  While regression tasks aim at interpolating a relation on the entire input
space, they often have to be solved with a limited amount of training data.
Still, if the hypothesis functions can be sketched well with the data, one can
hope for identifying a generalizing model.
  In this work, we introduce with the Neural Restricted Isometry Property
(NeuRIP) a uniform concentration event, in which all shallow $\mathrm{ReLU}$
networks are sketched with the same quality. To derive the sample complexity
for achieving NeuRIP, we bound the covering numbers of the networks in the
Sub-Gaussian metric and apply chaining techniques. In case of the NeuRIP event,
we then provide bounds on the expected risk, which hold for networks in any
sublevel set of the empirical risk. We conclude that all networks with
sufficiently small empirical risk generalize uniformly.
