# Quantization Aware Factorization for Deep Neural Network Compression

arXiv: https://arxiv.org/abs/2308.04595 · HTML: https://mlsanity.com/paper/2308.04595/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 8 Aug 2023.

## Builds on (most cited first, 20 of 20)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [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)
- [Bayesian Bits: Unifying Quantization and Pruning](https://mlsanity.com/paper/2005.07093/) (2020)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [Extremely Low Bit Neural Network: Squeeze the Last Bit Out with ADMM](https://mlsanity.com/paper/1707.09870/) (2017)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Towards Efficient Tensor Decomposition-Based DNN Model Compression with Optimization Framework](https://mlsanity.com/paper/2107.12422/) (2021)
- [Same, Same But Different - Recovering Neural Network Quantization Error Through Weight Factorization](https://mlsanity.com/paper/1902.01917/) (2019)
- [A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization](https://mlsanity.com/paper/1506.04209/) (2015)
- [T-Net: Parametrizing Fully Convolutional Nets with a Single High-Order Tensor](https://mlsanity.com/paper/1904.02698/) (2019)
- [Active Subspace of Neural Networks: Structural Analysis and Universal Attacks](https://mlsanity.com/paper/1910.13025/) (2019)
- [A General System for Heuristic Solution of Convex Problems over Nonconvex Sets](https://mlsanity.com/paper/1601.07277/) (2016)
- [Parallel Algorithms for Constrained Tensor Factorization via the Alternating Direction Method of Multipliers](https://mlsanity.com/paper/1409.2383/) (2014)
- [Reduced-Order Modeling of Deep Neural Networks](https://mlsanity.com/paper/1910.06995/) (2019)
- [Generalized Higher-Order Tensor Decomposition via Parallel ADMM](https://mlsanity.com/paper/1407.1399/) (2014)

## Built on by (most cited first, 6 of 6)

- [Synchronized Video-to-Audio Generation via Mel Quantization-Continuum Decomposition](https://mlsanity.com/paper/2503.06984/) (2025)
- [Addition is almost all you need: Compressing large language models with double binary factorization](https://mlsanity.com/paper/2505.11076/) (2025)
- [Post-Training Network Compression for 3D Medical Image Segmentation: Reducing Computational Efforts via Tucker Decomposition](https://mlsanity.com/paper/2404.09683/) (2024)
- [Frugal Machine Learning for Energy-efficient, and Resource-aware Artificial Intelligence](https://mlsanity.com/paper/2506.01869/) (2025)
- [NanoQuant: Efficient Sub-1-Bit Quantization of Large Language Models](https://mlsanity.com/paper/2602.06694/) (2026)
- [Distribution-Aware Tensor Decomposition for Compression of Convolutional Neural Networks](https://mlsanity.com/paper/2511.04494/) (2025)

## Abstract (arXiv)

Tensor decomposition of convolutional and fully-connected layers is an effective way to reduce parameters and FLOP in neural networks. Due to memory and power consumption limitations of mobile or embedded devices, the quantization step is usually necessary when pre-trained models are deployed. A conventional post-training quantization approach applied to networks with decomposed weights yields a drop in accuracy. This motivated us to develop an algorithm that finds tensor approximation directly with quantized factors and thus benefit from both compression techniques while keeping the prediction quality of the model. Namely, we propose to use Alternating Direction Method of Multipliers (ADMM) for Canonical Polyadic (CP) decomposition with factors whose elements lie on a specified quantization grid. We compress neural network weights with a devised algorithm and evaluate it's prediction quality and performance. We compare our approach to state-of-the-art post-training quantization methods and demonstrate competitive results and high flexibility in achiving a desirable quality-performance tradeoff.