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Constructive TT-representation of the tensors given as index interaction functions with applications
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Constructive TT-representation of the tensors given as index interaction functions with applications
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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.
Forward citations
Cited by 2 Pith papers
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Tractable Shapley Values and Interactions via Tensor Networks
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.
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SeeMPS: A Python-based Matrix Product State and Tensor Train Library
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.
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