arXiv research

Investigates projective Finsler metrizability for non-isotropic SODEs.

We create real-time geodesic rendering for non-isotropic geometries.

In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…

Private adaptive methods improve on traditional SGD for convex optimization.

Study on stability of geodesic maps in non-isotropic manifolds.

Paper improves learning efficiency by focusing on effective dimensionality.

New method improves representation learning from non-i.i.d. and non-isotropic data.

Novel guarantees for PCA in noisy data with correlated noise and missing data.

New blurring diffusion models bridge heat dissipation and denoising.

A new probabilistic approach improves deep metric learning by considering image uncertainties and class-specific variances.

We study singularities of geodesics flows in two-dimensional generalized Finsler spaces (pseudo-Finsler spaces). Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional. This allows to consider isotropic lines as (unparametrized…

Study closed G2-structures with T3-symmetry, classifying them into types and deriving hypersymplectic structures.

The paper proposes using non-isotropic distances for more accurate trace link recommendation.

New method finds vector fields with maximal Jacobi operator rank in manifolds.

We develop a flexible framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple bootstrap algorithm. Effectively, our procedure seeks an autoencoding basis for the observed matrix that is stable with respect to the specified noise model; we call the resul…

We give a positive answer to the Chavel's conjecture [J. Diff. Geom. 4 (1970), 13-20]: a simply connected rank one normal homogeneous space is symmetric if any pair of conjugate points are isotropic. It implies that all simply connected rank one normal homogeneous space with the property that the isotropy action is var…

To each non-isotropic almost-complex immersion of a 2-torus into $S ^ 6$ we associate an algebraic curve, called the spectral curve, and a linear flow in the intersection of two Prym varieties on this spectral curve. We show that generically the spectral curve is smooth and compute the dimension of the moduli space o…

SGD implicitly performs variational inference for deep networks, converging to limit cycles.

Study on spin random fields using chaos decomposition for cosmic microwave background modeling.

Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification o…

Heat kernel analysis on a specific sub-Riemannian manifold yields precise asymptotics.

Fundamental solutions found for PDEs in Finsler geometry.

We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature…

This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map off it. The same ideas allow one to construct (pluri)-harmonic maps of finite ty…

We describe the local structure of self-dual gradient Ricci solitons in neutral signature. If the Ricci soliton is non-isotropic then it is locally conformally flat and locally isometric to a warped product of the form $I\times_\varphi N(c)$, where $N(c)$ is a space of constant curvature. If the Ricci soliton is isotro…

Estimates shared linear subspace from noisy data with multiple users.

Researchers interpret SGD using diffusion metrics for clearer geometric understanding.

New findings show cosmological constant as initial condition for non-isotropic spacetimes.

New bounds for SGLD show error decreases with more data.

Polynomial networks converge to Gaussian processes at a rate of O(n^(-1/2)).

A Dirac structure is a Lagrangian subbundle of a Courant algebroid, $L\subset\mathbb{E}$, which is involutive with respect to the Courant bracket. In particular, $L$ inherits the structure of a Lie algebroid. In this paper, we introduce the more general notion of a pseudo-Dirac structure: an arbitrary subbundle, $W\sub…

The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant…

Least symmetry breaking principle explains SGD's local minima in shallow ReLU networks.

Graph neural network constructs a sparse latent point cloud from dense point clouds.

Develops non-Markovian couplings for sub-Riemannian Brownian motions.

Enhances traffic forecasting with dynamic regression incorporating error modeling.

Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.

New algorithm recovers sparse signals robustly against Gaussian noise and adaptive adversaries.

We introduce a wrapped Gaussian for SPD matrices, enhancing data analysis.

New CLT for SGD in high-dimensional regression provides online inference.

The paper addresses online prediction in marginally stable systems with bounded perturbations.

Framework uses unlabeled out-of-domain data to improve semi-supervised classification.

The paper analyzes optimal implicit bias in linear regression for over-parameterized models.

New chaos formula simplifies variance calculation for Gaussian nodal volumes.

McDiarmid's inequality under dependence via approximate tensorization of entropy

New quasi space forms solve Thurston's geometrical space form problem.

Study of cosmic microwave background polarization using spin random fields.

New approach connects supergravity, string actions, and generalized geometry via graded Poisson structures.