18 accepted papers
CoVariance Neural Networks (VNNs) perform graph convolutions on the empirical covariance matrix of signals defined over finite-dimensional Hilbert spaces, motivated by robustness and transferability properties. Yet, little is known about how these arguments extend to infinite-dimensional Hilbert spa…
Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses this limitation by leveraging combinatorial topological spaces, such as simplicial or cell complexes. However, existing TDL…
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue. TDL enables the principled modeling of arbitrary multi-way,…
Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell complexes. Although many complex systems have an asymmetric relational structure, most TDL models forcibly symmetrize these…
Recent advances in *artificial intelligence* reveal the limits of purely predictive systems and call for a shift toward causal *and* collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the *relativity of causal knowledge*, which posits struct
Graph Neural Networks (GNNs) effectively learn from relational data by leveraging graph symmetries. However, many real-world systems---such as biological or social networks---feature multi-way interactions that GNNs fail to capture. Topological Deep Learning (TDL) addresses this by modeling and leve…
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…
In this work, we study the problem of stability of Graph Convolutional Neural Networks (GCNs) under random small perturbations in the underlying graph topology, i.e. under a limited number of insertions or deletions of edges. We derive a novel bound on the expected difference between the outputs of…
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 a…
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…
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 ta…
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 pre…
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 se…
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 t…
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 a…
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 s…
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…
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 ea…