# Proximal Mean-field for Neural Network Quantization

## TL;DR

This paper introduces a novel neural network quantization method based on a proximal mean-field approach, enabling efficient optimization that maintains high accuracy in fully-quantized models.

## Contribution

It formulates NN quantization as a discrete labeling problem and connects it to a proximal mean-field method, bridging classical MRF optimization with neural network compression.

## Key findings

- Achieves near-floating-point accuracy with fully-quantized networks.
- Demonstrates effectiveness on standard datasets like MNIST and CIFAR.
- Provides an efficient iterative optimization procedure for network quantization.

## Abstract

Compressing large Neural Networks (NN) by quantizing the parameters, while maintaining the performance is highly desirable due to reduced memory and time complexity. In this work, we cast NN quantization as a discrete labelling problem, and by examining relaxations, we design an efficient iterative optimization procedure that involves stochastic gradient descent followed by a projection. We prove that our simple projected gradient descent approach is, in fact, equivalent to a proximal version of the well-known mean-field method. These findings would allow the decades-old and theoretically grounded research on MRF optimization to be used to design better network quantization schemes. Our experiments on standard classification datasets (MNIST, CIFAR10/100, TinyImageNet) with convolutional and residual architectures show that our algorithm obtains fully-quantized networks with accuracies very close to the floating-point reference networks.