A practical theory for designing very deep convolutional neural networks

Going deep is essential for deep learning. However it is not easy, there are many ways of going deep but most of them are ineffective. In this work, we propose two novel constrains in the design of deep structure to guarantee the performance gain when going deep. Firstly, for each convolutional layer, its capacity of learning more complex patterns should be guaranteed; Secondly, the receptive field of the topmost layer should be no larger than the image region. Given these two constrains, we cast the task of designing deep convolutional neural network into a constrained optimization problem. We present an analytic optimal solution under certain conditions.