Ok, but the the backward method of SumTo1 does not seem to map the whole \mathbb R^{n-1} into the simplex. E.g.:
>>> SumTo1().backward_val(np.ones(2))
array([ 1., 1., -1.])
And the support of logp() of the Dirichlet distribution is only the simplex, while ADVI models a paramter distribution on \mathbb R^{n-1}.