Related papers: Neural Operator: Graph Kernel Network for Partial …
Interest has been rising lately towards methods representing data in non-Euclidean spaces, e.g. hyperbolic or spherical, that provide specific inductive biases useful for certain real-world data properties, e.g. scale-free, hierarchical or…
Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while…
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 Convolutional Networks (GCNs) have emerged as powerful tools for learning on network structured data. Although empirically successful, GCNs exhibit certain behaviour that has no rigorous explanation -- for instance, the performance of…
Kernel methods in machine learning use a kernel function that takes two data points as input and returns their inner product after mapping them to a Hilbert space, implicitly and without actually computing the mapping. For many kernel…
Graph neural tangent kernels give a principled infinite-width theory for graph neural networks, but inherit a basic limitation of graph models: they see only pairwise structure. Many relational systems contain higher-order interactions that…
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…
Graph learning is naturally well suited for use in symbolic, object-centric planning due to its ability to exploit relational structures exhibited in planning domains and to take as input planning instances with arbitrary numbers of…
Seminal works on graph neural networks have primarily targeted semi-supervised node classification problems with few observed labels and high-dimensional signals. With the development of graph networks, this setup has become a de facto…
This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…
Solving partial differential equations (PDEs) is an important research means in the fields of physics, biology, and chemistry. As an approximate alternative to numerical methods, PINN has received extensive attention and played an important…
Neural tangent kernels (NTKs) provide a theoretical regime to analyze the learning and generalization behavior of over-parametrized neural networks. For a supervised learning task, the association between the eigenvectors of the NTK kernel…
Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…
Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world…
Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of…
Deep learning's successes are often attributed to its ability to automatically discover new representations of the data, rather than relying on handcrafted features like other learning methods. We show, however, that deep networks learned…
We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…
Learning the principal eigenfunctions of an integral operator defined by a kernel and a data distribution is at the core of many machine learning problems. Traditional nonparametric solutions based on the Nystr{\"o}m formula suffer from…
Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…
An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is…