Related papers: Redundancy for localized and Gabor frames
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
Our work builds on known results for k-uniform hypergraphs including the existence of limits, a Regularity Lemma and a Removal Lemma. Our main tool here is a theory of measures on ultraproduct spaces which establishes a correspondence…
We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea…
Let $X$ be a rearrangement-invariant space over a non-atomic $\sigma$-finite measure space $(\mathscr{R},\mu)$ and let $\alpha\in(0,\infty)$. We define the functional \begin{equation*} \|f\|_{X^{\langle \alpha \rangle}} =…
We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces…
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several…
In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…
Conditional inference on arbitrary subsets of variables is a core problem in probabilistic inference with important applications such as masked language modeling and image inpainting. In recent years, the family of Any-Order Autoregressive…
Linearity and ramification constraints have been widely used to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions. We show that fine-tuning these two…
It is now well known that the performance of a linear code $C$ under iterative decoding on a binary erasure channel (and other channels) is determined by the size of the smallest stopping set in the Tanner graph for $C$. Several recent…
Let $R$ be a standard graded Noetherian algebra over an infinite field $K$ and $M$ a finitely generated $\mathbb{Z}$-graded $R$-module. Then for any graded ideal $I\subseteq R_+$ of $R$, we show that there exist integers $e_1\geq e_2$ such…
Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically…
In this paper we consider on the notion of continuous frame of subspace and define a new concept of continuous frame, entitled {\it continuous atomic resolution of identity}, for arbitrary Hilbert space $\h$ which has a countable…
We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…
Inclusion of redundant fundamental quantities in SI system has resulted in lot of ambiguities and confusion in modern theories. The incompatibilities between the existing theories can possibly be due to incorrect assumption of fundamental…
This survey offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice. The goal is to collect the most important characterizations of Gabor frames and offer a systematic exposition…
Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly…
We construct a uniformly discrete sequence $\{\lambda_1 < \lambda_2 < \cdots\} \subset \mathbb{R}$ and functions $g$ and $\{g_n^*\}$ in $L^2(\mathbb{R})$, such that every $f \in L^2(\mathbb{R})$ admits a series expansion \[ f(x) =…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…