Riemannian geometry is the study of manifolds endowed with Riemannian metrics, which
are, roughly speaking, rules for measuring lengths of tangent vectors and angles between …

Existing equivariant neural networks require prior knowledge of the symmetry group and
discretization for continuous groups. We propose to work with Lie algebras (infinitesimal …

Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-
case (ie, adversarial) perturbations of the datapoints. On the other hand, it has been …

In this chapter, we begin by introducing the simplest type of manifolds, the topological
manifolds, which are topological spaces with three special properties that encode what we …

Graph convolutional networks (GCNs) have received considerable research attention
recently. Most GCNs learn the node representations in Euclidean geometry, but that could …

Graph neural network (GNN) has shown superior performance in dealing with structured
graphs, which has attracted considerable research attention recently. Most of the existing …

We present a new Riemannian metric, termed Log-Cholesky metric, on the manifold of
symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a …

Recently, the format of TT tensors (Hackbusch and Kühn in J Fourier Anal Appl 15: 706–722,
2009; Oseledets in SIAM J Sci Comput 2009, submitted; Oseledets and Tyrtyshnikov in SIAM …

Isotropic Gaussian random fields on the sphere are characterized by Karhunen–Loève
expansions with respect to the spherical harmonic functions and the angular power …

A bstract Starting from the asymptotic kinematics of massless scalar fields near null infinity in
any spacetime dimension, we build two higher-spin extensions of the Carrollian definition of …