A Provably Correct Algorithm for Deep Learning that Actually Works
This work addresses the challenge of provable convergence in deep learning for researchers, but it is incremental as it matches rather than surpasses existing methods.
The paper tackles the problem of training deep convolutional networks with a provably correct algorithm, achieving results comparable to standard CNNs on CIFAR, though with assumptions that may not fully reflect natural images.
We describe a layer-by-layer algorithm for training deep convolutional networks, where each step involves gradient updates for a two layer network followed by a simple clustering algorithm. Our algorithm stems from a deep generative model that generates mages level by level, where lower resolution images correspond to latent semantic classes. We analyze the convergence rate of our algorithm assuming that the data is indeed generated according to this model (as well as additional assumptions). While we do not pretend to claim that the assumptions are realistic for natural images, we do believe that they capture some true properties of real data. Furthermore, we show that our algorithm actually works in practice (on the CIFAR dataset), achieving results in the same ballpark as that of vanilla convolutional neural networks that are being trained by stochastic gradient descent. Finally, our proof techniques may be of independent interest.