This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in statistics and signal processing, low-rank tensor decompositions, and Tucker decompositions. It also includes a new family of null patterns -- not known to be detectable by current methods -- that can be thought of as continuous decompositions approximating curves and surfaces. We present a general algorithm to detect null patterns in each class using a parameter we call a \textit{chisel} that tunes the search to patterns of a prescribed shape. We also show that the patterns output by the algorithm are essentially unique.

翻译：本文介绍了一类针对张量数据的高效可计算零模式。该类模式包含统计学与信号处理中常见的块对角分解、低秩张量分解及Tucker分解等经典模式，同时涵盖了一类新的零模式族——这些模式可视为逼近曲线与曲面的连续分解，且当前方法尚未能有效检测。我们提出了一种通用算法，通过称为\textit{凿子}的参数来调整搜索过程以匹配特定形状的模式，从而检测各类零模式。此外，我们证明了算法输出的模式具有本质唯一性。