# Tensor Shape Search for Optimum Data Compression

arXiv: https://arxiv.org/abs/2205.10651 · HTML: https://mlsanity.com/paper/2205.10651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 21 May 2022.

## Builds on (most cited first, 13 of 13)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [Model Compression with Adversarial Robustness: A Unified Optimization Framework](https://mlsanity.com/paper/1902.03538/) (2019)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [Bayesian Tensorized Neural Networks with Automatic Rank Selection](https://mlsanity.com/paper/1905.10478/) (2019)
- [Towards Compact Neural Networks via End-to-End Training: A Bayesian Tensor Approach with Automatic Rank Determination](https://mlsanity.com/paper/2010.08689/) (2020)
- [Understanding Generalization in Deep Learning via Tensor Methods](https://mlsanity.com/paper/2001.05070/) (2020)
- [On-FPGA Training with Ultra Memory Reduction: A Low-Precision Tensor Method](https://mlsanity.com/paper/2104.03420/) (2021)
- [Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion](https://mlsanity.com/paper/1505.02343/) (2015)
- [Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition](https://mlsanity.com/paper/1407.3023/) (2014)
- [High-Dimensional Uncertainty Quantification via Tensor Regression with Rank Determination and Adaptive Sampling](https://mlsanity.com/paper/2103.17236/) (2021)

## Abstract (arXiv)

Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the error and the compression ratio. In this work, we study the effect of the tensor shape on the tensor decomposition and propose an optimization model to find an optimum shape for the tensor train (TT) decomposition. The proposed optimization model maximizes the compression ratio of the TT decomposition given an error bound. We implement a genetic algorithm (GA) linked with the TT-SVD algorithm to solve the optimization model. We apply the proposed method for the compression of RGB images. The results demonstrate the effectiveness of the proposed evolutionary tensor shape search for the TT decomposition.