In this paper, we propose a novel deep sparse coding network (SCN) capable of efficiently adapting its own regularization parameters for a given application. The network is trained end-to-end with a supervised task-driven learning algorithm via error backpropagation. During training, the network learns both the dictionaries and the regularization parameters of each sparse coding layer so that the reconstructive dictionaries are smoothly transformed into increasingly discriminative representations. In addition, the adaptive regularization also offers the network more flexibility to adjust sparsity levels. Furthermore, we have devised a sparse coding layer utilizing a 'skinny' dictionary. Integral to computational efficiency, these skinny dictionaries compress the high dimensional sparse codes into lower dimensional structures. The adaptivity and discriminability of our fifteen-layer sparse coding network are demonstrated on five benchmark datasets, namely Cifar-10, Cifar-100, STL-10, SVHN and MNIST, most of which are considered difficult for sparse coding models. Experimental results show that our architecture overwhelmingly outperforms traditional one-layer sparse coding architectures while using much fewer parameters. Moreover, our multilayer architecture exploits the benefits of depth with sparse coding's characteristic ability to operate on smaller datasets. In such data-constrained scenarios, our technique demonstrates highly competitive performance compared to the deep neural networks.