新的界限揭示了球体上浅层 ReLU 网络配置相关的近似极限

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-11 04:00

研究人员为浅层 ReLU$^k$ 神经网络在球体上运行时所能达到的近似能力建立了新的理论界限。研究结果表明，近似精度取决于网络内部参数的配置，特别是两极分离距离。对于某些参数配置，这些网络可以优于传统的有限元方法，但这种优势存在固有的局限性。 AI

排序理由这是一篇发表在 arXiv 上的研究论文，详细介绍了关于神经网络的理论发现。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.LG TIER_1 English(EN) · Tong Mao, Jinchao Xu · 2026-09-11 04:00

基于配置的浅层ReLU$^k$网络在球体上近似的下界

arXiv:2510.04060v3 Announce Type: replace-cross Abstract: We establish two related but logically distinct results for shallow ReLU$^k$ neural networks on the unit sphere $\SS^d$. First, for an arbitrary set of inner neural-network parameters, the best $\mathcal{L}^2(\SS^d)$ appro…