A Greedy Algorithm for Quantizing Neural Networks

TL;DR

This paper introduces a simple, efficient greedy algorithm for quantizing neural network weights that works across different architectures without complex retraining, and demonstrates error decay with network over-parameterization.

Contribution

The paper presents a deterministic, greedy quantization method applicable to various neural networks, with theoretical stability analysis and empirical validation on multiple datasets.

Findings

Quantization error decreases as layer width increases.

Method performs well on MNIST, CIFAR10, and ImageNet datasets.

No complex retraining needed for effective quantization.

Abstract

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.