Next-generation real-time compute-intensive applications, such as extended reality, multi-user gaming, and autonomous transportation, are increasingly composed of heterogeneous AI-intensive functions with diverse resource requirements and stringent latency constraints. While recent advances have enabled very efficient algorithms for joint service placement, routing, and resource allocation for increasingly complex applications, current models fail to capture the non-linear relationship between delay and resource usage that becomes especially relevant in AI-intensive workloads. In this paper, we extend thecloud network flowoptimization framework to support queueing-delay-aware orchestration of distributed AI applications over edge-cloud infrastructures. We introduce two execution models, Guaranteed-Resource (GR) and Shared-Resource (SR), that more accurately capture how computation and communication delays emerge from system-level resource constraints. These models incorporate M/M/1 and M/G/1 queue dynamics to represent dedicated and shared resource usage, respectively. The resulting optimization problem is non-convex due to the non-linear delay terms. To overcome this, we develop SPARQ, an iterative approximation algorithm that decomposes the problem into two convex sub-problems, enabling joint optimization of service placement, routing, and resource allocation under nonlinear delay constraints. The modeling approach is validated against real-world data. Simulation results demonstrate that the SPARQ not only offers a more faithful representation of system delays, but also substantially improves resource efficiency and the overall cost-delay tradeoff compared to existing state-of-the-art methods.

In the Edge Inference (EI) paradigm, where a Deep Neural Network (DNN) is split across the transceivers to wirelessly communicate goal-defined features in solving a computational task, the wireless medium has been commonly treated as a source of noise. In this paper, motivated by the emerging technologies of Reconfigurable Intelligent Surfaces (RISs) and Stacked Intelligent Metasurfaces (SIM) that offer programmable propagation of wireless signals, either through controllable reflections or diffractions, we optimize the RIS/SIM-enabled smart wireless environment as a means of over-the-air computing, resembling the operations of DNN layers. We propose a framework of Metasurfaces-Integrated Neural Networks (MINNs) for EI incorporating RIS/SIM over-the-air computations as a hidden layer alongside traditional digital DNN modules, presenting its modeling, training through a backpropagation variation for fading channels, and deployment aspects. The overall end-to-end DNN architecture is general enough to admit RIS and SIM devices, through controllable reconfiguration before each transmission or fixed configurations after training, while both channel-aware and channel-agnostic transceivers are considered. Our numerical evaluation showcases metasurfaces as instrumental in performing image classification under link budgets that impede conventional communications or metasurface-free systems. It is demonstrated that our MINN framework can significantly simplify EI requirements, achieving near-optimal performance with a 50 dB lower testing signal-to-noise ratio compared to that used in training, even without transceiver channel knowledge.

Structural causal models (SCMs) allow us to investigate complex systems at multiple levels of resolution. The causal abstraction (CA) framework formalizes the mapping between high- and low-level SCMs. We address CA learning in a challenging and realistic setting, where SCMs are inaccessible, interventional data is unavailable, and sample data is misaligned. A key principle of our framework is *semantic embedding*, formalized as the high-level distribution lying on a subspace of the low-level one. This principle naturally links linear CA to the geometry of the *Stiefel manifold*. We present a category-theoretic approach to SCMs that enables the learning of a CA by finding a morphism between the low- and high-level probability measures, adhering to the semantic embedding principle. Consequently, we formulate a general CA learning problem. As an application, we solve the latter problem for linear CA; considering Gaussian measures and the Kullback-Leibler divergence as an objective. Given the nonconvexity of the learning task, we develop three algorithms building upon existing paradigms for Riemannian optimization. We demonstrate that the proposed methods succeed on both synthetic and real-world brain data with different degrees of prior information about the structure of CA.

Semantic communications focus on prioritizing the understanding of the meaning behind transmitted data and ensuring the successful completion of tasks that motivate the exchange of information. However, when devices rely on different languages, logic, or internal representations, semantic mismatches may occur, potentially hindering mutual understanding. This paper introduces a novel approach to addressing latent space misalignment in semantic communications, exploiting multiple-input multiple-output (MIMO) communications. Specifically, our method learns a MIMO precoder/decoder pair that jointly performs latent space compression and semantic channel equalization, mitigating both semantic mismatches and physical channel impairments. We explore two solutions: (i) a linear model, optimized by solving a biconvex optimization problem via the alternating direction method of multipliers (ADMM); (ii) a neural network-based model, which learns semantic MIMO precoder/decoder under transmission power budget and complexity constraints. Numerical results demonstrate the effectiveness of the proposed approach in a goal-oriented semantic communication scenario, illustrating the main trade-offs between accuracy, communication burden, and complexity of the solutions.

Foundation models for computer vision built on Vision Transformer (ViT) architectures have become increasingly widespread. However, their fine-tuning process is resource-intensive, slowing their adoption in edge or low-energy applications. We introduce ALaST ( Adaptive Layer Selection for ViT Fine-Tuning ), a novel approach that dynamically optimizes the fine-tuning process to significantly reduce computational cost, memory consumption, and training time. Our method is founded on the critical observation that during fine-tuning, the importance of individual layers and tokens varies substantially across training iterations and depends on the specific mini-batch being processed. ALaST leverages this insight by adaptively estimating layer importance at each fine-tuning step and allocating computational resources—or “compute budgets”—proportionally. Layers assigned lower budgets are either trained with a reduced token set or temporarily frozen. Through comprehensive empirical evaluation on standard benchmarks, we demonstrate that ALaST achieves substantial efficiency gains: up to 1.3 × reduction in training time, 1.5 × reduction in FLOPs, and 2 × decrease in memory requirements, all while maintaining model performance within 0.5 % of full fine-tuning. Notably, our approach provides an automatic schedule for distributing computational resources across layers and can be combined with existing parameter-efficient fine-tuning techniques, offering an orthogonal dimension of optimization for Vision Transformers.

Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes) and allow for decentralized implementation through localized communications over different neighborhoods. Existing TNN architectures have not yet been considered in realistic communication scenarios, where channel effects typically introduce disturbances such as fading and noise. This paper aims to propose a novel TNN design, operating on regular cell complexes, that performs over-the-air computation, incorporating the wireless communication model into its architecture. Specifically, during training and inference, the proposed method considers channel impairments such as fading and noise in the topological con-volutional filtering operation, which takes place over different signal orders and neighborhoods. Numerical results illustrate the architecture’s robustness to channel impairments during testing and the superior performance with respect to existing architectures, which are either communication-agnostic or graph-based.

Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a given graph topology by dynamically learning it. However, most of LGI methods assume to have a (noisy, incomplete, improvable, ...) input graph to rewire and can solely learn regular graph topologies. In the wake of the success of Topological Deep Learning (TDL), we study Latent Topology Inference (LTI) for learning higher-order cell complexes (with sparse and not regular topology) describing multi-way interactions between data points. To this aim, we introduce the Differentiable Cell Complex Module (DCM), a novel learnable function that computes cell probabilities in the complex to improve the downstream task. We show how to integrate DCM with cell complex message-passing networks layers and train it in an end-to-end fashion, thanks to a two-step inference procedure that avoids an exhaustive search across all possible cells in the input, thus maintaining scalability. Our model is tested on several homophilic and heterophilic graph datasets and it is shown to outperform other state-of-the-art techniques, offering significant improvements especially in cases where an input graph is not provided.

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

This paper introduces topological Slepians, i.e., a novel class of signals defined over topological spaces (e.g., simplicial complexes) that are maximally concentrated on the topological domain (e.g., over a set of nodes, edges, triangles, etc.) and perfectly localized on the dual domain (e.g., a set of frequencies). These signals are obtained as the principal eigenvectors of a matrix built from proper localization operators acting over topology and frequency domains. Then, we suggest a principled procedure to build dictionaries of topological Slepians, which theoretically provide non-degenerate frames. Finally, we evaluate the effectiveness of the proposed topological Slepian dictionary in two applications, i.e., sparse signal representation and denoising of edge flows.

Weighing the topological domain over which data can be represented and analysed is a key strategy in many signal processing and machine learning applications, enabling the extraction and exploitation of meaningful data features and their (higher order) relationships. Our goal in this paper is to present topological signal processing tools for weighted simplicial complexes. Specifically, relying on the weighted Hodge Laplacian theory, we propose efficient strategies to jointly learn the weights of the complex and the filters for the solenoidal, irrotational and harmonic components of the signals defined over the complex. We numerically assess the effectiveness of the proposed procedures.

In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use this convolution operation to define tangent bundle filters and tangent bundle neural networks (TNNs), novel continuous architectures operating on tangent bundle signals, i.e. vector fields over manifolds. We discretize TNNs both in space and time domains, showing that their discrete counterpart is a principled variant of the recently introduced Sheaf Neural Networks. We formally prove that this discrete architecture converges to the underlying continuous TNN. We numerically evaluate the effectiveness of the proposed architecture on a denoising task of a tangent vector field over the unit 2-sphere.

The goal of this paper is to introduce pooling strategies for simplicial convolutional neural networks. Inspired by graph pooling methods, we introduce a general formulation for a simplicial pooling layer that performs: i) local aggregation of simplicial signals; ii) principled selection of sampling sets; iii) downsampling and simplicial topology adaptation. The general layer is then customized to design four different pooling strategies (i.e., max, top-k, self-attention, and separated top-k) grounded in the theory of topological signal processing. Also, we leverage the proposed layers in a hierarchical architecture that reduce complexity while representing data at different resolutions. Numerical results on real data benchmarks (i.e., flow and graph classification) illustrate the advantage of the proposed methods with respect to the state of the art.

In this paper, we propose a novel algorithm for energy-efficient, low-latency, accurate inference at the wireless edge, in the context of 6G networks endowed with reconfigurable intelligent surfaces (RISs). We consider a scenario where new data are continuously generated/collected by a set of devices and are handled through a dynamic queueing system. Building on the marriage between Lyapunov stochastic optimization and deep reinforcement learning (DRL), we devise a dynamic learning algorithm that jointly optimizes the data compression scheme, the allocation of radio resources (i.e., power, transmission precoding), the computation resources (i.e., CPU cycles), and the RIS reflectivity parameters (i.e., phase shifts), with the aim of performing energy-efficient edge classification with end-to-end (E2E) delay and inference accuracy constraints. The proposed strategy enables dynamic control of the system and of the wireless propagation environment, performing a low-complexity optimization on a per-slot basis while dealing with time-varying radio channels and task arrivals, whose statistics are unknown. Numerical results assess the performance of the proposed RIS-empowered edge inference strategy in terms of trade-off between energy, delay, and accuracy of a classification task.

Since their introduction, graph attention networks achieved outstanding results in graph representation learning tasks. However, these networks consider only pairwise relations between features associated to the nodes and then are unable to fully exploit higher-order and long-range interactions present in many real world data-sets. In this paper, we introduce a neural architecture operating on data defined over the nodes and the edges of a graph, represented as the 1-skeleton of a regular cell complex, able to capture insightful higher-order and long-range interactions. In particular, we exploit the lower and upper neighborhoods, as encoded in the cell complex, to design two independent masked self-attention mechanisms, thus generalizing the conventional graph attention strategy. The approach used is hierarchical and it incorporates the following steps: i) a lifting algorithm that learns (additional) edge features from node features; ii) a cell attention mechanism to find the optimal combination of edge features over both lower and upper neighbors; iii) a hierarchical edge pooling mechanism to extract a compact meaningful set of features. The experimental results show that this method compares favorably with state of the art results on graph-based learning tasks while maintaining a low complexity.

In band Network Telemetry (INT) is a technique aiming at collecting telemetry information by inserting it inside the data packets, instead of relying on classical centralized monitoring elements that periodically query the network devices. The main drawback of INT is represented by the introduced per-packet overhead, that could negatively affect some traffic flows, especially those having stringent QoS requirements. To deal with the increase in the packet length caused by INT, in this paper we introduce the Sampling and Recovering paradigm to overcome the classical Collect Everything approach where all the INT data must be gathered. The proposed approach hinges on signal processing strategies to sample and recover sparse flow signals. The key idea is to reduce the number of INT data to collect and exploit signal reconstruction algorithms to obtain the unseen samples. The preliminary performance evaluation shows that the 18% of INT data are enough to get an accurate reconstruction of the overall network situation, while allowing for 90% of overhead reduction with respect to the Collect Everything case.

This work lies at the intersection of two cutting edge technologies envisioned to proliferate in future 6G wireless systems: Multi-access Edge Computing (MEC) and Reconfigurable Intelligent Surfaces (RISs). While the former will bring a powerful information technology environment at the wireless edge, the latter will enhance communication performance, thanks to the possibility of adapting wireless propagation as per end users' convenience, according to specific service requirements. We propose a joint optimization of radio, computing, and wireless environment reconfiguration through an RIS, with the goal of enabling low power computation offloading services with reliability guarantees. Going beyond previous works on this topic, multi-carrier frequency selective RIS elements' responses and wireless channels are considered. This opens new challenges in RIS optimization, accounting for frequency dependent RIS response profiles, which strongly affect RIS-aided wireless links and, as a consequence, MEC service performance. We formulate an optimization problem accounting for short and long-term constraints involving device transmit power allocation across multiple subcarriers and local computing resources, as well as RIS reconfiguration parameters according to a recently developed Lorentzian model. Besides a theoretical optimization framework, numerical results show the effectiveness of the proposed method in enabling low power reliable computation offloading over RIS-aided frequency selective channels.

The aim of this work is to propose a novel dynamic resource allocation strategy for adaptive Federated Learning (FL), in the context of beyond 5G networks endowed with Reconfigurable Intelligent Surfaces (RISs). Due to time-varying wireless channel conditions, communication resources (e.g., set of transmitting devices, transmit powers, bits), computation parameters (e.g., CPU cycles at devices and at server) and RISs reflectivity must be optimized in each communication round, in order to strike the best trade-off between power, latency, and performance of the FL task. Hinging on Lyapunov stochastic optimization, we devise an online strategy able to dynamically allocate these resources, while controlling learning performance in a fully data-driven fashion. Numerical simulations implement distributed training of deep convolutional neural networks, illustrating the effectiveness of the proposed FL strategy endowed with multiple reconfigurable intelligent surfaces.

This work aims to propose a novel architecture and training strategy for graph convolutional networks (GCN). The proposed architecture, named Autoencoder-Aided GCN (AA-GCN), compresses the convolutional features in an information-rich embedding at multiple hidden layers, exploiting the presence of autoencoders before the point-wise nonlinearities. Then, we propose a novel end-to-end training procedure that learns different graph representations per layer, jointly with the GCN weights and auto-encoder parameters. As a result, the proposed strategy improves the computational scalability of the GCN, learning the best graph representations at each layer in a data-driven fashion. Several numerical results on synthetic and real data illustrate how our architecture and training procedure compares favorably with other state-of-the-art solutions, both in terms of robustness and learning performance.

Whenever communication takes place to fulfill a goal, an effective way to encode the source data to be transmitted is to use an encoding rule that allows the receiver to meet the requirements of the goal. A formal way to identify the relevant information with respect to a goal can be obtained exploiting the information bottleneck (IB) principle. In this paper, we propose a goal-oriented communication system, based on the combination of IB and stochastic optimization. The IB principle is used to design the encoder in order to find an optimal balance between representation complexity and relevance of the en-coded data with respect to the goal. Stochastic optimization is then used to adapt the parameters of the IB to find an efficient resource allocation of communication and computation resources. Our goal is to minimize the average energy consumption under constraints on average service delay and accuracy of the learning task applied to the received data in a dynamic scenario. Numerical results assess the performance of the proposed strategy in two cases: regression from Gaussian random variables, where we can exploit closed-form solutions, and image classification using deep neural networks, with adaptive network splitting between transmit and receive sides.

We propose a dynamic resource allocation algorithm in the context of future wireless networks endowed with edge computing, to enable accurate energy efficient classification with end-to-end delay guarantees. In our scenario, sensor devices continuously upload data to an Edge Server (ES) for classification purposes. Merging Lyapunov stochastic optimization and ensemble inference, we propose DEsIreE, a low-complexity method that dynamically selects the data quantization level, the device transmit power, and the ES's CPU scheduling, without any prior knowledge of the statistics of wireless channels and data arrivals. Numerical simulations run on two real datasets assess the effectiveness of our algorithm in optimizing sensors' energy consumption and classification accuracy, with the ensemble yielding considerable gain.

The aim of this paper is to propose a novel dynamic resource allocation strategy for energy-efficient federated learning at the wireless network edge, with latency and learning performance guarantees. We consider a set of devices collecting local data and uploading processed information to an edge server, which runs stochastic gradient descent (SGD) to perform distributed learning and adaptation. Hinging on Lyapunov stochastic optimization tools, we dynamically optimize radio parameters (i.e., set of transmitting devices, transmit powers) and computation resources (i.e., CPU cycles at devices and at server) in order to strike the best trade-off between energy, latency, and performance of the federated learning task. The general framework is then customized to the case of federated least mean squares (LMS) estimation. Numerical results illustrate the effectiveness of our strategy to perform energy-efficient, low-latency, federated machine learning at the wireless network edge.

The aim of this paper is to propose a method for online learning of time-varying graphs from noisy observations of smooth graph signals collected over the vertices. Starting from an initial graph, and assuming that the topology can undergo the perturbation of a small percentage of edges over time, the method is able to track the graph evolution by exploiting a small perturbation analysis of the Laplacian matrix eigendecomposition, while assuming that the graph signal is bandlimited. The proposed method alternates between estimating the time-varying graph signal and recovering the dynamic graph topology. Numerical results corroborate the effectiveness of the proposed learning strategy in the joint online recovery of graph signal and topology.

We study decentralized estimation of time-varying signals at a fusion center, when energy harvesting sensors transmit sampled data over rate-constrained links. We propose dynamic strategies to select radio parameters, sampling set, and harvested energy at each node, with the aim of estimating a time-varying signal while ensuring: 1) the accuracy of the recovery procedure and 2) the stability of the batteries around a prescribed operating level. The approach is based on stochastic optimization tools, which enable adaptive optimization without the need of apriori knowledge of the statistics of radio channels and energy arrivals processes. Numerical results validate the proposed approach for decentralized signal estimation under communication and energy constraints typical of Internet-of-Things scenarios.

The aim of this paper is to propose a novel distributed strategy for tensor completion, where (partial) data are collected over a network of agents with sparse, but connected, topology. The method hinges on the canonical polyadic decomposition, also known as PARAFAC, to complete the low-rank tensor in a distributed fashion. To deal with the nonconvex and distributed nature of the learning problem, we exploit a convexification/decomposition technique based on successive convex approximations, while using dynamic consensus to diffuse information over the network and force asymptotic agreement among the agents. Asymptotic convergence to stationary solutions of the centralized problem is established under mild conditions. Finally, numerical results assess the performance of the proposed method over both synthetic and real data.

The aim of this work is to develop a dynamic optimization strategy to allocate communication and computation resources in a Multi-access Edge Computing (MEC) scenario, where Unmanned Aerial Vehicles (UAVs) act as flying base station platforms endowed with computation capabilities to provide edge cloud services on demand. Hinging on stochastic optimization tools, we propose a dynamic algorithmic framework that minimizes the overall energy spent by the system, while imposing latency constraints, and optimizing the altitude of the UAV in an online fashion. The method does not require a priori knowledge of channels and/or task arrival statistics. Numerical results illustrate the advantages of the proposed approach.

In this paper, we address the problem of dynamic allocation of communication and computation resources for Edge Machine Learning (EML) exploiting Multi-Access Edge Computing (MEC). In particular, we consider an IoT scenario, where sensor devices collect data from the environment and upload them to an edge server that runs a learning algorithm based on Stochastic Gradient Descent (SGD). The aim is to explore the optimal tradeoff between the overall system energy consumption, including IoT devices and edge server, the overall service latency, and the learning accuracy. Building on stochastic optimization tools, we devise an algorithm that jointly allocates radio and computation resources in a dynamic fashion, without requiring prior knowledge of the statistics of the channels, task arrivals, and input data. Finally, we test our algorithm in the specific case the edge server runs a Least Mean Squares (LMS) algorithm on the data acquired by each sensor device.

A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.

Real-world networks are typically described in terms of nodes, links, and communities, having signal values often associated with them. The aim of this letter is to introduce a novel Compound Markov random field model (Compound MRF, or CMRF) for signals defined over graphs, encompassing jointly signal values at nodes, edge weights, and community labels. The proposed CMRF generalizes Markovian models previously proposed in the literature, since it accounts for different kinds of interactions between communities and signal smoothness constraints. Finally, the proposed approach is applied to (joint) graph learning and signal recovery. Numerical results on synthetic and real data illustrate the competitive performance of our method with respect to other state-of-the-art approaches.

This paper proposes a novel algorithmic solution for dynamic computation offloading, aimed at reducing the energy consumption of a mobile network endowed with multi-access edge computing. The dynamic evolution of the system is modeled through three queues: a local queue at the user side, a computation queue at the edge server, and a queue of results at the network access point. The optimization problem is cast as the minimization of the long-term average energy consumption of the whole system, comprising user devices, servers, and access points. Quality of service constraints for end users are imposed in terms of probability that the \textit{sum of the queues} exceeds a given threshold. A suitable weighting parameter can be tuned to drive the system toward a user-centric, a network-centric, or a hybrid solution. Exploiting stochastic optimization tools, the problem is solved thanks to a dynamic optimization algorithm, based on the solution of deterministic convex problems in each time slot. The algorithm does not assume any knowledge on the task input and output random sizes and the radio channel statistics. Several numerical results illustrate the advantages of the proposed method.

We study decentralized estimation of time-varying signals at a fusion center (FC), when energy harvesting sensors transmit sampled data over rate-constrained links. We propose a dynamic strategy based on stochastic optimization for selecting radio parameters, sampling set, and harvested energy at each node, with the aim of estimating a time-varying signal with guaranteed performance while ensuring stability of the batteries around a prescribed operating level. Numerical results validate the proposed approach for dynamic signal estimation under communication and energy constraints.

We study distributed processing of subspace-constrained signals in multi-agent networks with sparse connectivity. We introduce the first optimization framework based on distributed subspace projections, aimed at minimizing a network cost function depending on the specific processing task, while imposing subspace constraints on the final solution. The proposed method hinges on (sub)gradient techniques while leveraging distributed projections as a mechanism to enforce subspace constraints in a cooperative and distributed fashion. Asymptotic convergence to optimal solutions of the problem is established under different assumptions (e.g., nondifferentiability, nonconvexity, etc.) on the objective function. Finally, numerical tests assess the performance of the proposed distributed strategy.

Multi-Access Edge Computing (MEC) is one of the key technology enablers of the 5G ecosystem, in combination with the high speed access provided by mmWave communications. In this paper, among all services enabled by MEC, we focus on computation offloading, devising an algorithm to optimize computation and communication resources jointly with the assignment of mobile users to Access Points and Mobile Edge Hosts, in a dynamic scenario where computation tasks are continuously generated according to (unknown) random arrival processes at each user. To formulate and solve the dynamic allocation/assignment problem, we merge tools from stochastic optimization and matching theory, thus developing a low complexity algorithmic solution that works in an online fashion. Numerical results illustrate the potential advantages of the proposed approach.

We study centralized interpolation of bandlimited graph signals at a fusion center (FC), when sampled data are transmitted over rate-constrained links. In such a scenario, the performance of the reconstruction task is inevitably affected by several sources of errors such as observation noise and quantization due to source encoding. In this paper, we propose two strategies for optimally selecting transmission powers, quantization bits, and the sampling set, with the aim of interpolating a graph signal with guaranteed performance. Numerical results validate the proposed approach for interpolation of bandlimited graph signals under communication constraints.

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of nonconvex optimization, going under the general name of successive convex approximation techniques. The basic idea is to iteratively replace the original (nonconvex, highly dimensional) learning problem with a sequence of (strongly convex) approximations, which are both accurate and simple to optimize. Different from similar ideas (e.g., quasi-Newton algorithms), the approximations can be constructed using only first-order information of the NN function, in a stochastic fashion, while exploiting the overall structure of the learning problem for a faster convergence. We discuss several use cases, based on different choices for the loss function (e.g., squared loss and cross-entropy loss), and for the regularization of the NN's weights. We experiment on several medium-sized benchmark problems and on a large-scale data set involving simulated physical data. The results show how the algorithm outperforms the state-of-the-art techniques, providing faster convergence to a better minimum. Additionally, we show how the algorithm can be easily parallelized over multiple computational units without hindering its performance. In particular, each computational unit can optimize a tailored surrogate function defined on a randomly assigned subset of the input variables, whose dimension can be selected depending entirely on the available computational power.

A key tool to analyze signals defined over a graph is the so called Graph Fourier Transform (GFT). Alternative definitions of GFT have been proposed, based on the eigen-decomposition of either the graph Laplacian or adjacency matrix. In this paper, we introduce an alternative approach, valid for the general case of directed graphs, that builds the graph Fourier basis as the set of orthonormal vectors that minimize a well-defined continuous extension of the graph cut size, known as Lovász extension. To cope with the non-convexity of the problem, we exploit a recently developed method devised for handling orthogonality constraints, with provable convergence properties.

In this paper we introduce a novel algorithmic framework for non-convex distributed optimization in multi-agent networks with time-varying (nonsymmetric) topology. The proposed method hinges on successive convex approximation (SCA) techniques while leveraging dynamic consensus as a mechanism to diffuse information: each agent first solves (possibly inexactly) a local convex approximation of the nonconvex original problem, and then performs local averaging operations. Asymptotic convergence to (stationary) solutions of the nonconvex problem is established. Finally, the framework is applied to a distributed nonlinear regression problem.

The goal of this paper is to propose a network formation game where strategic agents decide whether to form or sever a link with other agents depending on the net balance between the benefit resulting from the additional information coming from the new link and the cost associated to establish the link. Differently from previous works, where the benefits are functions of the distances among the involved agents, in our work the benefit is a function of the mutual information that can be exchanged among the agents, conditioned to the information already available before setting up the link. An interesting result of our network formation game is that, under certain conditions, the final network topology tends to match the topology of the Markov graph describing the conditional independencies among the random variables observed in each node, at least when the cost of forming a link is small.

In this paper we propose distributed strategies for the estimation of sparse vectors over adaptive networks. The measurements collected at different nodes are assumed to be spatially correlated and distributed according to a Gaussian Markov random field (GMRF) model. We derive optimal sparsity-aware algorithms that incorporate prior information about the statistical dependency among observations. Simulation results show the potential advantages of the proposed strategies for online recovery of sparse vectors.

Polynomial-Phase Signals (PPS) appear in a variety of applications and several algorithms are available to estimate their parameters in the presence of noise. Among the available tools, the Product High order Ambiguity Function (PHAF) has the merit of performing well in the presence of a superposition of PPS's. In this work, we generalize the PHAF to handle two-dimensional PPS's. Then we show an example of application motivating such an extension: the high resolution imaging of moving targets from synthetic aperture radars (SAR). Using the 2D-PHAF, we will propose an algorithm that compensates jointly for the range cell migration and the phase modulation induced by the relative radar-target motion in order to produce a focused image of the moving target.

In this paper, we propose a decentralized algorithm for the estimation and control of connectivity of random ad hoc networks. First, we introduce a novel stochastic power iteration method that allows each node to estimate and track the expected algebraic connectivity of a random graph. The proposed method is then used to adapt the power transmitted by each node in order to drive the network connectivity toward a desired value. Numerical results illustrate the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures.

The goal of this letter is to propose an adaptive and distributed approach to cooperative sensing for wireless small cell networks. The method uses a basis expansion model of the power spectral density (PSD) to be estimated, and exploits spectral sparsity to improve estimation accuracy and adaptation capabilities. An estimator of the model coefficients is developed based on sparse diffusion strategies, which are able to exploit and track sparsity while at the same time processing data in real-time and in a fully decentralized manner. Simulation results illustrate the advantages of the proposed sparsity-aware strategies for cooperative spectrum sensing applications.

The goal of this paper is to propose diffusion LMS techniques for distributed estimation over adaptive networks, which are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing, to improve the performance of the diffusion strategies. We provide convergence and performance analysis of the proposed method, showing under what conditions it outperforms the unregularized diffusion version. Simulation results illustrate the advantage of the proposed filter under the sparsity assumption on the true coefficient vector.

This paper proposes a distributed resource allocation strategy for cognitive radio networks based on a swarming model that incorporates random link failures and quantized communications. The swarming mechanism is used to minimize the interference produced by the cognitive users, take advantage of cooperative sensing, avoid collisions among the users and limit the spread of resources in the time-frequency domain. The mechanism assumes only local exchange of data among nearby nodes. The communications among the nodes are assumed to be affected by noise and random fading. Packet drops are taken into account as inducing a random topology, where a link is on or off depending on the decision errors. Using classical results from stochastic approximation theory, we prove that the swarm always converges in probability to a final allocation even in the presence of non ideal communications among the nodes. Numerical results show how the convergence rate of the algorithm is affected by the probability of link failures. The proposed procedure is applied to a bi-dimensional allocation in the time-frequency plane where the primary users' activity is modeled as a set of continuous-time Markov processes.