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Heavy review Summary: The paper concerns multi-class problems with a large number of classes. It introduces a novel label tree classifier that learns and predicts in logarithmic time in the number of classes. Theoretical guarantees in terms of a boosting-like theorem have been proven. Moreover, not only node classifiers, but also the structure of the tree is trained online. Additionally, the authors show a simple subtree swapping procedure that ensures proper balancing of the tree.