  This paper defines linear range as the range of parameter perturbations which
lead to approximately linear perturbations in the states of a network. We
compute linear range from the difference between actual perturbations in states
and the tangent solution. Linear range is a new criterion for estimating the
effectivenss of gradients and thus having many possible applications. In
particular, we propose that the optimal learning rate at the initial stages of
training is such that parameter changes on all minibatches are within linear
range. We demonstrate our algorithm on two shallow neural networks and a
ResNet.
