Related papers: Topo-MLP : A Simplicial Network Without Message Pa…

Hypergraphs are vital in modelling data with higher-order relations containing more than two entities, gaining prominence in machine learning and signal processing. Many hypergraph neural networks leverage message passing over hypergraph…

Recently, message-passing Neural networks (MPNN) provide a promising tool for dealing with molecular graphs and have achieved remarkable success in facilitating the discovery and materials design with desired properties. However, the…

Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as oversquashing in topological message-passing remain understudied and lack theoretical…

Graph Neural Networks based on the message-passing (MP) mechanism are a dominant approach for handling graph-structured data. However, they are inherently limited to modeling only pairwise interactions, making it difficult to explicitly…

Graph Neural Network (GNN) has been demonstrated its effectiveness in dealing with non-Euclidean structural data. Both spatial-based and spectral-based GNNs are relying on adjacency matrix to guide message passing among neighbors during…

Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…

Real-world graphs exhibit increasing heterophily, where nodes no longer tend to be connected to nodes with the same label, challenging the homophily assumption of classical graph neural networks (GNNs) and impeding their performance.…

Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…

Message Passing Neural Networks (MPNNs) have emerged as the {\em de facto} standard in graph representation learning. However, when it comes to link prediction, they often struggle, surpassed by simple heuristics such as Common Neighbor…

Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…

Hypergraphs are crucial for modelling higher-order interactions in real-world data. Hypergraph neural networks (HNNs) effectively utilise these structures by message passing to generate informative node features for various downstream tasks…

The most prevalent class of neural networks operating on graphs are message passing neural networks (MPNNs), in which the representation of a node is updated iteratively by aggregating information in the 1-hop neighborhood. Since this…

We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs,…

Semantic communication enables intelligent agents to extract meaning (or semantics) of information via interaction, to carry out collaborative tasks. In this paper, we study semantic communication from a topological space perspective, in…

Given the large volume of side information from different modalities, multimodal recommender systems have become increasingly vital, as they exploit richer semantic information beyond user-item interactions. Recent works highlight that…

This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplicial complexes connected by simplicial maps, that captures…

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…

In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on…

Topological deep learning (TDL) is a rapidly growing field that seeks to leverage topological structure in data and facilitate learning from data supported on topological objects, ranging from molecules to 3D shapes. Most TDL architectures…