Given the task definition and input, reply with output. In this task, you are given a paper review. Based on the review, your job is to identify language and generate "en" if the review is in English or generate "es" if the review is in Spanish. Note that URLs in the text have been replaced with [Link].

The authors propose to combine a CCA objective with a downstream loss.  This is a really nice and natural idea.  However, both the execution and presentation leave a lot to be desired in the current version of the paper.  It is not clear what the overall objective is.  This was asked in a pre-review question but the answer did not fully clarify it for me.  Is it the sum of the CCA objective and the final (top-layer) objective, including the CCA constraints?  Is there some interpolation of the two objectives?    By saying that the top-layer objective is "cosine distance" or "squared cosine distance", do you really mean you are just minimizing this distance between the matched pairs in the two views?  If so, then of course that does not work out of the box without the intervening CCA layer:  You could minimize it by setting all of the projections to a single point.  A better comparison would be against a contrastive loss like the Hermann & Blunsom one mentioned in the reviewer question, which aims to both minimize the distance for matched pairs and separate mismatched ones (where "mismatched" ones can be uniformly drawn, or picked in some cleverer way).  But other discriminative top-layer objectives that are tailored to a downstream task could make sense.  There is some loose terminology in the paper.  The authors refer to the "correlation" and "cross-correlation" between two vectors.  "Correlation" normally applies to scalars, so you need to define what you mean here.  "Cross-correlation" typically refers to time series.  In eq. (2) you are taking the max of a matrix.  Finally I am not too sure in what way this approach is "fully differentiable" while regular CCA is not -- perhaps it is worth revisiting this term as well.  Also just a small note about the relationship between cosine distance and correlation:  they are related when we view the dimensions of each of the two vectors as samples of a single random variable.  In that case the cosine distance of the (mean-normalized) vectors is the same as the correlation between the two corresponding random variables.  In CCA we are viewing each dimension of the vectors as its own random variable.  So I fear the claim about cosine distance and correlation is a bit of a red herring here.  A couple of typos:  "prosed" --> "proposed" "allong" --> "along"

en