Tensor Network-Constrained Kernel Machines as Gaussian Processes

arXiv:2403.19500v1 Announce Type: new
Abstract: Tensor Networks (TNs) have recently been used to speed up kernel machines by constraining the model weights, yielding exponential computational and storage savings. In this paper we prove that the outputs of Canonical Polyadic Decomposition (CPD) and Tensor Train (TT)-constrained kernel machines recover a Gaussian Process (GP), which we fully characterize, when placing i.i.d. priors over their parameters. We analyze the convergence of both CPD and TT-constrained models, and show how TT yields models exhibiting …

abstract arxiv canonical computational cs.lg gaussian processes kernel machines network networks paper process processes prove speed stat.ml storage tensor train type