Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC decomposition (CPD), this value is known as the canonical rank and greatly affects the quality of the results. Existing methods use heuristics or Bayesian methods to estimate this value by repeatedly calculating the CPD, making them extremely computationally expensive. In this work, we propose FRAPPE and Self-FRAPPE: a cheaply supervised and a self-supervised method to estimate the canonical rank of a tensor without ever having to compute the CPD. We call FRAPPE cheaply supervised because it uses a fully synthetic training set without requiring real-world examples. We evaluate these methods on synthetic tensors, real tensors of known rank, and the weight tensor of a convolutional neural network. We show that FRAPPE and Self-FRAPPE offer large improvements in both effectiveness and speed, with a respective $15\%$ and $10\%$ improvement in MAPE and an $4000\times$ and $13\times$ improvement in evaluation speed over the best-performing baseline.

翻译：然而,这些方法大多需要一个关键参数:想要的部件的数量。在CANDECOMP/PARAFAC的分解(CPD)中,这一数值被称为罐头级,极大地影响了结果的质量。现有方法使用重力或巴耶斯方法,通过反复计算CPD来估计这一数值,使其在计算上极其昂贵。在这项工作中,我们提议FRAPPE和自制FRAPPPE:一种廉价的、受监督的和自制的估算高压罐罐的罐头等级的方法,而无需计算CPD。我们称之为低调监督FRAPAPE,因为它使用完全合成的成套培训,而不需要现实世界的实例。我们评估这些方法对合成的强力、已知级的真力,以及革命性神经网络的重量。我们表明,FRAPE和自制FRAPPPE在效率和速度两方面都大有改进,在MAPE13年和4000年业绩基准中提高了15美元和1 000美元。