  The parameters of a neural network are naturally organized in groups, some of
which might not contribute to its overall performance. To prune out unimportant
groups of parameters, we can include some non-differentiable penalty to the
objective function, and minimize it using proximal gradient methods. In this
paper, we derive the weighted proximal operator, which is a necessary component
of these proximal methods, of two structured sparsity inducing penalties.
Moreover, they can be approximated efficiently with a numerical solver, and
despite this approximation, we prove that existing convergence guarantees are
preserved when these operators are integrated as part of a generic adaptive
proximal method. Finally, we show that this adaptive method, together with the
weighted proximal operators derived here, is indeed capable of finding
solutions with structure in their sparsity patterns, on representative examples
from computer vision and natural language processing.
