text: The paper proposes to use a regularizer for tensor completion problems that can be written in a similar fashion as the variational factorization formulation of the trace norm aka nuclear norm for matrices. The paper introduces the regularizer with the nice argument that the gradient of the L3 norm to the power of 3rd will be easy to compute, but if we were raising the L2 norm to the 3rd power it would not be the case. They mention that their argument can generalize from D=3 to higher order tensors. Authors mention the paper by Friedland and Lim that introduces this norm and provides first theoretical results on it. Authors develop on the tensor equivalent of the matrix max norm which is built with the motivation of bringing robustness to heavy nodes in the graph (very popular content). This is again straightforward on the technical side. Empirical results are fine but do not show huge improvements compared to baselines so I do not think this is a strong argument for accepting the paper. On the scalability, authors do not show that their approach is better suited than baselines.