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We describe a layer-by-layer algorithm for training deep convolutionalnetworks, where each step involves gradient updates for a two layer networkfollowed by a simple clustering algorithm. Our algorithm stems from a deepgenerative model that generates mages level by level, where lower resolutionimages correspond to latent semantic classes. We analyze the convergence rateof our algorithm assuming that the data is indeed generated according to thismodel (as well as additional assumptions). While we do not pretend to claimthat the assumptions are realistic for natural images, we do believe that theycapture some true properties of real data. Furthermore, we show that ouralgorithm actually works in practice (on the CIFAR dataset), achieving resultsin the same ballpark as that of vanilla convolutional neural networks that arebeing trained by stochastic gradient descent. Finally, our proof techniques maybe of independent interest.

A Provably Correct Algorithm for Deep Learning that Actually Works