Beyond ReLU: How Activations Affect Neural Kernels and Random Wide Networks

ArXi:2506.22429v2 Announce Type: replace-cross In recent years, the neural tangent kernel (NTK) and neural network Gaussian process kernel (NNGP) have given theoreticians tractable limiting cases of fully connected neural networks. However, the property of these kernels are poorly understood for activation functions other than powers of the ReLU. Our main contribution is a characterization of the RKHS of these kernels for activation functions whose only non-smoothness is at zero. This extends existing theory to numerous commonly used activation functions such as SELU, ELU, or LeakyReLU.