Deep Networks from the Principle of Rate Reduction
Authors: Kwan Ho Ryan Chan, Yaodong Yu, Chong You, Haozhi Qi, John Wright, Yi Ma
Abstract: This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for maximizing the rate reduction of learned features naturally leads to a deep network, one iteration per layer. The architectures, operators (linear or nonlinear), and parameters of the network are all explicitly constructed layer-by-layer in a forward propagation fashion. All components of this ``white box'' network have precise optimization, statistical, and geometric interpretation. Our preliminary experiments indicate that such a network can already learn a good discriminative deep representation without any back propagation training. Moreover, all linear operators of the so-derived network naturally become multi-channel convolutions when we enforce classification to be rigorously shift-invariant. The derivation also indicates that such a convolutional network is significantly more efficient to learn and construct in the spectral domain.