# A simple approach for quantizing neural networks

arXiv: https://arxiv.org/abs/2209.03487 · HTML: https://mlsanity.com/paper/2209.03487/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 7 Sep 2022.

## Builds on (most cited first, 12 of 12)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [Improving Neural Network Quantization without Retraining using Outlier Channel Splitting](https://mlsanity.com/paper/1901.09504/) (2019)
- [A Survey on Methods and Theories of Quantized Neural Networks](https://mlsanity.com/paper/1808.04752/) (2018)
- [A Deterministic Linear Program Solver in Current Matrix Multiplication Time](https://mlsanity.com/paper/1910.11957/) (2019)
- [Post-training Quantization for Neural Networks with Provable Guarantees](https://mlsanity.com/paper/2201.11113/) (2022)
- [A Greedy Algorithm for Quantizing Neural Networks](https://mlsanity.com/paper/2010.15979/) (2020)
- [Approximation of functions with one-bit neural networks](https://mlsanity.com/paper/2112.09181/) (2021)

## Built on by (most cited first, 8 of 8)

- [MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantization](https://mlsanity.com/paper/2406.00800/) (2024)
- [Unified Stochastic Framework for Neural Network Quantization and Pruning](https://mlsanity.com/paper/2412.18184/) (2024)
- [Frame Quantization of Neural Networks](https://mlsanity.com/paper/2404.08131/) (2024)
- [Compressing Recurrent Neural Networks for FPGA-accelerated Implementation in Fluorescence Lifetime Imaging](https://mlsanity.com/paper/2410.00948/) (2024)
- [SPFQ: A Stochastic Algorithm and Its Error Analysis for Neural Network Quantization](https://mlsanity.com/paper/2309.10975/) (2023)
- [Computability of Classification and Deep Learning: From Theoretical Limits to Practical Feasibility through Quantization](https://mlsanity.com/paper/2408.06212/) (2024)
- [Low-Bit Quantization of Bandlimited Graph Signals via Iterative Methods](https://mlsanity.com/paper/2601.18782/) (2026)
- [Astro: Activation-guided Structured Regularization for Outlier-Robust LLM Post-Training Quantization](https://mlsanity.com/paper/2602.07596/) (2026)

## Abstract (arXiv)

In this short note, we propose a new method for quantizing the weights of a fully trained neural network. A simple deterministic pre-processing step allows us to quantize network layers via memoryless scalar quantization while preserving the network performance on given training data. On one hand, the computational complexity of this pre-processing slightly exceeds that of state-of-the-art algorithms in the literature. On the other hand, our approach does not require any hyper-parameter tuning and, in contrast to previous methods, allows a plain analysis. We provide rigorous theoretical guarantees in the case of quantizing single network layers and show that the relative error decays with the number of parameters in the network if the training data behaves well, e.g., if it is sampled from suitable random distributions. The developed method also readily allows the quantization of deep networks by consecutive application to single layers.