What is the weak hypotheses generated during boosting?
I'm guessing that you mean the weak classifiers that are combined in boosting? Often these are decision trees only a few layers deep. They are trained, one after another, on the dataset weighted such that data points the last classifier got wrong are given more weight.
Check these notes from a UPenn machine learning class for more information:
http://alliance.seas.upenn.edu/~cis520/wiki/index.php?n=Lectures.Boosting
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