Abstract--In this paper, we analyze the performance of the estimation of Laplacian matrices under general observatio n models. Laplacian matrix estimation involves structural c on-straints, including symmetry and null-space properties, a long with matrix sparsity. By exploiting a linear reparametriza tion that enforces the structural constraints, we derive closed -form matrix expressions for the Cram er-Rao Bound (CRB) specifically tailored to Laplacian matrix estimation. We further extend the derivation to the sparsity-constrained case, introduc ing two oracle CRBs that incorporate prior information of the suppo rt set, i.e. the locations of the nonzero entries in the Laplaci an matrix. We examine the properties and order relations betwe en the bounds, and provide the associated Slepian-Bangs formu la for the Gaussian case. We demonstrate the use of the new CRBs in three representative applications: (i) topology identi fication in power systems, (ii) graph filter identification in diffuse d models, and (iii) precision matrix estimation in Gaussian M arkov random fields under Laplacian constraints. The CRBs are eval - uated and compared with the mean-squared-errors (MSEs) of the constrained maximum likelihood estimator (CMLE), whic h integrates both equality and inequality constraints along with sparsity constraints, and of the oracle CMLE, which knows the locations of the nonzero entries of the Laplacian matrix . We perform this analysis for the applications of power syste m topology identification and graphical LASSO, and demonstra te that the MSEs of the estimators converge to the CRB and oracle CRB, given a sufficient number of measurements. Graph-structured data and signals arise in numerous applications, including power systems, communications, finance, social networks, and biological networks, for analysis and inference of networks [ 2 ], [ 3 ]. In this context, the Laplacian matrix, which captures node connectivity and edge weights, serves as a fundamental tool for clustering [ 4 ], modeling graph diffusion processes [ 5 ], [ 6 ], topology inference [ 6 ]-[ 12 ], anomaly detection [ 13 ], graph-based filtering [ 14 ]-[ 18 ], and analyzing smoothness on graphs [ 19 ]. M. Halihal and T. Routtenberg are with the School of Electric al and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel, e-mail: moradha@post.bgu.ac.il, tirzar@b gu.ac.il.

Network optimization is a fundamental challenge in the Internet of Things (IoT) network, often characterized by complex features that make it difficult to solve these problems. Recently, generative diffusion models (GDMs) have emerged as a promising new approach to network optimization, with the potential to directly address these optimization problems. However, the application of GDMs in this field is still in its early stages, and there is a noticeable lack of theoretical research and empirical findings. In this study, we first explore the intrinsic characteristics of generative models. Next, we provide a concise theoretical proof and intuitive demonstration of the advantages of generative models over discriminative models in network optimization. Based on this exploration, we implement GDMs as optimizers aimed at learning high-quality solution distributions for given inputs, sampling from these distributions during inference to approximate or achieve optimal solutions. Specifically, we utilize denoising diffusion probabilistic models (DDPMs) and employ a classifier-free guidance mechanism to manage conditional guidance based on input parameters. We conduct extensive experiments across three challenging network optimization problems. By investigating various model configurations and the principles of GDMs as optimizers, we demonstrate the ability to overcome prediction errors and validate the convergence of generated solutions to optimal solutions. We provide code and data at https://github.com/qiyu3816/DiffSG.

In federated learning (FL), heterogeneity among the local dataset distributions of clients can result in unsatisfactory performance for some, leading to an unfair model. To address this challenge, we propose an over-the-air fair federated learning algorithm (OTA-FFL), which leverages over-the-air computation to train fair FL models. By formulating FL as a multi-objective minimization problem, we introduce a modified Chebyshev approach to compute adaptive weighting coefficients for gradient aggregation in each communication round. To enable efficient aggregation over the multiple access channel, we derive analytical solutions for the optimal transmit scalars at the clients and the de-noising scalar at the parameter server. Extensive experiments demonstrate the superiority of OTA-FFL in achieving fairness and robust performance compared to existing methods.

To alleviate the training burden in federated learning while enhancing convergence speed, Split Federated Learning (SFL) has emerged as a promising approach by combining the advantages of federated and split learning. However, recent studies have largely overlooked competitive situations. In this framework, the SFL model owner can choose the cut layer to balance the training load between the server and clients, ensuring the necessary level of privacy for the clients. Additionally, the SFL model owner sets incentives to encourage client participation in the SFL process. The optimization strategies employed by the SFL model owner influence clients' decisions regarding the amount of data they contribute, taking into account the shared incentives over clients and anticipated energy consumption during SFL. To address this framework, we model the problem using a hierarchical decision-making approach, formulated as a single-leader multi-follower Stackelberg game. We demonstrate the existence and uniqueness of the Nash equilibrium among clients and analyze the Stackelberg equilibrium by examining the leader's game. Furthermore, we discuss privacy concerns related to differential privacy and the criteria for selecting the minimum required cut layer. Our findings show that the Stackelberg equilibrium solution maximizes the utility for both the clients and the SFL model owner.

Optimization is crucial for MEC networks to function efficiently and reliably, most of which are NP-hard and lack efficient approximation algorithms. This leads to a paucity of optimal solution, constraining the effectiveness of conventional deep learning approaches. Most existing learning-based methods necessitate extensive optimal data and fail to exploit the potential benefits of suboptimal data that can be obtained with greater efficiency and effectiveness. Taking the multi-server multi-user computation offloading (MSCO) problem, which is widely observed in systems like Internet-of-Vehicles (IoV) and Unmanned Aerial Vehicle (UAV) networks, as a concrete scenario, we present a Graph Diffusion-based Solution Generation (GDSG) method. This approach is designed to work with suboptimal datasets while converging to the optimal solution large probably. We transform the optimization issue into distribution-learning and offer a clear explanation of learning from suboptimal training datasets. We build GDSG as a multi-task diffusion model utilizing a Graph Neural Network (GNN) to acquire the distribution of high-quality solutions. We use a simple and efficient heuristic approach to obtain a sufficient amount of training data composed entirely of suboptimal solutions. In our implementation, we enhance the backbone GNN and achieve improved generalization. GDSG also reaches nearly 100\% task orthogonality, ensuring no interference between the discrete and continuous generation tasks. We further reveal that this orthogonality arises from the diffusion-related training loss, rather than the neural network architecture itself. The experiments demonstrate that GDSG surpasses other benchmark methods on both the optimal and suboptimal training datasets. The MSCO datasets has open-sourced at http://ieee-dataport.org/13824, as well as the GDSG algorithm codes at https://github.com/qiyu3816/GDSG.

Multi-connectivity involves dynamic cluster formation among distributed access points (APs) and coordinated resource allocation from these APs, highlighting the need for efficient mobility management strategies for users with multi-connectivity. In this paper, we propose a novel mobility management scheme for unmanned aerial vehicles (UAVs) that uses dynamic cluster reconfiguration with energy-efficient power allocation in a wireless interference network. Our objective encompasses meeting stringent reliability demands, minimizing joint power consumption, and reducing the frequency of cluster reconfiguration. To achieve these objectives, we propose a hierarchical multi-agent deep reinforcement learning (H-MADRL) framework, specifically tailored for dynamic clustering and power allocation. The edge cloud connected with a set of APs through low latency optical back-haul links hosts the high-level agent responsible for the optimal clustering policy, while low-level agents reside in the APs and are responsible for the power allocation policy. To further improve the learning efficiency, we propose a novel action-observation transition-driven learning algorithm that allows the low-level agents to use the action space from the high-level agent as part of the local observation space. This allows the lower-level agents to share partial information about the clustering policy and allocate the power more efficiently. The simulation results demonstrate that our proposed distributed algorithm achieves comparable performance to the centralized algorithm. Additionally, it offers better scalability, as the decision time for clustering and power allocation increases by only 10% when doubling the number of APs, compared to a 90% increase observed with the centralized approach.

Second-order methods are widely adopted to improve the convergence rate of learning algorithms. In federated learning (FL), these methods require the clients to share their local Hessian matrices with the parameter server (PS), which comes at a prohibitive communication cost. A classical solution to this issue is to approximate the global Hessian matrix from the first-order information. Unlike in idealized networks, this solution does not perform effectively in over-the-air FL settings, where the PS receives noisy versions of the local gradients. This paper introduces a novel second-order FL framework tailored for wireless channels. The pivotal innovation lies in the PS's capability to directly estimate the global Hessian matrix from the received noisy local gradients via a non-parametric method: the PS models the unknown Hessian matrix as a Gaussian process, and then uses the temporal relation between the gradients and Hessian along with the channel model to find a stochastic estimator for the global Hessian matrix. We refer to this method as Gaussian process-based Hessian modeling for wireless FL (GP-FL) and show that it exhibits a linear-quadratic convergence rate. Numerical experiments on various datasets demonstrate that GP-FL outperforms all classical baseline first and second order FL approaches.

In this paper, we consider a point-to-point integrated sensing and communication (ISAC) system, where a transmitter conveys a message to a receiver over a channel with memory and simultaneously estimates the state of the channel through the backscattered signals from the emitted waveform. Using Massey's concept of directed information for channels with memory, we formulate the capacity-distortion tradeoff for the ISAC problem when sensing is performed in an online fashion. Optimizing the transmit waveform for this system to simultaneously achieve good communication and sensing performance is a complicated task, and thus we propose a deep reinforcement learning (RL) approach to find a solution. The proposed approach enables the agent to optimize the ISAC performance by learning a reward that reflects the difference between the communication gain and the sensing loss. Since the state-space in our RL model is \`a priori unbounded, we employ deep deterministic policy gradient algorithm (DDPG). Our numerical results suggest a significant performance improvement when one considers unbounded state-space as opposed to a simpler RL problem with reduced state-space. In the extreme case of degenerate state-space only memoryless signaling strategies are possible. Our results thus emphasize the necessity of well exploiting the memory inherent in ISAC systems.

In wireless communications, efficient image transmission must balance reliability, throughput, and latency, especially under dynamic channel conditions. This paper presents an adaptive and progressive pipeline for learned image compression (LIC)-based architectures tailored to such environments. We investigate two state-of-the-art learning-based models: the hyperprior model and Vector Quantized Generative Adversarial Network (VQGAN). The hyperprior model achieves superior compression performance through lossless compression in the bottleneck but is susceptible to bit errors, necessitating the use of error correction or retransmission mechanisms. In contrast, the VQGAN decoder demonstrates robust image reconstruction capabilities even in the absence of channel coding, enhancing reliability in challenging transmission scenarios. We propose progressive versions of both models, enabling partial image transmission and decoding under imperfect channel conditions. This progressive approach not only maintains image integrity under poor channel conditions but also significantly reduces latency by allowing immediate partial image availability. We evaluate our pipeline using the Kodak high-resolution image dataset under a Rayleigh fading wireless channel model simulating dynamic conditions. The results indicate that the progressive transmission framework enhances reliability and latency while maintaining or improving throughput compared to non-progressive counterparts across various Signal-to-Noise Ratio (SNR) levels. Specifically, the progressive-hyperprior model consistently outperforms others in latency metrics, particularly in the 99.9th percentile waiting time-a measure indicating the maximum waiting time experienced by 99.9% of transmission instances-across all SNRs, and achieves higher throughput in low SNR scenarios. where Adaptive WebP fails.

Inspired by biological processes, neuromorphic computing utilizes spiking neural networks (SNNs) to perform inference tasks, offering significant efficiency gains for workloads involving sequential data. Recent advances in hardware and software have demonstrated that embedding a few bits of payload in each spike exchanged between the spiking neurons can further enhance inference accuracy. In a split computing architecture, where the SNN is divided across two separate devices, the device storing the first layers must share information about the spikes generated by the local output neurons with the other device. Consequently, the advantages of multi-level spikes must be balanced against the challenges of transmitting additional bits between the two devices. For this system, we present the design of digital and analog modulation schemes optimized for an orthogonal frequency division multiplexing (OFDM) radio interface. Simulation and experimental results using software-defined radios provide insights into the performance gains of multi-level SNN models and the optimal payload size as a function of the quality of the connection between a transmitter and receiver. D. Wu and B. Rajendran are with the King's Laboratory for Intelligent Computing (KLIC) lab within the Centre for Intelligent Information Processing Systems (CIIPS) at the Department of Engineering, King's College London, London, WC2R 2LS, UK (email:{dengyu.wu, J. Chen and O. Simeone are with the King's Communications, Learning and Information Processing (KCLIP) lab within the CIIPS at the Department of Engineering, King's College London, London, WC2R 2LS, UK (email:{jiechen.chen,