We prove that the reproducing kernel Hilbert spaces (RKHS) of a deep neural tangent kernel and the Laplace kernel include the same set of functions, when both kernels are restricted to the sphere $\mathbb{S}^{d-1}$. Additionally, we prove that the exponential power kernel with a smaller power (making the kernel more non-smooth) leads to a larger RKHS, when it is restricted to the sphere $\mathbb{S}^{d-1}$ and when it is defined on the entire $\mathbb{R}^d$.

中文翻译：

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Deep Neural Tangent Kernel 和 Laplace Kernel 具有相同的 RKHS

我们证明了深度神经切线核和拉普拉斯核的再生核希尔伯特空间 (RKHS) 包括相同的函数集，当两个核都被限制在球体 $\mathbb{S}^{d-1}$ 时。此外，我们证明了具有较小幂的指数幂内核（使内核更不光滑）导致更大的 RKHS，当它被限制在球体 $\mathbb{S}^{d-1}$ 和当它是在整个 $\mathbb{R}^d$ 上定义的。