Given the task definition and input, reply with output. In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

This paper studies the problem of learning weighted automata from a finite labeled training sample. We consider several general families of weighted automata defined in terms of three different measures: the norm of an automaton's weights, the norm of the function computed by an automaton, or the norm of the corresponding Hankel matrix. We present new data-dependent generalization guarantees for learning weighted automata expressed in terms of the Rademacher complexity of these families. We further present upper bounds on these Rademacher complexities, which reveal key new data-dependent terms related to the complexity of learning weighted automata.
Generalization Bounds for Weighted Automata