# FRAPPE: underlineFast underlineRank underlineApproximation with underlineExplainable Features for Tensors

arXiv: https://arxiv.org/abs/2206.09316 · HTML: https://mlsanity.com/paper/2206.09316/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 19 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Identifying and Alleviating Concept Drift in Streaming Tensor Decomposition](https://mlsanity.com/paper/1804.09619/) (2018)
- [Unsupervised Machine Learning Based on Non-Negative Tensor Factorization for Analyzing Reactive-Mixing](https://mlsanity.com/paper/1805.06454/) (2018)
- [A Neural Network for Determination of Latent Dimensionality in Nonnegative Matrix Factorization](https://mlsanity.com/paper/2006.12402/) (2020)
- [Automatic Unsupervised Tensor Mining with Quality Assessment](https://mlsanity.com/paper/1503.03355/) (2015)

## Built on by (most cited first, 2 of 2)

- [TRAWL: Tensor Reduced and Approximated Weights for Large Language Models](https://mlsanity.com/paper/2406.17261/) (2024)
- [Tensor Methods: A Unified and Interpretable Approach for Material Design](https://mlsanity.com/paper/2602.10392/) (2026)

## Abstract (arXiv)

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), the ideal value for the number of components is known as the canonical rank and greatly affects the quality of the decomposition 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, the first method to estimate the canonical rank of a tensor without having to compute the CPD. This method is the result of two key ideas. First, it is much cheaper to generate synthetic data with known rank compared to computing the CPD. Second, we can greatly improve the generalization ability and speed of our model by generating synthetic data that matches a given input tensor in terms of size and sparsity. We can then train a specialized single-use regression model on a synthetic set of tensors engineered to match a given input tensor and use that to estimate the canonical rank of the tensor - all without computing the expensive CPD. FRAPPE is over 24 times faster than the best-performing baseline and exhibits a 10% improvement in MAPE on a synthetic dataset. It also performs as well as or better than the baselines on real-world datasets.