相关论文: Guarantees for the Kronecker Fast Johnson-Lindenst…

We show that sufficiently low tensor rank for the balanced tripartitioning tensor $P_d(x,y,z)=\sum_{A,B,C\in\binom{[3d]}{d}:A\cup B\cup C=[3d]}x_Ay_Bz_C$ for a large enough constant $d$ implies uniform arithmetic circuits for the matrix…

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…

Let $Q$ be a relatively compact subset in a Hilbert space $V$. For a given $\e>0$ let $N(\e,Q)$ be the minimal number of linear measurements, sufficient to reconstruct any $x \in Q$ with the accuracy $\e$. We call $N(\e,Q)$ a sampling…

The scalar-tensor theory is plagued by nagging questions if different conformal frames, in particular the Jordan and Einstein conformal frames, are equivalent to each other. As a closely related question, there are opposing views on which…

Controlling the spectral norm of the Jacobian matrix, which is related to the convolution operation, has been shown to improve generalization, training stability and robustness in CNNs. Existing methods for computing the norm either tend to…

Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this…

We recently formulated important Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Modular Johnson-Lindenstrauss Flattening Conjecture in the Appendix of \textit{[arXiv: 2207.12799.v1]}. For the sake of wide accessibility…

We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…

Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary…

Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…

We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy,…

The aim of this paper is to use the methods and results of symplectic homogenization (see [V4]) to prove existence of periodic orbits and invariant measures with rotation number depending on the differential of the Homogenized Hamiltonian.…

This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…

We here deduce Lorentz transformation (LT) as a member of a class of time-dependent coordinate transformations, complementary to those already known as spatial translations and rotations. This exercise validates the principle of physical…

In this work, we analyze dimension reduction algorithms based on the Kac walk and discrete variants. (1) For $n$ points in $\mathbb{R}^{d}$, we design an optimal Johnson-Lindenstrauss (JL) transform based on the Kac walk which can be…

Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…

We show that if a permutation statistic can be written as a linear combination of bivincular patterns, then its moments can be expressed as a linear combination of factorials with constant coefficients. This generalizes a result of…

Taking the anti-de Sitter minimum of KKLT and the large volume scenario at face value, we argue for the existence of logarithmic quantum corrections to AdS swampland conjectures. If these conjectures receive such corrections, it is natural…

This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. Then, sparse random…

We provide another approach to Friedland's result that the topological entropy $h$ of a symmetric nearest-neighbor subshift is computable. Instead of the previous algebraic technique, our approach is mostly combinatorial and involves only…