  We consider the problem of learned transform compression where we learn both,
the transform as well as the probability distribution over the discrete codes.
We utilize a soft relaxation of the quantization operation to allow for
back-propagation of gradients and employ vector (rather than scalar)
quantization of the latent codes. Furthermore, we apply similar relaxation in
the code probability assignments enabling direct optimization of the code
entropy. To the best of our knowledge, this approach is completely novel. We
conduct a set of proof-of concept experiments confirming the potency of our
approaches.
