mlsanityData to 14 Oct 2026

Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks

arXiv 2210.03828 ↗First posted 7 Oct 2022math.NA cs.LG cs.NAcited by 2

Not on the map. Why?

Abstract (arXiv)

We show how to develop sampling-based alternating least squares (ALS) algorithms for decomposition of tensors into any tensor network (TN) format. Provided the TN format satisfies certain mild assumptions, resulting algorithms will have input sublinear per-iteration cost. Unlike most previous works on sampling-based ALS methods for tensor decomposition, the sampling in our framework is done according to the exact leverage score distribution of the design matrices in the ALS subproblems. We implement and test two tensor decomposition algorithms that use our sampling framework in a feature extraction experiment where we compare them against a number of other decomposition algorithms.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 10 of its 34 references that are in the map. First posted on arXiv 7 Oct 2022.

Builds on

10 of 34 references.

References · 10

  1. 2014Sketching as a Tool for Numerical Linear Algebracited by 288
  2. 2016Tensor Ring Decompositioncited by 127
  3. 2016TensorLy: Tensor Learning in Pythoncited by 104
  4. 2017Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectivescited by 54
  5. 2019Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstructioncited by 11
  6. 2021More Efficient Sampling for Tensor Decomposition With Worst-Case Guaranteescited by 7
  7. 2022Subquadratic Kronecker Regression with Applications to Tensor Decompositioncited by 6
  8. 2022Optimizing Tensor Network Contraction Using Reinforcement Learningcited by 5
  9. 2022Cost-efficient Gaussian Tensor Network Embeddings for Tensor-structured Inputscited by 5
  10. 2022Fast algorithms for least square problems with Kronecker lower subsetscited by 1

Built on by

Cited by year

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

2 papers.

  1. 2024Tensor Decomposition with Unaligned Observationscited by 1
  2. 2025Fast Tensor Completion via Approximate Richardson Iterationcited by 0