitly omitted. My review of the full text confirms this gap. Section III.B.3 presents equations (21)–(27) for a forward-reverse process, but then states that the forward phase is not integrated because no optimal x0 is available. This leaves Algorithm 1 dependent on an undefined εδ, so the algorithm cannot be implemented. Moreover, Algorithm 2 does not explain how sampled latent variables map to feasible task offloading, IRS phase shift, and resource allocation decisions, making the search space and constraints ill-defined. These are not cosmetic omissions: they are the core mechanism by which the paper claims to find 'optimal solutions.' Without a well-defined algorithm, the simulation results in Section IV lack a reproducible basis, and the comparison to baselines cannot support the central claim. The reader's verdict of REJECT is consistent with my assessment. I add no additional concern beyond this central gap, and no independent support (e.g., code, formal verification, or parameter-free derivation) appears in the manuscript to mitigate the missing training specification.","tokens_in":9759,"tokens_out":2784,"duration_ms":29389,"concrete_test":"Settle the concern by attempting to instantiate GDMSG from the manuscript alone: specify the εδ architecture, loss function, and training loop using only Section III. If no such specification can be written without adding new content, the algorithm is under-specified. Then run the only testable degenerate variant (εδ ≡ 0) on the Fig. 2 scenario; if its performance matches the reported GDMSG curves, the claimed gains are not attributable to learned diffusion; if it does not match, the missing trained model must be released to replicate. Releasing code and a trained checkpoint, followed by rerunning Fig. 2, would settle the question.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim that GDMSG achieves outstanding performance depends on a working generative diffusion optimizer. The only description of that optimizer is the reverse sampling loop in Algorithm 1, centered on the denoising function εδ(xt, t). No architecture, initialization, loss function, optimizer, dataset, training loop, or hyperparameters for εδ are given. More seriously, Section III.B.3 explicitly states that the forward phase is not integrated 'due to the lack of an optimal decision strategy (i.e., x0 in the forward phase) for the problem.' In standard DDPM, the reverse network is trained using noisy samples generated from real x0 by the forward process. Without x0 and without the forward process, there is no training signal from which εδ could learn. Therefore Algorithm 1 cannot be executed as specified, and the GDMSG curves in Fig. 2 cannot be reproduced from the manuscript. In addition, Algorithm 2 says the leader strategy Fj is obtained 'from x0' and follower strategies θj and Oj are 'obtained based on' Fj, but no mapping from a sampled x0 to feasible (O, θ, F) satisfying constraints (13b)–(13h) is specified, so the optimization space and constraint handling are undefined. Because the simulated algorithm is not a well-defined object, the simulation results cannot support the abstract's 'outstanding performance' claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper considers an IRS-assisted MEC vehicular network in which a base station allocates computation resources and an IRS adjusts phase shifts to support task offloading from vehicles. It formulates a multi-objective MINLP problem (P) that minimizes total delay and total energy under offloading, resource, and phase constraints, then reformulates P as a Stackelberg game with the BS as leader and vehicles as followers, and proposes the GDMSG algorithm that uses a denoising diffusion probabilistic model to generate strategies. The abstract and conclusion claim that GDMSG outperforms four benchmarks in delay, QoE, and BS revenue. In my reading, the system model and problem formulation are coherent, but the diffusion model component is not fully specified: the forward process is intentionally omitted, the noise predictor \\epsilon_\\delta is never defined or trained, and no mapping from the sampled latent variable to feasible decision variables is given. The reported simulations therefore cannot substantiate the central performance claim.","tokens_in":10032,"tokens_out":5668,"duration_ms":56547,"significance":"If the GDMSG were complete and validated, the paper would be a moderate contribution to applying generative models to wireless resource allocation: the Stackelberg reformulation of a mixed-integer resource allocation problem is a reasonable structural idea, and diffusion-based strategy generation is currently of interest. The paper's strengths are its clear system model, explicit benchmark definitions, and the correct identification of the main problem as MINLP/NP-hard. However, as submitted, the central algorithmic object is underspecified and untrained, and no code, proofs, or statistical evidence are provided; the significance for a journal audience is therefore not established.","major_comments":[{"comment":"The reverse sampling loop is centered on the learned noise predictor \\epsilon_\\delta, but the paper provides no architecture, loss function, optimizer, training set, training loop, or hyperparameters for \\epsilon_\\delta. The text explicitly states that the forward phase is not integrated 'due to the lack of an optimal decision strategy (i.e., x0 in the forward phase) for the problem' and only the reverse phase is used. In a standard DDPM, \\epsilon_\\delta is trained using noisy samples obtained from known x0 through the forward process; without x0 and without a forward process there is no training signal. Consequently Algorithm 1 cannot be executed as written, and the GDMSG curves in Fig. 2 are not reproducible from the manuscript.","section":"Section III.B.3, Eqs. (21)-(27), Algorithm 1"},{"comment":"The algorithm assumes that x0 produced by Algorithm 1 translates into a leader strategy F_j and then into follower strategies \\theta_j and O_j, but no decoding or projection from x0 to feasible variables satisfying constraints (13b)-(13h) is defined. Since x0 is not even described as a vector of O, \\theta, or F entries, the optimization space and constraint-handling mechanism are undefined. This makes the claimed optimal strategies returned on Line 19 meaningless as specified.","section":"Algorithm 2, Lines 4-8"},{"comment":"The simulation evidence consists of single curves without error bars, confidence intervals, number of runs, or statistical tests. Moreover, Eq. (20) defines the reward as the improvement in the same total utility U that the paper reports as QoE and revenue; evaluating the method only on the objective it is rewarded to increase is not circular in a formal sense, but it cannot by itself establish optimality or 'outstanding performance' without comparison to known-optimal solutions for small instances, an exhaustive or relaxation bound, or an ablation that isolates the GDM's contribution.","section":"Section IV.B, Fig. 2, Eq. (20)"},{"comment":"The paper states that reformulating P as a Stackelberg game 'simplifies' the problem, but it never states or proves a formal relation between a Stackelberg equilibrium of (18)-(19) and a Pareto-optimal solution of P (13). Without such a relation, optimizing the game utilities may yield results that do not minimize the original total delay and energy objectives, so the GDMSG solution is not grounded in the original problem P.","section":"Section III.A, Eqs. (18)-(19)"}],"minor_comments":[{"comment":"The notation is inconsistent: Eq. (25) calls the predictor \\epsilon_\\delta(x_t) while Eq. (26) and Algorithm 1 use \\epsilon_\\delta(x_t,t); please make the dependence on t consistent.","section":"Section III.B.3, Eqs. (25)-(26)"},{"comment":"In Eq. (16), the offloading utility uses E^{tran}_{i,b}, but Eq. (15) defines the offloading cost with E^o_i, which includes both transmission and BS computation energy; clarify which energy terms are actually paid by the vehicle.","section":"Section II.C and Eq. (16)"},{"comment":"Line 13 says 'Calculate R_j based on a using Eq. (20)', but no variable a is defined in the algorithm; this appears to be a typo for 'based on Eq. (20)'.","section":"Algorithm 2, Line 13"},{"comment":"The simulation setup does not state the diffusion hyperparameters (T, \\beta_min, \\beta_max), the utility weights w_i and w_b, the constant c in Eq. (14), or the number K of IRS elements, although these parameters are free in the model.","section":"Section IV.A"},{"comment":"Fig. 2 reports results over 'Time (s)' from 10 to 50 s, but the system model uses N time slots of duration \\delta t; please specify N and \\delta t and explain why the x-axis starts at 10 s.","section":"Fig. 2"},{"comment":"The paper asserts that problem P is NP-hard but gives no proof or citation for that specific claim; a reference or a short reduction would help.","section":"Section II.D"}],"recommendation":"reject","confidential_remarks":"This is a case where the central algorithm is not executable as specified, so the main experimental claim cannot be checked. Filling in the missing \\epsilon_\\delta network, its training procedure, and a valid decoding from x0 to feasible strategies would constitute essentially a new technical development, not a local revision. I recommend rejection rather than major revision for this reason, while noting that the system model and problem formulation could be reused in a future, more complete submission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this one has a load-bearing hole. The GDMSG algorithm that supposedly produces all the results is not actually specified. The forward diffusion phase is explicitly omitted, and the denoising network εδ gets no architecture, no loss function, no training procedure, and no hyperparameters. Algorithm 1 samples from Gaussian noise and calls the result x0, but there is no mapping from a sampled x0 to feasible (O, θ, F) either. The simulation curves in Fig. 2 cannot be reproduced from the manuscript, and the 'outstanding performance' claim rests on an undefined object.\n\nWhat the paper does well is set up the IRS-assisted MEC system model. The delay, energy, and QoE/revenue functions are clearly written, and the Stackelberg reformulation is a reasonable way to separate BS and vehicle decisions. The benchmark ladder (random, partial-random, PPO-DRL) is sensible for an applied-heuristic paper.\n\nThe soft spots are exactly where the reviewer and stress-test point. Section III.B.3 states the forward phase is not integrated 'due to the lack of an optimal decision strategy (i.e., x0 in the forward phase).' That omission kills the DDPM training signal, because standard DDPM learns εδ from noisy samples of real x0. Without that, εδ is an empty symbol. Algorithm 2 also claims to obtain leader strategy Fj from x0, but no constraint projection or mapping to (O, θ, F) is specified. The reward in Eq. (20) is circular: it rewards improvement in the same total utility the game is optimizing, so the algorithm is validated only on its own objective. Simulations have no error bars, no statistical tests, and no comparison to an optimal solver on a small instance. The NP-hardness claim is fine but no lower-bound comparison is attempted.\n\nWho is this for? The system model could be a useful reference for someone building an IRS-MEC simulation, but the core method is not a method. I would not cite it for the algorithm, and I would not send it to a serious referee in its current form. If the authors actually implement εδ, provide code and data, and compare against known-optimal solutions on small instances, then it becomes a normal heuristic paper worth a look. As it stands, it is a proposal, not a completed result.\n\nMy call: desk reject, or ask for major revision demanding a fully specified and trained diffusion model. The central claim is unsupported.","headline":"The system model is solid but the proposed GDM optimizer is never actually defined, so the simulation results and central claim don't hold up.","tokens_in":10577,"tokens_out":2816,"would_cite":false,"duration_ms":25782,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A diffusion-based Stackelberg game is claimed to jointly optimize offloading, IRS phase shifts, and resource allocation in vehicular edge networks.","keywords":["intelligent reflecting surfaces","mobile edge computing","vehicular networks","generative diffusion model","Stackelberg game","task offloading","resource allocation","NP-hard optimization"],"falsifier":"Run Algorithm 1 on a small instance where the joint problem can be solved exactly by enumeration, using a concrete instantiation of the denoiser $\\epsilon_\\delta$; if the generated strategies are no better than strategies drawn directly from the Gaussian prior, the performance claim is unsupported.","tokens_in":9519,"feed_emoji":"🚗","tokens_out":7105,"duration_ms":62750,"temperature":0.7,"pith_summary":"The paper tackles a multi-objective optimization problem in an IRS-assisted mobile edge computing network for vehicles: minimize total task completion delay and energy consumption by choosing task offloading, IRS phase-shift vector, and computation resource allocation. Because the problem is a mixed-integer nonlinear program and NP-hard, the authors reformulate it as a Stackelberg game, with the base station as leader setting resource allocations and vehicles as followers choosing offloading and phase shifts, and solve both levels with a generative diffusion model. The paper's central claim is that this GDMSG approach achieves outstanding performance in delay, vehicle QoE, and base-station revenue against random, equal-resource, and deep-reinforcement-learning baselines in simulation. A sympathetic reader would take the claim as: a diffusion-sampling heuristic can produce good joint strategies for this NP-hard problem without enumerating the combinatorial offloading decisions.","feed_headline":"Diffusion-game solver cuts delay and lifts revenue in vehicular nets","feed_subtitle":"A Stackelberg game with diffusion-generated strategies sets offloading, phase shifts, and computing resources together.","key_machinery":"The central machinery is a Stackelberg game decomposition paired with a denoising diffusion probabilistic model (DDPM) used as a strategy sampler. The game splits the joint problem into a leader problem (base station revenue maximization over $F$) and follower problems (vehicle utility maximization over $O$ and $\\theta$), with a reward mechanism that reinforces increases in total utility. For each decision level, Algorithm 1 samples a candidate strategy by reverse diffusion: it starts from $x_T \\sim \\mathcal{N}(0,I)$ and iteratively applies the mean function $\\mu_\\delta(x_t,t)$ built from a noise-prediction network $\\epsilon_\\delta$ to produce $x_0$. The paper explicitly omits the forward diffusion phase because no ground-truth optimal strategy $x_0$ is available, so the denoiser's parameters $\\delta$ are never trained by a conventional diffusion objective; the reverse sampler is nonetheless the component that is supposed to 'efficiently derive optimal solutions.'","core_discovery":"The paper claims that jointly optimizing task offloading, IRS phase shifts, and computation resource allocation in a vehicular IRS-assisted MEC network can be handled by recasting the NP-hard MINLP as a Stackelberg game and generating decisions with a diffusion model. In this game, the base station leads by allocating computation resources $F$, and each vehicle follows by choosing its offloading mode $O$ and the IRS phase-shift vector $\\theta$; the diffusion model supplies the strategies by sampling a reverse diffusion process that starts from Gaussian noise and denoises to a candidate strategy. The authors report that the resulting GDMSG algorithm outperforms random offloading/phase-shift/resource allocation, equal resource allocation with GDMSG decisions elsewhere, and a deep reinforcement learning baseline on total task completion delay, vehicle QoE, and base-station revenue, at the cost of somewhat higher energy consumption that they judge acceptable. The paper frames this as a way to 'efficiently derive optimal solutions' despite the problem's combinatorial hardness.","pith_inferences":["The paper's reverse-only sampler leaves the denoiser undefined; a direct test would be to instantiate $\\epsilon_\\delta$ as a small neural net and train it on solutions from a conventional solver, then compare sampling quality against untrained noise.","The same leader-follower diffusion template could be applied to other MEC settings where a central authority prices resources and users respond, such as UAV-assisted or satellite-edge networks, as long as a valid reward signal exists.","Because the forward phase is omitted, the generated $x_0$ is not a denoised version of any real strategy; replacing the sampler with plain random search in the same reward loop would be a minimal control experiment to isolate the diffusion model's contribution."],"forward_implications":["If GDMSG works as claimed, the binary offloading decisions do not need to be enumerated; the diffusion sampler produces complete strategies directly from the reverse process.","The Stackelberg decomposition turns a single multi-objective MINLP into two coupled single-level games, each with a narrower variable set, which is the mechanism by which the paper claims lower solution cost.","The reward mechanism that credits only positive changes in total utility pushes the sampler toward strategies that improve joint performance, which is why the authors expect revenue and QoE gains.","The reported complexity $\\mathcal{O}(J_{\\text{iter}} N V T)$ suggests the approach scales linearly in iterations, time slots, and vehicles, which the authors interpret as good scalability.","The paper accepts higher energy consumption as a trade-off for lower delay and higher QoE and revenue, so a correct GDMSG would need to be evaluated on application-specific cost weights."],"supporting_citations":[{"why":"Supplies the DDPM reverse-sampling equations and the noise-prediction parameterization used in Algorithm 1.","marker":"[15]"},{"why":"Provides the task-completion revenue form $\\log(c+T_{\\max}-T_i)$ used in the vehicle utility function.","marker":"[14]"},{"why":"The DRL resource-scheduling approach the paper compares against and classifies as a benchmark.","marker":"[8]"},{"why":"The bisection-search alternate optimization baseline for joint IRS-MEC design that motivates the need for the diffusion-based method.","marker":"[7]"},{"why":"Grounds IRS beamforming for vehicular communication as the channel-enhancement mechanism the system model builds on.","marker":"[4]"},{"why":"Survey of generative diffusion models that motivates using GDM to model complex distributions in optimization.","marker":"[9]"},{"why":"Rician fading model used for IRS-related channel gains.","marker":"[12]"}],"fun_headline_variants":["Diffusion-model Stackelberg game optimizes IRS-MEC vehicular nets","Diffusion game jointly optimizes offloading, IRS phases, and resources","GDMSG diffusion game cuts delay and boosts QoE in vehicular MEC","Generative diffusion Stackelberg beats DRL baselines for IRS-MEC vehicles"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"For the proposed method to work, the noise-prediction network inside the reverse diffusion sampler must be able to generate near-optimal strategies, yet the paper never defines that network's architecture, loss function, or training procedure, and it explicitly discards the forward phase that would normally train it.","fun_headline_variants_meta":{"raw":{"variants":["Diffusion-model Stackelberg game optimizes IRS-MEC vehicular nets","Diffusion game jointly optimizes offloading, IRS phases, and resources","GDMSG diffusion game cuts delay and boosts QoE in vehicular MEC","Generative diffusion Stackelberg beats DRL baselines for IRS-MEC vehicles"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000321,"raw_usage":{"total_tokens":1793,"prompt_tokens":919,"completion_tokens":874,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":535,"completion_tokens_details":{"reasoning_tokens":790}},"tokens_in":535,"tokens_out":874,"duration_ms":8566,"temperature":1.0,"reasoning_tokens":790,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T19:11:27.142066+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run Algorithm 1 on a small instance where the joint problem can be solved exactly by enumeration, using a concrete instantiation of the denoiser $\\epsilon_\\delta$; if the generated strategies are no better than strategies drawn directly from the Gaussian prior, the performance claim is unsupported.","supporting_citations":[{"cited_title":"Joint task offloading and resource allocation for fog-based intelligent trans- portation systems: A UA V-enabled multi-hop collaboration paradigm,","cited_arxiv_id":null,"evidence_quote":"Provides the task-completion revenue form $\\log(c+T_{\\max}-T_i)$ used in the vehicle utility function."},{"cited_title":"MARS: A drl-based multi-task resource scheduling framework for UA V with irs-assisted mobile edge computing system,","cited_arxiv_id":null,"evidence_quote":"The DRL resource-scheduling approach the paper compares against and classifies as a benchmark."},{"cited_title":"Min- max fairness based joint optimal design for IRS-assisted MEC systems,","cited_arxiv_id":null,"evidence_quote":"The bisection-search alternate optimization baseline for joint IRS-MEC design that motivates the need for the diffusion-based method."},{"cited_title":"Roadside irs-aided vehicular communication: Efficient channel estimation and low-complexity beam- forming design,","cited_arxiv_id":null,"evidence_quote":"Grounds IRS beamforming for vehicular communication as the channel-enhancement mechanism the system model builds on."},{"cited_title":"A survey on generative diffusion models,","cited_arxiv_id":null,"evidence_quote":"Survey of generative diffusion models that motivates using GDM to model complex distributions in optimization."},{"cited_title":"Performance analysis of mixed-adc massive MIMO systems over rician fading channels,","cited_arxiv_id":null,"evidence_quote":"Rician fading model used for IRS-related channel gains."}],"review_version":1}