Deep transform and metric learning network: Wedding deep dictionary learning and neural network

Abstract

On account of its many successes in inference tasks and imaging applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. In DL area, most solutions are focused on single-layer dictionaries, whose reliance on handcrafted features achieves a somewhat limited performance. With the rapid development of deep learning, improved DL methods called Deep DL (DDL), have been recently proposed an end-to-end flexible inference solution with a much higher performance. The proposed DDL techniques have, however, also fallen short on a number of issues, namely, computational cost and the difficulties in gradient updating and initialization. While a few differential programming solutions have been proposed to speed-up the single-layer DL, none of them could ensure an efficient, scalable, and robust solution for DDL methods. To that end, we propose herein, a novel differentiable programming approach, which yields an efficient, competitive and reliable DDL solution. The novel DDL method jointly learns deep transforms and deep metrics, where each DL layer is theoretically reformulated as a combination of one linear layer and a Recurrent Neural Network (RNN). The RNN is also shown to flexibly account for the layer-associated approximation together with a learnable metric. Additionally, our proposed work unveils new insights into Neural Network (NN) and DDL, bridging the combinations of linear and RNN layers with DDL methods. Extensive experiments on image classification problems are carried out to demonstrate that the proposed method can not only outperform existing DDL several counts including, efficiency, scaling and discrimination, but also achieve better accuracy and increased robustness against adversarial perturbations than CNNs.