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[formerly titled "Why and When Can Deep – but Not Shallow – Networks Avoid the Curse of Dimensionality: a Review"] The paper reviews and extends an emerging body of theoretical results on deep learning including the ...

[previously titled "Theory of Deep Learning III: Generalization Properties of SGD"] In Theory III we characterize with a mix of theory and experiments the generalization properties of Stochastic Gradient Descent in ...

The general features of the optimization problem for the case of overparametrized nonlinear networks have been clear for a while: SGD selects with high probability global minima vs local minima. In the overparametrized ...

In Theory IIb we characterize with a mix of theory and experiments the optimization of deep convolutional networks by Stochastic Gradient Descent. The main new result in this paper is theoretical and experimental evidence ...

Deep networks are usually trained and tested in a regime in which the training classification error is not a good predictor of the test error. Thus the consensus has been that generalization, defined as convergence of the ...

THIS MEMO IS REPLACED BY CBMM MEMO 90 A main puzzle of deep networks revolves around the absence of overfitting despite overparametrization and despite the large capacity demonstrated by zero training error on randomly ...