  We present a novel layerwise optimization algorithm for the learning
objective of Piecewise-Linear Convolutional Neural Networks (PL-CNNs), a large
class of convolutional neural networks. Specifically, PL-CNNs employ piecewise
linear non-linearities such as the commonly used ReLU and max-pool, and an SVM
classifier as the final layer. The key observation of our approach is that the
problem corresponding to the parameter estimation of a layer can be formulated
as a difference-of-convex (DC) program, which happens to be a latent structured
SVM. We optimize the DC program using the concave-convex procedure, which
requires us to iteratively solve a structured SVM problem. This allows to
design an optimization algorithm with an optimal learning rate that does not
require any tuning. Using the MNIST, CIFAR and ImageNet data sets, we show that
our approach always improves over the state of the art variants of
backpropagation and scales to large data and large network settings.
