This paper introduces ALL0CORE, a new form of probabilistic non-negative tensor decomposition. ALL0CORE is a Tucker decomposition where the number of non-zero elements (i.e., the L0-norm) of the core tensor is constrained to a preset value Q much smaller than the size of the core. While the user dictates the total budget Q, the locations and values of the non-zero elements are latent variables and allocated across the core tensor during inference. ALL0CORE -- i.e., allocated L0-constrained core -- thus enjoys both the computational tractability of CP decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that ALL0CORE typically requires only tiny fractions (e.g.,~1%) of the full core to achieve the same results as full Tucker decomposition at only a correspondingly tiny fraction of the cost.

翻译：本文提出了ALL0CORE——一种新的概率非负张量分解形式。ALL0CORE是一种Tucker分解，其核心张量中非零元素数量（即L0范数）被约束为预设值Q，且该值远小于核心张量的整体规模。虽然用户指定Q的总预算，但非零元素的位置和数值作为隐变量在推理过程中被动态分配至核心张量中。ALL0CORE（即分配式L0约束核心）因此既具备CP分解的计算高效性，又保留了Tucker分解在定性层面的潜在结构优势。在一系列真实数据实验中，我们证明ALL0CORE通常仅需使用完整核心的极小比例（如约1%）即可达到完整Tucker分解的同等效果，而计算成本相应降至极低水平。