I am reading through a paper (https://www.mitpressjournals.org/doi/pdf/10.1162/0891201053630273) where they describe logloss as a ranking function and can be simplified to the margin of the training data $X$. I am not sure what the transformation is in each step and could use a bit of help.
A precursor to this ranking loss is standard logloss which may clarify my understanding as well:
In this loss I only get from step 2 to here:
And here is the full ranking loss I am having trouble on: