Zobrazeno 1 - 10
of 32 514
pro vyhledávání: '"P A Barron"'
Autor:
García, Jonathan, Petersen, Philipp
We prove that a classifier with a Barron-regular decision boundary can be approximated with a rate of high polynomial degree by ReLU neural networks with three hidden layers when a margin condition is assumed. In particular, for strong margin conditi
Externí odkaz:
http://arxiv.org/abs/2412.07312
Akademický článek
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This paper presents a method for finding a sparse representation of Barron functions. Specifically, given an $L^2$ function $f$, the inverse scale space flow is used to find a sparse measure $\mu$ minimising the $L^2$ loss between the Barron function
Externí odkaz:
http://arxiv.org/abs/2312.02671
Autor:
Liao, Yulei, Ming, Pingbing
We prove the sharp embedding between the spectral Barron space and the Besov space. Given the spectral Barron space as the target function space, we prove a dimension-free result that if the neural network contains $L$ hidden layers with $N$ units pe
Externí odkaz:
http://arxiv.org/abs/2309.00788
Autor:
Wu, Lei
Publikováno v:
Journal of Machine Learning, 2023
An important problem in machine learning theory is to understand the approximation and generalization properties of two-layer neural networks in high dimensions. To this end, researchers have introduced the Barron space $\mathcal{B}_s(\Omega)$ and th
Externí odkaz:
http://arxiv.org/abs/2305.19082
The approximation properties of infinitely wide shallow neural networks heavily depend on the choice of the activation function. To understand this influence, we study embeddings between Barron spaces with different activation functions. These embedd
Externí odkaz:
http://arxiv.org/abs/2305.15839
Akademický článek
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Autor:
Abrahamsen, Nilin, Lin, Lin
A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The Barron space consists of high-dimensional functions that can be parameterized by infinite neural network
Externí odkaz:
http://arxiv.org/abs/2303.12856
Autor:
Voigtlaender, Felix
In this paper, we consider Barron functions $f : [0,1]^d \to \mathbb{R}$ of smoothness $\sigma > 0$, which are functions that can be written as \[ f(x) = \int_{\mathbb{R}^d} F(\xi) \, e^{2 \pi i \langle x, \xi \rangle} \, d \xi \quad \text{with} \qua
Externí odkaz:
http://arxiv.org/abs/2208.07605
Publikováno v:
J. Func. Anal. 284(2023),109747
In this paper, we obtain the maximal estimate for the Weyl sums on the torus $\mathbb{T}^d$ with $d\geq 2$, which is sharp up to the endpoint. We also consider two variants of this problem which include the maximal estimate along the rational lines a
Externí odkaz:
http://arxiv.org/abs/2201.12840