Statistical guarantees for sparse deep learning

Abstract Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further by developing statistical guarantees for sparse deep learning. contrast to previous work, consider different types sparsity, such as few active connections, nodes, other norm-based sparsity. Moreover, theories cover important aspects that have neglected, multiple outputs, regularization, $$\ell_{2}$$ ℓ 2 -loss. The a mild dependence on network widths depths, which means they support the application wide from perspective. Some concepts tools use derivations uncommon learning and, hence, might be additional interest.