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Constructive TT-representation of the tensors given as index interaction functions with applications

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arxiv 2206.03832 v2 pith:45BXZFYW submitted 2022-06-08 math.NA cs.NA

Constructive TT-representation of the tensors given as index interaction functions with applications

classification math.NA cs.NA
keywords applicationsmethodmethodsoptimalproblemstensorsasymptoticsbuild
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments show that our method outperforms the existing ones in several practical applications, including game theory problems. Theoretical estimations of the number of operations show that in some problems, such as permanent calculation, our methods are close to the known optimal asymptotics, which are obtained by a completely different type of methods.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Tractable Shapley Values and Interactions via Tensor Networks

    cs.LG 2025-10 conditional novelty 5.0

    TN-SHAP extracts exact Shapley values and k-way interactions of a multilinear tensor-network surrogate from O(n) probe evaluations, replacing O(2^n) coalition enumeration.

  2. SeeMPS: A Python-based Matrix Product State and Tensor Train Library

    quant-ph 2026-01 conditional novelty 4.0

    SeeMPS is a Python MPS/TT library offering a BLAS/LAPACK-style API for compressed linear algebra, from DMRG and time evolution to PDE solving and Fourier transforms.