Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to their data-dependent nature and their ability to capture algorithmic and geometric properties of learned models. However, most existing results rely on isotropic Gaussian posteriors, heavy use of spectral-norm concentration for weight perturbations, and largely architecture-agnostic analyses, which together limit both the tightness and practical relevance of the resulting bounds. To address these limitations, in this work, we propose a unified framework for PAC-Bayesian norm-based generalization by reformulating the derivation of generalization bounds as a stochastic optimization problem over anisotropic Gaussian posteriors. The key to our approach is a sensitivity matrix that quantifies the network outputs with respect to structured weight perturbations, enabling the explicit incorporation of heterogeneous parameter sensitivities and architectural structures. By imposing different structural assumptions on this sensitivity matrix, we derive a family of generalization bounds that recover several existing PAC-Bayesian results as special cases, while yielding bounds that are comparable to or tighter than state-of-the-art approaches. Such a unified framework provides a principled and flexible way for geometry-/structure-aware and interpretable generalization analysis in deep learning.

The space-air-ground integrated network (SAGIN) has garnered significant attention in recent years due to its capability to extend communication networks from terrestrial environments to near-ground and space contexts. The application of SAGIN enables to achieve a high-quality, multi-functional, and complex communication requirements, which are essential for sixth-generation communication systems. This paper presents a topology aware (TA) framework to leverage the topological structure in SAGIN to address the multi-functional communication challenge, particularly the integrated sensing, communication, and power transfer (ISCPT) problem. To take advantage of the topological structure, we initially establish the topology according to the criteria of visibility and channel strength. The ISCPT problem can be reformulated into a topological structure as a mixed integer linear program, providing valuable insights from the objectives and constraints. Results demonstrate the superior performance of our solution compared to the benchmarks.

This paper investigates the joint uplink scheduling and power control problem in a coordinated multicell wireless network, where at most one single-antenna user is allowed to access the single-antenna base station in each cell simultaneously. The resulting weighted sum-rate (WSR) maximization problem is a mixed discrete-continuous, nonconvex optimization problem that is notoriously difficult to solve directly. Classical fractional programming (FP) methods tackle this problem by leveraging the Lagrangian dual transform (LDT) followed by the quadratic transform (QT), yielding a tractable closed-form solution for scheduling and power control, with the LDT playing a crucial role in handling discrete variables. In this paper, we revisit the LDT from a minorization-maximization (MM) perspective and observe that its induced surrogate is somehow conservative due to the reciprocal-coordinate construction. Motivated by this observation, we propose a novel reciprocal-inversion transform (RIT) that constructs a tighter first-order Taylor expansion lower bound for the logarithmic rate function. The proposed RIT remains fully compatible with the QT, leading to a surrogate-enhanced FP (SEFP) algorithm for joint uplink scheduling and power control. The proposed SEFP algorithm retains the desirable per-cell separability of the classical FP framework and admits closed-form updates for the auxiliary variables, scheduling decisions, and transmit powers. Simulation results demonstrate that the SEFP algorithm consistently outperforms the classical FP method and other baselines for different network utilities.

In sixth-generation and beyond, space-air-ground integrated networks (SAGINs) extend network connectivity to space, thereby enabling broader service coverage. This paper proposes a topology-aware SAGIN framework to address the integrated sensing, communication, and wireless power transfer (ISCPT) problem, leveraging the distinctive visibility of satellite-terrestrial and satellite-satellite users as well as their constructing in-between channel strengths. By modeling the topology of the SAGIN as a bipartite graph, we formulate the ISCPT problem as a multi-objective joint optimization problem with specified topological structures to reflect connection relationships of satellite-terrestrial and satellite-satellite users. The ISCPT problem is then reformulated and carefully decomposed as several mixed-integer linear programs (MILPs) by leveraging the network topology to individually optimize sensing, communication, and power transfer. To reduce the computational complexity of the proposed method, a greedy algorithm deal with generalized multi-assignment problem (GMAP) is developed. Simulation results demonstrate superior performance in communication and sensing, with a tolerable trade-off in wireless power transfer.

This paper studies the multi-access coded caching (MACC) problem with arbitrary user-cache access topology, which extends existing MACC models that rely on highly structured and combinatorially designed topologies. We consider a MACC system consisting of a single server, Λ cache-nodes, and K user-nodes. The server stores N equal-size files, each cache-node has a storage capacity of M files, and each user-node k∈[K] can access an arbitrary subset of cache-nodes 𝒜_k⊆[Λ] and retrieve the cached content stored in cache-nodes 𝒜_k. The objective is to design a universal framework for the MACC delivery problem. Decoding conflicts among the requested packets are captured by a conflict graph, and the design of the delivery is reduced to a graph coloring problem, where achieving a lower transmission load corresponds to coloring the graph using fewer colors. Under this formulation, the classical DSatur algorithm achieves a transmission load close to the index-coding (IC) converse bound, thereby providing a practical benchmark. However, its computational complexity becomes prohibitive for large-scale graphs. To overcome this limitation, we develop a learning-driven approach using graph neural networks (GNNs) that efficiently constructs coded multicast transmissions with performance close to the theoretical bounds and generalizes across different user-cache access topologies and numbers of users. In addition, we extend the IC converse bound to MACC systems with arbitrary access topology and propose a low-complexity greedy approximation that closely matches the IC converse bound. Numerical results demonstrate that the proposed approach achieves performance close to the DSatur algorithm and the IC converse bound, while significantly reducing computational complexity, making it well-suited for large-scale MACC systems.

In moderate- to high-mobility scenarios, channel state information (CSI) varies rapidly and becomes temporally non-stationary, leading to severe performance degradation in the massive multiple-input multiple-output (MIMO) transmissions. To address this issue, we propose a tensor-structured approach to dynamic channel prediction (TS-DCP) for massive MIMO systems with temporal non-stationarity, exploiting both dual-timescale and cross-domain correlations. Specifically, due to inherent spatial consistency, non-stationary channels over long-timescales can be approximated as stationary on short-timescales, decoupling complicated temporal correlations into more tractable dual-timescale ones. To exploit such property, we propose the sliding frame structure composed of multiple pilot orthogonal frequency-division multiplexing (OFDM) symbols, which capture short-timescale correlations within frames by Doppler domain modeling and long-timescale correlations across frames by Markov/autoregressive processes. Building on this, we develop the Tucker-based spatial-frequency-temporal domain channel model, incorporating angle-delay-Doppler (ADD) domain channels and factor matrices parameterized by ADD domain grids. Furthermore, we model cross-domain correlations of ADD domain channels within each frame, induced by clustered scattering, through the Markov random field and tensor-coupled Gaussian distribution that incorporates high-order neighborhood structures. Following these probabilistic models, we formulate the TS-DCP problem as variational free energy (VFE) minimization, and unify different inference rules through the structure design of trial beliefs. This formulation results in the dual-layer VFE optimization process and yields the online TS-DCP algorithm, where the computational complexity is reduced by exploiting tensor-structured operations. Numerical simulations demonstrate the significant superiority of the proposed algorithm over benchmarks in terms of channel prediction performance.

In the multi-cell multiuser multi-input multi-output (MU-MIMO) systems, fractional programming (FP) has demonstrated considerable effectiveness in optimizing beamforming vectors, yet it suffers from high computational complexity. Recent improvements demonstrate reduced complexity by avoiding large-dimension matrix inversions (i.e., FastFP) and faster convergence by learning to unfold the FastFP algorithm (i.e., DeepFP).

Whilst the vulnerability of graph neural networks (GNNs) to adversarial attacks poses a critical threat to graph representation learning, the understanding of the robust generalization behavior remains a fundamental challenge in the adversarial setting. Recently, PAC-Bayesian margin-based generalization analysis substantially advances this line of research by providing a flexible and data-dependent analytical framework. However, existing robust analyses often rely on isotropic Gaussian posteriors and control weight perturbations in the full parameter space, which limits the ability to capture heterogeneous parameter sensitivity yet hinges on hidden-width-dependent complexity terms, resulting in not-tight-enough generalization bounds. In this paper, we extend a recently proposed sensitivity-aware PAC-Bayesian framework from deep neural networks to message passing GNNs (MPGNNs) and derive a tighter robust generalization bound in the adversarial setting. Specifically, we first quantify how sensitive the perturbations across different parameter blocks are to the network outputs by deriving the output Jacobians with respect to the weight parameters. Exploiting the fact that these Jacobian matrices have rank at most K in K-class graph classification, we then construct Jacobian-aligned sensitivity matrices and use anisotropic Gaussian posteriors with optimized covariances to upper bound the KL divergence in a tight way. Notably, by refining the spectral-norm dependence on the learned weights and reducing the leading dimension factor from hidden-width-dependent terms to the number of classes K, our analysis yields much tighter robust generalization guarantees for MPGNNs, thereby guiding their designs to enhance adversarial robustness.

This paper investigates the multi-access coded caching (MACC) problem with arbitrary user-cache access topology, extending previous models that rely on structured topologies. The MACC system consists of a single server storing N equal-size files, Λ cache-nodes, and K users, where each cache-node stores M files, and each user retrieves the content by accessing its connected cache-nodes. The objective is to design a universal and low-complexity delivery scheme for arbitrary access topology. We introduce a universal framework to model the MACC delivery problem, where decoding conflicts are captured by a conflict graph and the delivery design is reduced to a graph coloring problem. The classical DSatur algorithm serves as a practical benchmark, achieving transmission loads close to the index-coding (IC) converse bound, but suffering from high computational complexity for large-scale graphs. To address this limitation, we develop a learning-driven approach that efficiently produces near-optimal multicast transmissions and generalizes across diverse user-cache access topologies. In addition, we extend the IC converse bound to MACC systems with arbitrary access topology and propose a low-complexity greedy approximation. Experiments show that the proposed approach achieves performance close to the DSatur algorithm and the IC converse bound, while substantially reducing computational time, making it well-suited for large-scale MACC systems.

While massive multiple-input multiple-output (MIMO) promises high data rates and link reliability, the massive number of antennas introduces critical challenges in downlink (DL) channel estimation and precoding, especially in frequency-division duplex (FDD) systems, due to the lack of instantaneous channel reciprocity. Going beyond compressed sensing-aided approaches, active channel sparsification (ACS) has emerged as a promising candidate to realize joint DL channel estimation and precoding with limited pilot budget, relaxing the reliance of the level of channel sparsity. However, the complex combinatorial optimization problem inherent in the ACS methodology incurs prohibitive computational costs, hindering itself from potential practical deployment. To overcome these challenges, this paper proposes a novel ACS-GRL framework to produce sparsified channel representation via a bipartite graph neural network (GNN) architecture together with deep reinforcement learning (DRL). As such, leveraging second-order channel statistics, the proposed ACS-GRL framework generates a sparsifying pre-beamforming matrix that maps the multiuser channels to a sparsified one, which can be estimated effectively with a limited DL pilot budget, and at the same time yields sparsifying DL precoding vectors to maximize the effective multiplexing gain. Preliminary experimental results demonstrate the superiority of the proposed scheme over the existing ACS methods in improving the sum rate performance.

Graph neural networks have demonstrated excellent applicability to a wide range of domains, including social networks, biological systems, recommendation systems, and wireless communications. Yet a principled theoretical understanding of their generalization behavior remains limited, particularly for graph classification tasks where complex interactions between model parameters and graph structure play a crucial role. Among existing theoretical tools, PAC-Bayesian norm-based generalization bounds provide a flexible and data-dependent framework; however, current results for GNNs often restrict the exploitation of graph structures. In this work, we propose a topology-aware PAC-Bayesian norm-based generalization framework for graph convolutional networks (GCNs) that extends a previously developed framework to graph-structured models. Our approach reformulates the derivation of generalization bounds as a stochastic optimization problem and introduces sensitivity matrices that measure the response of classification outputs with respect to structured weight perturbations. By imposing different structures on sensitivity matrices from both spatial and spectral perspectives, we derive a family of generalization error bounds with graph structures explicitly embedded. Such bounds could recover existing results as special cases, while yielding bounds that are tighter than state-of-the-art PAC-Bayesian bounds for GNNs. Notably, the proposed framework explicitly integrates graph structural properties into the generalization analysis, enabling a unified inspection of GNN generalization behavior from both spatial aggregation and spectral filtering viewpoints.

Power control in Device-to-Device networks is still a challenging learn-to-optimize problem, although recent AI-empowered approaches (e.g., PCGNN/GRLinQ/UFPLinQ) have made remarkable progress regarding effectiveness and in-domain generalization. There is still some concern about whether or not purely data-driven approaches are generalizable across domains with diverse interference patterns. To clear such a concern, we propose a powerful data-driven approach, PCGFormer, enabled by a novel graph transformer architecture with fast attention mechanisms, answering the question in the affirmative. By extensive experiments in both strong and weak interference regimes, PCGFormer exhibits excellent sum rate performance comparable to the state-of-the-art model-based/driven methods, e.g., FPLinQ and UFPLinQ, with substantially reduced computational complexity. More impressively, PCGFormer demonstrates excellent cross-domain generalization across diverse interference patterns-scaling law still rocks-breaking through a key bottleneck of small-scale data-driven approaches, e.g., PCGNN. These findings establish PCGFormer as a practical and powerful candidate for large-scale wireless resource allocation.

The PAC-Bayesian generalization has demonstrated particular promise in understanding deep learning due to its data-dependent nature and the ability to capture algorithmic and geometric properties of learned models. However, most existing results rely on isotropic Gaussian posteriors, spectral-norm concentration, and architecture-agnostic analyses, which together limit both the tightness and practical relevance of the resulting generalization bounds. To address these limitations, in this work, we propose a unified framework for PAC-Bayesian norm-based generalization by reformulating the derivation of generalization bounds as a stochastic optimization problem over anisotropic Gaussian posteriors. The key is a sensitivity matrix that quantifies network outputs with respect to structured weight perturbations, enabling the explicit incorporation of heterogeneous parameter sensitivities and architectural structures. By imposing different designs of sensitivity matrices, we derive a family of generalization bounds that recover several existing PAC-Bayesian results as special cases, while yielding bounds that are comparable to or tighter than state-of-the-art approaches. Such a unified framework provides a principled and flexible way for structure-aware and interpretable generalization analysis in deep learning.

In practical Multiuser Multiple-Input Multiple-Output (MU-MIMO) systems, symbol detection remains challenging due to severe inter-user interference and sensitivity to Channel State Information (CSI) uncertainty. In contrast to the mostly studied belief propagation-type model-driven methods, which incur high computational complexity, Soft Interference Cancellation (SIC) strikes a good balance between performance and complexity. To further address CSI mismatch and nonlinear effects, the recently proposed data-driven deep neural receivers, such as DeepSIC, leverage the advantages of deep neural networks for interference cancellation and symbol detection, demonstrating strong empirical performance. However, there is still a lack of theoretical underpinning for why and to what extent DeepSIC could generalize with the number of training samples. This paper proposes inspecting the fully data-driven DeepSIC detection within a Network-of-MLPs architecture, which is composed of multiple interconnected MLPs via outer and inner Directed Acyclic Graphs (DAGs). Within such an architecture, DeepSIC can be upgraded as a graph-based message-passing process using Graph Neural Networks (GNNs), termed GNNSIC, with shared model parameters across users and iterations. Notably, GNNSIC achieves excellent expressivity comparable to DeepSIC with substantially fewer trainable parameters, resulting in improved sample efficiency and enhanced user generalization. By conducting a norm-based generalization analysis using Rademacher complexity, we reveal that an exponential dependence on the number of iterations for DeepSIC can be eliminated in GNNSIC due to parameter sharing. Simulation results demonstrate that GNNSIC attains comparable or improved Symbol Error Rate (SER) performance to DeepSIC with significantly fewer parameters and training samples.

Despite impressive capability in learning over graph-structured data, graph neural networks (GNN) suffer from adversarial topology perturbation in both training and inference phases. While adversarial training has demonstrated remarkable effectiveness in image classification tasks, its suitability for GNN models has been doubted until a recent advance that shifts the focus from transductive to inductive learning. Still, GNN robustness in the inductive setting is under-explored, and it calls for deeper understanding of GNN adversarial training. To this end, we introduce a concept of graph subspace energy (GSE)-a generalization of graph energy that measures graph stability-of the adjacency matrix, as an indicator of GNN robustness against topology perturbations. To further demonstrate the effectiveness of such concept, we propose an adversarial training method with the perturbed graphs generated by maximizing the GSE regularization term, referred to as AT-GSE. To deal with the local and global topology perturbations raised respectively by LRBCD and PRBCD, we employ randomized SVD (RndSVD) and Nystr & ouml;m low-rank approximation to favor the different aspects of the GSE terms. An extensive set of experiments shows that AT-GSE outperforms consistently the state-of-the-art GNN adversarial training methods over different homophily and heterophily datasets in terms of adversarial accuracy, whilst more surprisingly achieving a superior clean accuracy on non-perturbed graphs.

Upper mid-band massive multiple-input multiple-output (MIMO) offers a favorable capacity-coverage trade-off for next-generation wireless systems, but its large antenna arrays, wide bandwidths, and faster temporal variation substantially increase the pilot overhead required for accurate channel state information (CSI) acquisition. To reduce this overhead, this paper establishes a tensor-structured multi-domain channel extrapolation framework that exploits the limited-scattering nature of practical propagation environments to recover complete CSI across the spatial-frequency-temporal (SFT) domains from limited observations. Specifically, we develop a Tucker-based SFT-domain signal model to represent the complete CSI, where the factor matrices are parameterized by angle-delay-Doppler (ADD)-domain grids. Thanks to this representation, we reveal that limited SFT-domain observations imposed by uniform pilot patterns and antenna-port selection inherently induce ADD-domain aliasing, so that multiple physically distinct ADD-domain components become indistinguishable within structured ADD aliasing groups. To tackle this issue, we introduce a support-prior-assisted ADD-domain de-aliasing mechanism that leverages coarse-grained support information. Since exact closed-form characterization of this mechanism is difficult to derive, we propose a tensor-structure-aware axial-attention neural network (TANN), which integrates axis-wise attention with a lightweight multi-scale CNN-based gating module to incorporate support priors for ADD-domain de-aliasing. With tensor-structure modeling and mixed-configuration training over different pilot decimation factors, TANN yields a unified model that generalizes across pilot configurations without retraining. Numerical results demonstrate the effectiveness and strong generalization of the proposed framework over benchmark methods under diverse scenarios.

In this paper, we propose a learning-to-unfold algorithm named EGAT-FP for the weighted sum-rate maximization problem in the multi-cell massive multi-input multi-output downlink scenario. By unfolding the classical iterative fractional programming (FP) algorithms, we reformulate the beamforming subproblem in each iteration into a homogenized single-variable Quadratic Constrained Quadratic Programming (QCQP) problem, which is then embedded into an edge-featured graph with a hierarchical sparsity property. As such, an edge-featured graph attention network (EGAT) is then developed to solve the problem efficiently, with a set of theoretical analyses of how the GNN approximation error affects the iterative FP updates. Experiments demonstrate that the proposed EGAT-FP algorithm not only approaches the FP extremely close in terms of the weighted sum-rate (WSR), but also exhibits distinct advantages of ultra-low computational latency and significant compactness in model size.

Low-altitude wireless networks (LAWNs) are expected to consist of multi-tier, heterogeneous terrestrial and non-terrestrial devices, where effective coordination is essential to fully unlock the complementary capabilities of diverse systems from different vendors. To address this issue, we propose a novel multi-functional coordination framework that enables seamless cooperation within the LAWN while supporting efficient execution of diverse network functions. In the proposed architecture, each device or infrastructure element is assigned to a specific functional role, namely, edge mobile terminal (E-MT), distributed MT (D-MT), or computing center. E-MTs are equipped with lightweight, independent signal processing and computing capabilities, while D-MTs and the computing center handle regional and global coordination, respectively. To enhance the overall network efficiency, we model the LAWN as a sparse graph, where nodes represent network nodes and edges are defined according to a set of controllable connection rules. This topology-aware (TA) representation allows for efficiently solving various coordination tasks across the network. Numerical results show that the proposed TA coordination framework outperforms baseline approaches that lack topological insights, achieving higher efficiency in multi-task coordination. Finally, we discuss key technical challenges and outline potential solutions for future deployment.

Whilst spectral graph neural networks (GNNs) are theoretically well-founded in the spectral domain, their practical reliance on polynomial approximation implies a profound linkage to the spatial domain. As previous studies rarely examine spectral GNNs from the spatial perspective, their spatial-domain interpretability remains elusive, e.g., what information is essentially encoded by spectral GNNs in the spatial domain? In this article, to answer this question, we investigate the theoretical connection between spectral filtering and spatial aggregation, unveiling an intrinsic interaction that spectral filtering implicitly leads the original graph to an adapted new graph, explicitly computed for spatial aggregation. Both theoretical and empirical investigations reveal that the adapted new graph not only exhibits nonlocality but also accommodates signed edge weights to reflect label consistency among nodes. These findings highlight the interpretable role of spectral GNNs in the spatial domain and inspire us to rethink graph spectral filters beyond the fixed-order polynomials, which limit the effective propagation range and hinder their ability to capture long-range dependencies. Built upon the theoretical findings, we revisit the state-of-the-art spectral GNNs and propose a novel spatially adaptive filtering (SAF) framework, which leverages the adapted new graph by spectral filtering for an auxiliary nonlocal aggregation. Notably, our SAF comprehensively models both node similarity and dissimilarity from a global perspective, therefore alleviating persistent deficiencies of GNNs related to long-range dependencies and graph heterophily. Extensive experiments over 13 node classification benchmarks demonstrate the superiority of our proposed framework to the state-of-the-art methods.

Spectrum sharing is one of the most crucial problems for device-to-device (D2D) communications, for which link scheduling and power control are the most common approaches for large-scale D2D networks. While both optimization-based and learning-to-optimize approaches in the literature yield high-quality solutions for link scheduling and power control, there remains a challenging task to achieve near-optimal performance, low-latency, and cross-scenario adaptivity simultaneously. This paper proposes a novel D2D spectrum sharing approach, named GDiffLinQ, leveraging graph neural networks and diffusion models for generating high-quality solution distributions, and simultaneously enhancing scalability and generalization. By an extensive set of simulations, GDiffLinQ demonstrates superior sum rate performance to the best FPLinQ solutions that were believed to be numerically optimal, and more remarkably, possesses strong scalability and generalizability in both in-distribution and out-of-distribution large-scale network scenarios.