Exploiting Layerwise Convexity of Rectifier Networks with Sign Constrained Weights
This work provides a method for analyzing pattern structures in neural networks, but it is incremental as it builds on existing MM algorithms and focuses on specific network architectures.
The paper tackles the problem of training rectifier networks efficiently by introducing sign constraints on weights, resulting in SCRNs that can separate any disjoint pattern sets and decompose class patterns into convexly separable clusters.
By introducing sign constraints on the weights, this paper proposes sign constrained rectifier networks (SCRNs), whose training can be solved efficiently by the well known majorization-minimization (MM) algorithms. We prove that the proposed two-hidden-layer SCRNs, which exhibit negative weights in the second hidden layer and negative weights in the output layer, are capable of separating any two (or more) disjoint pattern sets. Furthermore, the proposed two-hidden-layer SCRNs can decompose the patterns of each class into several clusters so that each cluster is convexly separable from all the patterns from the other classes. This provides a means to learn the pattern structures and analyse the discriminant factors between different classes of patterns.