{"id":"8787c6d4-0c45-46c6-a90f-eacd25f0314f","arxiv_id":"2608.12849","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A joint optimization of agent positions, fluid antenna ports, and transmit powers raises energy efficiency in multi-cell interference channels with mobile embodied AI agents.","lead":"This paper designs an algorithm that jointly chooses where mobile AI agents stand, which fluid antenna port each base station uses, and how much power each transmits, to maximize energy efficiency in an interfering wireless network. It reports simulations showing gains over simpler baselines.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (8) minimizes to τ0 times Euclidean distance, but Eqs. (9), (10), and (14) use τ0 times squared distance; the EE objective and all simulation numbers are built on this misspecified movement-energy model.","rationale":"The power-control derivation in Section III-A is correct: for fixed X and E, the QoS constraints yield p ≥ Fp + u; with ρ(F) < 1, the componentwise-minimum feasible vector p* = (I - F)^{-1} u maximizes the EE because each term p_k L_k / R_k is increasing in p_k. Lemma 1's Sherman-Morrison update is algebraically sound. The load-bearing problem is in the movement-energy model. Eq. (8) derives the optimal speed v* for a fixed distance and correctly obtains min_v C(v) = τ0, so the bound should be E_k^move ≥ τ0 d. Writing ≥ τ0 d^2 is dimensionally inconsistent and propagates into (9), (10), and (14). Because the simulations use the squared form, the EE numbers, the optimal positions, and the feasibility comparisons in Fig. 2 are not for the model described by Eq. (8). This is testable by re-deriving the minimization and rerunning with linear distance. The framework is robust enough that a fix is plausible, hence CONDITIONAL rather than REJECT.","tokens_in":9713,"tokens_out":16853,"duration_ms":170842,"concrete_test":"Independently minimize (τ_r + τ_a v^2 + τ_c/v) d over v for fixed d; the minimum is τ0 d, not τ0 d^2. Then rerun the Section IV simulations with the corrected linear denominator τ0 ||a_k - a0_k|| in Eqs. (9), (10), and (14), keeping all other parameters and seeds identical, and compare EE curves and feasibility thresholds in Fig. 2. If the curves or the -60 dBm feasibility point shift materially, the validation is tied to the misspecified squared-distance energy model. If the authors intended squared-distance energy, Eq. (8) and the minimization over v should be rewritten with an energy model that is quadratic in distance.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Equations (8)-(10) contain an internal inconsistency in the movement-energy model. In Eq. (8), E_k^move = (τ_r + τ_a v^2 + τ_c/v) d_k(a_k, a0_k), with d_k the Euclidean distance. Minimizing the factor C(v) = τ_r + τ_a v^2 + τ_c/v over v yields min_v C(v) = τ_r + 3/2^{2/3} (τ_a τ_c^2)^{1/3} = τ0, so the bound should be E_k^move ≥ τ0 ||a_k - a0_k||, linear in distance. The paper instead writes ≥ τ0 ||a_k - a0_k||^2 and uses the squared distance in the denominators of Eq. (9), problem (10), and the reformulation (14). Since the central EE objective determines the optimal movement/port/power trade-off, all reported EE values and the claimed gains over benchmarks are computed for an objective different from the stated physics and from the cited vehicle-energy model [18]. This is not merely an external modeling assumption; it is an internal mismatch between the stated minimization in Eq. (8) and the objective subsequently optimized.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a downlink interference channel with K base station (BS)-agent pairs, where each BS is equipped with a fluid antenna system (FAS) and each embodied AI agent can move within a region using a channel-to-interference-plus-noise map. The authors formulate a sum energy-efficiency (EE) maximization problem jointly over agent positions, FAS port selections, and transmit powers. For fixed positions and ports they derive the optimal power vector in closed form as p* = (I-F)^{-1}u, based on the fact that the objective is strictly decreasing in each power component. They then propose an iterative algorithm with exhaustive or alternating FAS-port optimization, sequential agent-position optimization, and a Sherman-Morrison based low-complexity power update. Monte Carlo simulations compare the proposed scheme with fixed-position, random-position, and random-power benchmarks, reporting higher EE and an extended feasible noise range.","tokens_in":9996,"tokens_out":9446,"duration_ms":102597,"significance":"The closed-form power-control result for fixed positions and ports is correct and is the strongest technical contribution: the objective is componentwise decreasing in transmit powers, and p* is the minimum feasible power vector satisfying the QoS constraints. Lemma 1's Sherman-Morrison update is also correctly derived and provides a genuine complexity reduction for the position-search step. The overall framework, combining FAS port selection and agent mobility in an interference channel, is timely and relevant. However, the quantitative claims rest on a movement-energy model that is internally inconsistent (the stated minimization gives a bound linear in distance, while the optimization uses squared distance), and the simulation section omits key parameters needed to reproduce the results. These issues affect the central EE numbers and the claimed gains over benchmarks, so the results in their current form are not reliable.","major_comments":[{"comment":"The movement-energy model is internally inconsistent. Minimiizing C(v)=τ_r+τ_a v²+τ_c/v over v gives min_v C(v)=τ_0, so the correct lower bound is E_k^move ≥ τ_0 ||a_k-a_0^k||, linear in distance. The manuscript instead writes E_k^move ≥ τ_0||a_k-a_0^k||² and uses the squared distance in the denominators of Eq. (9), problem (10), and the reformulation (14). Since this term is part of the EE objective being optimized, all reported EE values and the claimed gains over benchmarks are computed for a model different from the one stated and from the cited vehicle-energy model [18]. Please correct the model to the linear distance form, rerun the simulations, and re-examine whether the qualitative conclusions still hold.","section":"Section II-B, Eq. (8)"},{"comment":"The convergence of Algorithm 1 is asserted without proof. The updates in (15)-(17) each maximize Φ over a finite set with all other variables fixed, so Φ is nondecreasing and bounded, but the paper should state this explicitly and provide a rigorous termination argument: either exact convergence after finitely many strict improvements, or an ε-tolerance with a bound on the number of iterations. As written, the repeat-until conditions in lines 3-18 could in principle cycle at equal objective values, and no guarantee is given that the returned point is a local optimum of (10).","section":"Section III-D, Algorithm 1"},{"comment":"Key parameters needed to reproduce the results are missing. The section specifies K=4, M=200×200, N=4, W=1, P_max=30 dBm, σ²=-90 dBm, B=3 MHz, N_th=1e5, and R_min=1 Mbps, but it does not give the movement coefficients τ_r, τ_a, τ_c (or τ_0), the path-loss exponent β, the reference constant C_0, the Gamma distribution parameters for ψ_{k,j}, the small-scale fading model, or how the channel-to-interference-plus-noise map is generated. Without these values, the EE magnitudes in Fig. 2 and the benchmark comparisons are not reproducible and cannot be verified.","section":"Section IV, Simulation Results"}],"minor_comments":[{"comment":"The label '(a)' is attached to the inequality sign, but the text then says 'The equality (a) holds because...'; there is no equality in the displayed chain. Please re-label the step and correct the wording.","section":"Section II-B, Eq. (8)"},{"comment":"The claim that the objective is strictly decreasing in each transmit power component is stated without proof. A short derivative argument would make the derivation self-contained and rule out any ambiguity about the componentwise minimum power being optimal.","section":"Section III-A, Eqs. (11)-(13)"},{"comment":"The initialization of Algorithm 1 is not described. The input requires feasible p(0), X(0), and E(0), but no heuristic for choosing these is given, even though the simulation section must rely on some initialization strategy. Please specify it.","section":"Section III-D, Algorithm 1"},{"comment":"The zoom-in insets are difficult to read, especially the annotations 'Proposed vs FPA near -80 dBm' and 'FPA vs RP 1e3 Best near -75 dBm'. Consider using separate panels or explicit markers for the feasibility boundaries.","section":"Section IV, Fig. 2(c)"},{"comment":"The state of the art for MEAN and FAS is dominated by the authors' own prior work (refs. [5], [12], [13], [14]). Please position the contribution against at least one external FAS-positioning or mobility-aware resource-allocation work to help readers assess novelty.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The self-citation density and the lack of external baselines may make the novelty harder to judge; I would ask the authors to broaden the related-work discussion. More importantly, the squared-distance movement-energy error is load-bearing for the numerical claims. If it is corrected, the optimal positions and the EE comparisons in Fig. 2 may change materially, so I would not recommend acceptance until the model is fixed and all simulations are rerun with complete parameter reporting."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper has one genuinely useful result—the closed-form optimal power vector for fixed positions and ports—and a neat Sherman–Morrison update that makes position search cheap. But the movement-energy model in Eq. (8) is internally inconsistent, and that flaw sits at the center of the paper.\n\nWhat is new: the joint optimization of agent positions, FAS port selections, and transmit powers for EE over interference channels. The power-control derivation is correct: for fixed X and E the objective is strictly decreasing in each power component, so the QoS-constrained optimum is the componentwise minimal power p* = (I−F)^{-1}u, with ρ(F)<1 as the feasibility condition. Lemma 1 is correct and is a legitimate computational contribution.\n\nThe soft spot is not small. Eq. (8) writes E_k^move = (τ_r + τ_a v^2 + τ_c/v) d_k and then claims the lower bound is τ0 ||a_k − a0_k||^2. Minimizing the speed-dependent factor gives min C(v) = τ0, so the bound is τ0 times the Euclidean distance, not its square. The squared distance then appears in the denominators of (9), problem (10), and reformulation (14), so all reported EE numbers and the gains over benchmarks are computed for an objective different from the stated physics and from the cited vehicle model [18]. This is not an external modeling assumption; it is an internal contradiction with the paper's own equation.\n\nAlso: Algorithm 1's convergence is asserted without proof, and the simulations are not reproducible from the manuscript—no code, and the coefficients τ_r, τ_a, τ_c are never specified. The perfect CINM and obstacle-free straight-line movement assumptions are optimistic but standard for this literature.\n\nProportionate verdict: the power-control half of the paper is sound and worth building on. The movement-energy mismatch is fixable, but it requires redoing the formulation and the simulations. The paper should go to peer review: a good referee will catch this, and the core ideas deserve a revised version.","headline":"A useful power-control result and a neat matrix-update trick, but the movement-energy model is internally inconsistent (linear bound turned into squared distance), so the reported EE numbers are for a different objective.","tokens_in":10482,"tokens_out":3215,"would_cite":false,"duration_ms":32003,"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":"Moving agents, switching fluid-antenna ports, and holding power at the minimum rate-feasible vector maximize energy efficiency in the studied interference-limited downlink, beating fixed-antenna and random benchmarks in simulation.","keywords":["fluid antenna system","mobile embodied AI network","energy efficiency","interference channel","power control","agent position optimization","channel-to-interference-plus-noise map","QoS constraints"],"falsifier":"The central claim would be tested by a deployment in which the channel-to-interference-plus-noise map is refreshed slowly while agents roam: measure whether the proposed scheme still beats fixed-antenna and random-position baselines, since the optimality of $p^* = (I - F)^{-1}u$ assumes the map matches the true interference at the moment of transmission. If a stale map erases the energy-efficiency gain, the reported advantage rests on the map-accuracy premise rather than on the optimization structure.","tokens_in":9568,"feed_emoji":"📡","tokens_out":15119,"duration_ms":114281,"temperature":0.7,"pith_summary":"This paper claims that in a multipair downlink where each base station has a fluid antenna (a small grid of switchable ports sharing one radio chain) and each mobile embodied agent can move to a better spot, the energy-efficiency problem separates cleanly: once agent positions and antenna ports are fixed, the transmit power that maximizes energy efficiency is simply the lowest power vector that meets every pair's minimum-rate constraint, given in closed form by $p^* = (I - F)^{-1}u$. The paper then alternates between optimizing the discrete port choices and the discrete agent positions, and shows in simulation that this three-way joint design beats fixed-antenna, random-position, and random-power baselines in bits per joule. A side benefit is a wider feasible noise range: the scheme still finds a working configuration at noise levels where fixed-antenna baselines cannot meet the rate constraints. If true, this gives a practical recipe for controlling interference-limited embodied-AI networks while budgeting the energy cost of movement alongside transmission power.","feed_headline":"Closed-form power rule lifts energy efficiency in embodied-AI downlink","feed_subtitle":"Jointly choosing agent spots, antenna ports, and transmit powers keeps links alive where fixed antennas fail.","key_machinery":"The load-bearing object is the minimum-power feasibility equation: writing the per-agent minimum-rate constraint as $p \\ge F p + u$, where $F$ captures interference-to-desired-signal ratios and $u$ normalizes noise, yields the closed-form power vector $p^* = (I - F)^{-1}u$ for fixed positions and ports, with feasibility controlled by the spectral radius $\\rho(F) < 1$ via the Perron-Frobenius theorem. This single identity collapses the power dimension of the problem and makes the remaining objective an explicit function of the discrete position and port variables. The algorithm's second prop is a Sherman-Morrison update (Lemma 1) that recomputes $p^*$ after moving one agent to a candidate position at $O(K)$ cost instead of a fresh matrix inversion, which is what makes the sequential position sweep over tens of thousands of candidate points computationally tractable.","core_discovery":"On the paper's own terms, the central finding is that for given agent positions and FAS port selections, the optimal transmit power vector in the energy-efficiency problem is the unique minimum QoS-feasible vector $p^* = (I - F)^{-1}u$, provided the spectral radius $\\rho(F) < 1$; every component of the objective is strictly decreasing in each transmit power, so pushing each power down to the boundary set by the rate constraints is optimal. With this closed form, the mixed-integer nonlinear problem reduces to maximizing an explicit function $\\Phi(X,E)$ over position assignments and port selections, and the paper proposes an iterative algorithm that exhaustively or alternately searches ports depending on the size of the search space, then sequentially moves agents along positions using a rank-one (Sherman-Morrison) update of the power solution. Simulations over 4 BS-agent pairs, 40,000 candidate positions, and varying port counts, data sizes, and noise powers show the proposed design achieves the best energy efficiency among the considered benchmarks and remains feasible at -60 dBm noise where a fixed-antenna version cannot satisfy the rate constraints.","pith_inferences":["The same $p^* = (I - F)^{-1}u$ structure would carry over to outage-based formulations: replacing the deterministic channel-to-interference-plus-noise map with a distribution over maps turns the feasibility condition $\\rho(F) < 1$ into a probability-of-feasibility constraint, so the algorithm could be re-derived for robust operation.","The power solution is the classic minimum-power vector of interference-coupled systems, so the paper's energy-efficiency objective inherits known convergence behavior and fragility to channel-estimation error from that literature, even though the paper does not analyze imperfect channel state information.","If movement energy is dominated by route length rather than Euclidean distance (as in obstacle-filled indoor plans), the optimization structure still holds — only the distance metric in the objective changes — which makes the framework portable to logistics and warehouse robots.","A testable online variant would optimize agent positions only within the freshness region of the map, accepting a small loss in nominal energy efficiency to guard against stale maps."],"forward_implications":["For fixed agent positions and FAS ports, the closed-form power vector $p^* = (I - F)^{-1}u$ is the unique energy-efficiency-optimal power assignment, so power control needs no iterative search.","Simulated over 4 BS-agent pairs with 40,000 candidate positions, the joint design delivers higher bits per joule than fixed-antenna, random-position, and random-power baselines at every tested port count, data load, and noise level.","FAS port selection extends the feasible operating range: the proposed scheme still meets minimum-rate constraints at -60 dBm noise, where the fixed-antenna baseline stops being feasible near -75 dBm.","The Sherman-Morrison power update cuts the cost of evaluating a candidate position to O(K) vector operations, making a sequential sweep over 40,000 positions practical.","Energy-efficiency gains from adding FAS ports saturate as ports become strongly correlated within a fixed aperture, so moderate port counts capture most of the benefit."],"supporting_citations":[{"why":"Supplies the Perron-Frobenius argument that (I-F)^{-1}u is the minimum QoS-feasible power vector, making rho(F)<1 the feasibility criterion that the closed-form power solution rests on.","marker":"[19]"},{"why":"Provides the Sherman-Morrison identity used in Lemma 1, which lets the algorithm recompute the optimal power after moving one agent without re-inverting the matrix.","marker":"[20]"},{"why":"Gives the spatial correlation function (spherical Bessel, j0) between FAS ports, which defines the channel structure that the port-selection and position optimization act on in simulation.","marker":"[17]"},{"why":"Supplies the movement-energy model with its distance-dependent cost, the term that makes agent relocation comparable against transmission power in the energy-efficiency objective.","marker":"[18]"},{"why":"Defines the small-scale fading model for the FAS channels that enter the SINR expression and hence the QoS constraint.","marker":"[14]"}],"fun_headline_variants":["Closed-form power rule lifts energy efficiency in FAS-aided embodied-AI links","Optimal power closed form maximizes EE in mobile embodied-AI FAS networks","Joint port-position-power optimization boosts FAS downlink energy efficiency","Energy-efficient FAS downlink solved with closed-form power allocation","FAS-assisted embodied-AI downlink achieves optimal energy efficiency via closed form"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The design assumes the channel-to-interference-plus-noise map is accurate for every candidate position and that agents move along obstacle-free straight lines with energy cost set by Euclidean distance; if the map is stale, noisy, or blocked, the optimized positions and ports are no longer optimal and the reported energy-efficiency gains can shrink.","fun_headline_variants_meta":{"raw":{"variants":["Closed-form power rule lifts energy efficiency in FAS-aided embodied-AI links","Optimal power closed form maximizes EE in mobile embodied-AI FAS networks","Joint port-position-power optimization boosts FAS downlink energy efficiency","Energy-efficient FAS downlink solved with closed-form power allocation","FAS-assisted embodied-AI downlink achieves optimal energy efficiency via closed form"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000837,"raw_usage":{"total_tokens":3662,"prompt_tokens":967,"completion_tokens":2695,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":583,"completion_tokens_details":{"reasoning_tokens":2603}},"tokens_in":583,"tokens_out":2695,"duration_ms":19528,"temperature":1.0,"reasoning_tokens":2603,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:59:11.242510+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"The central claim would be tested by a deployment in which the channel-to-interference-plus-noise map is refreshed slowly while agents roam: measure whether the proposed scheme still beats fixed-antenna and random-position baselines, since the optimality of $p^* = (I - F)^{-1}u$ assumes the map matches the true interference at the moment of transmission. If a stale map erases the energy-efficiency gain, the reported advantage rests on the map-accuracy premise rather than on the optimization structure.","supporting_citations":[{"cited_title":"Performance of optimum transmitter power control in cellular radio systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the Perron-Frobenius argument that (I-F)^{-1}u is the minimum QoS-feasible power vector, making rho(F)<1 the feasibility criterion that the closed-form power solution rests on."},{"cited_title":"An information-theoretic characterization of MIMO-FAS: Optimization, diversity-multiplexing tradeoff and q-outage capacity,","cited_arxiv_id":null,"evidence_quote":"Gives the spatial correlation function (spherical Bessel, j0) between FAS ports, which defines the channel structure that the port-selection and position optimization act on in simulation."},{"cited_title":"Neural network-based modeling of electric vehicle energy demand and all electric range,","cited_arxiv_id":null,"evidence_quote":"Supplies the movement-energy model with its distance-dependent cost, the term that makes agent relocation comparable against transmission power in the energy-efficiency objective."},{"cited_title":"Energy efficient fluid antenna relay (FAR)-assisted wireless communi- cations,","cited_arxiv_id":null,"evidence_quote":"Defines the small-scale fading model for the FAS channels that enter the SINR expression and hence the QoS constraint."}],"review_version":1}