  We present an efficient block-diagonal ap- proximation to the Gauss-Newton
matrix for feedforward neural networks. Our result- ing algorithm is
competitive against state- of-the-art first order optimisation methods, with
sometimes significant improvement in optimisation performance. Unlike
first-order methods, for which hyperparameter tuning of the optimisation
parameters is often a labo- rious process, our approach can provide good
performance even when used with default set- tings. A side result of our work
is that for piecewise linear transfer functions, the net- work objective
function can have no differ- entiable local maxima, which may partially explain
why such transfer functions facilitate effective optimisation.
