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When Attention is Beneficial for Learning Wireless Resource Allocation Efficiently?

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Attention is beneficial in learned resource allocation exactly when interference exists in a dimension and that interference is not visible in the measurable environmental parameters; in that case the GNN's first recursion along that…

desk verdict A useful design rule for when to put attention in GNNs for wireless resource allocation, but the rule's algorithm-independence rests on omitted proofs; deserves a serious referee, not yet a settled result. read the letter →

arxiv 2507.02427 v1 pith:QI6BEBUI submitted 2025-07-03 eess.SP

Jia Guo , Chenyang Yang This is my paper · ORCID
classification eess.SP
keywords attentionmechanismgraphneuralnetworkspermutationequivariancerecursivepolicystructurewirelessresourceallocationprecodingdesignsizegeneralizabilityinterferencemodeling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether the attention mechanism is genuinely needed in graph neural networks that learn wireless resource-allocation policies, and it argues that the answer is a structural rule rather than a design heuristic. It first proves that every permutation-equivariant function on a set can be written recursively using one of two building blocks: one whose processor sees only the other element ($q_I(x_j)$), and one whose processor sees a pair ($q_{II}(x_k,x_j)$), the attention processor. It then re-expresses the iterative updates of numerical solvers for several wireless problems in the same recursive form and finds that attention appears only along the dimension where interference acts and where that interference is absent from the measurable channel parameters. If the paper is right, attention should be placed in the first recursion of the interfering dimension and ordinary processors everywhere else, giving a direct GNN design rule that preserves size generalizability and avoids quadratic complexity in non-interfering dimensions.

What carries the argument

The machinery is a decomposition of permutation-equivariant functions into four one-set PE functions: APE-I, $y_k = f_I(x_k, \sum_{j\ne k} q_I(x_j))$, which uses an ordinary processor; APE-II, $y_k = f_{II}(x_k, \sum_{j\ne k} q_{II}(x_k,x_j))$, which uses an attention processor; and nested-set analogues NPE-I and NPE-II. These blocks compose recursively, one recursion per set, so a multi-set function can be aligned with the permutation symmetries of the problem. The key move is to rewrite each numerical algorithm's iteration as a re-expressed iterative equation (RIE) built from these blocks; the RIE's shape, and the location of its attention processors, then dictates the GNN update equation.

What would settle it

Re-express an alternative solver for the same MU-MISO precoding problem (for instance fractional programming or gradient descent) in the paper's recursive notation and inspect the first recursion. If the first recursion can lie along the antenna dimension rather than the user dimension, or if an attention processor in a later recursion still captures the multi-user interference terms, the placement rule is falsified.

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Extended reading notes

Core claim

The paper's central discovery is an equivalence between two seemingly unrelated things: the recursive structure of permutation-equivariant functions and the recursive structure of iterative solvers like WMMSE. For each representative problem (MU-MISO precoding, MU-MIMO precoding, power control, OFDMA bandwidth/power allocation), the iteration is rewritten as a re-expressed iterative equation (RIE) composed of one-set PE functions; comparing the RIEs shows that an attention processor is required exactly when interference exists in a dimension and is not reflected in the environmental parameters, and in that case the attention processor sits in the first recursion along the interfering dimension. The same structure holds, the paper asserts, for fractional programming and gradient descent solvers and for other objectives, because the structure is fixed by the sets and their permutation relations rather than by the algorithm. Guided by this, the paper proposes a design procedure that determines from the optimization problem itself how many recursions the GNN should have, which one-set PE function belongs in each recursion, and which processors should be attention processors.

Load-bearing premise

The argument assumes that the recursive form of the update equations is an intrinsic property of the resource-allocation problem itself, not of the particular algorithm used to solve it; if another solver for the same problem has a different recursive form, the attention-placement rule would need to be rechecked.

Editorial extensions

If this is right

  • A GNN for a new wireless policy can be designed from the problem statement: identify the sets, their types and relations, and the dimension where interference is not visible in the inputs; that set becomes the first recursion and gets the attention processor.
  • Quadratic attention cost is confined to one dimension: for the paper's RIS-aided hybrid precoding example, an all-attention design costs roughly $1.5\times 10^7$ times more FLOPs than the structure-aligned design.
  • Size generalizability follows from the recursion: processors and combiners in the deepest recursion are invariant to all set sizes, so the trained network can be evaluated on larger problem instances without retraining.
  • When the environmental parameters already contain the interference terms (as in power control with the full channel matrix), attention processors provide no benefit and ordinary processors suffice.
  • A single-set attention model such as an encoder-only Transformer can approximate what an ordinary-processor GNN does on one set, but it cannot efficiently handle nested or multi-set policies because it satisfies only one permutation property.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The placement rule likely transfers to any permutation-equivariant learned policy whose inputs omit pairwise couplings: attention is doing the work of a missing interaction term, and the cheap design is to expose that term in the input rather than infer it.
  • A testable middle ground is partial reflection of interference: varying how much of the interference (for example channel magnitudes but not phases) is included in the environmental parameters should continuously shift the attention load, letting a designer trade quadratic attention cost against measurement cost.
  • If the symmetry claim is right, sample-efficiency comparisons among GNN variants are only fair when all variants follow the same recursive placement; otherwise a mismatch in permutation properties, not the processor choice, explains the gap.
  • The same recursion analysis could prescribe where to insert other pairwise operations, such as message passing or cross-attention, in non-wireless permutation-equivariant systems whenever a hidden pairwise interaction must be inferred.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper asks when attention is needed in GNNs for learning wireless resource allocation policies, and answers with a structural analysis of permutation-equivariant functions and of iterative optimization algorithms. It defines APE/NPE function classes, proves representational results (Propositions 1-5), and re-expresses iterative algorithms such as WMMSE, FP, and GD for representative problems in recursive form. The central conclusion is that attention should be placed along a dimension exactly when interference (MUI, IDI, ICI) exists in that dimension and is not reflected in the environmental parameters; this is implemented as a GNN design rule in Procedure 1. The rule is validated by a RIS-aided hybrid precoding example, showing that user-dimension attention outperforms RF-dimension or no attention and provides size generalizability.

Significance. If the central claim holds, the paper gives a principled replacement for trial-and-error attention placement in wireless GNNs and can yield enormous complexity savings; the paper estimates a reduction of about 1.5e7 in FLOPs relative to attention in all recursions. The paper also provides concrete, written proofs of the basic function-structure results (Propositions 1-5), a clear design procedure, and an empirical ablation in Fig. 5 that supports the proposed placement. The main significance is therefore contingent on whether the algorithm-independence and first-recursion claims in Section III-C can be substantiated rather than asserted; currently the most load-bearing part of the framework rests on omitted proofs.

major comments (3)
  1. [Section III-C, Remark 3, Remark 5, Procedure 1] The central design rule depends on the claim that 'the structure of an RIE is determined by the sets, and does not depend on specific algorithms and specific objective function/constraints.' This is load-bearing because Procedure 1 uses only the sets and the presence of interference to place attention. However, the completed proofs cover the GD example in Appendix E, while Propositions 6, 7, and 8 state 'Proof omitted', and Remark 3 explicitly says that the FP, GD, and max-min fairness proofs are not provided. Remark 5 then concedes that the structure is identified only from several algorithms. If another algorithm for the same problem has a different recursive structure, the proposed attention placement and the resulting GNN design would need to be revised. Please supply the missing proofs or explicitly restrict the framework to the family of algorithms for which the RIE structure has been verified.
  2. [Appendix A, Proposition 1] The proof of Proposition 1 claims that the vector [x1,...,x_{k-1},x_{k+1},...] can be recovered from sum_{j≠k} qI(xj) because qI has K-dimensional output. This is not justified: the sum is permutation-invariant and therefore cannot recover an ordered list in general. The cited Deep Sets result [26] provides representations of invariant functions, not a mechanism for recovering an ordered vector from a sum. The equivalence of (3) and (2) may still be true for other reasons, but the written proof is not valid as it stands and should be corrected or replaced by a direct argument.
  3. [Section III-C and Fig. 5] The empirical validation of the general rule is an ablation of a single instance. Fig. 5 compares attention on the user dimension, attention on the RF dimension, and no attention for one RIS-aided hybrid precoding problem; it does not test a GNN derived from a different algorithm for the same problem, nor does it test the predicted absence of attention when interference is reflected in the environmental parameters (as in P-C). As a result, the experiments support the weaker conclusion that user-dimension attention helps in this particular design, but they do not by themselves validate the general algorithm-independence and first-recursion claims that justify Procedure 1.
minor comments (5)
  1. [Eq. (3) and surrounding text] In (3), qII(xk, xj) is written with type R -> R, but it takes two scalar arguments; the type should be R x R -> R (or the text should clarify that the scalar notation is shorthand).
  2. [Eq. (17b)] The term uH_pj Hj HH_k u_mk appears to contain a typo; the channel matrix indices should likely be H_k^H H_k rather than H_j H_k^H, matching the structure of (17a).
  3. [Throughout] There are several typographical and wording errors, e.g., 'Hadmard' for Hadamard, 'uauslly' for usually, and 'nest set' for nested set; these should be corrected in revision.
  4. [Fig. 5] The x-axis labels '5001000' and '10000' are visually unclear; use standard scientific notation or separated tick labels.
  5. [Remark 6] The sentence 'the converse statement may not be true' is ambiguous about whether it concerns approximation capability or learning performance; please clarify.

Circularity Check

0 steps flagged · score 2.0 of 10

No constructional circularity: the attention-placement rule is read off from the algorithms' RIE and tested by an independent ablation; the algorithm-independence generalization is an unproven induction, not a circular reduction.

full rationale

The derivation chain is not circular in the constructional sense. Section II builds on external representation theorems (Deep Sets, Zaheer et al.) to define APE/NPE function-I/II, and Section III re-expresses GD and WMMSE update equations as RIEs; the appearance of a pairwise processor in the interference dimension is obtained by algebraically rewriting those update equations, not by fitting a parameter and then predicting the same parameter. The framework in Section IV converts the RIE structures into GNN update equations, and Section V validates the design with an ablation that varies the attention placement (Fig. 5) plus size-generalization tests (Fig. 6). That ablation is an independent empirical check, so the design rule is not a fitted input called a prediction. The main concern is the load-bearing claim at Section III-C: 'The structure of an RIE is determined by the sets, and does not depend on specific algorithms and specific objective function/constraints.' This is supported only by Observations 2-4 for WMMSE on three problems, while Remark 3 says the FP/GD and max-min fairness proofs 'are not provided due to the limited space', and Remark 5 concedes 'Such a structure of the RIE (and hence the policy with permutation property) is identified only from several algorithms of several problems.' That is a support gap for an inductive generalization, not a circular reduction: no equation in the paper makes the attention-placement conclusion equivalent to its input by construction. The self-citations ([12], [22], [30]) supply set-identification and recursive-GNN machinery from prior published work, but they are not used to assume the attention-placement conclusion, so they are not load-bearing circularity. Overall, the paper's central empirical claim has independent content and is tested by ablation; the omitted-proof generalization affects certainty, not circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The core claim introduces no fitted constants and no new physical entities. It relies on cited representation theorems, the high-SNR Taylor approximation, a definitional boundary between environmental parameters and derived interference, and an unproven generality assumption about algorithm independence.

assumptions (4)
  • standard math Any APE function can be written as y_k = f(x_k, sum_{j!=k} q(x_j)) with q: R -> R^K (Lemma 2, [35]); any API function can be written as y = f(sum_j q(x_j)) (Lemma 1, [26]).
    Used in Appendix B to prove Proposition 2 and in Appendix A to convert attention form to pooled form. These representation theorems are cited, not re-proved.
  • domain assumption The WMMSE iteration for MU-MIMO precoding can be approximated by (17a)-(17b) under a high-SNR assumption and Taylor expansion of the matrix inverse.
    Stated before Eq. (17). The RIE and the attention-placement conclusion for P-M inherit this approximation; no error bound is given.
  • ad hoc to paper The RIE structure of a policy is determined solely by the sets and their relations, independent of the optimization algorithm and objective function.
    Asserted in Section III-C after analyzing a few WMMSE cases, with proofs for FP/GD and other objectives omitted. This is load-bearing for Procedure 1 and Table I.
  • domain assumption The boundary between environmental parameters and interference is defined by whether the inter-user products appear explicitly in the input (G in P-C) or only derivable from it (H in P-S/P-M).
    The attention criterion depends on this classification; it is a modeling choice in Section III-B, not derived.

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Pith. "Pith review of When Attention is Beneficial for Learning Wireless Resource Allocation Efficiently?." pith.science (2026). https://pith.science/paper/QI6BEBUI

@misc{pith2026250702427,
  author       = {Pith},
  title        = {Pith review of: When Attention is Beneficial for Learning Wireless Resource Allocation Efficiently?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QI6BEBUI}},
  note         = {Machine review of arXiv:2507.02427}
}
read the original abstract

Owing to the use of attention mechanism to leverage the dependency across tokens, Transformers are efficient for natural language processing. By harnessing permutation properties broadly exist in resource allocation policies, each mapping measurable environmental parameters (e.g., channel matrix) to optimized variables (e.g., precoding matrix), graph neural networks (GNNs) are promising for learning these policies efficiently in terms of scalability and generalizability. To reap the benefits of both architectures, there is a recent trend of incorporating attention mechanism with GNNs for learning wireless policies. Nevertheless, is the attention mechanism really needed for resource allocation? In this paper, we strive to answer this question by analyzing the structures of functions defined on sets and numerical algorithms, given that the permutation properties of wireless policies are induced by the involved sets (say user set). In particular, we prove that the permutation equivariant functions on a single set can be recursively expressed by two types of functions: one involves attention, and the other does not. We proceed to re-express the numerical algorithms for optimizing several representative resource allocation problems in recursive forms. We find that when interference (say multi-user or inter-data stream interference) is not reflected in the measurable parameters of a policy, attention needs to be used to model the interference. With the insight, we establish a framework of designing GNNs by aligning with the structures. By taking reconfigurable intelligent surface-aided hybrid precoding as an example, the learning efficiency of the proposed GNN is validated via simulations.

Figures

Figures reproduced from arXiv: 2507.02427 by the authors.

Figure 1
Figure 1. An example of permuted vector, M = 2, K = 3, where both the sub-vectors and the elements of each sub-vector are re-ordered. 3) PE property induced by two sets: While the two sets can either be normal sets, nested sets or their combination, we only define the functions on two normal sets for easy exposition. A function on two normal sets satisfies 2D-PE property if the elements in the two sets can be permuted indepen… view at source ↗
Figure 2
Figure 2. Structure of the RIE of the WMMSE algorithm for problem [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. We can see that only the diagonal blocks in the tensor [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Structure of the RIE of the WMMSE algorithm for problem [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Learning performance, NB = NRE = 8, NRF = 6, K = 3. The SE ratio of the BCD algorithm is 100%. In [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Size generalizability of GNN (User attention). [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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Forward citations

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Reference graph

Works this paper leans on

40 extracted references · 37 canonical work pages · cited by 1 Pith paper

  1. [26]

    Deep sets,

    M. Zaheer, S. Kottur, S. Ravanbakhsh et al., “Deep sets,” NeuIPS, 2017

    work page 2017

  2. [1]

    GPT-4 technical report,

    J. Achiam, S. Adler, S. Agarwal et al. , “GPT-4 technical report,” arXiv:2303.08774, 2023

    arXiv 2023

  3. [2]

    Transformer-empowered 6G intelligent networks: From massive MIMO processing to semantic communication,

    Y . Wang, Z. Gao, D. Zhenget al., “Transformer-empowered 6G intelligent networks: From massive MIMO processing to semantic communication,” IEEE Wireless Commun., vol. 30, no. 6, pp. 127–135, June 2023

    work page 2023

  4. [3]

    Large language model enhanced multi-agent systems for 6G communications,

    F. Jiang, Y . Peng, L. Dong et al. , “Large language model enhanced multi-agent systems for 6G communications,” IEEE Wireless Commun., vol. 31, no. 6, pp. 48–55, June 2024

    work page 2024

  5. [4]

    Attention is all you need,

    A. Vaswani, N. Shazeer, N. Parmar et al., “Attention is all you need,” NeurIPS, 2017

    work page 2017

  6. [5]

    Parallel attention-based transformer for channel estimation in RIS-aided 6G wireless communications,

    J. Guo, G. Liu, Q. Wu et al., “Parallel attention-based transformer for channel estimation in RIS-aided 6G wireless communications,” IEEE Trans. Veh. Tech., vol. 73, no. 11, pp. 15 927–15 940, Nov. 2024

    work page 2024

  7. [6]

    Pay less but get more: A dual-attention- based channel estimation network for massive MIMO systems with low-density pilots,

    B. Zhou, X. Yang, S. Ma et al., “Pay less but get more: A dual-attention- based channel estimation network for massive MIMO systems with low-density pilots,” IEEE Trans. Wireless Commun. , vol. 23, no. 6, pp. 6061–6076, Jun. 2024

    work page 2024

  8. [7]

    Transformer network based channel prediction for CSI feedback enhancement in AI-native air interface,

    T. Zhou, X. Liu, Z. Xiang et al., “Transformer network based channel prediction for CSI feedback enhancement in AI-native air interface,” IEEE Trans. Wireless Commun. , vol. 23, no. 9, pp. 11 154–11 167, Mar. 2024

    work page 2024

Show all 40 references
  1. [8]

    Transformer-based channel prediction for rate-splitting multiple access-enabled vehicle-to-everything communication,

    S. Zhang, S. Zhang, Y . Mao et al. , “Transformer-based channel prediction for rate-splitting multiple access-enabled vehicle-to-everything communication,” IEEE Trans. Wireless Commun. , vol. 23, no. 10, pp. 12 717–12 730, Oct. 2024

    2024

  2. [9]

    HPE Transformer: Learning to optimize multi-group multicast beamforming under nonconvex QoS constraints,

    Y . Li and Y . Liu, “HPE Transformer: Learning to optimize multi-group multicast beamforming under nonconvex QoS constraints,” IEEE Trans. Commun., vol. 72, no. 9, pp. 5581–5594, Sept. 2024

    2024

  3. [10]

    Transformer-based power optimization for max-min fairness in cell-free massive MIMO,

    I. Chafaa, G. Bacci, and L. Sanguinetti, “Transformer-based power optimization for max-min fairness in cell-free massive MIMO,” IEEE Wireless Commun. Lett., 2025, Early access

    2025

  4. [11]

    Learning precoding in multi-user multi- antenna systems: Transformer or graph transformer?

    Y . Duan, J. Guo, and C. Yang, “Learning precoding in multi-user multi- antenna systems: Transformer or graph transformer?” arXiv:2503.02998, 2025

    2025 arXiv

  5. [12]

    Multidimensional graph neural networks for wireless communications,

    S. Liu, J. Guo, and C. Yang, “Multidimensional graph neural networks for wireless communications,” IEEE Trans. Wireless Commun. , vol. 23, no. 4, pp. 3057–3073, April 2024

    2024

  6. [13]

    Improving learning efficiency for wireless resource allocation with symmetric prior,

    C. Sun, J. Wu, and C. Yang, “Improving learning efficiency for wireless resource allocation with symmetric prior,” IEEE Wireless Commun. , vol. 29, no. 2, pp. 162–168, April 2022

    2022

  7. [14]

    Understanding the performance of learning precoding policies with graph and convolutional neural networks,

    B. Zhao, J. Guo, and C. Yang, “Understanding the performance of learning precoding policies with graph and convolutional neural networks,” IEEE Trans. Commun. , vol. 72, no. 9, pp. 5657–5673, Sept. 2024

    2024

  8. [15]

    Optimal wireless resource allocation with random edge graph neural networks,

    M. Eisen and A. Ribeiro, “Optimal wireless resource allocation with random edge graph neural networks,” IEEE Trans. Signal Process. , vol. 68, no. 10, pp. 2977–2991, 2020

    2020

  9. [16]

    Graph neural networks for scalable radio resource management: Architecture design and theoretical analysis,

    Y . Shen, Y . Shi, J. Zhang et al., “Graph neural networks for scalable radio resource management: Architecture design and theoretical analysis,” IEEE J. Sel. Areas Commun. , vol. 39, no. 1, pp. 101–115, Jan. 2021

    2021

  10. [17]

    Heterogeneous graph neural network for power allocation in multicarrier-division duplex cell-free massive MIMO systems,

    B. Li, L.-L. Yang, R. G. Maunder et al., “Heterogeneous graph neural network for power allocation in multicarrier-division duplex cell-free massive MIMO systems,” IEEE Trans. Wireless Commun., vol. 23, no. 2, pp. 962–977, Feb. 2024

    2024

  11. [18]

    Distributed graph-based learning for user association and beamforming design in multi-ris multi-cell networks,

    B. Lim and M. Vu, “Distributed graph-based learning for user association and beamforming design in multi-ris multi-cell networks,” IEEE Trans. Wireless Commun., 2025, Early access

    2025

  12. [19]

    Graph embedding-based wireless link scheduling with few training samples,

    M. Lee, G. Yu, and G. Y . Li, “Graph embedding-based wireless link scheduling with few training samples,” IEEE Trans. Wireless Commun. , vol. 20, no. 4, pp. 2282–2294, April 2021

    2021

  13. [20]

    Learning power allocation for multi-cell-multi-user systems with heterogeneous graph neural network,

    J. Guo and C. Yang, “Learning power allocation for multi-cell-multi-user systems with heterogeneous graph neural network,” IEEE Trans. Wireless Commun., vol. 21, no. 2, pp. 884–897, Feb. 2022

    2022

  14. [21]

    Graph neural network aided power control in partially connected cell-free massive MIMO,

    S. Mishra, L. Salaun, H. Yang et al., “Graph neural network aided power control in partially connected cell-free massive MIMO,” IEEE Trans. Wireless Commun., vol. 23, no. 9, pp. 12 412–12 423, Sept. 2024

    2024

  15. [22]

    Recursive GNNs for learning precoding policies with size-generalizability,

    J. Guo and C. Yang, “Recursive GNNs for learning precoding policies with size-generalizability,” IEEE Trans. Mach. Learn. Commun. Netw. , vol. 2, pp. 1558–1579, Oct. 2024

    2024

  16. [23]

    GNN-based beamforming for sum-rate maximization in MU-MISO networks,

    Y . Li, Y . Lu, B. Ai et al. , “GNN-based beamforming for sum-rate maximization in MU-MISO networks,” IEEE Trans. Wireless Commun. , vol. 23, no. 8, pp. 9251–9264, Aug. 2024

    2024

  17. [24]

    ENGNN: A general edge-update empowered GNN architecture for radio resource management in wireless networks,

    Y . Wang, Y . Li, Q. Shi et al. , “ENGNN: A general edge-update empowered GNN architecture for radio resource management in wireless networks,” IEEE Trans. Wireless Commun., vol. 23, no. 6, pp. 5330–5344, June 2024

    2024

  18. [25]

    Equivariance through parameter-sharing,

    S. Ravanbakhsh, J. Schneider, and B. Poczos, “Equivariance through parameter-sharing,” International Conference on Machine Learning, 2017

    2017

  19. [27]

    Structure of deep neural networks with a priori information in wireless tasks,

    J. Guo and C. Yang, “Structure of deep neural networks with a priori information in wireless tasks,” IEEE ICC, 2020

    2020

  20. [28]

    Beamforming design and association scheme for multi-RIS multi-user mmwave systems through graph neural networks,

    M. Liu, C. Huang, A. Alhammadi, M. D. Renzo, M. Debbah, and C. Yuen, “Beamforming design and association scheme for multi-RIS multi-user mmwave systems through graph neural networks,” IEEE Trans. Wireless Commun., 2025, Early access

    2025

  21. [29]

    A bipartite graph neural network approach for scalable beamforming optimization,

    J. Kim, H. Lee, S.-E. Hong et al. , “A bipartite graph neural network approach for scalable beamforming optimization,” IEEE Trans. Wireless Commun., vol. 22, no. 1, pp. 333–347, 2023

    2023

  22. [30]

    A size-generalizable graph neural network for learning multi-user multi-stream MIMO precoding,

    J. Guo and C. Yang, “A size-generalizable graph neural network for learning multi-user multi-stream MIMO precoding,” IEEE MLSP, 2024

    2024

  23. [31]

    Joint spectrum, precoding, and phase shifts design for RIS-aided multiuser MIMO THz systems,

    A. Mehrabian and V . W. Wong, “Joint spectrum, precoding, and phase shifts design for RIS-aided multiuser MIMO THz systems,” IEEE Trans. Commun., vol. 72, no. 8, pp. 5087–5101, Aug. 2024

    2024

  24. [32]

    Graph attention networks,

    P. Veliˇckovi´c, G. Cucurull, A. Casanova et al., “Graph attention networks,” ICLR, 2017

    2017

  25. [33]

    Graph attention network-based precoding for reconfigurable intelligent surfaces aided wireless communication systems,

    J. Yang, J. Xu, Y . Zhanget al., “Graph attention network-based precoding for reconfigurable intelligent surfaces aided wireless communication systems,” IEEE Trans. Veh. Tech., vol. 73, no. 6, pp. 9098–9102, June 2024

    2024

  26. [34]

    Weighted sum-rate maximization for reconfigurable intelligent surface aided wireless networks,

    H. Guo, Y .-C. Liang, J. Chen et al., “Weighted sum-rate maximization for reconfigurable intelligent surface aided wireless networks,” IEEE Trans. Wireless Commun., vol. 19, no. 5, pp. 3064–3076, May 2020

    2020

  27. [35]

    Universal approximations of permutation invariant/equivariant functions by deep neural networks,

    A. Sannai, Y . Takai, and M. Cordonnier, “Universal approximations of permutation invariant/equivariant functions by deep neural networks,” arXiv:1903.01939, 2019

    1903 arXiv

  28. [36]

    S. P. Boyd and L. Vandenberghe, Convex optimization. Cambridge university press, 2004

    2004

  29. [37]

    An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,

    Q. Shi, M. Razaviyayn, Z. Luo et al., “An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,” IEEE Trans. Signal Process. , vol. 59, no. 9, Sept. 2011

    2011

  30. [38]

    J. N. Franklin, Matrix theory. Courier Corporation, 2012

    2012

  31. [39]

    Transformers are graph neural networks,

    C. Joshi, “Transformers are graph neural networks,” The Gradient, vol. 12, p. 17, 2020

    2020

  32. [40]

    Learning beamforming for RIS-aided systems with permutation equivariant graph neural networks,

    B. Zhao and C. Yang, “Learning beamforming for RIS-aided systems with permutation equivariant graph neural networks,” IEEE VTC-Spring, 2023

    2023

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