Theoretical Exploration of Solutions of Feedforward ReLU networks

This paper aims to interpret the mechanism of feedforward ReLU networks by exploring their solutions for piecewise linear functions through basic rules. The constructed solutions should be universal enough to explain the network architectures of engineering. In order for that, we borrow the methodology of theoretical physics to develop the theories. Some of the consequences of our theories include: Under geometric backgrounds, the solutions of both three-layer networks and deep-layer networks are presented, and the solution universality is ensured by several ways; We give clear and intuitive interpretations of each component of network architectures, such as the parameter-sharing mechanism for multi-output, the function of each layer, the advantage of deep layers, the redundancy of parameters, and so on. We explain three typical network architectures: the subnetwork of last three layers of convolutional networks, multi-layer feedforward networks, and the decoder of autoencoders. This paper is expected to provide a basic foundation of theories of feedforward ReLU networks for further investigations.