mlsanityData to 7 Oct 2026

Tensor Network-Constrained Kernel Machines as Gaussian Processes

arXiv 2403.19500 ↗First posted 28 Mar 2024cs.LG stat.MLcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 24 of its 49 references that are in the map. First posted on arXiv 28 Mar 2024.

Builds on

24 of 49 references.

References · 24

  1. 2017Deep Neural Networks as Gaussian Processescited by 617
  2. 2013Gaussian Processes for Big Datacited by 377
  3. 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 314
  4. 2014Speeding up Convolutional Neural Networks with Low Rank Expansionscited by 283
  5. 2015Tensorizing Neural Networkscited by 246
  6. 2014Scalable Variational Gaussian Process Classificationcited by 226
  7. 2014Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decompositioncited by 199
  8. 2015Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)cited by 175
  9. 2018Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processescited by 164
  10. 2018Deep Convolutional Networks as shallow Gaussian Processescited by 137
  11. 2015On the Expressive Power of Deep Learning: A Tensor Analysiscited by 97
  12. 2016Variational Fourier features for Gaussian processescited by 85
12 more
  1. 2019A Tensorized Transformer for Language Modelingcited by 85
  2. 2017Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectivescited by 53
  3. 2017Learning Compact Recurrent Neural Networks with Block-Term Tensor Decompositioncited by 33
  4. 2017Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decompositioncited by 28
  5. 2022High-Order Pooling for Graph Neural Networks with Tensor Decompositioncited by 24
  6. 2022Additive Gaussian Processes Revisitedcited by 19
  7. 2016Parallelized Tensor Train Learning of Polynomial Classifierscited by 16
  8. 2021Large-Scale Learning with Fourier Features and Tensor Decompositionscited by 14
  9. 2016Tensor Network alternating linear scheme for MIMO Volterra system identificationcited by 13
  10. 2022Improvements to Gradient Descent Methods for Quantum Tensor Network Machine Learningcited by 6
  11. 2021Faster Kernel Interpolation for Gaussian Processescited by 5
  12. 2023Beyond IID weights: sparse and low-rank deep Neural Networks are also Gaussian Processescited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 1.

2 papers.

  1. 2024No-Free-Lunch Theories for Tensor-Network Machine Learning Modelscited by 0
  2. 2026Accelerated Learning of High Dimensional Functions with a Tensor-Featured Training Networkcited by 0