相关论文: Spectral Convergence of Complexon Shift Operators

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…

In this study, we analyze the feasibility of distributed phase synchronization for coherent signal superposition, a fundamental enabler for paradigms such as coherent over-the-air computation (OAC), distributed beamforming, and interference…

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…

The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive…

Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graph-structured data. To address its scalability issue due to the recursive embedding of neighboring features, graph topology sampling has been…

Spectral Graph Neural Networks have demonstrated superior performance in graph representation learning. However, many current methods focus on employing shared polynomial coefficients for all nodes, i.e., learning node-unified filters,…

Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…

This paper introduces a $\textit{canonical}$ graph signal model defined by a $\textit{canonical}$ graph and a $\textit{canonical}$ shift, the $\textit{companion}$ graph and the $\textit{companion}$ shift. These are canonical because, under…

Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…

The notion of translation (shift) is straightforward in classical signal processing, however, it is challenging on an irregular graph structure. In this work, we present an approach to characterize the translation operator in various signal…

Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the…

Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties…

Since its introduction in 2017, Transformer has emerged as the leading neural network architecture, catalyzing revolutionary advancements in many AI disciplines. The key innovation in Transformer is a Self-Attention (SA) mechanism designed…

The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are general conditions under which the partition function is tractable? The answer leads to a new…

Graph signal processing (GSP) is an emerging field developed for analyzing signals defined on irregular spatial structures modeled as graphs. Given the considerable literature regarding the resilience of infrastructure networks using graph…

Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for…

Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions…

In digital signal processing, shift-invariant filters can be represented as a polynomial expansion of a shift operation,that is, the Z-transform representation. When extended to graph signal processing (GSP), this would mean that a…