论文标题
深神经切线内核和拉普拉斯内核具有相同的RKHS
Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS
论文作者
论文摘要
我们证明，当两个内核都仅限于Sphere $ \ Mathbb {s}^{d-1-1} $时，我们的深神经切线内核和Laplace内核的复制核Hilbert空间（RKHS）包括相同的功能。此外，我们证明，具有较小功率的指数功率内核（使内核降低平滑）会导致较大的RKHS，而当它仅限于Sphere $ \ Mathbb {s}^{D-1} $时，并且当它在整个$ \ Mathbb {r}^d $中定义时。
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 less 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 $\mathbb{R}^d$.
