  This work considers a challenging Deep Neural Network(DNN) quantization task
that seeks to train quantized DNNs without involving any full-precision
operations. Most previous quantization approaches are not applicable to this
task since they rely on full-precision gradients to update network weights. To
fill this gap, in this work we advocate using Evolutionary Algorithms (EAs) to
search for the optimal low-bits weights of DNNs. To efficiently solve the
induced large-scale discrete problem, we propose a novel EA based on
cooperative coevolution that repeatedly groups the network weights based on the
confidence in their values and focuses on optimizing the ones with the least
confidence. To the best of our knowledge, this is the first work that applies
EAs to train quantized DNNs. Experiments show that our approach surpasses
previous quantization approaches and can train a 4-bit ResNet-20 on the
Cifar-10 dataset with the same test accuracy as its full-precision counterpart.
