arXiv research

Low-entropy surfaces can be flowed into spheres and cylinders.

Paper resolves Huisken's conjecture without strict genus drop theorem.

This is a continuation of our first paper in [WY16]. There are two purposes of this paper: One is to give a proof of the main result in [WY16] without going through the argument depending on numerical effectiveness. The other one is to provide a proof of our conjecture, mentioned in [TY], where the assumption of negati…

Paper proposes a new binary quantization method for faster DNN inference.

Hyperplanes, hyperspheres and hypercylinders in $\Bbb R^n$ with suitable densities are proved to be weighted minimizing by a calibration argument. Also calibration method is used to prove a weighted minimal hypersurface is weighted area-minimizing locally.

Proposes a new feature preprocessing method using kernel density integral transformation.

We describe some problems, observations, and conjectures concerning thickness and packing density of knots and links in $\sp^3$ and $\R^3$. We prove the thickness of a nontrivial knot or link in $\sp^3$ is no more than $\fracπ{4}$, the thickness of a Hopf link. We also give arguments and evidence supporting the conject…

Study geodesics on Grushin spaces, proving upper bounds on conjugate times.

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model complexity, representational capacity and overfitting. In this work, we propose …

Revisits Finsler spacetimes from inertial observer perspective.

We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some density $r_x$. Our tests, formulated with a Stein operator, can be applied to any…

Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \frac{\om^p}{p!}$ is a calibration. More generally, dropping the closedness assumption on $\om$, we get an almost hermitian manifold $(M, \om, …

New noncompact Coxeter polytopes found in various dimensions.

We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a consequence and as part of the arguments we obtain perturbed harmonic maps with constant density.

When working with asymptotically hyperbolic initial data sets for general relativity it is convenient to assume certain simplifying properties. We prove that the subset of initial data sets with such properties is dense in the set of physically reasonable asymptotically hyperbolic initial data sets. More specifically, …

In this short note, we prove that conformal classes which are small perturbations of a product conformal class on a product with a standard sphere admit a metric extremal for some Laplace eigenvalue. As part of the arguments we obtain perturbed harmonic maps with constant density.

Researchers calculate the price of a perpetual put option in Lévy models.

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price process is driven by Brownian motion, an associated "master equation" for the dynam…

We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target distribution, and therefore does not perform its full power on truncated distribu…

Round balls minimize liquid drop model volumes ≤ 1.

Proves regularity for stable varifolds near specific cones.

We investigate the role of networks of alliances in preventing (multilateral) interstate wars. We first show that, in the absence of international trade, no network of alliances is peaceful and stable. We then show that international trade induces peaceful and stable networks: trade increases the density of alliances s…

Empirical study shows GANs overfit and drop modes when training is deterministic.

Overfitting frequently occurs in deep learning. In this paper, we propose a novel regularization method called Drop-Activation to reduce overfitting and improve generalization. The key idea is to drop nonlinear activation functions by setting them to be identity functions randomly during training time. During testing, …

The study examines mass drop and multiplicity in mean curvature flow.

DO-EM framework for quantum models improves generative tasks.

This paper analyzes the configurations of shapes that shows a spacelike liquid drop in Minkowski space deposited over a spacelike plane $Π$. We assume the presence of a uniform gravity field directed toward $Π$ and that the volume of the drop is prescribed. Our interest are the liquid drops that are critical points of …

Deep neural networks have dramatically achieved great success on a variety of challenging tasks. However, most successful DNNs have an extremely complex structure, leading to extensive research on model compression.As a significant area of progress in model compression, traditional gradual pruning approaches involve an…

A new robust PCA estimator combining M-estimators and minimum divergence estimators.

A method for eliciting expert beliefs using preferential questions and normalizing flows.

In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the dr…

Study guarantees convergence of mean shift mode estimation.

Minimal action of mapping class group on character variety.

One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function is known, mode is an argument of the maximum value of the density function and o…

Formula for critical points of chi fields on manifolds.

We extend the Jang equation proof of the positive energy theorem due to R. Schoen and S.-T. Yau from dimension $n=3$ to dimensions $3 \leq n <8$. This requires us to address several technical difficulties that are not present when $n=3$. The regularity and decay assumptions for the initial data sets to which our argume…

Deep neural networks (DNNs) have been proven to have many redundancies. Hence, many efforts have been made to compress DNNs. However, the existing model compression methods treat all the input samples equally while ignoring the fact that the difficulties of various input samples being correctly classified are different…

A faster method for density estimation using denoising score matching with random Fourier features.

Transfer learning has recently attracted significant research attention, as it simultaneously learns from different source domains, which have plenty of labeled data, and transfers the relevant knowledge to the target domain with limited labeled data to improve the prediction performance. We propose a Bayesian transfer…

The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational characterizations that naturally suggest a two-step scheme for their optimizatio…

Study on liquidation games with market drop-out, proving unique equilibria.

Study on how reparametrization affects neural nets' parameter spaces from a geometric perspective.

T-EMDE bridges the heterogeneity gap between image and text modalities.

Dual-ISL improves implicit generative model training with convex optimization and explicit density approximation.

New analysis of annealing paths in sampling and estimation.

We analyze convergence of Fermat distances and their application in clustering.

RDIS fills missing values in time series data explicitly.

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method …