Deep Learning with Low Precision by Half-wave Gaussian Quantization

TL;DR

This paper introduces a low-precision neural network quantization method using Half-wave Gaussian Quantization (HWGQ), which closely approximates full-precision networks and is efficiently implementable, improving performance over previous low-precision approaches.

Contribution

The paper proposes HWGQ for forward activation approximation and investigates backward approximators, resulting in HWGQ-Net that significantly improves low-precision neural network performance.

Findings

HWGQ-Net achieves performance close to full-precision models.

Efficient implementation leveraging activation statistics and batch normalization.

Outperforms previous low-precision networks with binary weights and 2-bit activations.

Abstract

The problem of quantizing the activations of a deep neural network is considered. An examination of the popular binary quantization approach shows that this consists of approximating a classical non-linearity, the hyperbolic tangent, by two functions: a piecewise constant sign function, which is used in feedforward network computations, and a piecewise linear hard tanh function, used in the backpropagation step during network learning. The problem of approximating the ReLU non-linearity, widely used in the recent deep learning literature, is then considered. An half-wave Gaussian quantizer (HWGQ) is proposed for forward approximation and shown to have efficient implementation, by exploiting the statistics of of network activations and batch normalization operations commonly used in the literature. To overcome the problem of gradient mismatch, due to the use of different forward and backward approximations, several piece-wise backward approximators are then investigated. The implementation of the resulting quantized network, denoted as HWGQ-Net, is shown to achieve much closer performance to full precision networks, such as AlexNet, ResNet, GoogLeNet and VGG-Net, than previously available low-precision networks, with 1-bit binary weights and 2-bit quantized activations.