Zobrazeno 1 - 10
of 17 411
pro vyhledávání: '"The optimal approximation"'
Autor:
Hong, Ruiyang, Kratsios, Anastasis
The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that need not generalize, while the latter considers classes that generalize b
Externí odkaz:
http://arxiv.org/abs/2409.12335
Autor:
Yang, Yunfei
This paper studies the problem of how efficiently functions in the Sobolev spaces $\mathcal{W}^{s,q}([0,1]^d)$ and Besov spaces $\mathcal{B}^s_{q,r}([0,1]^d)$ can be approximated by deep ReLU neural networks with width $W$ and depth $L$, when the err
Externí odkaz:
http://arxiv.org/abs/2409.00901
Autor:
Trunschke, Philipp, Nouy, Anthony
This manuscript addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a sufficiently
Externí odkaz:
http://arxiv.org/abs/2407.06674
Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational uncertainty quantification. The approximation of such functions from
Externí odkaz:
http://arxiv.org/abs/2310.16940
This paper introduces deep super ReLU networks (DSRNs) as a method for approximating functions in Sobolev spaces measured by Sobolev norms $W^{m,p}$ for $m\in\mathbb{N}$ with $m\ge 2$ and $1\le p\le +\infty$. Standard ReLU deep neural networks (ReLU
Externí odkaz:
http://arxiv.org/abs/2310.10766
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP). Concretely, we pro
Externí odkaz:
http://arxiv.org/abs/2310.00526
Autor:
Siegel, Jonathan W.
We study the following two related problems. The first is to determine to what error an arbitrary zonoid in $\mathbb{R}^{d+1}$ can be approximated in the Hausdorff distance by a sum of $n$ line segments. The second is to determine optimal approximati
Externí odkaz:
http://arxiv.org/abs/2307.15285
Autor:
Lin, Shao-Bo
This paper focuses on approximation and learning performance analysis for deep convolutional neural networks with zero-padding and max-pooling. We prove that, to approximate $r$-smooth function, the approximation rates of deep convolutional neural ne
Externí odkaz:
http://arxiv.org/abs/2308.03259
Theoretical guarantees in reinforcement learning (RL) are known to suffer multiplicative blow-up factors with respect to the misspecification error of function approximation. Yet, the nature of such \emph{approximation factors} -- especially their op
Externí odkaz:
http://arxiv.org/abs/2307.13332
Autor:
Vavpetič, Aleš, Žagar, Emil
In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic B\'ezier patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal approximation of s
Externí odkaz:
http://arxiv.org/abs/2303.04434