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Shallow supervised 1-hidden layer neural networks have a number of favorableproperties that make them easier to interpret, analyze, and optimize than theirdeep counterparts, but lack their representational power. Here we use 1-hiddenlayer learning problems to sequentially build deep networks layer by layer,which can inherit properties from shallow networks. Contrary to previousapproaches using shallow networks, we focus on problems where deep learning isreported as critical for success. We thus study CNNs on image classificationtasks using the large-scale ImageNet dataset and the CIFAR-10 dataset. Using asimple set of ideas for architecture and training we find that solvingsequential 1-hidden-layer auxiliary problems lead to a CNN that exceeds AlexNetperformance on ImageNet. Extending this training methodology to constructindividual layers by solving 2-and-3-hidden layer auxiliary problems, we obtainan 11-layer network that exceeds several members of the VGG model family onImageNet, and can train a VGG-11 model to the same accuracy as end-to-endlearning. To our knowledge, this is the first competitive alternative toend-to-end training of CNNs that can scale to ImageNet. We illustrate severalinteresting properties of these models theoretically and conduct a range ofexperiments to study the properties this training induces on the intermediatelayers.

Greedy Layerwise Learning Can Scale to ImageNet