  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.
