相关论文: Shrinking target horospherical equidistribution vi…

We study the dynamics of stochastic families of rational maps on the projective line. As such families can be infinite and may not typically be defined over a single number field, we introduce the concept of generalized adelic measures,…

In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty. Specifically, we consider a mean-variance formulation of the control objective and employ a…

We use the Herschel SPIRE color-color diagram to study the spectral energy distribution (SED) and the redshift estimation of high-z galaxies. We compiled a sample of 57 galaxies with spectroscopically confirmed redshifts and SPIRE…

Over-parameterized neural networks incur prohibitive memory and computational costs for resource-constrained deployment. The Strong Lottery Ticket (SLT) hypothesis suggests that randomly initialized networks contain sparse subnetworks…

Previous work has shown that one can often greatly speed up static analysis by computing data flows not for every edge in the program's control-flow graph but instead only along definition-use chains. This yields a so-called sparse static…

The recently proposed Lottery Ticket Hypothesis of Frankle and Carbin (2019) suggests that the performance of over-parameterized deep networks is due to the random initialization seeding the network with a small fraction of favorable…

In the random geometric graph model $\mathsf{Geo}_d(n,p)$, we identify each of our $n$ vertices with an independently and uniformly sampled vector from the $d$-dimensional unit sphere, and we connect pairs of vertices whose vectors are…

In this paper, we investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a…

T-distributed stochastic neighbor embedding (t-SNE) is a well-known algorithm for visualizing high-dimensional data by finding low-dimensional representations. In this paper, we study the convergence of t-SNE with generalized kernels and…

Transfer Learning is an area of statistics and machine learning research that seeks answers to the following question: how do we build successful learning algorithms when the data available for training our model is qualitatively different…

We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described…

We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…

We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…

The t-distributed Stochastic Neighbor Embedding (t-SNE) is a powerful and popular method for visualizing high-dimensional data. It minimizes the Kullback-Leibler (KL) divergence between the original and embedded data distributions. In this…

Non-equilibrium Monte Carlo simulations based on Jarzynski's equality are a well-understood method to compute differences in free energy and also to sample from a target probability distribution without the need to thermalize the system…

Time-frequency distributions (TFDs) play a vital role in providing descriptive analysis of non-stationary signals involved in realistic scenarios. It is well known that low time-frequency (TF) resolution and the emergency of cross-terms…

Given $f:\{-1, 1\}^n \rightarrow \{-1, 1\}$, define the \emph{spectral distribution} of $f$ to be the distribution on subsets of $[n]$ in which the set $S$ is sampled with probability $\widehat{f}(S)^2$. Then the Fourier Entropy-Influence…

The central limit theorem suggests Gaussian convolution as a generic blur model for images. Since Gaussian convolution is equivalent to homogeneous diffusion filtering, one way to deblur such images is to diffuse them backwards in time.…

Diffusion models with continuous stochastic differential equations (SDEs) have shown superior performances in image generation. It can serve as a deep generative prior to solving the inverse problem in magnetic resonance (MR)…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…