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An important characteristic of neural networks is their ability to learnrepresentations of the input data with effective features for prediction, whichis believed to be a key factor to their superior empirical performance. Tobetter understand the source and benefit of feature learning in neuralnetworks, we consider learning problems motivated by practical data, where thelabels are determined by a set of class relevant patterns and the inputs aregenerated from these along with some background patterns. We prove that neuralnetworks trained by gradient descent can succeed on these problems. The successrelies on the emergence and improvement of effective features, which arelearned among exponentially many candidates efficiently by exploiting the data(in particular, the structure of the input distribution). In contrast, nolinear models on data-independent features of polynomial sizes can learn to asgood errors. Furthermore, if the specific input structure is removed, then nopolynomial algorithm in the Statistical Query model can learn even weakly.These results provide theoretical evidence showing that feature learning inneural networks depends strongly on the input structure and leads to thesuperior performance. Our preliminary experimental results on synthetic andreal data also provide positive support.

A Theoretical Analysis on Feature Learning in Neural Networks: Emergence from Inputs and Advantage over Fixed Features