# Tensor network compressibility of convolutional models

arXiv: https://arxiv.org/abs/2403.14379 · HTML: https://mlsanity.com/paper/2403.14379/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 21 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (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)
- [Segmentation-Based Deep-Learning Approach for Surface-Defect Detection](https://mlsanity.com/paper/1903.08536/) (2019)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [Towards Efficient Tensor Decomposition-Based DNN Model Compression with Optimization Framework](https://mlsanity.com/paper/2107.12422/) (2021)
- [CompactifAI: Extreme Compression of Large Language Models using Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/2401.14109/) (2024)
- [Einconv: Exploring Unexplored Tensor Network Decompositions for Convolutional Neural Networks](https://mlsanity.com/paper/1908.04471/) (2019)
- [ADA-Tucker: Compressing Deep Neural Networks via Adaptive Dimension Adjustment Tucker Decomposition](https://mlsanity.com/paper/1906.07671/) (2019)
- [Convolutions and More as Einsum: A Tensor Network Perspective with Advances for Second-Order Methods](https://mlsanity.com/paper/2307.02275/) (2023)

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

- [Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks](https://mlsanity.com/paper/2505.20132/) (2025)
- [Tensorization of neural networks for improved privacy and interpretability](https://mlsanity.com/paper/2501.06300/) (2025)

## Abstract (arXiv)

Convolutional neural networks (CNNs) are one of the most widely used neural network architectures, showcasing state-of-the-art performance in computer vision tasks. Although larger CNNs generally exhibit higher accuracy, their size can be effectively reduced by ``tensorization'' while maintaining accuracy, namely, replacing the convolution kernels with compact decompositions such as Tucker, Canonical Polyadic decompositions, or quantum-inspired decompositions such as matrix product states, and directly training the factors in the decompositions to bias the learning towards low-rank decompositions. But why doesn't tensorization seem to impact the accuracy adversely? We explore this by assessing how textittruncating the convolution kernels of textitdense (untensorized) CNNs impact their accuracy. Specifically, we truncated the kernels of (i) a vanilla four-layer CNN and (ii) ResNet-50 pre-trained for image classification on CIFAR-10 and CIFAR-100 datasets. We found that kernels (especially those inside deeper layers) could often be truncated along several cuts resulting in significant loss in kernel norm but not in classification accuracy. This suggests that such ``correlation compression'' (underlying tensorization) is an intrinsic feature of how information is encoded in dense CNNs. We also found that aggressively truncated models could often recover the pre-truncation accuracy after only a few epochs of re-training, suggesting that compressing the internal correlations of convolution layers does not often transport the model to a worse minimum. Our results can be applied to tensorize and compress CNN models more effectively.