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Abstract:
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Deep neural networks have improved state-of-the-art performance for prediction problems across an impressive range of application areas, and they have become a central ingredient in AI systems. This talk considers the statistical properties of deep networks, in particular, how their performance on training data compares to predictive accuracy, and how to measure the complexity of functions computed by these networks. For multiclass classification problems, we present margin-based misclassification probability bounds that scale with a certain margin-normalized "spectral complexity," involving the product of the spectral norms of the weight matrices in the network. We show how these bounds give insight into the observed performance of these networks in practical problems.
Joint work with Matus Telgarsky and Dylan Foster.
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