@Reviewer1:$ We will provide in appendix the SGD algorithm for our model (complex) with update equations. @Reviewer2: We will visually emphasize in Table 4 the antisymmetric relations, and use a multi-dimensional scaling (such as PCA or t-SNE) to visualize a 2d projection of the complex embeddings versus real embeddings. @Reviewer3: 1) That's right, we should refer U as orthogonal, not unitary. we will correct it. 2) The discussion about matrices that are not normal will be expanded and clarified. 3) As the FB and WN datasets are partially observed we cannot directly check XX^T == X^TX, and we are actually designing an experiment to check experimentally for which relation this hypothesis is statistically significant. Also, in the discussion on the triangular matrices (point 2), we will mention examples of non-normal relations, and their link to triangular matrices. 4) It is very possible that with a more adapted regularization for RESCAL can manage better prediction accuracy. But even if it becomes competitive in terms of prediction, the main drawback of RESCAL is that its quadratic complexity in both memory and time makes it hardly scalable to datasets with numerous relations. This was partly why we did not investigate further on this model. 5) We were also surprised by the fact that RESCAL overfits so quickly. The main reason is the size of the relations embeddings that introduces too many parameters for the simplicity of the relations nature (symmetry and antisymmetry). We will investigate the minimum required number of examples for each model to generalize correctly. 6) We will add results on WN and FB with the CP (canonical polyadic) model which corresponds to the decoupled subject and object embeddings.