  Larger and deeper networks generalise well despite their increased capacity
to overfit. Understanding why this happens is theoretically and practically
important. One recent approach looks at the infinitely wide limits of such
networks and their corresponding kernels. However, these theoretical tools
cannot fully explain finite networks as the empirical kernel changes
significantly during gradient-descent-based training in contrast to infinite
networks. In this work, we derive an iterative linearised training method as a
novel empirical tool to further investigate this distinction, allowing us to
control for sparse (i.e. infrequent) feature updates and quantify the frequency
of feature learning needed to achieve comparable performance. We justify
iterative linearisation as an interpolation between a finite analog of the
infinite width regime, which does not learn features, and standard gradient
descent training, which does. Informally, we also show that it is analogous to
a damped version of the Gauss-Newton algorithm -- a second-order method. We
show that in a variety of cases, iterative linearised training surprisingly
performs on par with standard training, noting in particular how much less
frequent feature learning is required to achieve comparable performance. We
also show that feature learning is essential for good performance. Since such
feature learning inevitably causes changes in the NTK kernel, we provide direct
negative evidence for the NTK theory, which states the NTK kernel remains
constant during training.
