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arXiv · 2608.17135

Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions

Xiao Wang·Tomohiro Hashizume·Pia Siegl·Dieter Jaksch
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Abstract

Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise evaluation of elementary and nonlinear filtering functions on data encoded as tensor trains (TTs), a class of tensor networks. Our approach operates entirely in the compressed domain, enabling efficient computation on exponentially large datasets while maintaining a controlled computational cost. We demonstrate its power in two key areas: (I) evaluating highly nonlinear elementary and filtering functions on a 3D reactive flow field, enabling high-fidelity reaction rate computation and region filtering, and (II) finding extrema in complex optimization problems, such as solving Max-SAT instances on spaces up to $2^{70}$ configurations. These results establish ITNT as a foundational tool that provides tensor network methods with the capability for general-purpose data science and large-scale optimization.

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Xiao Wang, Tomohiro Hashizume, Pia Siegl, Dieter Jaksch. 2026-08-17. Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions. https://arxiv.org/abs/2608.17135

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