text: The paper studies different methods for defining hypergraph embeddings, i.e. defining vectorial representations of the set of hyperedges of a given hypergraph.  It should be noted that the framework does not allow to compute a vectorial representation of a set of nodes not already given as an hyperedge.  A set of methods is presented : the first one is based on an auto-encoder technique ;  the second one is based on tensor decomposition ;  the third one derives from sentence embedding methods.  The fourth one extends over node embedding techniques  and the last one use spectral methods.  The two first methods use plainly the set structure of hyperedges.  Experimental results are provided on semi-supervised regression tasks.  They show very similar performance for all methods and variants.  Also run-times are compared  and the results are expected.  In conclusion, the paper gives an overview of methods for computing hypernode embeddings.  This is interesting in its own.  Nevertheless, as the target problem on hypergraphs is left unspecified,  it is difficult to infer conclusions from the study.  Therefore, I am not convinced that the paper should be published in ICLR'18. * typos * Recent surveys on graph embeddings have been published in 2017 and should be cited as "A comprehensive survey of graph embedding ..." by Cai et al * Preliminaries. The occurrence number R(g_i) are not modeled in the hypergraphs.  A graph N_a is defined but not used in the paper. * Section 3.1. the procedure for sampling hyperedges in the lattice shoud be given.  At least, you should explain how it is made efficient when the number of nodes is large. * Section 3.2. The method seems to be restricted to cases where the cardinality of hyperedges can take a small number of values.  This is discussed in Section 3.6  but the discussion is not convincing enough. * Section 3.3 The term Sen2vec is not common knowledge * Section 3.3 The length of the sentences depends on the number of permutations of $k$ elements.  How can you deal with large k ? * Section 3.4 and Section 3.5. The methods proposed in these two sections should be related with previous works on hypergraph kernels.  I.e. there should be mentions on the clique expansion and star expansion of hypergraphs.  This leads to the question why graph embeddings methods on these expansions have not be considered in the paper. * Section 4.1. Only hyperedeges of cardinality in [2,6] are considered.  This seems a rather strong limitation  and this hypothesis does not seem pertinent in many applications.  * Section 4. For online multi-player games, hypernode embeddings only allow to evaluate existing teams, i.e. already existing as hyperedges in the input hypergraph.  One of the most important problem for multi-player games is team making where team evaluation should be made for all possible teams. * Section 5. Seems redundant with the Introduction.