English(EN) Deep ReLU Networks Can Fail the Best Approximation Property for Continuous Target Functions

研究发现深度ReLU网络无法满足最佳逼近性质

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-23 04:00

一篇新论文表明，深度ReLU网络可能无法实现连续目标函数的最佳逼近性质。研究人员构建了一个在二维域上的特定连续函数，其中具有两个隐藏层和(2,2,1,1)架构的网络无法达到最小的L^2逼近误差。这一发现与浅层神经网络形成对比，在浅层神经网络中，ReLU激活通常能确保回归任务的全局最小值，其原因归结于更深层网络中断线的弯曲。 AI

影响强调了深度ReLU网络的一个理论局限性，可能影响其在某些逼近任务中的应用。

排序理由在arXiv上发表的学术论文，详细介绍了关于神经网络性质的理论发现。[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) · Sebastian Kassing · 2026-10-23 04:00

Deep ReLU Networks Can Fail the Best Approximation Property for Continuous Target Functions

arXiv:2610.31264v1 Announce Type: new Abstract: We construct a continuous function on $[-1,1]^2$ for which the infimum of the $L^2$-approximation error over the class of ReLU networks with two hidden layers and architecture $(2,2,1,1)$ is not attained. This counterexample shows t…

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Deep ReLU Networks Can Fail the Best Approximation Property for Continuous Target Functions

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