  The foundational concept of Max-Margin in machine learning is ill-posed for
output spaces with more than two labels such as in structured prediction. In
this paper, we show that the Max-Margin loss can only be consistent to the
classification task under highly restrictive assumptions on the discrete loss
measuring the error between outputs. These conditions are satisfied by
distances defined in tree graphs, for which we prove consistency, thus being
the first losses shown to be consistent for Max-Margin beyond the binary
setting. We finally address these limitations by correcting the concept of
Max-Margin and introducing the Restricted-Max-Margin, where the maximization of
the loss-augmented scores is maintained, but performed over a subset of the
original domain. The resulting loss is also a generalization of the binary
support vector machine and it is consistent under milder conditions on the
discrete loss.
