In this paper, we propose a novel multitask learning method based on the deep convolutional network. The proposed deep network has four convolutional layers, three max-pooling layers, and two parallel fully connected layers. To adjust the deep network to multitask learning problem, we propose to learn a low-rank deep network so that the relation among different tasks can be explored. We proposed to minimize the number of independent parameter rows of one fully connected layer to explore the relations among different tasks, which is measured by the nuclear norm of the parameter of one fully connected layer, and seek a low-rank parameter matrix. Meanwhile, we also propose to regularize another fully connected layer by sparsity penalty so that the useful features learned by the lower layers can be selected. The learning problem is solved by an iterative algorithm based on gradient descent and back-propagation algorithms. The proposed algorithm is evaluated over benchmark datasets of multiple face attribute prediction, multitask natural language processing, and joint economics index predictions. The evaluation results show the advantage of the low-rank deep CNN model over multitask problems.
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