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Yes, they do. This paper provides the first empirical demonstration that deepconvolutional models really need to be both deep and convolutional, even whentrained with methods such as distillation that allow small or shallow models ofhigh accuracy to be trained. Although previous research showed that shallowfeed-forward nets sometimes can learn the complex functions previously learnedby deep nets while using the same number of parameters as the deep models theymimic, in this paper we demonstrate that the same methods cannot be used totrain accurate models on CIFAR-10 unless the student models contain multiplelayers of convolution. Although the student models do not have to be as deep asthe teacher model they mimic, the students need multiple convolutional layersto learn functions of comparable accuracy as the deep convolutional teacher.

Do Deep Convolutional Nets Really Need to be Deep and Convolutional?