  Highly overparametrized neural networks can display curiously strong
generalization performance - a phenomenon that has recently garnered a wealth
of theoretical and empirical research in order to better understand it. In
contrast to most previous work, which typically considers the performance as a
function of the model size, in this paper we empirically study the
generalization performance as the size of the training set varies over multiple
orders of magnitude. These systematic experiments lead to some interesting and
potentially very useful observations; perhaps most notably that training on
smaller subsets of the data can lead to more reliable model selection decisions
whilst simultaneously enjoying smaller computational costs. Our experiments
furthermore allow us to estimate Minimum Description Lengths for common
datasets given modern neural network architectures, thereby paving the way for
principled model selection taking into account Occams-razor.
