The trace norm is widely used in multi-task learning as it can discover low-rank structures among tasks in terms of model parameters. Nowadays, with the emerging of big datasets and the popularity of deep learning techniques, tensor trace norms have been used for deep multi-task models. However, existing tensor trace norms cannot discover all the low-rank structures and they require users to manually determine the importance of their components. To solve those two issues together, in this paper, we propose a Generalized Tensor Trace Norm (GTTN). The GTTN is defined as a convex combination of matrix trace norms of all possible tensor flattenings and hence it can discover all the possible low-rank structures. In the induced objective function, we will learn combination coefficients in the GTTN to automatically determine the importance. Experiments on real-world datasets demonstrate the effectiveness of the proposed GTTN.
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