text: The authors present a neural embedding technique using a hyperbolic space. The idea of embedding data into a space that is not Euclidean is not new. There have been attempts to project onto (hyper)spheres. Also, the proposal bears some resemblance with what is done in t-SNE, where an (exponential) distortion of distances is induced.  Discussing this potential similarity would certainly broaden the readership of the paper. The organisation of the paper might be improved, with a clearer red line and fewer digressions. The call to the very small appendix via eq. 17 is an example. The position of Table in the paper is odd as well. The order of examples in Fig.5 differs from the order in the list. The experiments are well illustrative but rather small sized. The qualitative assessment is always interesting  and it is completed with some label prediction task. Due the geometrical consideretations developed in the paper, other quality criteria like e.g. how well neighbourhoods are preserved in the embeddings would give some more insights. All in all the idea developed in the paper sounds interesting  but the paper organisation seems a bit loose  and additional aspects should be investigated.