As pointed out in Finkel and Manning (2009), there is a simple equivalence between hierarchical regularization as described here and the addition of new tied features in a "flat" model with zero-meaned Gaussian regularization on all parameters.
instead of parameterizing the objective in Section 2.4 in terms of multiple sets of weights, one at each node in the phylogeny (the hierarchical parameterization, described in Section 2.4), it is equivalent to parameterize this same objective in terms of a single set of weights on a larger of group features (the flat parameterization).