Deep Learning with Low Precision by Half-wave Gaussian Quantization
This addresses the challenge of reducing computational and memory costs for deep learning deployment, though it is incremental as it builds on existing quantization methods.
The paper tackles the problem of quantizing deep neural network activations by proposing a half-wave Gaussian quantizer (HWGQ) for ReLU non-linearities, achieving performance close to full-precision networks like AlexNet and ResNet with 1-bit binary weights and 2-bit quantized activations.
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.