Quantized deep neural networks (QDNNs) are attractive due to their much lower
memory storage and faster inference speed than their regular full precision
counterparts. To maintain the same performance level especially at low
bit-widths, QDNNs must be retrained. Their training involves piecewise constant
activation functions and discrete weights, hence mathematical challenges arise.
We introduce the notion of coarse gradient and propose the blended coarse
gradient descent (BCGD) algorithm, for training fully quantized neural
networks. Coarse gradient is generally not a gradient of any function but an
artificial ascent direction. The weight update of BCGD goes by coarse gradient
correction of a weighted average of the full precision weights and their
quantization (the so-called blending), which yields sufficient descent in the
objective value and thus accelerates the training. Our experiments demonstrate
that this simple blending technique is very effective for quantization at
extremely low bit-width such as binarization. In full quantization of ResNet-18
for ImageNet classification task, BCGD gives 64.36\% top-1 accuracy with binary
weights across all layers and 4-bit adaptive activation. If the weights in the
first and last layers are kept in full precision, this number increases to
65.46\%. As theoretical justification, we show convergence analysis of coarse
gradient descent for a two-linear-layer neural network model with Gaussian
input data, and prove that the expected coarse gradient correlates positively
with the underlying true gradient.

提出了混合粗微分下降算法 (BCGD)，该算法利用了人工升高方向的粗微分来进行系数的权重更新，从而在目标值上产生足够的下降，加速了量化训练效果，并在 ImageNet 分类任务中全量化 ResNet-18 网络汇报了 64.36％的 top-1 准确率。