相关论文: Barron Space for Graph Convolution Neural Networks
Heterogeneous Graph Neural Network (HGNN) has been successfully employed in various tasks, but we cannot accurately know the importance of different design dimensions of HGNNs due to diverse architectures and applied scenarios. Besides, in…
Graph Neural Networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph…
Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural…
Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage…
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are…
We study the approximation power of Graph Neural Networks (GNNs) on latent position random graphs. In the large graph limit, GNNs are known to converge to certain "continuous" models known as c-GNNs, which directly enables a study of their…
While artificial neural networks are known as universal approximators for continuous functions, many modern approaches rely on overparameterized architectures with high computational cost. In this work, we introduce the Barycentric Neural…
While Graph Neural Networks (GNNs) are powerful models for learning representations on graphs, most state-of-the-art models do not have significant accuracy gain beyond two to three layers. Deep GNNs fundamentally need to address: 1).…
Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to…
Graph representation learning has attracted much attention in supporting high quality candidate search at scale. Despite its effectiveness in learning embedding vectors for objects in the user-item interaction network, the computational…
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by…
Sparse matrix computations are ubiquitous in scientific computing. With the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NN). Unfortunately, multi-layer…
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…
Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…
We investigate machine learning approaches to approximating the \emph{domination number} of graphs, the minimum size of a dominating set. Exact computation of this parameter is NP-hard, restricting classical methods to small instances. We…
Graph neural networks have demonstrated excellent applicability to a wide range of domains, including social networks, biological systems, recommendation systems, and wireless communications. Yet a principled theoretical understanding of…
The popularity of deep learning techniques renewed the interest in neural architectures able to process complex structures that can be represented using graphs, inspired by Graph Neural Networks (GNNs). We focus our attention on the…
We present a joint graph convolution-image convolution neural network as our submission to the Brain Tumor Segmentation (BraTS) 2021 challenge. We model each brain as a graph composed of distinct image regions, which is initially segmented…
Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…
A common theoretical approach to understanding neural networks is to take an infinite-width limit, at which point the outputs become Gaussian process (GP) distributed. This is known as a neural network Gaussian process (NNGP). However, the…