What are the limmitations of reparametrization gradients for discrete random variables? (Gumbel-softmax) We know that one approach for re-parametrizing gradients for variational inference is taking the Gumbel-softmax estimator proposed in [1] and [2].
In [3], that is a talk on SVI, D. Blei at around 29:31 mentions that there is no re-parametrization for discrete variables for VI (also on the slides). The talk is one year after the papers. Since I find it highly unlikely that something like that would have gotten under the radar of a leading expert what am I missing? 
More concretely, the questions I have are the following:


*

*Is the Gumbel softmax trick considered to have solved in a satisfying manner the issue of low-variance gradients in SVI with re-parametrization or not?

*Is the statement in the talk simply inaccurate?


This is not to be perceived as a criticism of the talk - I highly recommend it by the way. I am truly asking to clarify my confusion on the subject.
[1]: Categorical Reparametrization with Gumbel-Softmax  (https://arxiv.org/pdf/1611.01144.pdf)
[2]: The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables  (https://arxiv.org/abs/1611.00712)
[3]: Talk by D. Blei on SVI: https://www.youtube.com/watch?v=-H2N4tVDK7I
 A: Is the Gumbel softmax trick considered to have solved in a satisfying manner the issue of low-variance gradients in SVI with re-parametrization or not?
I think in [1], at first Gumbel-max trick is used which is an exact method to obtain samples from the categorical distribution. But, Gumbel-max trick (eqn 1 in paper [1]) introduces arg-max which needs is approximated by using the softmax function (eqn. 2 in paper [1]). Basically, this approximation enables automatic differentiation but also introduces a hyperparameter $\tau$ which determines the variance. If $\tau$ is small, the arg-max approximation is accurate but it leads to gradients with high variance. Conversely, if $\tau$ is large, the arg-max approximation may become inaccurate (see figure 1 and section 2.1 in paper [1]).
The paper introduces a novel method that solves gradient backpropagation problem for discrete latent variables but I think the solution is not perfect (as there is an approximation for arg-max)
2)Is the statement in the talk simply inaccurate?
I think the statement in the talk is correct. The solution is not perfect or exact as in Auto-Encoding Variational Bayes (Diederik P Kingma, Max Welling).
