相关论文: Barron Space for Graph Convolution Neural Networks

Recently, there have been some breakthroughs in graph analysis by applying the graph neural networks (GNNs) following a neighborhood aggregation scheme, which demonstrate outstanding performance in many tasks. However, we observe that the…

Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper we discuss how the theory of reproducing kernel Banach spaces can be used to tackle this challenge. In…

Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs…

Characterizing the function spaces defined by neural networks helps understanding the corresponding learning models and their inductive bias. While in some limits neural networks correspond to function spaces that are Hilbert spaces, these…

One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approximation and estimation…

Recent works have characterized the function-space inductive bias of infinite-width bounded-norm single-hidden-layer neural networks as a kind of bounded-variation-type space. This novel neural network Banach space encompasses many…

Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing deep learning to arbitrary non-regular domains. Most of the existing GCNs follow a neighborhood aggregation scheme, where the representation of a…

Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the…

Graph Neural Networks (GNNs) have achieved tremendous success in graph representation learning. Unfortunately, current GNNs usually rely on loading the entire attributed graph into network for processing. This implicit assumption may not be…

In this paper, we introduce a generalization of Reproducing Kernel Banach Spaces (RKBS), which we term \emph{Generalized Reproducing Kernel Banach Spaces} (GRKBS). The motivation stems from recent results showing that classical fully…

The current success of Graph Neural Networks (GNNs) usually relies on loading the entire attributed graph for processing, which may not be satisfied with limited memory resources, especially when the attributed graph is large. This paper…

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…

Universal approximation theorems show that neural networks can approximate any continuous function; however, the number of parameters may grow exponentially with the ambient dimension, so these results do not fully explain the practical…

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…

Graph Neural Networks (GNNs) have emerged as a powerful and flexible framework for representation learning on irregular data. As they generalize the operations of classical CNNs on grids to arbitrary topologies, GNNs also bring much of the…

Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the properties that (1) B possesses an l1 norm in the sense that it is isometrically isomorphic to the Banach space of integrable functions on…

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…

Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive…

Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a…