浅层 ReLU-s 网络逼近与泛化研究

作者 PulseAugur 编辑部 · [2 个来源] · 2026-05-18 14:27

研究人员发表了一篇论文，详细介绍了 L^p 型和 Sobolev 空间中浅层 ReLU-s 网络的逼近界限。该研究利用球谐分析来建立这些界限，在某些参数范围内显示出优于现有随机特征率的改进。此外，该论文在非参数回归场景中提出了路径范数正则化网络的极小极大最优泛化界限。 AI

影响为浅层神经网络的逼近能力和泛化特性提供了理论见解，可能为未来的模型设计提供信息。

排序理由一篇在 arXiv 上发表的学术论文，详细介绍了神经网络逼近和泛化方面的理论进展。

AI 生成摘要 · Google Gemini · 来自 2 个来源。我们如何撰写摘要 →

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arXiv stat.ML TIER_1 English(EN) · Weizhao Li, Fanghui Liu, Lei Shi · 2026-05-19 04:00

浅层 ReLU 网络在 $L^p$ 型和 Sobolev 空间中的逼近与路径范数控制泛化

arXiv:2605.18468v1 Announce Type: new Abstract: We study approximation by shallow ReLU$^s$ networks, $\sigma_s(t)=\max{0,t}^s$, and the generalization behavior of such networks under $\ell_1$ path-norm control. For the $L^p$-type integral spaces $\widetilde{\mathcal{F}}_{p,\tau_d…
arXiv stat.ML TIER_1 English(EN) · Lei Shi · 2026-05-18 14:27

浅层 ReLU 网络在 $L^p$ 型和 Sobolev 空间中的逼近与路径范数控制泛化

We study approximation by shallow ReLU$^s$ networks, $σ_s(t)=\max{0,t}^s$, and the generalization behavior of such networks under $\ell_1$ path-norm control. For the $L^p$-type integral spaces $\widetilde{\mathcal{F}}_{p,τ_d,s}$, $1\le p\le2$, we establish approximation bounds fo…