Tensor Network-Constrained Kernel Machines as Gaussian Processes

Frederiek Wesel, Kim Batselier
3/28/2024
cs.LGstat.ML

No official code found. Best implementation: fwesel/TensorGP (1 star, MIT, last commit 2025-02-11).

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 more GP behavior compared to CPD, for the same number of model parameters. We empirically observe this behavior in two numerical experiments where we respectively analyze the convergence to the GP and the performance at prediction. We thereby establish a connection between TN-constrained kernel machines and GPs.

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Code Implementations(1)

fwesel/TensorGPCommunity100%
MIT

This repository allows for the reproducibility of the experimentsi in the omonimous paper.

11PythonFeb 11, 20251 years agoMIT

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Cite this paper

@article{wesel2024tensor,
  title  = {Tensor Network-Constrained Kernel Machines as Gaussian Processes},
  author = {Frederiek Wesel and Kim Batselier},
  year   = {2024},
  eprint = {2403.19500},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2403.19500v1}
}

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