Stability analysis of feed-forward neural network using topological soliton

Abstract

As perceptrons, the generalization power of layered feed-forward neural network(MLP) on the variations in test data is important for practical use of the neural networks. For the analysis of these stabilities in the MLP, we changed the feed-forward of neural network as cascade of $φ^4$ field theory with corresponding field Lagrangian without losing any properties of the network. Using this well-known topological soliton solution of field theory model, the stability of neural network is interpreted as topological stability of kink-type soliton solutions of $φ^4$ field theory. An explicit example, a simple three-class recognition problem, is shown with their theoretical field Lagrangian for practical manner.