Related papers: Topological Neural Networks go Persistent, Equivar…

This paper explores the applications and challenges of graph neural networks (GNNs) in processing complex graph data brought about by the rapid development of the Internet. Given the heterogeneity and redundancy problems that graph data…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

Recurrent Neural Networks (RNNs) are very successful at solving challenging problems with sequential data. However, this observed efficiency is not yet entirely explained by theory. It is known that a certain class of multiplicative RNNs…

This paper studies semi-supervised graph classification, a crucial task with a wide range of applications in social network analysis and bioinformatics. Recent works typically adopt graph neural networks to learn graph-level representations…

Graph neural networks (GNNs) have achieved remarkable success in node classification. Building on this progress, heterogeneous graph neural networks (HGNNs) integrate relation types and node and edge semantics to leverage heterogeneous…

Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…

Deep learning methods are achieving ever-increasing performance on many artificial intelligence tasks. A major limitation of deep models is that they are not amenable to interpretability. This limitation can be circumvented by developing…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

Hypergraphs offer a generalized framework for capturing high-order relationships between entities and have been widely applied in various domains, including healthcare, social networks, and bioinformatics. Hypergraph neural networks, which…

We introduce TopoNets, end-to-end probabilistic deep networks for modeling semantic maps with structure reflecting the topology of large-scale environments. TopoNets build a unified deep network spanning multiple levels of abstraction and…

Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…

Graph neural tangent kernels give a principled infinite-width theory for graph neural networks, but inherit a basic limitation of graph models: they see only pairwise structure. Many relational systems contain higher-order interactions that…

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in…

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is…

In this era of artificial intelligence, deep neural networks like Convolutional Neural Networks (CNNs) have emerged as front-runners, often surpassing human capabilities. These deep networks are often perceived as the panacea for all…

Convolutional Neural Networks (CNNs) excel at extracting local features hierarchically, but their performance in capturing complex correlations hinges heavily on deep architectures, which are usually computationally demanding and difficult…

Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured…

The growing use of deep learning necessitates efficient network design and deployment, making neural predictors vital for estimating attributes such as accuracy and latency. Recently, Graph Neural Networks (GNNs) and transformers have shown…

Graph Neural Networks (GNNs) are characterized by their capacity of processing graph-structured data. However, due to the sparsity of labels under semi-supervised learning, they have been found to exhibit biased performance on specific…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…