Summary of Tensor Network-constrained Kernel Machines As Gaussian Processes, by Frederiek Wesel et al.
Tensor Network-Constrained Kernel Machines as Gaussian Processes
by Frederiek Wesel, Kim Batselier
First submitted to arxiv on: 28 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores the connection between Tensor Networks (TNs) constrained kernel machines and Gaussian Processes (GPs). Specifically, it proves that the outputs of Canonical Polyadic Decomposition (CPD) and Tensor Train (TT)-constrained kernel machines recover a GP when placing i.i.d. priors over their parameters. The authors analyze the convergence of both CPD and TT-constrained models, showing how TT yields models exhibiting more GP behavior compared to CPD. They also empirically observe this behavior in two numerical experiments. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper shows that using Tensor Networks (TNs) can help speed up kernel machines by reducing the number of model weights needed. Researchers found that when they used certain techniques, called Canonical Polyadic Decomposition (CPD) and Tensor Train (TT), they got outputs that looked like a type of mathematical function called a Gaussian Process (GP). The authors studied how these methods worked and found that one method, TT, produced models that behaved more like GPs than the other. They tested their ideas on some data and found it to be true. |
