{"id":"0f037d95-fc2e-44da-8449-442e4f42151f","arxiv_id":"2504.21409","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A three-tier DNN partitioning and MIMO beamforming optimization for ISCC networks is presented, with an invalid majorization-minimization bound in the beamforming update.","lead":"This paper proposes a three-tier cloud-edge-device setup where ISAC devices, edge servers, and a cloud server split a pre-trained neural network to speed up sensing inference. The authors design an optimization algorithm for DNN partitioning, beamforming, and computing resources, but a key mathematical step in the beamforming solver appears invalid.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The MM lower bound in Eq. (34) is directionally wrong: Cauchy–Schwarz shows the claimed surrogate is an upper bound rather than a lower bound, so Algorithm 1's convergence and the BnB-matching optimality claim rest on an invalid inequality.","rationale":"The reader’s weakest-assumption analysis identifies exactly the load-bearing flaw: Eq. (34) is presented as a Jensen lower bound but is in fact an upper bound by Cauchy–Schwarz, with equality only at the current point. The paper provides no machine-checked proof or reproducible code, and the simulations in Fig. 4 and Fig. 9 do not by themselves validate a surrogate that can lie above the true objective. The resource-allocation and OPP pieces are reasonable, and the three-tier DNN partitioning concept may have practical value, but the convergence and near-optimality claims of the joint algorithm collapse unless the MM surrogate is corrected. I therefore agree with the reader’s REJECT verdict and recommend no change.","tokens_in":20219,"tokens_out":9435,"duration_ms":104757,"concrete_test":"Evaluate Eq. (34) at the explicit counterexample: K=2, o_1=o_2=1, R_1^{it}=R_2^{it}=1, R=(1, 1.5). If LHS = 0.6 < RHS = 0.625, the surrogate is not a lower bound. Then replace the surrogate with a correct minorizer, re-derive the inner beamforming update, and rerun the Fig. 4(a) convergence trace and the Fig. 9 BnB comparison. If the corrected algorithm no longer decreases latency monotonically or no longer matches BnB, the central optimality claim fails; if it still does, the paper’s conclusion can be restored with a revised derivation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (34) is the keystone of the inner beamforming update, and it is not a valid minorizer. Writing x_k = o_k(l_1)/R_k and S = Σ x_k, the claimed bound reads 1/S ≥ (Σ (x_k^{it})^2/x_k)/(S^{it})^2. Cauchy–Schwarz gives (Σ x_k^{it})^2 ≤ (Σ x_k)(Σ (x_k^{it})^2/x_k), i.e. the right-hand side is generally ≥ 1/S, with equality only when x = x^{it}. A concrete failure: K=2, o_1=o_2=1, R_1^{it}=R_2^{it}=1, and R=(1, 1.5) gives LHS = 1/(1+2/3) = 0.6 and RHS = (1+1.5)/4 = 0.625, so Eq. (34) is false as a lower bound. Because Algorithm 1 maximizes this surrogate at each MM iteration, the monotone-convergence argument for the beamforming update is unsupported; the claimed near-optimality in Fig. 9 is therefore not established even though the KKT resource-allocation closed forms and the OPP update are individually sound. A valid minorizer would contain negative 1/R_k terms (e.g., the tangent 1/S ≥ 2/S^{it} − (1/(S^{it})^2)Σ o_k/R_k), so the subsequent WMMSE/OPP derivation would need to be reworked. Until Eq. (34) is replaced or independently justified, the central claim cannot be accepted.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a three-tier cloud-edge-device collaborative inference framework for integrated sensing, communication, and computing (ISCC) networks. Each ISAC device runs part of a pre-trained DNN locally and offloads intermediate features to a MEC server and cloud server, while the same transmitted signal is used for sensing. The authors formulate a mixed-integer nonlinear program that jointly optimizes DNN partition points, ISAC beamforming matrices, and computational resource allocation, subject to a sensing beampattern covariance constraint. The proposed solution is a two-layer algorithm: an inner layer with closed-form CPU allocation and an MM-WMMSE-OPP-based beamforming update, and an outer layer using a cross-entropy (CE) method to search over partition choices. Simulations compare the proposed scheme with two-tier baselines and with a branch-and-bound (BnB) benchmark.","tokens_in":20596,"tokens_out":11257,"duration_ms":108128,"significance":"The paper addresses a timely and relevant problem in the ISCC literature, and the high-level problem decomposition into an inner continuous optimization and an outer discrete search is sensible. The closed-form resource allocation solutions in Eqs. (28) and (31) are correct, and the CE-based outer loop is a standard and reproducible approach. However, the central beamforming algorithm rests on the MM surrogate in Eq. (34), which is not a valid minorizer of the reciprocal-latency objective. Since the convergence of Algorithm 1 and the near-optimality comparison in Fig. 9 both depend on this inequality, the main contribution of the paper is not supported by the provided derivation. The paper cannot be accepted while this load-bearing error remains.","major_comments":[{"comment":"The claimed lower-bound surrogate in Eq. (34) is mathematically false. Setting x_k = o_k(l_1)/R_k and x_k^{it} = o_k(l_1)/R_k^{it}, the inequality reads 1/(sum x_k) >= (sum (x_k^{it})^2 / x_k) / (sum x_k^{it})^2. Cauchy-Schwarz gives (sum x_k^{it})^2 <= (sum x_k)(sum (x_k^{it})^2 / x_k), which implies the opposite inequality, i.e., the right-hand side is generally an upper bound, not a lower bound, with equality only at x = x^{it}. A concrete counterexample is K=2, o_1=o_2=1, R_1^{it}=R_2^{it}=1, R_1=1, R_2=1.5, for which the left-hand side is 0.6 and the right-hand side is 0.625. Therefore the MM update in Algorithm 1 is not a valid minorization step, and the monotone-convergence argument for the beamforming update is unsupported.","section":"III-B-3, Eq. (34)"},{"comment":"Because the surrogate in Eq. (34) is not a lower bound, the convergence of Algorithm 1 is not established, and the claimed near-optimality of the beamforming update is unproven. The comparison against the BnB baseline in Fig. 9 evaluates both algorithms with the same inner-layer solver, so the observed match only shows that the CE search and BnB agree on the same (possibly suboptimal) inner-layer solutions; it does not validate the optimality of the beamforming update itself. The paper's central claim that the proposed algorithm substantially reduces inference latency therefore rests on an invalid algorithmic step.","section":"III-B-4 and IV-D, Fig. 9"},{"comment":"In the MSE expression (36) and the MMSE receiver (38), the interference covariance is written as sum_i U_k H_i \\hat{R}_k^{pre} H_i^H U_k^H and sum_i H_i \\hat{R}_k^{pre} H_i^H, respectively, but the covariance of the i-th user is \\hat{R}_i^{pre}, not \\hat{R}_k^{pre}. As written, the formulas are dimensionally inconsistent (\\hat{R}_k^{pre} is used for every i) and the receiver is not the correct MMSE receiver. If this is a typesetting error, it must be corrected, because the subsequent WMMSE-OPP derivation relies on these expressions.","section":"III-B-3, Eqs. (36) and (38)"}],"minor_comments":[{"comment":"The algorithm states that feasible samples satisfying constraints (21a)-(21b) are generated from the Bernoulli distribution in (50), but no rejection or conditioning mechanism is described. Since independent Bernoulli draws can yield sum_{l} beta_{kl} = 0 or >2 for some device, the sampling procedure is not fully specified.","section":"III-C, Algorithm 2"},{"comment":"The complexity expression O(it_I it_O V (N_t^3 + M^2 N_t + N_t^2 M)) does not explicitly account for the inner BCD loop in Algorithm 1, which itself requires multiple iterations to converge. The stated complexity should include the number of BCD iterations or clarify that it is absorbed into it_I.","section":"III-D, complexity analysis"},{"comment":"The sentence 'the proposed scheme ... acting as lower bound for ED-DP and CED-WDP' is ungrammatical and should be rewritten to state that the proposed scheme achieves lower latency than both baselines for the displayed range of F_M.","section":"IV-C, Fig. 5"}],"recommendation":"reject","confidential_remarks":"The invalidity of Eq. (34) is a direct mathematical error that undermines the main algorithmic claim. Even if the typos and sampling details were corrected, the core beamforming derivation would need to be reworked, likely changing the algorithm and the reported results. This goes beyond a minor revision, and the manuscript in its current form does not provide a sound basis for the proposed approach."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The three-tier DNN partitioning idea is worth a look, but the paper's central MM inequality is backwards, so the convergence and optimality claims don't hold as written. If you're skimming for novelty: this is the first ISCC formulation I know that splits a pre-trained DNN across device, MEC, and cloud, with MIMO ISAC beamforming and beampattern constraints. That is a real addition over the two-tier schemes in [29]–[32], and the latency model is carefully built. The closed-form resource allocations in (28) and (31) are standard KKT results and they're correct. The OPP step that gives the beamforming update (46) is also standard and cleanly derived.\n\nThe soft spot is Eq. (34), and it's load-bearing. The paper claims a Jensen lower bound: 1/(Σ o_k/R_k) ≥ (Σ o_k R_k/(R_k^it)^2)/(Σ o_k/R_k^it)^2. That's not a lower bound. Let x_k = o_k/R_k and x_k^it = o_k/R_k^it. Then the RHS equals (Σ (x_k^it)^2/x_k)/(Σ x_k^it)^2. Cauchy-Schwarz gives (Σ x_k^it)^2 ≤ (Σ x_k)(Σ (x_k^it)^2/x_k), which is exactly the reverse inequality. A concrete failure: K=2, o_1=o_2=1, R^it=(1,1), R=(1,1.5). LHS = 1/(1+2/3)=0.6, RHS = (1+1.5)/4=0.625. So the surrogate is an upper bound, not a lower bound. That breaks the monotone-convergence argument for Algorithm 1 and makes the beamforming update's objective a possibly increasing function of the true objective. Since this inner update is the core of the paper, the claims that the proposed algorithm matches BnB in Fig. 9 and outperforms two-tier benchmarks are not established. A valid minorizer would need negative 1/R_k terms, so the WMMSE/OPP chain would need rework.\n\nMinor point: the simulations are averaged over 200 trials, but no error bars or confidence intervals are shown, and the claimed \"identical\" performance to BnB is suspicious given the CE sampler is stochastic. The beampattern matching itself is fine because the equality constraint (21f) is imposed exactly.\n\nOverall: the paper is coherent and the system model is genuinely new, but the keystone inequality fails. It deserves a serious referee because the fix might be possible and the problem statement is useful. I'd send it to review with a request that the authors replace or correct the MM minorizer and re-run the experiments.","headline":"A useful three-tier ISCC/DNN-partitioning setup, undercut by a reversed MM inequality that leaves the convergence and near-optimality claims unsupported.","tokens_in":21164,"tokens_out":2733,"would_cite":false,"duration_ms":27731,"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":"Splitting a sensing DNN across device, edge, and cloud and jointly optimizing beamforming and computing resources minimizes inference latency and outperforms two-tier offloading.","keywords":["integrated sensing and communication","mobile edge computing","DNN partitioning","beamforming design","cross-entropy optimization","inference latency","three-tier collaborative inference","MIMO"],"falsifier":"Take $o_1=o_2=1$, $R_1^{it}=R_2^{it}=1$, $R_1=2$, and $R_2=1$; the claimed bound in (34) would require $2/3 \\ge 3/4$, which is false, so computing either side of (34) for such a configuration settles whether the MM surrogate is a true lower bound and whether the convergence argument can hold.","tokens_in":20033,"feed_emoji":"📡","tokens_out":8691,"duration_ms":86115,"temperature":0.7,"pith_summary":"This paper tries to show that a three-tier cloud–edge–device network can run a pre-trained deep neural network for radar sensing faster than any two-tier offloading scheme by splitting the DNN at two carefully chosen layers and transmitting only intermediate features over the air. It argues that jointly choosing the two partition points, the ISAC beamforming matrices, and the CPU cycles allocated at each device and the MEC server can minimize total sensing-task inference latency under a sensing beampattern constraint. The proposed two-layer algorithm—closed-form resource allocation in the inner layer and a cross-entropy search over partitioning strategies in the outer layer—is reported to match the branch-and-bound optimum while keeping runtime nearly flat as the number of devices grows, and to outperform two-tier baselines across MEC capacity, device capacity, bandwidth, and backhaul settings. If correct, this gives a practical way to push DNN-based sensing tasks into edge networks without sacrificing sensing quality.","feed_headline":"Three-tier DNN split cuts edge sensing latency","feed_subtitle":"Joint design of DNN split, beamforming, and compute beats two-tier offloading.","key_machinery":"The load-bearing object is the two-point DNN partition encoded by binary variables $\\beta_{kl}$: each device's DNN has one or two layers at which execution hands off to the next tier, and the FLOP counts $S_k^L$, $S_k^M$, $S_k^C$ and feature sizes $o_k(l_1)$, $o_k(l_2)$ are derived from that partition. The inner-layer beamforming solution is carried by the MM lower-bound surrogate in (34), by the WMMSE equivalence that turns weighted sum-rate maximization into weighted sum-MSE minimization, and by the orthogonal Procrustes transformation (Lemma 1) that gives a closed-form SVD-based update $\\hat{W}_k^{c*}=A(1:d)B^H$ under the covariance constraint $W_k W_k^H=\\hat{R}_k^{\\mathrm{pre}}$. The outer layer is carried by a Bernoulli-parameterized cross-entropy search that samples partitioning strategies, keeps elite samples, and updates the probability vector $\\omega$ via $\\omega^{(it+1)}=\\rho \\upsilon^{(it)}+(1-\\rho)\\omega^{(it)}$.","core_discovery":"The paper's central claim is that the inference latency of a sensing task executed by a pre-trained DNN can be minimized by allowing the DNN to be split at up to two layers across three computational tiers: the ISAC device runs early layers, the MEC server runs middle layers, and the cloud runs the remainder. Because only the output of the first partition layer ($o_k(l_1)$) is transmitted over the ISAC link and only the output of the second ($o_k(l_2)$) crosses the backhaul, offloading intermediate features rather than raw spectrograms cuts fronthaul load. The authors formulate this as a mixed-integer nonlinear program over binary partition decisions, beamforming matrices, and CPU frequencies, and solve it by decoupling into an inner continuous problem—KKT closed forms for resource allocation and an MM–WMMSE iteration with an orthogonal Procrustes step for beamforming—and an outer discrete search driven by cross-entropy. They report that the resulting scheme achieves lower average inference latency than two-tier partitioning and than non-partitioned three-tier offloading, tracks the branch-and-bound optimal DNN partitioning, and exposes a trade-off between sensing beampattern mainlobe width and latency.","pith_inferences":["Editorial extension: The same two-layer decomposition—closed-form continuous allocation under a discrete handoff-point search—applies to other split-inference settings, such as multiple DNN stages or hierarchical federated learning, wherever the cost separates additively across tiers.","Editorial extension: Because the model already lets each device have its own number of layers, layer FLOPs, and feature sizes, a mixed-device network with different DNN architectures is directly within the formulation, though the simulations use a shared AlexNet.","Editorial extension: Relaxing the equality sensing-covariance constraint to a bounded mismatch would enlarge the beamforming feasible region; the expected effect is lower latency for the same sensing quality, at the cost of a more complex constraint set."],"forward_implications":["If the central claim holds, ISAC devices can offload intermediate DNN features instead of raw sensing data, reducing fronthaul load while still completing the sensing task.","Jointly optimizing partition points, beamforming, and compute allocation yields lower inference latency than either two-tier DNN partitioning or non-partitioned three-tier offloading across the simulated ranges of MEC capacity, device capacity, bandwidth, and backhaul rate.","The cross-entropy outer loop reaches the same DNN partitioning as branch-and-bound in the tested cases while its runtime grows far more slowly with the number of devices, making near-optimal partitioning feasible for larger networks.","There is an explicit trade-off: widening the sensing beampattern mainlobe lowers latency by improving offloading rates, while narrowing it improves sensing gain at the cost of higher latency.","The closed-form resource allocation formulas and the SVD-based beamforming update give a low-complexity inner loop that can be embedded in each evaluation of a partitioning candidate."],"supporting_citations":[{"why":"Introduces DNN partitioning as a way to offload intermediate features rather than raw inputs, motivating the three-tier split.","marker":"[25]"},{"why":"Supplies the layer-wise FLOP formulas used to compute local, edge, and cloud workloads in (9).","marker":"[27]"},{"why":"Defines the least-squares procedure that produces the desired sensing covariance $\\hat{R}_k^{\\mathrm{pre}}$ enforced in (21f).","marker":"[34]"},{"why":"Provides the majorization–minimization framework and Jensen-inequality surrogate used in the inner beamforming update.","marker":"[36]"},{"why":"Gives the WMMSE equivalence that converts weighted sum-rate maximization into weighted sum-MSE minimization in (37).","marker":"[37]"},{"why":"Supplies the SVD closed form for the orthogonal Procrustes problem that yields the beamforming update (46)–(47).","marker":"[38]"},{"why":"Introduces the cross-entropy-based offloading learning algorithm adapted for the outer-layer partitioning search.","marker":"[39]"},{"why":"Defines the three-tier ISCC architecture and provides the non-partitioned three-tier benchmark (CED-WDP).","marker":"[17]"},{"why":"Provides the two-tier adaptive DNN splitting benchmark (ED-DP) used in the latency comparisons.","marker":"[32]"}],"fun_headline_variants":["3-tier DNN split trims edge sensing latency","Joint DNN split and beamforming minimize latency","Three-tier DNN beats two-tier offloading latency","Split DNN across 3 tiers to cut inference delay","3-tier DNN split beats two-tier latency"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire beamforming optimization rests on the inequality in Equation (34) being a valid lower bound on $1/\\sum_k o_k/R_k$, so if that inequality fails the inner-loop convergence and near-optimality results do not follow.","fun_headline_variants_meta":{"raw":{"variants":["3-tier DNN split trims edge sensing latency","Joint DNN split and beamforming minimize latency","Three-tier DNN beats two-tier offloading latency","Split DNN across 3 tiers to cut inference delay","3-tier DNN split beats two-tier latency"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001054,"raw_usage":{"total_tokens":4497,"prompt_tokens":1087,"completion_tokens":3410,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":703,"completion_tokens_details":{"reasoning_tokens":3335}},"tokens_in":703,"tokens_out":3410,"duration_ms":28294,"temperature":1.0,"reasoning_tokens":3335,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:05:18.394889+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take $o_1=o_2=1$, $R_1^{it}=R_2^{it}=1$, $R_1=2$, and $R_2=1$; the claimed bound in (34) would require $2/3 \\ge 3/4$, which is false, so computing either side of (34) for such a configuration settles whether the MM surrogate is a true lower bound and whether the convergence argument can hold.","supporting_citations":[{"cited_title":"Neurosurgeon: Collaborative intelligence betwe en the cloud and mobile edge,","cited_arxiv_id":null,"evidence_quote":"Introduces DNN partitioning as a way to offload intermediate features rather than raw inputs, motivating the three-tier split."},{"cited_title":"Wireless channel adaptive D NN split inference for resource-constrained edge devices,","cited_arxiv_id":null,"evidence_quote":"Supplies the layer-wise FLOP formulas used to compute local, edge, and cloud workloads in (9)."},{"cited_title":"An iterativ ely weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,","cited_arxiv_id":null,"evidence_quote":"Gives the WMMSE equivalence that converts weighted sum-rate maximization into weighted sum-MSE minimization in (37)."},{"cited_title":"A novel cross entropy approach for offloading learning in mobile edge comp uting,","cited_arxiv_id":null,"evidence_quote":"Introduces the cross-entropy-based offloading learning algorithm adapted for the outer-layer partitioning search."},{"cited_title":"Integrated sensing, comm unication, and computation with adaptive DNN splitting in multi-UA V ne tworks,","cited_arxiv_id":null,"evidence_quote":"Provides the two-tier adaptive DNN splitting benchmark (ED-DP) used in the latency comparisons."}],"review_version":1}