# A Greedy Algorithm for Quantizing Neural Networks

arXiv: https://arxiv.org/abs/2010.15979 · HTML: https://mlsanity.com/paper/2010.15979/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2020.

## Built on by (most cited first, 22 of 22)

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- [XnODR and XnIDR: Two Accurate and Fast Fully Connected Layers For Convolutional Neural Networks](https://mlsanity.com/paper/2111.10854/) (2021)
- [Approximation of functions with one-bit neural networks](https://mlsanity.com/paper/2112.09181/) (2021)
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- [Seeking Interpretability and Explainability in Binary Activated Neural Networks](https://mlsanity.com/paper/2209.03450/) (2022)
- [Unified Stochastic Framework for Neural Network Quantization and Pruning](https://mlsanity.com/paper/2412.18184/) (2024)
- [DiscQuant: A Quantization Method for Neural Networks Inspired by Discrepancy Theory](https://mlsanity.com/paper/2501.06417/) (2025)
- [AWP: Activation-Aware Weight Pruning and Quantization with Projected Gradient Descent](https://mlsanity.com/paper/2506.10205/) (2025)
- [Beacon: Post-Training Quantization with Integrated Grid Selection](https://mlsanity.com/paper/2508.20293/) (2025)
- [Optimal Post-Training Quantization Scales and Where to Find Them](https://mlsanity.com/paper/2606.10890/) (2026)
- [Frame Quantization of Neural Networks](https://mlsanity.com/paper/2404.08131/) (2024)
- [Theoretical Compression Bounds for Wide Multilayer Perceptrons](https://mlsanity.com/paper/2512.06288/) (2025)
- [GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation](https://mlsanity.com/paper/2606.01412/) (2026)
- [Algorithms for Discrepancy, Matchings, and Approximations: Fast, Simple, and Practical](https://mlsanity.com/paper/2209.01147/) (2022)
- [SPFQ: A Stochastic Algorithm and Its Error Analysis for Neural Network Quantization](https://mlsanity.com/paper/2309.10975/) (2023)
- [Post-Training Quantization of Generative and Discriminative LSTM Text Classifiers: A Study of Calibration, Class Balance, and Robustness](https://mlsanity.com/paper/2507.09687/) (2025)
- [Low-Bit Quantization of Bandlimited Graph Signals via Iterative Methods](https://mlsanity.com/paper/2601.18782/) (2026)

## Abstract (arXiv)

We propose a new computationally efficient method for quantizing the weights of pre- trained neural networks that is general enough to handle both multi-layer perceptrons and convolutional neural networks. Our method deterministically quantizes layers in an iterative fashion with no complicated re-training required. Specifically, we quantize each neuron, or hidden unit, using a greedy path-following algorithm. This simple algorithm is equivalent to running a dynamical system, which we prove is stable for quantizing a single-layer neural network (or, alternatively, for quantizing the first layer of a multi-layer network) when the training data are Gaussian. We show that under these assumptions, the quantization error decays with the width of the layer, i.e., its level of over-parametrization. We provide numerical experiments, on multi-layer networks, to illustrate the performance of our methods on MNIST and CIFAR10 data, as well as for quantizing the VGG16 network using ImageNet data.