Demystifying the world of deep networks

Friday, February 28, 2020 - 15:00 in Mathematics & Economics

Introductory statistics courses teaches us that, when fitting a model to some data, we should have more data than free parameters to avoid the danger of overfitting — fitting noisy data too closely, and thereby failing to fit new data. It is surprising, then, that in modern deep learning the practice is to have orders of magnitude more parameters than data. Despite this, deep networks show good predictive performance, and in fact do better the more parameters they have. Why would that be? It has been known for some time that good performance in machine learning comes from controlling the complexity of networks, which is not just a simple function of the number of free parameters. The complexity of a classifier, such as a neural network, depends on measuring the “size” of the space of functions that this network represents, with multiple technical measures previously suggested: Vapnik–Chervonenkis dimension, covering numbers, or...

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