Related papers: Improved Small Set Expansion in High Dimensional E…
We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fr\'echet sequence spaces.…
Given a family $X$ of subsets of $[n]$ and an ensemble of local functions $\{f_s:s\to\Sigma\; | \; s\in X\}$, an agreement test is a randomized property tester that is supposed to test whether there is some global function $G:[n]\to\Sigma$…
The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a…
We apply a dynamical systems approach to concatenation of quantum error correcting codes, extending and generalizing the results of Rahn et al. [1] to both diagonal and nondiagonal channels. Our point of view is global: instead of focusing…
We introduce a framework of layered subsets, and give a sufficient condition for when a set system supports an agreement test. Agreement testing is a certain type of property testing that generalizes PCP tests such as the plane vs. plane…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…
The LCDM cosmological model assumes the existence of a small cosmological constant in order to explain the observed accelerating cosmic expansion. Despite the dramatic improvement of the quality of cosmological data during the last decade…
Constructing active sets is a key part of the Multivariate Decomposition Method. An algorithm for constructing optimal or quasi-optimal active sets is proposed in the paper. By numerical experiments, it is shown that the new method can…
Learning the distance metric between pairs of samples has been studied for image retrieval and clustering. With the remarkable success of pair-based metric learning losses, recent works have proposed the use of generated synthetic points on…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
Query expansion has been widely used to improve the search results of first-stage retrievers, yet its influence on second-stage, cross-encoder rankers remains under-explored. A recent work of Weller et al. [44] shows that current expansion…
We study the statistical mechanics of classical Coulomb systems in a low coupling regime (Debye-Huckel regime) in a confined geometry with Dirichlet boundary conditions. We use a method recently developed by the authors which relates the…
A data augmentation methodology is presented and applied to generate a large dataset of off-axis iris regions and train a low-complexity deep neural network. Although of low complexity the resulting network achieves a high level of accuracy…
We propose a new mass-mapping algorithm, specifically designed to recover small-scale information from a combination of gravitational shear and flexion. Including flexion allows us to supplement the shear on small scales in order to…
We provide an asymptotic expansion of the maximal mean squared error (MSE) of the sample median to be attained on shrinking gross error neighborhoods about an ideal central distribution. More specifically, this expansion comes in powers of…
Image-mixing augmentations (e.g., Mixup and CutMix), which typically involve mixing two images, have become the de-facto training techniques for image classification. Despite their huge success in image classification, the number of images…
Data-parallel SGD is the de facto algorithm for distributed optimization, especially for large scale machine learning. Despite its merits, communication bottleneck is one of its persistent issues. Most compression schemes to alleviate this…
Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…
We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…
This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such…