  Estimating matrices in the symmetric positive-definite (SPD) cone is of
interest for many applications ranging from computer vision to graph learning.
While there exist various convex optimization-based estimators, they remain
limited in expressivity due to their model-based approach. The success of deep
learning has thus led many to use neural networks to learn to estimate SPD
matrices in a data-driven fashion. For learning structured outputs, one
promising strategy involves architectures designed by unrolling iterative
algorithms, which potentially benefit from inductive bias properties. However,
designing correct unrolled architectures for SPD learning is difficult: they
either do not guarantee that their output has all the desired properties, rely
on heavy computations, or are overly restrained to specific matrices which
hinders their expressivity. In this paper, we propose a novel and generic
learning module with guaranteed SPD outputs called SpodNet, that also enables
learning a larger class of functions than existing approaches. Notably, it
solves the challenging task of learning jointly SPD and sparse matrices. Our
experiments demonstrate the versatility of SpodNet layers.
