FRAPPE: $\underline{\text{F}}$ast $\underline{\text{Ra}}$nk $\underline{\text{App}}$roximation with $\underline{\text{E}}$xplainable Features for Tensors

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.