相关论文: Geodesic convolutional neural networks on Riemanni…

Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better…

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

Graph Neural Networks (GNNs) have recently been applied to graph learning tasks and achieved state-of-the-art (SOTA) results. However, many competitive methods run GNNs multiple times with subgraph extraction and customized labeling to…

Convolutional Neural Networks(CNNs) has achieved remarkable performance breakthrough in Euclidean structure data. Recently, aggregation-transformation based Graph Neural networks(GNNs) gradually produce a powerful performance on…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations…

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…

Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static…

Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…

Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or…

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii)…

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…

In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…

Graph Neural Networks (GNNs) have significant advantages in handling non-Euclidean data and have been widely applied across various areas, thus receiving increasing attention in recent years. The framework of GNN models mainly includes the…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional…

In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…

Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…