English(EN) Depth Separation for Neural Networks under Gaussian Measure

神经网络中的深度分离：证明深度为3的ReLU网络具有优越性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-22 04:00

研究人员证明了深度为3的ReLU神经网络可以在维度上以多项式大小逼近某些径向函数，而深度为2的网络则需要指数大小或亚指数界限的权重。这一发现建立在Eldan和Shamir以及Daniely的工作基础上，在Gausian测度下强调了网络深度对于高效逼近的重要性。这些定理的证明已通过Lean 4编程语言进行了形式化验证。 AI

影响这项研究有助于加深对神经网络表达能力和效率的理论理解，可能指导未来的架构设计。

排序理由关于神经网络理论的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

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arXiv cs.LG TIER_1 English(EN) · Cynthia Bortolotto, Francisco Ganacim, Roberto I. Oliveira · 2026-10-22 04:00

高斯测度下神经网络的深度分离

arXiv:2610.28800v1 Announce Type: cross Abstract: We revisit the problem of depth separation for neural networks, as studied by Eldan and Shamir, Daniely, and others. Specifically, we consider the natural setting of $L^2$ approximation of radial functions under the standard Gauss…

本文如何被排名

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高斯测度下神经网络的深度分离

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