# Semi-tensor Product-based TensorDecomposition for Neural Network Compression

arXiv: https://arxiv.org/abs/2109.15200 · HTML: https://mlsanity.com/paper/2109.15200/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 50 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Convolutional Neural Networks for Sentence Classification](https://mlsanity.com/paper/1408.5882/) (2014)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks](https://mlsanity.com/paper/1503.00075/) (2015)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [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)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [CondenseNet: An Efficient DenseNet using Learned Group Convolutions](https://mlsanity.com/paper/1711.09224/) (2017)
- [Accelerating Very Deep Convolutional Networks for Classification and Detection](https://mlsanity.com/paper/1505.06798/) (2015)
- [A Primer on Neural Network Models for Natural Language Processing](https://mlsanity.com/paper/1510.00726/) (2015)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [Ultimate tensorization: compressing convolutional and FC layers alike](https://mlsanity.com/paper/1611.03214/) (2016)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [Learning Compact Recurrent Neural Networks with Block-Term Tensor Decomposition](https://mlsanity.com/paper/1712.05134/) (2017)
- [T-Net: Parametrizing Fully Convolutional Nets with a Single High-Order Tensor](https://mlsanity.com/paper/1904.02698/) (2019)
- [Network Decoupling: From Regular to Depthwise Separable Convolutions](https://mlsanity.com/paper/1808.05517/) (2018)

## Built on by (most cited first, 3 of 3)

- [Activation Map Compression through Tensor Decomposition for Deep Learning](https://mlsanity.com/paper/2411.06346/) (2024)
- [Low Rank Optimization for Efficient Deep Learning: Making A Balance between Compact Architecture and Fast Training](https://mlsanity.com/paper/2303.13635/) (2023)
- [Efficient Resource-Constrained Training of Transformers via Subspace Optimization](https://mlsanity.com/paper/2510.09160/) (2025)

## Abstract (arXiv)

The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper, the semi-tensor product is used to generalize classical matrix product-based mode product to semi-tensor mode product. As it permits the connection of two factors with different dimensionality, more flexible and compact tensor decompositions can be obtained with smaller sizes of factors. Tucker decomposition, Tensor Train (TT) and Tensor Ring (TR) are common decomposition for low rank compression of deep neural networks. The semi-tensor product is applied to these tensor decompositions to obtained their generalized versions, i.e., semi-tensor Tucker decomposition (STTu), semi-tensor train(STT) and semi-tensor ring (STR). Experimental results show the STTu, STT and STR achieve higher compression factors than the conventional tensor decompositions with the same accuracy but less training times in ResNet and WideResNetcompression. With 2% accuracy degradation, the TT-RN (rank = 14) and the TR-WRN (rank = 16) only obtain 3 times and99t times compression factors while the STT-RN (rank = 14) and the STR-WRN (rank = 16) achieve 9 times and 179 times compression factors, respectively.