  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.
