Regularization with Dot-Product Kernels

By Alex Smola, Zoltán L. Óvári, Robert C. Williamson. 2000

134 citations recorded by the source corpus.

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Citations in the corpus

On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, methodology): “If X ⊂ R d +1 is the d -dimensional hypersphere { x ∈ R d +1 , k x k 22 = 1 , then speciﬁc kernels may be used, of the form k ( x, y ) = t ( x ⊤ y ) , where t has to have a positive Legendre expansion (Smola et al., 2001).”
Fastfood: Approximate Kernel Expansions in Loglinear Time (2014, methodology): “Since Smola et al. (2001) derive an incomplete characterization involving an unspeciﬁed radial contribution we give a detailed derivation below.”
Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks (2020, unknown): “Eigenvalues of the kernel scales with d as k ⇠ N(d, k) 1 (Smola et al., 2001) in the d ! 1 limit, as we verify numerically in Figure 1 for NTK.”
On the Inductive Bias of Neural Tangent Kernels (2019, methodology): “In order to balance our observations on smoothness, we also consider approximation properties for the NTK of two-layer ReLU networks, by characterizing the RKHS using a Mercer decomposition of the kernel in the basis of spherical harmonics [6, 46, 47].”
Supervised classification and mathematical optimization (2013, background): “However, many potential kernels, such as those found in [172, 207, 215], violate such assumptions.”
A Fine-Grained Spectral Perspective on Neural Networks (2019, methodology): “[54]’s observation that spherical harmonics diagonalize dot product kernels, with the latter two concurrent to us.”
A tutorial on support vector regression (2004, unknown): “For further details see [Berg et al., 1984, Smola et al., 2001].”
Learning with non-positive kernels (2004, background): “One such instance is the hyperbolic tangent kernel k ( x, x 0 ) = tanh( h x, x 0 i − 1) of Neural Networks, which is indeﬁnite for any range of parameters or dimensions (Smola et al., 2000).”