Group-Invariant Tensor Train Networks for Supervised Learning

DOI10.1137/22m1506857zbMath1527.15027arXiv2206.15051OpenAlexW4387500824MaRDI QIDQ6070296

Unnamed Author, Nick Vannieuwenhoven

Publication date: 20 November 2023

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.15051

zbMATH Keywords

supervised learningrepresentation theorytensor networksgroup invariancetensor trainsgroup equivariance

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Learning and adaptive systems in artificial intelligence (68T05) Representations of finite symmetric groups (20C30) Linear transformations, semilinear transformations (15A04) Multilinear algebra, tensor calculus (15A69) Computational aspects of data analysis and big data (68T09)

Cites Work

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• Tensor-Train Decomposition
• The density-matrix renormalization group in the age of matrix product states
• Multilinear algebra. 2nd ed
• A new scheme for the tensor representation
• Hierarchical Singular Value Decomposition of Tensors
• Algorithm 862
• Generalized Eigenvalue Problems for Rectangular Matrices
• A randomized algorithm for testing nonsingularity of structured matrices with an application to asserting nondefectivity of Segre varieties
• Hand-waving and interpretive dance: an introductory course on tensor networks
• Desingularization of Bounded-Rank Matrix Sets

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