arXiv research

The paper extends the spacetime positive mass theorem to multiple time dimensions.

Sparse OSEs achieve optimal embedding dimension of O(d).

Geometric pruning rules improve change point detection in multiple time series.

SKI accelerates GP inference with sparse grids to handle higher dimensions.

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

High-dimensional linear classifiers, such as the support vector machine (SVM) and distance weighted discrimination (DWD), are commonly used in biomedical research to distinguish groups of subjects based on a large number of features. However, their use is limited to applications where a single vector of features is mea…

In this note, we combine the work of Ilmanen and of Colding-Ilmanen-Minicozzi to observe a uniqueness property for tangent flows at the first singular time of a smooth mean curvature flow of a closed surface in 3-dimensional Euclidean space. Specifically, if, at a fixed singular point, one tangent flow is a positive in…

MetaGrad adapts multiple learning rates for faster online optimization.

Analyzes Kodaira-Iitaka dimension and multiplicity using intersection theory.

Many real-world applications involve multivariate, geo-tagged time series data: at each location, multiple sensors record corresponding measurements. For example, air quality monitoring system records PM2.5, CO, etc. The resulting time-series data often has missing values due to device outages or communication errors. …

SMTM improves MCMC sampling in high dimensions with multiple proposals and stereographic integration.

Memory is an important aspect of intelligence and plays a role in many deep reinforcement learning models. However, little progress has been made in understanding when specific memory systems help more than others and how well they generalize. The field also has yet to see a prevalent consistent and rigorous approach f…

Multidimensional data have become ubiquitous and are frequently encountered in situations where the information is aggregated over multiple data atoms. The aggregation can be over time or other features, such as geographical location. We often have access to multiple aggregated views of the same data, each aggregated i…

Given an initial $C^1$ hypersurface and a time-dependent vector field in a Sobolev space, we prove a time-global existence of a family of hypersurfaces which start from the given hypersurface and which move by the velocity equal to the mean curvature plus the given vector field. We show that the hypersurfaces are $C^1$…

In statistical learning, high covariate dimensionality poses challenges for robust prediction and inference. To address this challenge, supervised dimension reduction is often performed, where dependence on the outcome is maximized for a selected covariate subspace with smaller dimensionality. Prevalent dimension reduc…

In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a …

Singularities of the mean curvature flow of an embedded surface in R^3 are expected to be modelled on self-shrinkers that are compact, cylindrical, or asymptotically conical. In order to understand the flow before and after the singular time, it is crucial to know the uniqueness of tangent flows at the singularity. In …

The space of tensors of metric curvature type on a Euclidean vector space carries a two-parameter family of orthogonally invariant commutative nonassociative multiplications invariant with respect to the symmetric bilinear form determined by the metric. For a particular choice of parameters these algebras recover the p…

In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared loss of such CNNs is $\mathit{~locally~strongly~convex}$ in a basin of attraction…

We prove that a sequence of solutions of the Seiberg-Witten equation with multiple spinors in dimension three can degenerate only by converging (after rescaling) to a Fueter section of a bundle of moduli spaces of ASD instantons.

The problem of missing values in multivariable time series is a key challenge in many applications such as clinical data mining. Although many imputation methods show their effectiveness in many applications, few of them are designed to accommodate clinical multivariable time series. In this work, we propose a multiple…

Proposes a neural network for handling multi-sensor time series with varying input dimensions.

Estimates drift functions in SDEs using denoising diffusion models.

The paper confirms the existence of 5D regular static vacuum solutions with multiple black holes and Kasner asymptotics.

Proposes a method for evaluating multiple dimensions of organizational effectiveness using DEA.

Algorithm learns multiple LDS models from unlabeled short trajectories.

The paper strengthens a theorem on crossings under linear perturbations with Hausdorff measure estimates.

The Yamabe flow can blow up in infinite time with small perturbations.

The online problem of computing the top eigenvector is fundamental to machine learning. In both adversarial and stochastic settings, previous results (such as matrix multiplicative weight update, follow the regularized leader, follow the compressed leader, block power method) either achieve optimal regret but run slow,…

Pareto Testing optimizes model performance under multiple constraints.

In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize …

Bayesian Optimization (BO) is a data-efficient method for global black-box optimization of an expensive-to-evaluate fitness function. BO typically assumes that computation cost of BO is cheap, but experiments are time consuming or costly. In practice, this allows us to optimize ten or fewer critical parameters in up to…

A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data are limited to single population recordings, and can not identify dynamics embedde…

Generative model combines multi-dimensional annotations for more accurate ground truth estimation.

Study on multiplicities in length spectrum of Salem numbers.

This paper improves fairness in recommendation systems by learning individual preferences across multiple dimensions.

We show that any multiplicative bijection between the algebras of differentiable functions, defined on differentiable manifolds of positive dimension, is an algebra isomorphism, given by composition with a unique diffeomorphism.

We show that strictly stable components of Allen-Cahn minimal hypersurfaces always occur with multiplicity one. We also establish the uniqueness of solutions converging to nondegenerate hypersurfaces with multiplicity one. Our results work in all dimensions and without variational assumptions on the Allen-Cahn solution…

We develop an efficient algorithm to find confidence ellipsoids with volume guarantees in high dimensions.

Extends specific relative entropy to multidimensional continuous martingales.

Given a piecewise linear (PL) function $p$ defined on an open subset of $\R^n$, one may construct by elementary means a unique polyhedron with multiplicities $\D(p)$ in the cotangent bundle $\R^n\times \R^{n*}$ representing the graph of the differential of $p$. Restricting to dimension 2, we show that any smooth functi…

We present MDP Playground, a testbed for Reinforcement Learning (RL) agents with dimensions of hardness that can be controlled independently to challenge agents in different ways and obtain varying degrees of hardness in toy and complex RL environments. We consider and allow control over a wide variety of dimensions, i…

The paper finds multiple ways a special curvature can blow up in high dimensions.

We show that any 2-valued C^{1, α} (α\in (0, 1)) function u = {u_{1}, u_{2}} on an open ball B in {\mathbb R}^{n} with values u_{1}, u_{2} \in {\mathbb R}^{k} whose graph, viewed as a varifold with multiplicity 2 at points where u_{1} = u_{2} and with multiplicity 1 at points where u_{1}, u_{2} are distinct, is station…

It is shown that a hypersurface of a space form is the initial data for a solution to the mean curvature flow by parallel hypersurfaces if, and only if, it is isoparametric. By solving an ordinary differential equation, explicit solutions are given for all isoparametric hypersurfaces of space forms. In particular, for …

The paper introduces a method for forecasting corporate sales growth using multiple reference variables.

Consensus dimension reduction combines multiple visualizations to identify shared patterns.

A faster method for estimating effects in large data using fixed-point trees.