# Least squares binary quantization of neural networks Source: [Least squares binary quantization of neural networks]() Collection index: [llms.txt]() Data updated: 2025-10-25T22:21:05.859Z Authors: Hadi Pouransari, Zhucheng Tu, Oncel Tuzel Published: 2020-01-09T00:01:14.000Z ## Abstract Quantizing weights and activations of deep neural networks results in significant improvement in inference efficiency at the cost of lower accuracy. A source of the accuracy gap between full precision and quantized models is the quantization error. In this work, we focus on the binary quantization, in which values are mapped to -1 and 1. We provide a unified framework to analyze different scaling strategies. Inspired by the pareto-optimality of 2-bits versus 1-bit quantization, we introduce a novel 2-bits quantization with provably least squares error. Our quantization algorithms can be implemented efficiently on the hardware using bitwise operations. We present proofs to show that our proposed methods are optimal, and also provide empirical error analysis. We conduct experiments on the ImageNet dataset and show a reduced accuracy gap when using the proposed least squares quantization algorithms. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on ImageNet ILSVRC-2012 (val)](): Image Classification; ImageNet ILSVRC-2012 (val); Top-1 Accuracy: 66.1. ## Original sources and implementation [Original paper]() [PDF]()