I think that, if a phrase is meaningless, it is enough to explain why it is meaningless (because it proposes to make an 'exact' connexion between something rigorously defined and something that is not) without having to explain in what way the argument for it fails to fulfil that meaningless goal.

Nonetheless, it's surely also true that it would be nice to suggest a constructive remedy; and, fortunately, one need not go farther than the abstract to find (a better approximation to) the precise statement that the authors are making:

> We construct an exact mapping from the variational renormalization group, first introduced by Kadanoff, [to] deep learning architectures based on Restricted Boltzmann Machines (RBMs).