提出迭代张量网络变换，实现压缩数据中逐元素非线性计算。
Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions
- 在张量列车压缩域内迭代执行非线性函数运算
- 在3D反应流场上实现高保真反应速率计算与区域过滤
- 可求解高达2^70状态空间的Max-SAT优化问题
张量网络是压缩大规模数据的强大工具，但其在通用数据处理中的应用受限于难以执行非线性操作。本文提出迭代张量网络变换（ITNT），一种在张量列车（TT）编码的数据上进行逐元素基本函数和非线性滤波函数评估的通用算法框架。该方法完全在压缩域内运行，可在指数级大规模数据上高效计算，同时保持可控的计算成本。我们在两个关键领域验证了其能力：(I) 对3D反应流场中的高度非线性函数进行评估，实现高保真反应速率计算与区域过滤；(II) 在复杂优化问题中寻找极值，例如求解最多包含2^70种配置的Max-SAT实例。这些结果表明，ITNT为张量网络方法赋予了通用数据科学和大规模优化的能力，是一项基础性工具。
原文摘要 · Abstract (English)
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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