Related papers: A note on Riemann normal coordinates

We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function…

We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field…

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian…

We propose a novel Riemannian preconditioning approach for the tensor completion problem with rank constraint. A Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

Policy gradient algorithms are an important family of deep reinforcement learning techniques. Many past research endeavors focused on using the first-order policy gradient information to train policy networks. Different from these works, we…

We consider convex optimization problems with the objective function having Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new tensor method, which closes the gap between the lower…

We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in…

The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…

The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of…

Constant rescaling of a Riemannian metric appears in many computational settings, often through a global scale parameter that is introduced either explicitly or implicitly. Although this operation is elementary, its consequences are not…

Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…

This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian…

This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…