发表机构
Clarendon Laboratory, University of Oxford; The Hamburg Centre for Ultrafast Imaging; Institute for Quantum Physics, University of Hamburg; Institute of Software Methods for Product Virtualization, German Aerospace Center (DLR)（牛津大学克拉伦登实验室; 汉堡超快成像中心; 汉堡大学量子物理研究所; 德国航空航天中心产品虚拟化软件方法研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出迭代张量网络变换（ITNTs）框架，可在压缩域中对张量列编码的数据执行初等与滤波函数的逐元素评估，能高效处理大规模数据，在三维流场计算与Max-SAT问题求解中展现出应用价值。
AI 中文摘要
张量网络是压缩大规模数据的强大格式，但它们在通用数据处理中的应用受限于非线性运算的执行难度。本文提出迭代张量网络变换（ITNTs），这是一种通用算法框架，用于对编码为张量列（TTs，一类张量网络）的数据执行初等函数与非线性滤波函数的逐元素评估。我们的方法完全在压缩域中运行，可在指数级大规模数据集上实现高效计算，同时保持可控的计算成本。我们在两个关键领域验证其效能：（I）对三维反应流场执行高度非线性的初等函数与滤波函数评估，实现高保真反应速率计算与区域滤波；（II）在复杂优化问题中寻找极值，例如求解最多达2^70个配置空间的最大可满足性（Max-SAT）实例。这些结果确立了ITNT作为基础工具，为张量网络方法提供通用数据科学与大规模优化的能力。
英文摘要
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.
Comments23 pages, 10 figures
