English(EN) The minimal width of neural networks and immersions of real projective space

神经网络宽度与实射影空间浸入相关联

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-15 04:00

本文深入探讨了深度神经网络逼近连续函数所需的最小宽度。它将神经网络的逼近能力与微分拓扑学领域联系起来，特别是关于实射影空间的浸入。研究表明，在某些条件下，最小宽度至少为 n+min{n,m}，这在 n 为 2、3、4、7 或 8 的情况下，扩展了之前关于 ReLU 网络的发现。 AI

影响探索神经网络容量的理论极限，可能为未来的架构设计提供信息。

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

AI 生成摘要 · Google Gemini · 来自 1 个来源。我们如何撰写摘要 →

本文如何被排名

Signal score: 16 / 100; Composite score across the factors below. Higher = stronger signal that this story matters right now.
Newsworthiness bucket: Tool; 关于神经网络理论方面的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]
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AI-industry relevance: High; Clearly on-topic for AI-industry coverage.
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完整方法见我们的编辑标准。

arXiv cs.LG TIER_1 English(EN) · BaoZhi Chu, Ben Weinkove · 2026-10-15 04:00

神经网络的最小宽度与实射影空间的浸入

arXiv:2610.20229v1 Announce Type: cross Abstract: We investigate the minimal width of deep neural networks that can approximate all continuous functions from $\mathbb{R}^n$ to $\mathbb{R}^m$ in the topology of uniform convergence on compact subsets. We show that whenever the real…