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Learning polynomials with Neural Networks

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We study the effectiveness of learning low degree polynomials using neural networks by the gradient descent method. While neural networks have been shown to have great expressive power, and gradient descent has been widely used in prac- tice for learning neural networks, few theoretical guarantees are known for such methods. In particular, it is well known that gradient descent can get stuck at local minima, even for simple classes of target functions. In this paper, we present several positive theoretical results to support the effectiveness of neural networks. We focus on two- layer neural networks where the bottom layer is a set of non-linear hidden nodes, and the top layer node is a linear function, similar to Bar- ron (1993). We show that for a randomly initialized neural network with sufficiently many hidden units, the generic gradient descent algorithm learns any low degree polynomial, assuming we initialize the weights randomly

This talk is part of the Machine Learning Reading Group @ CUED series.

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