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Recently, over-parameterized neural networks have been extensively analyzedin the literature. However, the previous studies cannot satisfactorily explainwhy fully trained neural networks are successful in practice. In this paper, wepresent a new theoretical framework for analyzing over-parameterized neuralnetworks which we call neural feature repopulation. Our analysis cansatisfactorily explain the empirical success of two level neural networks thatare trained by standard learning algorithms. Our key theoretical result is thatin the limit of infinite number of hidden neurons, over-parameterized two-levelneural networks trained via the standard (noisy) gradient descent learns awell-defined feature distribution (population), and the limiting featuredistribution is nearly optimal for the underlying learning task under certainconditions. Empirical studies confirm that predictions of our theory areconsistent with the results observed in real practice.

Over Parameterized Two-level Neural Networks Can Learn Near Optimal Feature Representations