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of 154
pro vyhledávání: '"Iwen, Mark A."'
We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, this phenomenon has been studied in a number of works. A particular chal
Externí odkaz:
http://arxiv.org/abs/2410.16247
In this paper we prove the existence of H\"{o}lder continuous terminal embeddings of any desired $X \subseteq \mathbb{R}^d$ into $\mathbb{R}^{m}$ with $m=\mathcal{O}(\varepsilon^{-2}\omega(S_X)^2)$, for arbitrarily small distortion $\varepsilon$, whe
Externí odkaz:
http://arxiv.org/abs/2408.02812
We propose two provably accurate methods for low CP-rank tensor completion - one using adaptive sampling and one using nonadaptive sampling. Both of our algorithms combine matrix completion techniques for a small number of slices along with Jennrich'
Externí odkaz:
http://arxiv.org/abs/2403.09932
The celebrated Johnson-Lindenstrauss lemma states that for all $\varepsilon \in (0,1)$ and finite sets $X \subseteq \mathbb{R}^N$ with $n>1$ elements, there exists a matrix $\Phi \in \mathbb{R}^{m \times N}$ with $m=\mathcal{O}(\varepsilon^{-2}\log n
Externí odkaz:
http://arxiv.org/abs/2403.03969
In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements. Crucially, the proposed random measurement ensembles are both designed to be compactly
Externí odkaz:
http://arxiv.org/abs/2308.13709
We propose an adaptive and provably accurate tensor completion approach based on combining matrix completion techniques (see, e.g., arXiv:0805.4471, arXiv:1407.3619, arXiv:1306.2979) for a small number of slices with a modified noise robust version o
Externí odkaz:
http://arxiv.org/abs/2307.01297
Autor:
Gross, Craig, Iwen, Mark
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless march to
Externí odkaz:
http://arxiv.org/abs/2302.00752
The remarkable successes of neural networks in a huge variety of inverse problems have fueled their adoption in disciplines ranging from medical imaging to seismic analysis over the past decade. However, the high dimensionality of such inverse proble
Externí odkaz:
http://arxiv.org/abs/2208.13305
Autor:
Iwen, Mark A., Roach, Mark Philip
Let $\mathcal{M}$ be a compact $d$-dimensional submanifold of $\mathbb{R}^N$ with reach $\tau$ and volume $V_{\mathcal M}$. Fix $\epsilon \in (0,1)$. In this paper we prove that a nonlinear function $f: \mathbb{R}^N \rightarrow \mathbb{R}^{m}$ exists
Externí odkaz:
http://arxiv.org/abs/2206.03376
Let $M$ be a smooth, connected, compact submanifold of $\mathbb{R}^n$ without boundary and of dimension $k\geq 2$. Let $\mathbb{S}^k \subset \mathbb{R}^{k+1}\subset \mathbb{R}^n$ denote the $k$-dimesnional unit sphere. We show if $M$ has reach equal
Externí odkaz:
http://arxiv.org/abs/2202.06161