  In deep image compression, uniform quantization is applied to latent
representations obtained by using an auto-encoder architecture for reducing
bits and entropy coding. Quantization is a problem encountered in the
end-to-end training of deep image compression. Quantization's gradient is zero,
and it cannot backpropagate meaningful gradients. Many methods have been
proposed to address the approximations of quantization to obtain gradients.
However, there have not been equitable comparisons among them. In this study,
we comprehensively compare the existing approximations of uniform quantization.
Furthermore, we evaluate possible combinations of quantizers for the decoder
and the entropy model, as the approximated quantizers can be different for
them. We conduct experiments using three network architectures on two test
datasets. The experimental results reveal that the best approximated
quantization differs by the network architectures, and the best approximations
of the three are different from the original ones used for the architectures.
We also show that the combination of quantizers that uses universal
quantization for the entropy model and differentiable soft quantization for the
decoder is a comparatively good choice for different architectures and
datasets.
