A Greedy Algorithm for Quantizing Neural Networks
This work addresses the need for efficient quantization methods in neural networks, which is incremental as it builds on existing quantization techniques with a new deterministic approach.
The authors tackled the problem of quantizing neural network weights efficiently by proposing a greedy algorithm that deterministically quantizes layers without retraining, showing that quantization error decays with layer width under Gaussian data assumptions, and demonstrating performance on MNIST, CIFAR10, and ImageNet datasets.
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.