Trusting SVM for Piecewise Linear CNNs

We present a novel layerwise optimization algorithm for the learning objective of a large class of convolutional neural networks (CNNs). Specifically, we consider CNNs that 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. To this end, we extend the block-coordinate Frank-Wolfe (BCFW) algorithm in three important ways: (i) we include a trust-region for the parameters, which allows us to use the previous parameters as an initialization; (ii) we reduce the memory requirement of BCFW by potentially several orders of magnitude for the dense layers, which enables us to learn a large set of parameters; and (iii) we observe that, empirically, the optimal solution of the structured SVM problem can be obtained efficiently by solving a related, but significantly easier, multi-class SVM problem. Using publicly available data sets, we show that our approach outperforms the state of the art variants of backpropagation, and is also more robust to the hyperparameters of the learning objective.