arXiv research

Proposes TRNN for tensorial time series data analysis.

Tensorial Neural Networks improve neural network compression and performance.

Capsule Neural Networks classify graphs from categorical features and relationships.

Tensor networks and RNNs are equivalent, improving wave function encoding.

Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack the ability of tractable marginalization, and thus are not suitable for many ta…

Machine learning models accurately predict molecular magnetic anisotropy tensors.

LLoCa makes any network Lorentz-equivariant, achieving high accuracy and efficiency.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

A new tensorial metric describes geometry in 4D space.

The paper defines constraints for commuting endomorphisms in generalized tangent bundles.

We give a tensorial description of the Turaev cobracket on any genus 0 compact surface through the standard group-like expansion, where the Bernoulli numbers appear.

Study peels tensor equations on Schwarzschild spacetime.

New space of tensorial bodies defined, properties and representatives studied.

DAUM networks improve weather forecasting with attention and multistream features.

Developed a new symmetric hyperbolic formulation for Einstein-Yang-Mills system.

Proves energy estimates for tensorial wave equations, decoupling components for stability proof.

Paper shows invertibility of tensor X-ray transform on certain manifolds.

Study finds conditions for operator fields to be in strictly upper triangular form in small dimensions.

Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing an analogue of the Weyl tractor $W$ to the setting of smooth metric measure space…

Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.

The paper proves volume stability for hyperbolic manifolds and applies it to general relativity.

Kosmann-Lie derivatives in the bundle of Weyl spinors are considered. It is shown that the basic spin-tensorial fields of this bundle are constants with respect to these derivatives.

TACE unifies scalar and tensorial modeling in Cartesian space for accurate, stable, and efficient atomistic predictions.

In this paper, we consider various tensorial estimates in geometric Besov-type norms on a one-parameter foliation of surfaces with evolving geometries. Moreover, we wish to do this with only very weak control on these geometries. Several of these estimates were established in previous works by S. Klainerman and I. Rodn…

We derive a representation formula for the tensorial wave equation $\Box_\bg φ^I=F^I$ in globally hyperbolic Lorentzian spacetimes $(\M^{2+1}, \bg)$ by giving a geometric formulation of the method of descent which is applicable for any dimension.

Study non-homogeneous operators in 1+0 systems, classifying and analyzing their geometric properties.

Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the energy-momentum tensor of a massive spin 1/2 particle is shown.

Defines strongest integrability condition for skew-symmetric endomorphisms.

In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally construct a Markov trace on these algebras and from this trace we derive isotopy invariants for framed and classical knots and links in the so…

The paper introduces a tensor-based approach to improve neural models' aggregation of structural context.

A new geometric method approximates slow invariant manifolds without explicit time-scale separation.

New models predict interactions in multilayer networks more accurately.

Proposes a new kernel technique for tensor data in SVM.

A conformal structure on a manifold $M^n$ induces natural second order conformally invariant operators, called Möbius and Laplace structures, acting on specific weight bundles of $M$, provided that $n\ge 3$. By extending the notions of Möbius and Laplace structures to the case of surfaces and curves, we develop here th…

This paper consists of two parts. In the first part we show that in odd dimension, as well as in even dimension below the critical weight (i.e. half the dimension), the logarithmic singularities of Schwartz kernels and Green kernels of conformal invariant pseudodifferential operators are linear combinations of Weyl con…

Let $(\tilde Q,g)$ be a para-quaternionic Hermitian structure on the real vector space $V$. By referring to the tensorial presentation $(V, \tilde{Q},g) \simeq (H^2 \otimes E^{2n}, \mathfrak{sl}(H),ω^H \otimes ω^E)$, we give an explicit description, from an affine and metric point of view, of main classes of subspaces…

In a fibre bundle, natural derivatives of a section are defined as tangent vector fields on the image of a section of the fibre bundle. A local extension to vector fields in the tangent bundle leads to a direct proof of the formula expressing the curvature of a connection in terms of covariant derivatives. The result i…

Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.

Study fourth-order geometric flow of shape operator for co-dimension one immersions.

The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a "non-degeneracy" condition on the Weyl tensor \W. We investigate the geometry of the foliations …

Study proves global existence and decay for complex wave equations.

Tensor measures chirality for curves, even those with rough edges.

In this paper we characterize sprays that are metrizable by Finsler functions of constant flag curvature. By solving a particular case of the Finsler metrizability problem we provide the necessary and sufficient conditions that can be used to decide whether or not a given homogeneous system of second order ordinary dif…

Survey article analyzes pseudoholomorphic curves on symplectization via contact instantons.

We reformulate ten-dimensional type II supergravity as a generalised geometrical analogue of Einstein gravity, defined by an $O(9,1)\times O(1,9)\subset O(10,10)\times\mathbb{R}^+$ structure on the generalised tangent space. Using the notion of generalised connection and torsion, we introduce the analogue of the Levi-C…

Riemannian Manifolds may be $C^{1,1}$ and the geometry of these manifolds is investigated in \cite{Groah1}. Here, a similar analysis is given for pseudohermitian, torsion-free manifolds whereby, instead of assuming that the metric is parallel, it is assumed that the metric is pseudohermitian, a condition adopted by Ein…

Study on the topology of tensorial bodies, showing they are homeomorphic to a product space.

This research examines anisotropic conformal transformations of pseudo-Finsler surfaces.