  Model-based neural networks provide unparalleled performance for various
tasks, such as sparse coding and compressed sensing problems. Due to the strong
connection with the sensing model, these networks are interpretable and inherit
prior structure of the problem. In practice, model-based neural networks
exhibit higher generalization capability compared to ReLU neural networks.
However, this phenomenon was not addressed theoretically. Here, we leverage
complexity measures including the global and local Rademacher complexities, in
order to provide upper bounds on the generalization and estimation errors of
model-based networks. We show that the generalization abilities of model-based
networks for sparse recovery outperform those of regular ReLU networks, and
derive practical design rules that allow to construct model-based networks with
guaranteed high generalization. We demonstrate through a series of experiments
that our theoretical insights shed light on a few behaviours experienced in
practice, including the fact that ISTA and ADMM networks exhibit higher
generalization abilities (especially for small number of training samples),
compared to ReLU networks.
