12 research outputs found
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
Generalized Simplicial Attention Neural Networks
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:2203.0748
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.Comment: Preprint, under revie
Goal-oriented Communications for the IoT: System Design and Adaptive Resource Optimization
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
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
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 assess the effectiveness of the proposed procedures
Dynamic resource optimization for adaptive federated learning empowered by reconfigurable intelligent surfaces
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
Lyapunov-based Optimization of Edge Resources for Energy-Efficient Adaptive Federated Learning
International audienceThe aim of this paper is to propose a novel dynamic resource allocation strategy for energy-efficient adaptive 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-based algorithms to perform distributed learning and adaptation. Hinging on Lyapunov stochastic optimization tools, we dynamically optimize radio parameters (e.g., set of transmitting devices, transmit powers, bits, and rates) and computation resources (e.g., CPU cycles at devices and at server) in order to strike the best trade-off between power, latency, and performance of the federated learning task. The framework admits both a model-based implementation, where the learning performance metrics are available in closed-form, and a data-driven approach, which works with online estimates of the learning performance of interest. The method is then customized to the case of federated least mean squares (LMS) estimation, and federated training of deep convolutional neural networks. Numerical results illustrate the effectiveness of our strategy to perform energy-efficient, low-latency, adaptive federated learning at the wireless network edge
Energy-efficient classification at the wireless edge with reliability guarantees
International audienceLearning 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 resource to perform a classification task, with the minimum average end devices' energy consumption, under E2E delay and inference reliability constraints. Our method does not require 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 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
Performance analysis of SiRe next-generation sequencing panel in diagnostic setting: focus on NSCLC routine samples
Following the development for liquid biopsies of the SiRe next-generation sequencing (NGS) panel that covers 568 clinical relevant mutations in EGFR, KRAS, NRAS, BRAF, cKIT and PDGFRa genes, in this current study, we apply this small NGS panel on tissue samples of lung cancer