Related papers: Nonlinear Sheaf Diffusion in Graph Neural Networks

Deep neural networks can be powerful tools, but require careful application-specific design to ensure that the most informative relationships in the data are learnable. In this paper, we apply deep neural networks to the nonlinear…

Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…

Graph neural network (GNN) is achieving remarkable performances in a variety of application domains. However, GNN is vulnerable to noise and adversarial attacks in input data. Making GNN robust against noises and adversarial attacks is an…

Graph Neural Networks have gained huge interest in the past few years. These powerful algorithms expanded deep learning models to non-Euclidean space and were able to achieve state of art performance in various applications including…

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…

We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from…

Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task…

The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and…

With the advancement of computational network science, its research scope has significantly expanded beyond static graphs to encompass more complex structures. The introduction of streaming, temporal, multilayer, and hypernetwork approaches…

In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their…

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…

The increasing complexity of neural networks and the energy consumption associated with training and inference create a need for alternative neuromorphic approaches, e.g. using optics. Current proposals and implementations rely on physical…

Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…

Recent works have demonstrated the benefits of capturing long-distance dependency in graphs by deeper graph neural networks (GNNs). But deeper GNNs suffer from the long-lasting scalability challenge due to the neighborhood explosion problem…

We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…

Recent work in Topological Deep Learning (TDL) seeks to generalize graph learning's preeminent $message \ passing$ paradigm to more complex relational structures: simplicial complexes, cell complexes, hypergraphs, and combinations thereof.…

Understanding and predicting interface diffusion phenomena in materials is crucial for various industrial applications, including semiconductor manufacturing, battery technology, and catalysis. In this study, we propose a novel approach…

Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning research. In this paper, we replace the output activation function of DNNs, typically the…

Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with…

The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets…