We investigate the relationship between neural network Gaussian process kernels (NNGP) for infinitely large transform neural network architectures, and Laplace operators on the data sets where these networks are typically applied. NNGPs are equivalent to Bayesian neural networks in a particular limit, and provide a closed form for evaluation on new data points. This kernel is available for many network architectures, and we briefly study which kernels correspond to which networks, focusing on transformer networks. The integral operator equipped with the NNGP kernel of an infinite-width transform network spectrum is then studied and the transformation between bases is considered to derive the geometry induced on the data via the Laplace Beltrami operator. This induction is possible because all NNGP kernels are symmetric positive semidefinite kernels and thus can be used to span functional spaces on the data manifold on which the original network was trained. The Laplacian-based manifold learning approach is justified by the fact that the Laplace-Beltrami operator encodes all geometric information of a Riemannian manifold.