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This paper introduces Iterative Tensor Network Transformations (ITNTs), a framework that overcomes the historical limitation of tensor networks in handling nonlinear operations within compressed data domains. By enabling efficient element-wise evaluation on exponentially large datasets, this method bridges high-fidelity scientific simulation with general-purpose optimization tasks like Max-SAT solving at scales previously unattainable for classical or standard quantum approaches. The work represents a significant algorithmic advance that expands the utility of tensor networks beyond specific physics applications into broader data science and complex problem-solving contexts.
Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions
arXiv:2608.17135v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)
arXiv:2608.17135 [cs.LG]
(or arXiv:2608.17135v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.17135 arXiv-issued DOI via DataCite (pending registration)
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