arXiv:2505.00110stat.MLcs.LG2025-05被引 4
深度赫维赛德网络表达能力有限，加跳跃连接或线性单元可突破瓶颈。
On the expressivity of deep Heaviside networks
- 通过跳跃连接或线性神经元增强表达能力
- 给出VC维和逼近率的上下界
- 适用于非参数回归的统计收敛性分析
我们证明深度赫维赛德网络（DHNs）的表达能力受限，但可通过引入跳跃连接或线性激活神经元克服。本文给出了这类网络类的VC维与逼近率的上下界，并应用于非参数回归模型中，推导出DHN拟合的统计收敛速率。
原文摘要 · Abstract (English)
We show that deep Heaviside networks (DHNs) have limited expressiveness but that this can be overcome by including either skip connections or neurons with linear activation. We provide lower and upper bounds for the Vapnik-Chervonenkis (VC) dimensions and approximation rates of these network classes. As an application, we derive statistical convergence rates for DHN fits in the nonparametric regression model.
深度网络表达能力统计学习
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