arXiv research

Study of special Lorentzian Lie groups with 4D isometry group, finding all are non-gradient expanding Ricci solitons.

Study on non-gradient Ricci almost solitons in warped products.

Gradient Ricci solitons can be extended to non-gradient Ricci solitons using energy function.

The paper classifies quasi-Einstein 3-manifolds and their properties.

A1GM method improves efficiency in reconstructing missing data using KL divergence.

PairNets optimize AI models for fast IoT applications.

In this work, a non-gradient descent learning (NGDL) scheme was proposed for deep feedforward neural networks (DNN). It is known that an autoencoder can be used as the building blocks of the multi-layer perceptron (MLP) DNN, the MLP is taken as an example to illustrate the proposed scheme of pseudoinverse learning algo…

This research analyzes how input and output layers affect deep neural networks' resistance to adversarial attacks.

Study defends shallow neural networks from data-poisoning attacks.

We study $3$-dimensional Ricci solitons which project via a semi-conformal mapping to a surface. We reformulate the equations in terms of parameters of the map; this enables us to give an ansatz for constructing solitons in terms of data on the surface. A complete description of the soliton structures on all the $3$-di…

The three-dimensional Heisenberg group $H_3$ has three left-invariant Lorentz metrics $g_1$, $g_2$ and $g_3$. They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric $g_1$ as a Lorentz Ricci soliton. This Ricci soliton $g_1$ is a shrinking non-gradient Ricci soliton. Likew…

The paper classifies Ricci solitons and studies harmonic vector fields on a specific Thurston geometry.

Paper studies non-gradient almost Yamabe solitons and their properties.

In this paper, we briefly review the basic scheme of the pseudoinverse learning (PIL) algorithm and present some discussions on the PIL, as well as its variants. The PIL algorithm, first presented in 1995, is a non-gradient descent and non-iterative learning algorithm for multi-layer neural networks and has several adv…

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riema…

New quasi-Einstein metrics found on a sphere.

Study of Bach flow on specific nilmanifolds, converging to a soliton.

SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.

With a f-left-invariant Riemannian metric on a Lie group $G$, we mean a Riemannian metric which is conformally equivalent to a left-invariant Riemannian metric, with the conformal factor $f$. In this article, we study the geometry of such metrics and give a necessary and sufficient condition for an f-left-invariant Rie…

The purpose of this article is to study the existence and uniqueness of quasi-Einstein structures on $3$-dimensional homogeneous Riemannian manifolds. To this end, we use the eight model geometries for 3-dimensional manifolds identified by Thurston. First, we present here a complete description of quasi-Einstein metric…

Killing fields on compact m-quasi-Einstein manifolds are shown under specific curvature conditions.

Foundation for robust finance using rough path theory.

In this paper, we address a problem of machine learning system vulnerability to adversarial attacks. We propose and investigate a Key based Diversified Aggregation (KDA) mechanism as a defense strategy. The KDA assumes that the attacker (i) knows the architecture of classifier and the used defense strategy, (ii) has an…

The study explores $(m,ρ)$-quasi-Einstein structures on contact metric manifolds.

Gradient-enhanced deep GPs improve multifidelity model accuracy.

In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to change with both altitude and velocity. It is thus important to quantify these cha…

New algorithm improves online learning with reduced discretization.

E-LDA offers faster, interpretable LDA topic models.

New algorithm trains ReLU gates provably in linear time.

SOLO uses DNN to optimize complex topology problems with reduced FEM calculations.

The paper analyzes convergence of Langevin dynamics with time-dependent metrics.

Introduces new info-geometric structure for dynamics on graphs and hypergraphs.

New method reconstructs non-equilibrium stochastic systems from data.

Discovering quasipotential equations from data using machine learning.

New degree theory proves existence of solitons on 4D manifolds.