  In this paper, we design lightweight graph convolutional networks (GCNs)
using a particular class of regularizers, dubbed as phase-field models (PFMs).
PFMs exhibit a bi-phase behavior using a particular ultra-local term that
allows training both the topology and the weight parameters of GCNs as a part
of a single "end-to-end" optimization problem. Our proposed solution also
relies on a reparametrization that pushes the mask of the topology towards
binary values leading to effective topology selection and high generalization
while implementing any targeted pruning rate. Both masks and weights share the
same set of latent variables and this further enhances the generalization power
of the resulting lightweight GCNs. Extensive experiments conducted on the
challenging task of skeleton-based recognition show the outperformance of PFMs
against other staple regularizers as well as related lightweight design
methods.
