text: This paper proposes the concept of optimal representation space and suggests that a model should be evaluated in its optimal representation space to get good performance. It could be a good idea if this paper could suggest some ways to find the optimal representation space in general, instead of just showing two cases. It is disappointing, because this paper is named as "finding optimal representation spaces ...". In addition, one of the contributions claimed in this paper is about introducing the "formalism" of an optimal representation space. However, I didn't see any formal definition of this concept or theoretical justification. About FastSent or any other log-linear model, the reason that dot product (or cosine similarity) is a good metric is because the model is trained to optimize the dot product, as shown in equation 5 --- I think this simple fact is missed in this paper. The experimental results are not convincing, because I didn't find any consistent pattern that shows the performance is getting better once we evaluated the model in its optimal representation space. There are statements in this paper that I didn't agree with 1) Distributional hypothesis from Harris (1954) is about words not sentences. 2) Not sure the following line makes sense: "However, these unsupervised tasks are more interesting from a general AI point of view, as they test whether the machine truly understands the human notion of similarity, without being explicitly told what is similar"