  Current model quantization methods have shown their promising capability in
reducing storage space and computation complexity. However, due to the
diversity of quantization forms supported by different hardware, one limitation
of existing solutions is that usually require repeated optimization for
different scenarios. How to construct a model with flexible quantization forms
has been less studied. In this paper, we explore a one-shot network
quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which
aims to train a robust weight-sharing quantization supernet. First of all, we
propose an elastic quantization space (including elastic bit-width,
granularity, and symmetry) to adapt to various mainstream quantitative forms.
Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and
Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the
distribution for weights and output logits in the elastic quantization space
gap. Lastly, we incorporate genetic algorithms and the proposed Conditional
Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search
mixed-precision quantized neural networks in supernet. Extensive experiments
demonstrate that our EQ-Net is close to or even better than its static
counterparts as well as state-of-the-art robust bit-width methods. Code can be
available at
\href{https://github.com/xuke225/EQ-Net.git}{https://github.com/xuke225/EQ-Net}.
