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:

$$-\sum_{i=1}^n log(\frac{{e^{y_iF(x_i,\overline{a})}}}{1 + e^{yF(x,\overline{a})}})$$ $$=-\sum_{i=1}^ny_iF(x_i, \overline{a}) - log(1 + e^{yF(x,\overline{a})})$$ enter image description here

And here is the full ranking loss I am having trouble on:

enter image description here


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