Related papers: Topological Deep Learning: Going Beyond Graph Data
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.…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…
Graph-structured data consisting of objects (i.e., nodes) and relationships among objects (i.e., edges) are ubiquitous. Graph-level learning is a matter of studying a collection of graphs instead of a single graph. Traditional graph-level…
We propose a framework for constructing combinatorial complexes (CCs) from fMRI time series data that captures both pairwise and higher-order neural interactions through information-theoretic measures, bridging topological deep learning and…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…
Important advances have been made using convolutional neural network (CNN) approaches to solve complicated problems in areas that rely on grid structured data such as image processing and object classification. Recently, research on graph…
Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that…
Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…
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…
Graph Neural Networks (GNNs) excel at learning from graph-structured data but are limited to modeling pairwise interactions, insufficient for capturing higher-order relationships present in many real-world systems. Topological Deep Learning…
Graph Neural Networks (GNN) have emerged as a popular and standard approach for learning from graph-structured data. The literature on GNN highlights the potential of this evolving research area and its widespread adoption in real-life…
The standard cosmological model with cold dark matter posits a hierarchical formation of structures. We introduce topological neural networks (TNNs), implemented as message-passing neural networks on higher-order structures, to effectively…
Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. They also provide a…
Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…
Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented…
Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…
Deep learning, particularly convolutional neural networks (CNNs), have yielded rapid, significant improvements in computer vision and related domains. But conventional deep learning architectures perform poorly when data have an underlying…