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Recently, foundation models based on Vision Transformers (ViTs) have become widely available. However, their fine-tuning process is highly resource-intensive, and it hinders their adoption in several edge or low-energy applications. To this end, in this paper we introduce an efficient fine-tuning method for ViTs called $\textbf{ALaST}$ ($\textit{Adaptive Layer Selection Fine-Tuning for Vision Transformers}$) to speed up the fine-tuning process while reducing computational cost, memory load, and training time. Our approach is based on the observation that not all layers are equally critical during fine-tuning, and their importance varies depending on the current mini-batch. Therefore, at each fine-tuning step, we adaptively estimate the importance of all layers and we assign what we call ``compute budgets'' accordingly. Layers that were allocated lower budgets are either trained with a reduced number of input tokens or kept frozen. Freezing a layer reduces the computational cost and memory usage by preventing updates to its weights, while discarding tokens removes redundant data, speeding up processing and reducing memory requirements. We show that this adaptive compute allocation enables a nearly-optimal schedule for distributing computational resources across layers, resulting in substantial reductions in training time (up to 1.5x), FLOPs (up to 2x), and memory load (up to 2x) compared to traditional full fine-tuning approaches. Additionally, it can be successfully combined with other parameter-efficient fine-tuning methods, such as LoRA.

This paper investigates the advantages of representing and processing semantic knowledge extracted into graphs within the emerging paradigm of semantic communications. The proposed approach leverages semantic and pragmatic aspects, incorporating recent advances on large language models (LLMs) to achieve compact representations of knowledge to be processed and exchanged between intelligent agents. This is accomplished by using the cascade of LLMs and graph neural networks (GNNs) as semantic encoders, where information to be shared is selected to be meaningful at the receiver. The embedding vectors produced by the proposed semantic encoder represent information in the form of triplets: nodes (semantic concepts entities), edges(relations between concepts), nodes. Thus, semantic information is associated with the representation of relationships among elements in the space of semantic concept abstractions. In this paper, we investigate the potential of achieving high compression rates in communication by incorporating relations that link elements within graph embeddings. We propose sending semantic symbols solely equivalent to node embeddings through the wireless channel and inferring the complete knowledge graph at the receiver. Numerical simulations illustrate the effectiveness of leveraging knowledge graphs to semantically compress and transmit information., Comment: Accepted for publication at the 25th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

The plethora of wirelessly connected devices, whose deployment density is expected to largely increase in the upcoming sixth Generation (6G) of wireless networks, will naturally necessitate substantial advances in multiple access schemes. Reconfigurable Intelligent Surfaces (RISs) constitute a candidate 6G technology capable to offer dynamic over-the-air signal propagation programmability, which can be optimized for efficient non-orthogonal access of a multitude of devices. In this paper, we study the downlink of a wideband communication system comprising multiple multi-antenna Base Stations (BSs), each wishing to serve an associated single-antenna user via the assistance of a Beyond Diagonal (BD) and frequency-selective RIS. Under the assumption that each BS performs Orthogonal Frequency Division Multiplexing (OFDM) transmissions and exclusively controls a distinct RIS, we focus on the sum-rate maximization problem and present a distributed joint design of the linear precoders at the BSs as well as the tunable capacitances and the switch selection matrices at the multiple BD RISs. The formulated non-convex design optimization problem is solved via successive concave approximation necessitating minimal cooperation among the BSs. Our extensive simulation results showcase the performance superiority of the proposed cooperative scheme over non-cooperation benchmarks, indicating the performance gains with BD RISs via the presented optimized frequency selective operation for various scenarios., Comment: Submitted to an IEEE Journal

In this paper, we propose a novel design for AI-native goal-oriented communications, exploiting transformer neural networks under dynamic inference constraints on bandwidth and computation. Transformers have become the standard architecture for pretraining large-scale vision and text models, and preliminary results have shown promising performance also in deep joint source-channel coding (JSCC). Here, we consider a dynamic model where communication happens over a channel with variable latency and bandwidth constraints. Leveraging recent works on conditional computation, we exploit the structure of the transformer blocks and the multihead attention operator to design a trainable semantic token selection mechanism that learns to select relevant tokens (e.g., image patches) from the input signal. This is done dynamically, on a per-input basis, with a rate that can be chosen as an additional input by the user. We show that our model improves over state-of-the-art token selection mechanisms, exhibiting high accuracy for a wide range of latency and bandwidth constraints, without the need for deploying multiple architectures tailored to each constraint. Last, but not least, the proposed token selection mechanism helps extract powerful semantics that are easy to understand and explain, paving the way for interpretable-by-design models for the next generation of AI-native communication systems., Comment: 5 pages

The Information Bottleneck (IB) method is an information theoretical framework to design a parsimonious and tunable feature-extraction mechanism, such that the extracted features are maximally relevant to a specific learning or inference task. Despite its theoretical value, the IB is based on a functional optimization problem that admits a closed form solution only on specific cases (e.g., Gaussian distributions), making it difficult to be applied in most applications, where it is necessary to resort to complex and approximated variational implementations. To overcome this limitation, we propose an approach to adapt the closed-form solution of the Gaussian IB to a general task. Whichever is the inference task to be performed by a (possibly deep) neural-network, the key idea is to opportunistically design a regression sub-task, embedded in the original problem, where we can safely assume a (joint) multivariate normality between the sub-task's inputs and outputs. In this way we can exploit a fixed and pre-trained neural network to process the input data, using a tunable number of features, to trade data-size and complexity for accuracy. This approach is particularly useful every time a device needs to transmit data (or features) to a server that has to fulfil an inference task, as it provides a principled way to extract the most relevant features for the task to be executed, while looking for the best trade-off between the size of the feature vector to be transmitted, inference accuracy, and complexity. Extensive simulation results testify the effectiveness of the proposed method and encourage to further investigate this research line., Comment: To appear in IEEE Open Journal of the Communications Society, 2024

In future 6G wireless networks, semantic and effectiveness aspects of communications will play a fundamental role, incorporating meaning and relevance into transmissions. However, obstacles arise when devices employ diverse languages, logic, or internal representations, leading to semantic mismatches that might jeopardize understanding. In latent space communication, this challenge manifests as misalignment within high-dimensional representations where deep neural networks encode data. This paper presents a novel framework for goal-oriented semantic communication, leveraging relative representations to mitigate semantic mismatches via latent space alignment. We propose a dynamic optimization strategy that adapts relative representations, communication parameters, and computation resources for energy-efficient, low-latency, goal-oriented semantic communications. Numerical results demonstrate our methodology's effectiveness in mitigating mismatches among devices, while optimizing energy consumption, delay, and effectiveness.

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., Comment: Proceedings of the 41st International Conference on Machine Learning, Vienna, Austria. PMLR 235, 2024

Recent advances in AI technologies have notably expanded device intelligence, fostering federation and cooperation among distributed AI agents. These advancements impose new requirements on future 6G mobile network architectures. To meet these demands, it is essential to transcend classical boundaries and integrate communication, computation, control, and intelligence. This paper presents the 6G-GOALS approach to goal-oriented and semantic communications for AI-Native 6G Networks. The proposed approach incorporates semantic, pragmatic, and goal-oriented communication into AI-native technologies, aiming to facilitate information exchange between intelligent agents in a more relevant, effective, and timely manner, thereby optimizing bandwidth, latency, energy, and electromagnetic field (EMF) radiation. The focus is on distilling data to its most relevant form and terse representation, aligning with the source's intent or the destination's objectives and context, or serving a specific goal. 6G-GOALS builds on three fundamental pillars: i) AI-enhanced semantic data representation, sensing, compression, and communication, ii) foundational AI reasoning and causal semantic data representation, contextual relevance, and value for goal-oriented effectiveness, and iii) sustainability enabled by more efficient wireless services. Finally, we illustrate two proof-of-concepts implementing semantic, goal-oriented, and pragmatic communication principles in near-future use cases. Our study covers the project's vision, methodologies, and potential impact.

This paper investigates the role and the impact of control operations for dynamic mobile edge computing (MEC) empowered by Reconfigurable Intelligent Surfaces (RISs), in which multiple devices offload their computation tasks to an access point (AP) equipped with an edge server (ES), with the help of the RIS. While usually ignored, the control aspects related to channel estimation (CE), resource allocation (RA), and control signaling play a fundamental role in the user-perceived delay and energy consumption. In general, the higher the resources involved in the control operations, the higher their reliability; however, this introduces an overhead, which reduces the number of resources available for computation offloading, possibly increasing the overall latency experienced. Conversely, a lower control overhead translates to more resources available for computation offloading but impacts the CE accuracy and RA flexibility. This paper establishes a basic framework for integrating the impact of control operations in the performance evaluation of the RIS-aided MEC paradigm, clarifying their trade-offs through theoretical analysis and numerical simulations., Comment: Paper submitted to Asilomar Conference on Signals, Systems, and Computers 2023. Copyright may be transferred without further notice

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., Comment: IEEE GLOBECOM 2022

Deep Neural Network (DNN) splitting is one of the key enablers of edge Artificial Intelligence (AI), as it allows end users to pre-process data and offload part of the computational burden to nearby Edge Cloud Servers (ECSs). This opens new opportunities and degrees of freedom in balancing energy consumption, delay, accuracy, privacy, and other trustworthiness metrics. In this work, we explore the opportunity of DNN splitting at the edge of 6G wireless networks to enable low energy cooperative inference with target delay and accuracy with a goal-oriented perspective. Going beyond the current literature, we explore new trade-offs that take into account the accuracy degradation as a function of the Splitting Point (SP) selection and wireless channel conditions. Then, we propose an algorithm that dynamically controls SP selection, local computing resources, uplink transmit power and bandwidth allocation, in a goal-oriented fashion, to meet a target goal-effectiveness. To the best of our knowledge, this is the first work proposing adaptive SP selection on the basis of all learning performance (i.e., energy, delay, accuracy), with the aim of guaranteeing the accomplishment of a goal (e.g., minimize the energy consumption under latency and accuracy constraints). Numerical results show the advantages of the proposed SP selection and resource allocation, to enable energy frugal and effective edge AI., Comment: Submitted at EuCNC 2024

Despite the large research effort devoted to learning dependencies between time series, the state of the art still faces a major limitation: existing methods learn partial correlations but fail to discriminate across distinct frequency bands. Motivated by many applications in which this differentiation is pivotal, we overcome this limitation by learning a block-sparse, frequency-dependent, partial correlation graph, in which layers correspond to different frequency bands, and partial correlations can occur over just a few layers. To this aim, we formulate and solve two nonconvex learning problems: the first has a closed-form solution and is suitable when there is prior knowledge about the number of partial correlations; the second hinges on an iterative solution based on successive convex approximation, and is effective for the general case where no prior knowledge is available. Numerical results on synthetic data show that the proposed methods outperform the current state of the art. Finally, the analysis of financial time series confirms that partial correlations exist only within a few frequency bands, underscoring how our methods enable the gaining of valuable insights that would be undetected without discriminating along the frequency domain., Comment: Accepted at IEEE Transactions on Signal Processing

Internet of Things (IoT) applications combine sensing, wireless communication, intelligence, and actuation, enabling the interaction among heterogeneous devices that collect and process considerable amounts of data. However, the effectiveness of IoT applications needs to face the limitation of available resources, including spectrum, energy, computing, learning and inference capabilities. This paper challenges the prevailing approach to IoT communication, which prioritizes the usage of resources in order to guarantee perfect recovery, at the bit level, of the data transmitted by the sensors to the central unit. We propose a novel approach, called goal-oriented (GO) IoT system design, that transcends traditional bit-related metrics and focuses directly on the fulfillment of the goal motivating the exchange of data. The improvement is then achieved through a comprehensive system optimization, integrating sensing, communication, computation, learning, and control. We provide numerical results demonstrating the practical applications of our methodology in compelling use cases such as edge inference, cooperative sensing, and federated learning. These examples highlight the effectiveness and real-world implications of our proposed approach, with the potential to revolutionize IoT systems., Comment: Accepted for publication on IEEE Internet of Things Magazine, special issue on "Task-Oriented Communications and Networking for the Internet of Things"

The aim of this work is to introduce Generalized Simplicial Attention Neural Networks (GSANs), i.e., novel neural architectures designed to process data defined on simplicial complexes using masked self-attentional layers. Hinging on topological signal processing principles, we devise a series of self-attention schemes capable of processing data components defined at different simplicial orders, such as nodes, edges, triangles, and beyond. These schemes learn how to weight the neighborhoods of the given topological domain in a task-oriented fashion, leveraging the interplay among simplices of different orders through the Dirac operator and its Dirac decomposition. We also theoretically establish that GSANs are permutation equivariant and simplicial-aware. Finally, we illustrate how our approach compares favorably with other methods when applied to several (inductive and transductive) tasks such as trajectory prediction, missing data imputation, graph classification, and simplex prediction., Comment: arXiv admin note: text overlap with arXiv:2203.07485

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 a 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., Comment: Under review. 17 pages, 5 figures

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.

Edge Learning (EL) pushes the computational resources toward the edge of 5G/6G network to assist mobile users requesting delay-sensitive and energy-aware intelligent services. A common challenge in running inference tasks from remote is to extract and transmit only the features that are most significant for the inference task. From this perspective, EL can be effectively coupled with goal-oriented communications, whose aim is to transmit only the information {\it relevant} to perform the inference task, under prescribed accuracy, delay, and energy constraints. In this work, we consider a multi-user/single server wireless network, where the users can opportunistically decide whether to perform the inference task by themselves or, alternatively, to offload the data to the edge server for remote processing. The data to be transmitted undergoes a goal-oriented compression stage performed using a convolutional encoder, jointly trained with a convolutional decoder running at the edge-server side. Employing Lyapunov optimization, we propose a method to jointly and dynamically optimize the selection of the most suitable encoding/decoding scheme, together with the allocation of computational and transmission resources, across all the users and the edge server. Extensive simulations confirm the effectiveness of the proposed approaches and highlight the trade-offs between energy, latency, and learning accuracy., Comment: 15 pages, 11 figures

In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bundle filters and tangent bundle neural networks (TNNs) based on this convolution operation, which are novel continuous architectures operating on tangent bundle signals, i.e. vector fields over the manifolds. Tangent bundle filters admit a spectral representation that generalizes the ones of scalar manifold filters, graph filters and standard convolutional filters in continuous time. We then introduce a discretization procedure, both in the space and time domains, to make TNNs implementable, showing that their discrete counterpart is a novel principled variant of the very recently introduced sheaf neural networks. We formally prove that this discretized architecture converges to the underlying continuous TNN. Finally, we numerically evaluate the effectiveness of the proposed architecture on various learning tasks, both on synthetic and real data., Comment: arXiv admin note: substantial text overlap with arXiv:2210.15058

Reconfigurable Intelligent Surfaces (RISs) constitute the key enabler for programmable electromagnetic propagation environments, and are lately being considered as a candidate physical-layer technology for the demanding connectivity, reliability, localization, and sustainability requirements of next generation wireless networks. In this paper, we first present the deployment scenarios for RIS-enabled smart wireless environments that have been recently designed within the ongoing European Union Horizon 2020 RISE-6G project, as well as a network architecture integrating RISs with existing standardized interfaces. We identify various RIS deployment strategies and sketch the core architectural requirements in terms of RIS control and signaling, depending on the RIS hardware architectures and respective capabilities. Furthermore, we introduce and discuss, with the aid of simulations and reflectarray measurements, two novel metrics that emerge in the context of RIS-empowered wireless systems: the RIS bandwidth and area of influence. Their extensive investigation corroborates the need for careful deployment and planning of the RIS technology in future networks., Comment: 43 pages, 21 figures, sumbitted for a journal publication. arXiv admin note: text overlap with arXiv:2203.13478

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 asses 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 the convolution 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.

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., Comment: 6 pages, 3 figures

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.

Since their introduction, graph attention networks achieved outstanding results in graph representation learning tasks. However, these networks consider only pairwise relationships among nodes and then they are not able to fully exploit higher-order interactions present in many real world data-sets. In this paper, we introduce Cell Attention Networks (CANs), a neural architecture operating on data defined over the vertices of a graph, representing the graph as the 1-skeleton of a cell complex introduced to capture higher order 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 in CANs is hierarchical and it incorporates the following steps: i) a lifting algorithm that learns {\it edge features} from {\it node features}; ii) a cell attention mechanism to find the optimal combination of edge features over both lower and upper neighbors; iii) a hierarchical {\it edge pooling} mechanism to extract a compact meaningful set of features. The experimental results show that CAN is a low complexity strategy that compares favorably with state of the art results on graph-based learning tasks., Comment: Preprint, under review

The technology of Reconfigurable Intelligent Surfaces (RISs) has lately attracted considerable interest from both academia and industry as a low-cost solution for coverage extension and signal propagation control. In this paper, we study the downlink of a multi-cell wideband communication system comprising single-antenna Base Stations (BSs) and their associated single-antenna users, as well as multiple passive RISs. We assume that each BS controls a separate RIS and performs Orthogonal Frequency Division Multiplexing (OFDM) transmissions. Differently from various previous works where the RIS unit elements are considered as frequency-flat phase shifters, we model them as Lorentzian resonators and present a joint design of the BSs' power allocation, as well as the phase profiles of the multiple RISs, targeting the sum-rate maximization of the multi-cell system. We formulate a challenging distributed nonconvex optimization problem, which is solved via successive concave approximation. The distributed implementation of the proposed design is discussed, and the presented simulation results showcase the interplay of the various system parameters on the sum rate, verifying the performance boosting role of RISs., Comment: 5 pages, 1 figure. Presented in IEEE SPAWC 2022

The inference of causal structures from observed data plays a key role in unveiling the underlying dynamics of the system. This paper exposes a novel method, named Multiscale-Causal Structure Learning (MS-CASTLE), to estimate the structure of linear causal relationships occurring at different time scales. Differently from existing approaches, MS-CASTLE takes explicitly into account instantaneous and lagged inter-relations between multiple time series, represented at different scales, hinging on stationary wavelet transform and non-convex optimization. MS-CASTLE incorporates, as a special case, a single-scale version named SS-CASTLE, which compares favorably in terms of computational efficiency, performance and robustness with respect to the state of the art onto synthetic data. We used MS-CASTLE to study the multiscale causal structure of the risk of 15 global equity markets, during covid-19 pandemic, illustrating how MS-CASTLE can extract meaningful information thanks to its multiscale analysis, outperforming SS-CASTLE. We found that the most persistent and strongest interactions occur at mid-term time resolutions. Moreover, we identified the stock markets that drive the risk during the considered period: Brazil, Canada and Italy. The proposed approach can be exploited by financial investors who, depending to their investment horizon, can manage the risk within equity portfolios from a causal perspective.

The advent of Reconfigurable Intelligent Surfaces (RISs) in wireless communication networks unlocks the way to support high frequency radio access (e.g. in millimeter wave) while overcoming their sensitivity to the presence of deep fading and blockages. In support of this vision, this work exhibits the forward-looking perception of using RIS to enhance the connectivity of the communication links in edge computing scenarios, to support computation offloading services. We consider a multi-user MIMO system, and we formulate a long-term optimization problem aiming to ensure a bounded end-to-end delay with the minimum users average transmit power, by jointly selecting uplink user precoding, RIS reflectivity parameters, and computation resources at a mobile edge host. Thanks to the marriage of Lyapunov stochastic optimization, projected gradient techniques and convex optimization, the problem is efficiently solved in a per-slot basis, requiring only the observation of instantaneous realizations of time-varying radio channels and task arrivals, and that of communication and computing buffers. Numerical simulations show the effectiveness of our method and the benefits of the RIS, in striking the best trade-off between power consumption and delay for different blocking conditions, also when different levels of channel knowledge are assumed.

Learning at the edge is a challenging task from several perspectives, since data must be collected by end devices (e.g. sensors), possibly pre-processed (e.g. data compression), and finally processed remotely to output the result of training and/or inference phases. This involves heterogeneous resources, such as radio, computing and learning related parameters. In this context, we propose an algorithm that dynamically selects data encoding scheme, local computing resources, uplink radio parameters, and remote computing resources, to perform a classification task with the minimum average end devices' energy consumption, under E2E delay and inference reliability constraints. Our method does not assume any prior knowledge of the statistics of time varying context parameters, while it only requires the solution of low complexity per-slot deterministic optimization problems, based on instantaneous observations of these parameters and that of properly defined state variables. Numerical results on convolutional neural network based image classification illustrate the effectiveness of our method in striking the best trade-off between energy, delay and inference reliability., Comment: Accepted at IEEE ICC 2022, Workshop on Edge Artificial Intelligence for 6G

Whenever communication takes place to fulfil 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 encoded 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., Comment: Accepted at ICASSP 2022

In this paper, we propose a novel algorithm for energy-efficient, low-latency dynamic mobile edge computing (MEC), in the context of beyond 5G networks endowed with Reconfigurable Intelligent Surfaces (RISs). In our setting, new computing requests are continuously generated by a set of devices and are handled through a dynamic queueing system. Building on stochastic optimization tools, we devise a dynamic learning algorithm that jointly optimizes the allocation of radio resources (i.e., power, transmission rates, sleep mode and duty cycle), computation resources (i.e., CPU cycles), and RIS reflectivity parameters (i.e., phase shifts), while guaranteeing a target performance in terms of average end-to-end (E2E) delay. The proposed strategy is dynamic, since it performs a low-complexity optimization on a per-slot basis while dealing with time-varying radio channels and task arrivals, whose statistics are unknown. The presence and optimization of RISs helps boosting the performance of dynamic MEC, thanks to the capability to shape and adapt the wireless propagation environment. Numerical results assess the performance in terms of service delay, learning, and adaptation capabilities of the proposed strategy for RIS empowered MEC., Comment: Submitted to IEEE Transactions on Signal Processing

The design of 6th Generation (6G) wireless networks points towards flexible connect-and-compute technologies capable to support innovative services and use cases. Targeting the 2030 horizon, 6G networks are poised to pave the way for sustainable human-centered smart societies and vertical industries, such that wireless networks will be transformed into a distributed smart connectivity infrastructure, where new terminal types are embedded in the daily environment. In this context, the RISE-6G project aims at investigating innovative solutions that capitalize on the latest advances in the emerging technology of Reconfigurable Intelligent Surfaces (RISs), which offers dynamic and goal-oriented radio wave propagation control, enabling the concept of the wireless environment as a service. The project will focus on: i) the realistic modeling of RIS-assisted signal propagation, ii) the investigation of the fundamental limits of RIS-empowered wireless communications and sensing, and iii) the design of efficient algorithms for orchestrating networking RISs, in order to implement intelligent, sustainable, and dynamically programmable wireless environments enabling diverse services that go well beyond the 5G capabilities. RISE-6G will offer two unprecedented proof-of-concepts for realizing controlled wireless environments in near-future use cases., Comment: 6 pages, 5 figures, to be presented in 2021 Joint EuCNC & 6G Summit

We propose a novel strategy for energy-efficient dynamic computation offloading, in the context of edge-computing-aided beyond 5G networks. The goal is to minimize the energy consumption of the overall system, comprising multiple User Equipment (UE), an access point (AP), and an edge server (ES), under constraints on the end-to-end service delay and the packet error rate performance over the wireless interface. To reduce the energy consumption, we exploit low-power sleep operation modes for the users, the AP and the ES, shifting the edge computing paradigm from an always on to an always available architecture, capable of guaranteeing an on-demand target service quality with the minimum energy consumption. To this aim, we propose an online algorithm for dynamic and optimal orchestration of radio and computational resources called Discontinuous Computation Offloading (DisCO). In such a framework, end-to-end delay constraints translate into constraints on overall queueing delays, including both the communication and the computation phases of the offloading service. DisCO hinges on Lyapunov stochastic optimization, does not require any prior knowledge on the statistics of the offloading traffic or the radio channels, and satisfies the long-term performance constraints imposed by the users. Several numerical results illustrate the advantages of the proposed method., Comment: Accepted and published in the IEEE Transactions on Green Communications and Networking

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization., Comment: Published on IEEE Transactions on Signal and Information Processing over Networks

We study distributed stochastic nonconvex optimization in multi-agent networks. We introduce a novel algorithmic framework for the distributed minimization of the sum of the expected value of a smooth (possibly nonconvex) function (the agents' sum-utility) plus a convex (possibly nonsmooth) regularizer. The proposed method hinges on successive convex approximation (SCA) techniques, leveraging dynamic consensus as a mechanism to track the average gradient among the agents, and recursive averaging to recover the expected gradient of the sum-utility function. Almost sure convergence to (stationary) solutions of the nonconvex problem is established. Finally, the method is applied to distributed stochastic training of neural networks. Numerical results confirm the theoretical claims, and illustrate the advantages of the proposed method with respect to other methods available in the literature., Comment: Proceedings of 2019 Asilomar Conference on Signals, Systems, and Computers

Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse representation of the graph signal leading to a modular graph whose Laplacian matrix admits the found dictionary as its eigenvectors. The role of sparsity here is to induce a band-limited representation or, equivalently, a modular structure of the graph. The proposed strategy is composed of two optimization steps: i) learning an orthonormal sparsifying transform from the data; ii) recovering the Laplacian, and then topology, from the transform. The first step is achieved through an iterative algorithm whose alternating intermediate solutions are expressed in closed form. The second step recovers the Laplacian matrix from the sparsifying transform through a convex optimization method. Numerical results corroborate the effectiveness of the proposed methods over both synthetic data and real brain data, used for inferring the brain functionality network through experiments conducted over patients affected by epilepsy., Comment: Submitted to IEEE Transactions on Signal Processing, March 2018

One of the most crucial challenges in graph signal processing is the sampling of bandlimited graph signals, i.e., signals that are sparse in a well-defined graph Fourier domain. So far, the prior art is mostly focused on (sub)sampling single snapshots of graph signals ignoring their evolution over time. However, time can bring forth new insights, since many real signals like sensor measurements, biological, financial, and network signals in general, have intrinsic correlations in both domains. In this work, {we fill this lacuna} by jointly considering the graph-time nature of graph signals, named \emph{graph processes} for two main tasks: \emph{i)} observability of graph processes; and \emph{ii)} tracking of graph processes via Kalman filtering; both from a (possibly time-varying) subset of nodes. A detailed mathematical analysis ratifies the proposed methods and provides insights into the role played by the different actors, such as the graph topology, the process bandwidth, and the sampling strategy. Moreover, (sub)optimal sampling strategies that jointly exploit the nature of the graph structure and graph process are proposed. Several numerical tests on both synthetic and real data validate our theoretical findings and illustrate the performance of the proposed methods in coping with time-varying graph signals., Comment: Submitted to Transactions on Signal Processing

The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely, the least mean squares (LMS) and the recursive least squares (RLS) adaptive estimation strategies. For both methods, a detailed mean-square analysis illustrates the effect of random sampling on the adaptive reconstruction capability and the steady-state performance. Then, several probabilistic sampling strategies are proposed to design the sampling probability at each node in the graph, with the aim of optimizing the tradeoff between steady-state performance, graph sampling rate, and convergence rate of the adaptive algorithms. Finally, a distributed RLS strategy is derived and is shown to be convergent to its centralized counterpart. Numerical simulations carried out over both synthetic and real data illustrate the good performance of the proposed sampling and reconstruction strategies for (possibly distributed) adaptive learning of signals defined over graphs., Comment: Submitted to IEEE Transactions on Signal Processing, September 2017

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA) techniques. The basic idea is to iteratively replace the original (non-convex, highly dimensional) learning problem with a sequence of (strongly convex) approximations, which are both accurate and simple to optimize. Differently from similar ideas (e.g., quasi-Newton algorithms), the approximations can be constructed using only first-order information of the neural network 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 dataset involving simulated physical data. The results show how the algorithm outperforms 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., Comment: Preprint submitted to IEEE Transactions on Neural Networks and Learning Systems

The aim of this paper is to develop a general framework for training neural networks (NNs) in a distributed environment, where training data is partitioned over a set of agents that communicate with each other through a sparse, possibly time-varying, connectivity pattern. In such distributed scenario, the training problem can be formulated as the (regularized) optimization of a non-convex social cost function, given by the sum of local (non-convex) costs, where each agent contributes with a single error term defined with respect to its local dataset. To devise a flexible and efficient solution, we customize a recently proposed framework for non-convex optimization over networks, which hinges on a (primal) convexification-decomposition technique to handle non-convexity, and a dynamic consensus procedure to diffuse information among the agents. Several typical choices for the training criterion (e.g., squared loss, cross entropy, etc.) and regularization (e.g., $\ell_2$ norm, sparsity inducing penalties, etc.) are included in the framework and explored along the paper. Convergence to a stationary solution of the social non-convex problem is guaranteed under mild assumptions. Additionally, we show a principled way allowing each agent to exploit a possible multi-core architecture (e.g., a local cloud) in order to parallelize its local optimization step, resulting in strategies that are both distributed (across the agents) and parallel (inside each agent) in nature. A comprehensive set of experimental results validate the proposed approach., Comment: Published on Neural Networks (Elsevier), in press

The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment., Comment: Submitted to IEEE Transactions on Signal and Information Processing over Networks

We study nonconvex distributed optimization in multi-agent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and nonseparable) function - the agents' sum-utility - plus a convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually employed to enforce some structure in the solution, typically sparsity. The proposed method hinges on successive convex approximation techniques while leveraging dynamic consensus as a mechanism to distribute the computation among the agents: 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. Our algorithmic framework is then customized to a variety of convex and nonconvex problems in several fields, including signal processing, communications, networking, and machine learning. Numerical results show that the new method compares favorably to existing distributed algorithms on both convex and nonconvex problems., Comment: To appear on IEEE Transactions on Signal and Information Processing over Networks

The analysis of signals defined over a graph is relevant in many applications, such as social and economic networks, big data or biological networks, and so on. A key tool for analyzing these signals is the so called Graph Fourier Transform (GFT). Alternative definitions of GFT have been suggested in the literature, based on the eigen-decomposition of either the graph Laplacian or adjacency matrix. In this paper, we address the general case of directed graphs and we propose an alternative approach that builds the graph Fourier basis as the set of orthonormal vectors that minimize a continuous extension of the graph cut size, known as the Lov\'{a}sz extension. To cope with the non-convexity of the problem, we propose two alternative iterative optimization methods, properly devised for handling orthogonality constraints. Finally, we extend the method to minimize a continuous relaxation of the balanced cut size. The formulated problem is again non-convex and we propose an efficient solution method based on an explicit-implicit gradient algorithm., Comment: To appear in IEEE Journal of Selected Topics in Signal Processing, 2017

In many applications, from sensor to social networks, gene regulatory networks or big data, observations can be represented as a signal defined over the vertices of a graph. Building on the recently introduced Graph Fourier Transform, the first contribution of this paper is to provide an uncertainty principle for signals on graph. As a by-product of this theory, we show how to build a dictionary of maximally concentrated signals on vertex/frequency domains. Then, we establish a direct relation between uncertainty principle and sampling, which forms the basis for a sampling theorem of signals defined on graph. Based on this theory, we show that, besides sampling rate, the samples' location plays a key role in the performance of signal recovery algorithms. Hence, we suggest a few alternative sampling strategies and compare them with recently proposed methods., Comment: 6 pages, 3 figures. Asilomar Conference on Signals, Systems, and Computers, 8-11 November, 2015

In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of graph signals that are maximally concentrated on the graph domain and on its dual. Then, building on this framework, we derive an uncertainty principle for graph signals and illustrate the conditions for the recovery of band-limited signals from a subset of samples. We show an interesting link between uncertainty principle and sampling and propose alternative signal recovery algorithms, including a generalization to frame-based reconstruction methods. After showing that the performance of signal recovery algorithms is significantly affected by the location of samples, we suggest and compare a few alternative sampling strategies. Finally, we provide the conditions for perfect recovery of a useful signal corrupted by sparse noise, showing that this problem is also intrinsically related to vertex-frequency localization properties., Comment: This article is the revised version submitted to the IEEE Transactions on Signal Processing on May, 2016; first revision was submitted on January, 2016; original manuscript was submitted on July, 2015. The work includes 16 pages, 8 figures