arXiv subjects

Paolo Di Lorenzo

Publications and source records attributed to Paolo Di Lorenzo.

At least 73 records · Page 4Linked to original sources

arXiv2023

From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module

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.

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arXiv2023

Lyapunov-Driven Deep Reinforcement Learning for Edge Inference Empowered by Reconfigurable Intelligent Surfaces

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.

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arXiv2023

Multi-user Goal-oriented Communications with Energy-efficient Edge Resource Management

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.

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arXiv2023

RIS-Enabled Smart Wireless Environments: Deployment Scenarios, Network Architecture, Bandwidth and Area of Influence

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.

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arXiv2023

Topological Signal Processing over Weighted Simplicial Complexes

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.

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arXiv2022

Goal-Oriented Communication for Edge Learning based on the Information Bottleneck

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.

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arXiv2022

Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back

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.

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arXiv2022

Topological Slepians: Maximally Localized Representations of Signals over Simplicial Complexes

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.

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arXiv2022

Pooling Strategies for Simplicial Convolutional Networks

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.

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arXiv2022

Cell Attention Networks

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.

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arXiv2022

Distributed Sum-Rate Maximization of Cellular Communications with Multiple Reconfigurable Intelligent Surfaces

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.

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arXiv2022

Multiscale Causal Structure Learning

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.

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arXiv2022

Reconfigurable Intelligent Surface Aided Mobile Edge Computing over Intermittent mmWave Links

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.

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arXiv2022

Energy-Efficient Classification at the Wireless Edge with Reliability Guarantees

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.

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arXiv2021

Dynamic Edge Computing empowered by Reconfigurable Intelligent Surfaces

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.

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arXiv2021

Discontinuous Computation Offloading for Energy-Efficient Mobile Edge Computing

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.

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arXiv2021

Wireless Environment as a Service Enabled by Reconfigurable Intelligent Surfaces: The RISE-6G Perspective

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.

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arXiv2021

Distributed Training of Graph Convolutional Networks

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.

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