arXiv research

GeoAdaLer enhances geometric understanding of Adam for stochastic optimization.

Discusses new probabilistic morphisms and geometric methods in machine and statistical learning.

We survey some recent geometric methods for studying Heegaard splittings of 3-manifolds

Enhanced spectral clustering for geometric graphs improves clustering accuracy.

Geometrically reformulates the Laplace method for optimal transport.

Based on Nielsen fixed point theory and Gröbner-Shirshov basis, we obtain a simple method to compute geometric intersection numbers and self-intersection geometric numbers of loops on surfaces.

New method proves length spectrum rigidity in various geometric settings.

We investigate learning of the differential geometric structure of a data manifold embedded in a high-dimensional Euclidean space. We first analyze kernel-based algorithms and show that under the usual regularizations, non-probabilistic methods cannot recover the differential geometric structure, but instead find mostl…

New approach combines geometric and probabilistic methods to estimate manifold dimension in high-dimensional data.

We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convol…

Proves conjecture for hyperbolic-by-cyclic groups using geometric methods.

In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important geometric quantities under the…

In this paper, we are concerned with the 2D and 3D geometric shape generation by prescribing a set of characteristic values of a specific geometric body. One of the major motivations of our study is the 3D human body generation in various applications. We develop a novel method that can generate the desired body with c…

Adapts Stein's method for geometric inequalities, addressing boundary terms.

A new geometric method for clustering SPD data improves upon Euclidean and Riemannian approaches.

Geometric methods solve sampling, optimisation, inference, and adaptive decision-making.

Combines topological and geometric approaches to data analysis.

Randomized Geometric Algebra for Convex Neural Networks Optimizes Transfer Learning.

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\sqrtκ)$ and thus achieves the optimal …

The ABP method is used to prove geometric inequalities for submanifolds and tensors.

Proposes IIKL for preserving geometric properties of non-Euclidean data.

We use the methods of geometric control theory to study extremal trajectories of vertical rolling disk. We focus on the role of symmetries of the underlying geometric structures. We demonstrate the computations in the CAS Maple package DifferentialGeometry.

Investigates geometric mean reversion process using Lie symmetry method.

We present a brief spray theory necessary for the geometric method in hydrodynamics. We make use of the convenient calculus to complete a unitary approach started by P. Michor and A. Kriegl.

The paper integrates dissipative and curl forces using geometric methods.

Geometric method improves uncertainty estimation in real-time.

PackIt creates a virtual space for testing geometric planning skills.

This paper develops a general method for constructing Poisson integrators.

Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.

GD-VAEs learn dynamics from observations using geometric and topological information.

This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.

New geometrical method optimizes portfolio with minimal risk.

The paper constructs triangulations for double twist knots using geometric methods.

Study geometric singular solutions of generalized Monge-Ampère equations.

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.

We consider the hyperbolic geometric flow $\frac{\partial^2}{\partial t^2}g(t)=-2Ric_{g(t)}$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Using the techniques and ideas of S.Brendle [Br,BS], we derive evolution equations for the Levi-Civita connection and the curvature…

Paper compares stock price prediction models using Heston and Geometric Brownian Motion.

Survey on geometric foundations of data reduction methods.

New method improves matrix completion with functional maps.

Geometric interpretation improves VAE performance and robustness.

Study characterizes Einstein manifolds in almost Ricci solitons.

Enhances quantum circuit synthesis using deep learning and geometric methods.

In this paper, a type of integrable evolution equation--the generalized Landau-Lifshitz equation into $S^n$ is considered. We deal with this equation from a geometric point of view by rewriting it in a geometric form. Through the geometric energy method, we show the global well-posedness of the corresponding Cauchy pro…

Geometric Variational Inference improves efficiency in complex probability distributions.

In this paper, an unsupervised machine learning method for geometric constellation shaping is investigated. By embedding a differentiable fiber channel model within two neural networks, the learning algorithm is optimizing for a geometric constellation shape. The learned constellations yield improved performance to sta…

In a recent paper Hodgson and Kerckhoff prove a local rigidity theorem for finite volume, three dimensional hyperbolic cone-manifolds. In this paper we extend this result to geometrically finite cone-manifolds. Our methods also give a new proof of a local version of the classical rigidity theorem for geometrically fini…

New method learns dynamics from sparse data using geometric constraints.

The paper proposes methods for volumetric parameterization of 3D solid manifolds.