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The trace norm is widely used in multi-task learning as it can discoverlow-rank structures among tasks in terms of model parameters. Nowadays, withthe emerging of big datasets and the popularity of deep learning techniques,tensor trace norms have been used for deep multi-task models. However, existingtensor trace norms cannot discover all the low-rank structures and they requireusers to manually determine the importance of their components. To solve thosetwo 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 ofall possible tensor flattenings and hence it can discover all the possiblelow-rank structures. In the induced objective function, we will learncombination coefficients in the GTTN to automatically determine the importance.Experiments on real-world datasets demonstrate the effectiveness of theproposed GTTN.

Deep Multi-Task Learning via Generalized Tensor Trace Norm